Handbook on the Physics and Chemistry of Rare Earths

Handbook on the Physics and Chemistry of Rare Earths, volume 20 Elsevier, 1995

Edited by: Karl A. Gschneidner, Jr. and LeRoy Eyring ISBN: 978-0444820143

Handbook on the Physics and Chemistry of Rare Earths VoL 20 edited by K.A. Gschneidner, Jr. and L. Eyring © 1995 Elsevier Science B.V. All rights reserved

PREFACE

Karl A. G S C H N E I D N E R , Jr., and LeRoy EYRING

These elements perplex us in our rearches [sic], baffle us in our speculations, and haunt

us in our very dreams. They stretch like an unknown sea before us - mocking, mystifying,

and murmuring strange revelations and possibilities. Sir William Crookes (February 16, 1887)

This volume, which completes the second decade of volumes in this series, is focused on physical aspects of metallic compounds. Research efforts on metallic rare earth compounds started in earnest about 50 years ago and received a significant boost with the discovery of the RCo5 permanent magnets about 12 3(ears later. In this time much has been learned about the structure as well as the electrical, magnetic and thermal properties of ~2500 binary rare earth metallic compounds. But considering the possible true ternary compounds, and possible pseudo-binary ternary alloys formed by mixing two binary compounds, we have just begun to scratch the surface of the wealth of knowledge these yet-to-be discovered materials will bring to mankind. The information contained in this volume will be but a few footsteps in our journey to unravel the mysteries hidden in these unknown materials. Hopefully, the four chapters will serve as useful guides in our quest for this new knowledge.

The first chapter (135) in this volume, by Onuki and Hasegawa, deals with the Fermi surfaces of rare earth (Y, La, Ce, Pr, Nd, Sm, Gd and Yb) intermetallic compounds. Initially, the reader is introduced to the relevant theories required to describe the electronic behavior of the electrons near the Fermi surface, and then to the basic experimental techniques to study these surfaces. The main portion of the chapter is devoted to a comparison of the experimental results with the band structure calculations for a large number of compounds. The authors have found some systematics in the observed behaviors, and have grouped the compounds into several different classes: i.e. non-4f behaviors, including some cerium compounds; valence fluctuation compounds; Kondo regime materials; and magnetic materials with magnetic energy gaps etc. They also note that the more complicated the crystal structure the larger the discrepancy between theory and experiment.

Next, Gasgnier examines the world of thin films of rare earth metals, alloys, and compounds in chapter 136. The three main topics are the pure metals themselves, metallic

vi PREFACE

alloys and compounds, and metalloid compounds. Many of the metallic elements exhibit a "valence" change when they change from the vapor to solid or vice-versa and this has some strong influences on the physical properties, especially the vapor pressure. Another major problem is the easy way which the rare earth metal films can become contaminated especially by the strongly electronegative non-metallic elements, i.e. H, N, O. The reported results are critically examined by Gasgnier. Included in his coverage are the results on metallic alloy/compound thin films include permanent magnets, R-Ni and R-Co hydrogen storage alloys, modulated and multilayered structures, and superconducting materials. The metalloid films include those with the chalcogenides, bismuth, lead and their combinations.

The third chapter (137) in this volume, by Vajda, is devoted to hydrogen in metals and their binary compounds RH2 and R H 3 . One of the critical problems is the purity of the starting rare earth metal itself because phase relations can be greatly affected by impurities. Therefore, Vajda devotes some time discussing the preparation of specimens and the phase diagrams. The interesting structural properties, kinetics and thermodynamic behavior, as well as electronic, magnetic and thermal properties are reviewed. The occurrence of H-H pairs in zig-zag chains along the c-axis in the heavy lanthanides and Sc and Y terminal solid solution alloys is one of the unusual structural behaviors observed in these materials. The formation or annihilation of these pairs lead to some interesting kinetic effects and phase transitions during heating and cooling. Also examined is the profound influence of hydrogen on the magnetic properties by the mediation of RKKY interaction in these materials.

The final chapter (138) of this volume, by Gignoux and Schmitt, is an update on the magnetic behaviors of lanthanide intermetatlic compounds. This chapter builds on the review of Kirchmayr and Poldy in chapter 14 of volume 2 of this Handbook series. When one examines chapter 138, it will immediately be apparent that a great deal of science and technology has occurred in the past 15 years in the magnetic behaviors of lanthanide compounds. Gignoux and Schmitt divide their chapter into two main parts: one is devoted to 3d magnetism where both the 3d metal and the lanthanide element contribute to the magnetic behavior; and the second is concerned with lanthanide magnetism by itself. In the first group the major emphasis is on systems which exhibit collective electron metamagnetism. In addition, magnetocrystalline anistropy, and topological frustration and magnetic instability are reviewed. The section devoted to compounds with the lanthanide as a magnetic atom, deals with materials which exhibit metamagnetic processes from different origins. It is found that the majority of these compounds order antiferromagnetically with complex magnetic field vs. temperature phase diagrams. This is due to the long range and oscillatory nature of the RKKY exchange interaction.

C O N T E N T S

Preface v

Contents vii

Contents of Volumes 1-19 ix

135. Y. 0nuki and A. Hasegawa Fermi surfaces of intermetallic compounds 1

136. M. Gasgnier The intricate world of rare earth thin films." metals, alloys, intermetallics, chemical compounds . . . . 105

137. P. Vajda Hydrogen in rare-earth metals, including RH2+ x phases 207

138. D. Gignoux and D. Schmitt Magnetic properties of intermetallic compounds 293

Author Index 425

Subject Index 457

vii

CONTENTS OF VOLUMES 1-19

V O L U M E 1: Metals 1978, 1st repr. 1982, 2nd repr. 1991; ISBN 0-444-85020-1

1. 2. 3. 4. 5. 6. 7. 8. 9.

10. 11. 12.

Z.B. Goldschmidt, Atomic properties (free atom) 1 B.J. Beaudry and K.A. Gschneidner Jr, Preparation and basic properties of the rare earth metals 173 S.H. Liu, Electronic structure of rare earth metals 233 D.C. Koskenmaki and K.A. Gschneidner Jr, Cerium 337 L.J. Sundstr6m, Low temperature heat capacity of the rare earth metals 379 K.A. McEwen, Magnetic and transport properties of the rare earths 411 S.K. Sinha, Magnetic structures and inelastic neutron scattering." metals, alloys and compounds 489 T.E. Scott, Elastic and mechanical properties 591 A. Jayaraman, High pressure studies: metals, alloys and compounds 707 C. Probst and J. Wittig, Superconductivity: metals, alloys and compounds 749 M.B. Maple, L.E. DeLong and B.C. Sales, Kondo effect." alloys and compounds 797 M.E Dariel, Diffusion in rare earth metals 847 Subject index 877

V O L U M E 2: Alloys and intermetallics 1979, 1st repr. 1982, 2nd repr. 1991; ISBN 0-444-85021-X

13. A. Iandelli and A. Palenzona, Crystal chemistry ofintermetallic compounds l 14. H.R. Kirchmayr and C.A. Poldy, Magnetic properties of intermetallic compounds of rare earth

metals 55 15. A.E. Clark, Magnetostrictive RFe2 intermetallic compounds 231 16. J.J. Rhyne, Amorphous magnetic rare earth alloys 259 17. E Fulde, Crystalfields 295 18. R.G. Barnes, NMR, EPR and M6ssbauer effect: metals, alloys and compounds 387 19. E Wachter, Europium chalcogenides: EuO, EuS, EuSe and EuTe 507 20. A. Jayaraman, Valence changes in compounds 575

Subject Index 613

V O L U M E 3: Non-metall ic compounds - I 1979, 1st repr. 1984; ISBN 0-444-85215-8

21. L.A. Haskin and T.P. Paster, Geochemistry and mineralogy of the rare earths 1 22. J.E. Powell, Separation chemistry 81 23. C.K. Jorgensen, Theoretical chemistry of rare earths 111 24. W.T. Carnall, The absorption and fluorescence spectra of rare earth ions in solution 25. L.C. Thompson, Complexes 209 26. G.G. Libowitz and A.J. Maeland, Hydrides 299 27. L. Eyring, The binary rare earth oxides 337 28. D.J.M. Bevan and E. Summerville, Mixed rare earth oxides 401 29. C.P. Khattak and EEY. Wang, Perovskites and garnets 525 30. L.H. Brixne~ J.R. Barkley and W. Jeitschko, Rare earth molybdates (VI) 609

Subject index 655

171

ix

x CONTENTS OF VOLUMES 1-19

V O L U M E 4: N o n - m e t a l l i c c o m p o u n d s - I I 1979, 1st repr. 1984; ISBN 0-444-85216-6

31. 32. 33. 34. 35. 36. 37A. 37B. 37C. 37D. 37E. 37E 37G.

38. 39. 40.

J. Flahaut, Sulfides, selenides and tellurides 1 J.M. H~chke, Halides 89 E Hulliger, Rare earth pnictides 153 G. Blasse, Chemistry and physics of R-activated phosphors 237 M.J. Weber, Rare earth lasers 275 EK. Fong, Nonradiative processes of rare-earth ions in crystals 317 J.W. O'Laughlin, Chemical spectrophotometric and polarographic methods 341 S.R. Taylor, Trace element analysis of rare earth elements by spark source mass spectroscopy 359 R.J. Conzemius, Analysis of rare earth matrices by spark source mass spectrometry 377 E.L. DeKalb and V.A. Fassel, Optical atomic emission and absorption methods 405 A.P. D'Silva and V.A. Fassel, X-ray excited optical luminescence of the rare earths 441 EW.V. Boynton, Neutron activation analysis 457 S. Schuhmann and J.A. Philpotts, Mass-spectrometric stable-isotope dilution analysis for lanthanides in geochemical materials 471 J. Reuben and G.A. Elgavish, Shift reagents and NMR of paramagnetic lanthanide complexes 483 J. Reuben, Bioinorganic chemistry: lanthanides as probes in systems of biological interest 515 T.J. Haley, Toxicity 553 Subject index 587

VO LUM E 5 1982, 1st repr. 1984; ISBN 0-444-86375-3

41. M. Gasgnier, Rare earth alloys and compounds as thin films 1 42. E. Gratz and M.J. Zuckermann, Transport properties (electrical resitivity, thermoelectric power and

thermal conductivity) of rare earth intermetallic compounds 117 43. EP. Netzer and E. Bertel, Adsorption and catalysis on rare earth surfaces 217 44. C. Boulesteix, Defects and phase transformation near room temperature in rare earth sesquioxides 321 45. O. Greis and J.M. Haschke, Rare earth fluorides 387 46. C.A. Morrison and R.P. Leavitt, Spectroscopic properties of triply ionized lanthanides in transparent

host crystals 461 Subject index 693

VOLU M E 6 1984; ISBN 0-444-86592-6

47. K.H.J. Busehow, Hydrogen absorption in intermetallic compounds 1 48. E. Parth~ and B. Chabot, Crystal structures and crystal chemistry of ternary rare earth-transition metal

borides, silicides and homologues 113 49. P. Rogl, Phase equilibria in ternary and higher order systems with rare earth elements and boron 335 50. H.B. Kagan and J.L. Namy, Preparation of divalent ytterbium and samarium derivatives and their use

in organic chemistry 525 Subject index 567

V O L U M E 7 1984; ISBN 0-444-86851-8

51. P. Rogl, Phase equilibria in ternary and higher order systems with rare earth elements and silicon 52. K.H.J. Buschow, Amorphous alloys 265 53. H. Schumann and W Genthe, OrganametalIic compounds of the rare earths 446

Subject index 573

CONTENTS OF VOLUMES 1-19 xi

VOLUME 8 1986; ISBN 0-444-86971-9

54. K.A. Gschneidner Jr and EW. Calderwood, Intra rare earth binary alloys: phase relationships, lattice parameters and systematics 1

55. X. Gao, Polarographie analysis of the rare earths 163 56. M. Leskel~t and L. Niinist6, Inorganic complex compounds I 203 57. J.R. Long, Implications in organic synthesis 335

Errata 375 Subject index 379

VOLUME 9 1987; ISBN 0-444-87045-8

58. R. Reisfeld and C.K. Jorgensen, Excited state phenomena in vitreous materials 1 59. L. Niinist6 and M. Leskel~i, Inorganic complex compounds II 91 60. J.-C.G. Biinzli, Complexes with synthetic ionophores 321 61. Zhiquan Shen and Jun Ouyang, Rare earth coordination catalysis in stereospecific polymerization


395

VOLUME 10: High energy spectroscopy 1988; ISBN 0-444-87063-6

62. Y. Baer and W.-D. Schneider, High-energy spectroscopy of lanthanide materials - An overview 1 63. M. Campagna and EU. Hillebrecht, f-electron hybridization and dynamical screening of core holes in

intermetallic compounds 75 64. O. Gunnarsson and K. Sch6nhammer, Many-body formulation of spectra of mixed valence systems 103 65. A.J. Freeman, B.I. Min and M.R. Norman, Local density supercell theory ofphotoemission and inverse

photoemission spectra 165 66. D.W. Lynch and J.H. Weaver, Photoemission of Ce and its compounds 231 67. S. Hfifner, Photoemission in chalcogenides 301 68. J.E Herbst and J.W Wilkins, Calculation of 4f excitation energies in the metals and relevance to mixed

valence systems 321 69. B. Johansson and N. M~trtensson, Thermodynamic aspects of 4f levels in metals and compounds 361 70. EU. Hillebrecht and M. Campagna, Bremsstrahlung isochromat spectroscopy of alloys and mixed valent

compounds 425 71. J. R6hler, X-ray absorption and emission spectra 453 72. EP. Netzer and J.A.D. Matthew, Inelastic electron scattering measurements 547

Subject index 601

VOLUME 11: Two-hundred-year impact of rare earths on science t988; ISBN 0-444-87080-6

H.J. Svec, Prologue 1 73. E Szabadv~ry, The history of the discovery and separation of the rare earths 33 74. B.R. Judd, Atomic theory and optical spectroscopy 81 75. C.K. Jorgensen, Influence of rare earths on chemical understanding and classification 197 76. J.J. Rhyne, Highlights from the exotic phenomena of lanthanide magnetism 293 77. B. Bleaney, Magnetic resonance spectroscopy and hyperfine interactions 323 78. K.A. Gschneidner Jr and A.H. Daane, Physical metallurgy 409 79. S.R. Taylor and S.M. McLennan, The significance of the rare earths in geochemistry and

cosmochemistry 485 Errata 579 Subject index 581

xii CONTENTS OF VOLUMES 1-19

V O L U M E 12 1989; ISBN 0-444-87105-5

80. J.S. Abell, Preparation and crystal growth of rare earth elements and intermetallic compounds 1 81. Z. Fisk and J.E Remeika, Growth of single crystals from molten metal fluxes 53 82. E. Burzo and H.R. Kirchmayr, Physical properties of R2Fel4B-based alloys 71 83. A. Szytuta and J. Leciejewicz, Magnetic properties of ternary intermetallie eompounds of the RT2X2

type 133 84. H. Maletta and W. Zinn, Spin glasses 213 85. J. van Zytveld, Liquid metals and alloys 357 86. M.S. Chandrasekharaiah and K.A. Gingerich, Thermodynamic properties ofgaseoas species 409 87. W.M. Yen, Laser spectroscopy 433

Subject index 479

V O L U M E 13 1990; ISBN 0-444-88547-1

88. E.I. Gladyshevsky, O.I. Bodak and V.K. Pecharsky, Phase equilibria and crystal chemistry in ternary rare earth systems with metallic elements 1

89. A.A. Eliseev and G.M. Kuzmichyeva, Phase equilibrium and crystal chemistry in ternary rare earth systems with chalcogenide elements 191

90. N. Kimizuka, E. Takayama-Muromachi and K. Siratori, The systems R203-M203-MtO 283 91, R.S. Houk, Elemental analysis by atomic emission and mass spectrometry with inductively coupled

plasmas 385 92, P.H, Brown, A.H. Rathjen, R.D, Graham and D.E. Tribe, Rare earth elements in biologicalsystems 423


V O L U M E 14 1991; ISBN 0-444-88743-1

93. R. Osborn, S.W. Lovesey, A.D. Taylor and E. Balcar, Intermultiplet transitions using neutron spectroscopy 1

94. E. Dormann, NMR in intermetallic compounds 63 95. E. Zirngiebl and G. Giintherodt, Light scattering in intermetallic compounds 163 96. E Thalmeier and B. Liithi, The electron-phonon interaction in intermetallic compounds 225 97. N. Grewe and E Steglich, Heaoyfermions 343

Subject index 475

V O L U M E 15 1991; ISBN 0-444-88966-3

98. 99.

100. 101. 102.

103. 104.

J.G. Sereni, Low-temperature behaviour of cerium compounds 1 G.-y. Adachi, N. Imanaka and Zhang Fuzhong, Rare earth carbides 61 A. Simon, Hj. Mattausch, G.J. Miller, W. Bauhofer and R.K. Kremer, Metal-rich halides 191 R.M. Almeida, Fluoride glasses 287 K.L. Nash and J.C. Sullivan, Kinetics of complexation and redox reactions of the lanthanides in aqueous solutions 347 E.N. Rizkalla and G.R. Choppin, Hydration and hydrolysis oflanthanides 393 L.M. Vallarino, Macroeycle complexes of the lanthanide(llI) yttrium(IIl) and dioxouranium(VI) ions from metal-templated syntheses 443 Errata 513 Subject index 515

CONTENTS OF VOLUMES 1-19 xiii

M A S T E R INDEX, Vols. 1 -15 1993; ISBN 0-444-89965-0

V O L U M E 16 1993; ISBN 0-444-89782-8

105. M. Loewenhaupt and K.H. Fischer, Valence-fluctuation and heavy-fermion 4fsystems 1 106. I.A. Smirnov and V.S. Oskotski, Thermal conductivity of rare earth compounds 107 107. M.A. Subramanian and A.W. Sleight, Rare earthspyrochlores 225 108. R. Miyawaki and I. Nakai, Crystal structures of rare earth minerals 249 109. D.R. Chopra, Appearance potential spectroscopy of lanthanides and their intermetallics 519

Author index 547 Subject index 579

V O L U M E 17: Lanthanides/Act inides: Physics - I 1993; ISBN 0-444-81502-3

110. M.R. Norman and D.D. Koelling, Electronic structure, Fermi surfaces, and superconductivity in f electron metals 1

111. S.H. Liu, Phenomenological approach to heavy-fermion systems 87 112. B. Johansson and M.S.S. Brooks, Theory of cohesion in rare earths and actinides 149 113. U. Benedict and W.B. Holzapfel, High-pressure studies - Structural aspects 245 114. O. Vogt and K. Mattenberger, Magnetic measurements on rare earth and aetinide monopnictides and

monochaleogenides 301 115. J.M. Fournier and E. Gratz, Transport properties of rare earth and actinide intermetallies 409 116. W. Potzel, G.M. Kalvius and J. Gal, M6ssbauer studies on electronic structure of intermetallie

compounds 539 117. G.H. Lander, Neutron elastic scattering from actinides and anomalous lanthanides 635


V O L U M E 18: Lanthanides/Act inides: Chemistry 1994; ISBN 0-444-81724-7

118. G.T. Seaborg, Origin of the aetinide concept 1 119. K. Ba|asubramanian, Relativistic effects and electronic structure of lanthanide and actinide

molecules 29 120. J.V. Beitz, Similarities and differences in trivalent lanthanide- and actinide-ion solution absorption

spectra and luminescence studies 159 121. K.L. Nash, Separation chemistry for lanthanides and trivalent actinides 197 122. L.R. Morss, Comparative thermochemical and oxidation-reduction properties of lanthanides and

actinides 239 123. J.W. Ward and J.M. Haschke, Comparison o f4 fand 5felement hydride properties 293 124. H.A. Eiek, Lanthanide and aetinide halides 365 125. R.G. Haire and L. Eyring, Comparisons of the binary oxides 413 126. S.A. Kinkead, K.D. Abney and T.A. O'Donnell,f-element speciation in strongly acidic media: lanthanide

and mid-actinide metals, oxides, fluorides and oxide fluorides in superacids 507 127. E.N. Rizkalla and G.R. Choppin, Lanthanides and aetinides hydration and hydrolysis 529 128. G.R. Choppin and E.N. Rizkalla, Solution chemistry ofactinides and lanthanides 559 129. J.R. Duffield, D.M. Taylor and D.R. Williams, The biochemistry of the f-elements 591


xiv CONTENTS OF VOLUMES 1-19

V O L U M E 19: L a n t h a n i d e s / A c t i n i d e s : Phys ics - II 1994; ISBN 0-444-82015-9

130. E. Holland-Moritz and G.H. Lander, Neutron inelastic scattering from actinides and anomalous lanthanides 1

131. G. Aeppli and C. Broholm, Magnetic correlations in heavy-fermion systerr~." neutron scattering from single crystals 123

132. P. Wachter, Intermediate valence and heavy fermions 177 133. J.D. Thompson and J.M. Lawrence, High pressure studies - Physical properties of anomalous Ce, Yb

and U compounds 383 134. C. Colinet and A. Pasturel, Thermodynamic properties of metallic systems 479

Author Index 649 Subject Index 693

Handbook on the Physics and Chemistry of Rare Earths Vol. 20 edited by K.A. Gschneidner, Jr. and L. Eyring © 1995 Elsevier Science B.V. All rights reserved

Chapter 135

FERMI SURFACES OF INTERMETALLIC COMPOUNDS

Yoshichika Onuki Department of Physics, Faculty of Science, Osaka University, Toyonaka, Osaka 560, Japan

Akira Hasegawa Department of Physics, Faculty of Science, Niigata University, Niigata 950-21, Japan

C o ~ e ~ s

List of symbols and abbreviations 1. Introduction 2. Theory of energy band structure

2.1. Relativistic effect in the lanthanide atoms

2.2, Luttinger's theorem on the Fermi surface 2.3. Relativistic band theory

2.3.1. Kohn-Sham-Dirac one-electron equation

2.3.2. Self-consistent, symmetrized relativistic APW approach 16 2.3.2.1. APW matrix elements in

a symmetrized form 16 2,3.2.2. Determination of

eigenvalues and eigenfunctions 19

2.3.2.3. Electron density function 20 2.3.2.4. Self-consistent

calculation 21 2.4. Determination of the density of states,

the Fermi surface and the cyclotron effective mass 22

2.5. Mass enhancement factors 24 3. Transverse magnetoresistance and de Haas-

van Alphen effect 26 3.1. Transverse magnetoresistance 26 3.2. de Haas-van Alphen effect 27

1 4. Experimental results and comparisons with 2 band calculations 30 8 4.1. Fermi surfaces in the simple cubic

Brillouin zone 30 8 4.1.1. RB 6 30

11 4.1.2. LaAg and YZn 38 12 4.1.3. RIn 3 40

4.1.4. RSn 3 52 14 4.2. Fermi surfaces in the bcc Brillouin zone 59

5. Conclusions Acknowledgement References

4.2.1. RX 59 4.2.2. RAt 2 67

4.3. Fermi surfaces in the hexagonal Brillouin zone 70 4.3.1. RG% 70

4.4. Fermi surfaces in the tetragonal Bfillouin zone 74 4.4.1. RRu2Si 2 and RRu2Ge 2 74 4.4.2. CeCu2Si 2 81

4.5. Fermi surface in the orthorhombic Brillouin zone 82 4.5.1. RNi 82 4.5.2, RCu 2 87 4.5.3. RCu 6 90

95 98 98

List of symbols and abbreviations

a lattice constant AF1,2 antiferromagnetic states

2 Y. 0NUKI and A. HASEGAWA

APW augmented plane wave m* effective mass

c phase velocity of light m~ cyclotron effective mass

C specific heat Mosc oscillatory component of magnetization

dHvA de Haas-van Alphen MBZ magnetic Brillouin zone

e electronic charge N(EF) density of states at E F

E F Fermi energy n e number of electron carriers

Ef f level n h number of hole carriers

Eex exchange splitting energy RKKY Ruderman-Kittel-Kasuya-Yosida

E i eigenvalue of ~pi S extremal cross-sectional area of the F de Haas-van Alphen frequency Fermi surface

FFT fast Fourier transformation T absolute temperature

FS Fermi surface T c Curie temperature

g g factor for the spin of the conduction TD Dingle temperature electron TK Kondo temperature

gj Land6 g factor TN N6el temperature

H magnetic field TQ quadrupolar ordering temperature

H c critical field for the metamagnetic U Coulomb repulsive force transition v velocity of an electron

h Planck constant divided by 2~ v F Fermi velocity

Hex effective H including the exchange field v± velocity component perpendicular to the J current Fermi surface or cyclotron orbit

J total angular momentum V(r) external potential

J~ z-component of J V hybridized coupling constant

k wave vector 7 electronic specific heat coefficient

k magnitude of k 7b 7 calculated from the band model

kB Boltzmann constant )~ mass enhancement factor

k H magnitude of wave vector along the ~'m ~, due to electron-magnon interaction field direction ~,p ), due to electron-phonon interaction

kv~ Fermi vector along the three principal /t B Bohr magneton

axes (i = 1,2, 3) #x~[p(r)] exchange-correlation potential KKR Korringa-Kohn-Rostoker Ap/p magnetoresistance, LAFW linearized augmented plane wave Ap/p = [p(H)-p(O)]/p(O)

LDA local density approximation a(r) local spin density at r

LMTO linearized muffin-tin orbital z scattering lifetime

m0 free electron mass wc cyclotron frequency m b band mass

1. Introduction

T h e l a n t h a n i d e c o m p o u n d s are usua l ly t r ea ted in m a g n e t i s m by a n f - loca l ized mode l ,

bu t show var ious in te res t ing p h e n o m e n a such as va l ence f luctuat ions , gap states, K o n d o

latt ice, and h e a v y e lec t rons . T h e s e or ig ina te f r o m the 4 f e lec t rons in the l an than ide

c o m p o u n d s , w h i c h are e i the r b o u n d to the l an than ide a toms or de local ized , i nd ica t ing

FERMI SURFACES OF INTERMETALLIC COMPOUNDS 3

an itinerant nature. The 4f electrons in the atom are pushed deep into the interior of the closed 5s and 5p shells because of the strong centrifugal potential l(l + 1)/r 2, where l = 3 holds for the f electrons. This is why the 4f electrons possess an atomic-like character in the crystal. On the other hand, the tail of their wave function spreads to the outside of the closed 5s and 5p shells, which is highly influenced by the potential energy, the relativistic effect and the distance between the lanthanide atoms; this results in hybridization of the 4f electrons with the conduction electrons. These cause the various phenomena mentioned above.

The Coulomb repulsive force of the 4f electron (or the intra-atomic correlation energy) U at the same atomic site is so strong, for example U ~ 5 eV in Ce compounds, that occupancy of a same site by two 4f electrons is usually prohibited. The 4f partial density of states determined by resonant photoemission experiments shows a maximum below the Fermi level which corresponds to the binding energy or the level of the 4f electrons El. For example, the distance from this 4f level to the Fermi level is 7.0 eV and 1.2 eV in SmCu6, 5.5 eV in NdCu6, 3.5 eV in PrCu6 and 2.4eV in CeCu6 (Ishii et al. 1987). The tail of the 4f partial density of states extends to the Fermi level even at room temperature in CeCu6 and also slightly in PrCu6, while no trend of 4f states is observed around the Fermi level in NdCu6.

Near the Ce or Yb end of the R series, the 4f level thus approaches the Fermi level in energy and the 4f electrons hybridize more strongly with the conduction electrons with the kinetic energy Ek. This f-hybridized coupling constant is denoted by V. A theoretical treatment for such a system is called the periodic Anderson model (Anderson 1961). The parameters Ek, V, Ef and U predominantly control the dynamics of the system. These values depend actually on the crystal structure. The relation between the magnetic ordering temperature and the distance between the Ce (or U) atoms is known as a Hill plot (Hill 1970).

When U is strong and/or V is ignored, the freedom of the charge in the 4f electron is suppressed, while the freedom of the spin is retained, representing the 4f-localized state. Naturally, the degree of localization depends on El, where larger Ef helps to increase the localization. This situation is applied to most of the lanthanide compounds in which the RKKY interaction (Ruderman and Kittel 1954, Kasuya 1956, Yosida 1957) plays a predominant role in magnetism. Therefore, the mutual magnetic interaction between the 4f electrons occupying different atomic sites cannot be of a direct type, such as in 3d metal magnetism, but should be indirect, which occurs only through the conduction electrons.

In the RKKY interaction, a localized spin Si interacts with a conduction electron with spin s, which leads to a spin polarization of the conduction electron. This polarization interacts with another spin Sj localized on ion j and therefore creates an indirect interaction between the spins Si and Sj. This indirect interaction extends to the far distance and damps with a sinusoidal 2kv oscillation, where kv is half of the caliper dimension of the Fermi surface. When the number of 4f electrons increases in such a way that the lanthanide element changes from Ce to Gd or reversely from Yb to Gd in the compound, the magnetic moment becomes larger and the RKKY interaction stronger, leading to

4 Y. ONUKI and A. HASEGAWA

i00

0

o 50

" ~ " 1 , , , , , , , , i ' ' ' ' ' " ' 1 ' ~ ' ~ 1 ~ , ' , , , , q , ,

CexLal-xCu6 _X = J / / b - a x i s 0.50 . . . . . . . . . . . . . . . . . . . . _ ~ ~

-o .73 . . . . . .

- , /

90 . . . . . . . . . 0.01 0,1 1 10 100

Temperature (K)

Fig. 1. Temperature dependence of the electric resistivity in CexLa~_xCu 6 (Sumiyama et al. 1986).

magnetic order of which the ordering temperature roughly follows the de Gennes relation, (gj-1)2j(j + 1). Here gj and J are the Land6 g factor and the total angular momentum, respectively.

Contrary to what happens at large U, higher V tends to enhance the hybridization of 4f electrons with conduction electrons, thus accelerating the delocalization of the 4f electrons (Koelling et al. 1985). The delocalization of 4f electrons tends to make the 4fband wide. When Ef > V, we have still better localization and expect the Kondo regime in the Ce (or Yb) compounds.

The Kondo effect was studied for the first time in a dilute alloy where a ppm range of the 3d transition metal is dissolved in a pure metal of copper. Kondo (1964) showed that the third-order scattering of the conduction electron with the localized moment of the transition impurity diverges logarithmically with decreasing temperature, and clarified the origin of the long standing problem of the resistivity minimum. This became the start of the Kondo problem, and it took ten years for theorists to solve this divergence problem at the Fermi energy (Wilson 1975).

The many-body Kondo bound state is now understood as follows. For the simplest case of no orbital degeneracy, the localized spin S(T) is coupled antiferromagneti- tally with the spin of the conduction electron s(+). Consequently the singlet state {S(i") • s(J,) + S(1)" s(T)} is formed with binding energy kBTK. Here the Kondo temperature TK is the single energy scale. In other words, disappearance of the localized moment is thought to be due to the formation of a spin-compensating cloud of the conduction electron around the impurity moment.

Kondo-like behavior was observed in the ianthanide compounds, typically in Ce and Yb compounds (Buschow et al. 1971, Parks 1977, Falicov et al. 1981). For example, the electric resistivity in CexLal-xCu6 increases logarithmically with decreasing temperature for all the x-values (Sumiyama et al. 1986), as shown in fig. 1. The Kondo effect occurs independently at each cerium site even in a dense system. Therefore, this phenomenon was called the dense Kondo effect.


The Kondo temperature in the Ce (or Yb) compound is large compared to the magnetic ordering temperature based on the RKKY interaction. For example, the cerium ion is trivalent (J = 5/2), and the 4f energy level is split into three doublets by the crystalline electric field, namely possessing the splitting energies of A1 and A2. The Kondo temperature is given as follows (Yamada et al. 1984):

T~z=Dexp - 3 [JexlD(EF) when T > AI, A2, (1)

and

TK = A---~Dexp I&xlb(EF) when T < At, A2. (2)

Here D, [Jex [ and D(Ev) are the band width, exchange energy and density of states, respectively. If we postulate TK ~ 5 K, for D = 104 K, zll = 100 K and A2 = 200 K, the value of T~ ~ 50K is obtained, which is compared to the S = ½-Kondo temperature of 10 3 K defined as T ° = D exp(-1/IJex I D(EF)). These large values of Kondo temperatures shown in eqs. (1) and (2) are due to the orbital degeneracy of the 4f levels. Therefore, even at low temperatures the Kondo temperature is not T ° but TK shown in eq. (2).

On the other hand, the magnetic ordering temperature is about 5 K in the Ce (or Yb) compound, which can be simply estimated from the de Gennes relation under the consideration of the Curie temperature of about 300K in Gd. Therefore, T~ is much higher than the magnetic ordering temperature, but TK is close to it. Therefore, it depends on the compound whether or not magnetic ordering occurs at low temperatures (Brandt and Moshchalkov 1984). As shown in table 1, some compounds such as CeB6 or CeAI2 order antiferromagnetically below 5 K, while CeCu6 (TK = 4 K) does not order magnetically.

The ground-state properties of dense Kondo systems are interesting in magnetism, which is highly different from the dilute Kondo effect. In the cerium intermetallic compounds such as CeCu6, cerium ions are periodically aligned whose ground state cannot be a scattering state but becomes a coherent Kondo-lattice state. The electric resistivity p decreases steeply with decreasing temperature, following p ~ A T 2 with a large value of the coefficient A. The v/A-value is proportional to the effective mass of the carrier and thus inversely proportional to the Kondo temperature (Kadowaki and Woods 1986). Correspondingly, the electronic specific heat coefficient y roughly follows the simple relation y ~ 104/TK (mJ/K2mol). It reaches 1600mJ/K2mol for CeCu6 because of a small Kondo temperature (Satoh et al. 1989). The Ce Kondo- lattice compound with magnetic ordering also possesses the large y value even if the RKKY interaction overcomes the Kondo effect at low temperatures. For example, the ~, value of CeB6 is 250 mJ/K 2 mol, which is roughly one hundred times larger than that of LAB6, 2.6 mJ/K 2 tool. The conduction electrons possess large effective masses and thus move slowly in the crystal. These heavy electrons become superconductive in CeCuaSi2

Y. ONUKI and A. HASEGAWA

Table 1 Characteristic properties of Ce compounds ~

Compound Crystal a (.&) T n (K) T c (K) y (mJ/K 2 mol) H c (kOe) structure

(a) Non-Kondo lattice compounds with magnetic ordering CeGa 2 hexa 4.32 11.4 CeRu2Ge 2 tetra 4.27 8.5

(b) Kondo lattice compounds with magnetic ordering

CeSb cubic 4.54 16.2 Celn 3 cubic 4.69 10.2 CeA12 cubic 3.49 3.8 CeCu 2 ortho 3.57 3.4 CeB 6 cubic 4.14 2.3 b CeCu 2 Si 2 tetra 4.11 0.7 c

8.2 9

7.5 20

20 38 130 >150 135 53 82 18

250 15 1000 70

(c) Kondo lattice compounds without magnetic ordering CeCu 6 ortho 4.83 1600 CeRu2Si2 tetra 4.19 350 CeNi ortho 3.59 65-85 CeSn 3 cubic 4.72 53

20 80

" Symbols: a, distance between nearest Ce atoms; TN, N6el temperature; Tc, Curie temperature; TQ, quadrupolar ordering temperature; To, superconducting transition temperature; ~/, electronic specific heat coefficient; He, critical field for metamagnetic transition. b TQ=3.2K. e T0=0.7K '

(Steglich et al. 1980). Therefore, the Kondo-latt ice system is called a heavy-electron or heavy-Fermion system.

When Ef < V, the 4 f electrons may tend to be delocalized, manifesting the valence- fluctuation regime. CeSn3 and CeNi were once called valence-fluctuation compounds or mixed-valent compounds. The magnetic susceptibility in these compounds follows the Cur ie-Weiss law at higher temperatures than room temperature, possessing the magnetic moment near Ce 3+, while it becomes approximately temperature-independent with decreasing temperature, showing a broad maximum around 150-200 K (Gschneidner et al. 1985). Thus the valence o f Ce atoms seems to change from Ce 3+ into Ce 4+ (non-

magnetic state) with decreasing temperature. The ionic radius o f the lanthanide atom decreases with increasing number of

4 f electrons, which is well known as lanthanide contraction. A plot o f the lattice constant o f the lanthanide compound versus the atomic number of the lanthanide element shows a nearly straight line, except for some Ce, Sm, Eu, Tm and Yb compounds, where the lanthanides can take integral valencies different from 3 as in Ce 4÷ and Sm 2+, Eu 2+, Tm 2+, Yb z+. The valence change in these compounds is brought about by changing the constitution x (such as in Sml-xLaxB6 Kasaya et al. 1980) or by


introducing pressure (for SmS Jayaraman et al. 1970) or a magnetic field (YbB12 Sugiyama et al. 1988), as well as by changing the temperature as mentioned above for CeSn3 and CeNi.

The first insulating valence fluctuations were studied by Jayaraman et al. (1970) for SINS. An insulating black phase of SmS at ambient pressure changes into a metallic golden phase at high pressures. In other words, divalence of Sm 2+ changes into the intermediate valence between 2+ and 3+. The application of hydrostatic pressure is associated with a smaller volume, which introduces the 4f valence transition and consequently delocalization of 4f electrons.

Fermi surface studies are very important to know the ground-state properties of these various magnetic compounds (Norman and Koelling 1993, Onuki et al. 1991a). Even in the localized system, the presence of 4f electrons alters the Fermi surface through the 4f-electron contribution to the crystal potential and through the introduction of new Brillouin zone boundaries and magnetic energy gaps which occur when 4f electron moments order. The latter effect may be approximated by a band-folding procedure where the paramagnetic Fermi surface, which is roughly similar to the Fermi surface of the corresponding La compound, is folded into a smaller Brillouin zone based on the magnetic unit cell, which is larger than the chemical unit cell.

If the magnetic energy gaps associated with the magnetic structure are small enough, conduction electrons undergoing cyclotron motion in the presence of a magnetic field can tunnel through these gaps and circulate the orbits on the paramagnetic Fermi surface. If this magnetic breakthrough (or breakdown) occurs, the paramagnetic Fermi surface may be observed in the de Haas-van Alphen (dHvA) effect even in the presence of magnetic order.

For Kondo-lattice compounds with magnetic ordering, the Kondo effect is expected to have minor influence on the topology of the Fermi surface, representing that Fermi surfaces of the Ce compounds are roughly similar to those of the corresponding La compounds, but are altered by the magnetic Brillouin zone boundaries mentioned above. Nevertheless, the effective masses of the conduction carriers are extremely large compared to those of La compounds mentioned above. In this system a small amount of 4f electron most likely contributes to make a sharp density of states at the Fermi energy. Thus the energy band becomes flat around the Fermi energy, which brings about the large mass.

There is a big difference in f-electron character between the Kondo regime and the valence-fluctuation regime. One may be tempted to think that the 4f electrons in a Kondo lattice compound with a large value of TK are itinerant. This seems to be true, as shown later in detail for CeSn3 and CeNi or CeRu2 Si2.

In the following sections we present the dHvA results of the lanthanide compounds shown in table 2, which are compared to the results of energy band calculations. Comparisons of the dHvA experiments with band calculations are essentially important to determine the f character, namely whether the 4f electrons are itinerant or localized. These Fermi surface properties should shed light on the basic understanding of the strongly correlated 4f-electron system.

Y. (3NUKI and A. HASEGAWA

Table 2

Rare earth compounds for which dHvA results and energy band calculations are presented in the text.

Elements Y La Ce Pr Nd Sm Gd Yb

B LaB 6 CeB 6 PrB 6 NdB 6

Ag LaAg

Zn YZn

In Lain 3 Celn 3 Prln 3 Ndln 3 Smln 3 Gdln 3

Sn LaSh 3 CeSn 3

Bi LaBi CeBi

Sb LaSb CeSb PrSb SmSb GdSb

As CeAs YbAs

A1 YA12 LaA1 z CeAI z

Ga LaGa2 CeG% SmGa 2

Ru/Si LaRu2Si z CeRu2Si 2

Ru/Ge LaRu2Ge 2 CeRu2Ge z

Cu/Si CeCu2Si2

Ni LaNi CeNi PrNi

Cu YCu z CeCu 2 SmCu 2

LaCu 6 CeCu 6 PrCu 6 NdCu 6 SmCu 6

2. Theory of energy band structure

2.1. Relativistic effect in the lanthanide atoms

The lanthanide atoms have fairly large atomic numbers and their compounds contain other heavy atoms as the constituent elements. Therefore, it is essential to take into account the relativistic effect in calculations of the energy band structures for the lanthanide compounds. In this section, we explain how the energy and the wave function of an electron in these compounds may be influenced by relativity.

We treat the neutral cerium atom as an example, and explain the important effect of relativity on the electrons in its outer shells such as the 4f, 5d and 6s electrons. The electrons in the s states in both inner (the Xe core) and outer shells have finite probability amplitudes at the nucleus. As the nuclear potential is deep in the vicinity of the nucleus, electron velocity approaches light velocity and consequently the relativistic effect becomes appreciably large. Compared to the non-relativistic theory, the corresponding energy of all the s (l = 0) electrons decreases significantly, because the s electrons have relatively large probability amplitudes at the nucleus and their wave functions contract toward the nucleus. This direct relativistic effect on the s electrons induces an indirect effect on the other (l ~ 0) electrons. Namely, the s electrons tend to screen more effectively the nuclear potential which the 4f and 5d electrons feel, and therefore the latter would be bound more loosely. As a result, their energies increase and their wave functions tend to spread outward in contrast to the 6s electrons.


.72_

'<3

e v e

~ - 0 ,

~x7

o 1 2 3 4 5 D i s t a n c e ( a. u. )

Fig. 2. Electronic charge densities of the 4f, 5p, 5d and 6s orbits for the neutral Ce atom. The solid and dashed lines show the results of relativistic and non-relativistic calculations, respectively. In each orbit, except the 6s orbit, two solid curves distinguish the charge densities having different total angular momentum j, where the charge density with higher j spreads out more widely than with lower j . Units are arbitrary, but the normalization constant is the same for all states. Both calculations are performed for the configuration of 4f25p65d°6s 2, i.e. the 5d orbit is not occupied, although the result for the 5d state is added in the figure for the sake of comparison.

5d

-1 .0

V i ~

J i i i

i r

l

t ,

, I

i

1 I I I I i I I I i I I I I r

La Ce Pr Nd Pm Sm Eu Gd Tb DyHo Er Tm Yb Lu

Fig. 3. Relativistic (solid line) and non-relativistic (dashed line) calculations for the eigenvalues of the 4f, 5d and 6s states of the neutral lanthanide atoms.

It is now clear that in the many-electron atoms relativity causes a different effect on the energies and wave functions of electrons with different quantum numbers. Actually, they are so complicated that they cannot be taken into account correctly by the Pauli approximation nor by any other perturbation theories.

For the sake of illustration, we explain the electronic structure of the cerium atom by using the self-consistent field method of Liberman et al. (1965), which is based on the Dirac one-electron equation with the exchange and correlation interactions in the local- density approximation (Callaway and March 1984). A spherically symmetric potential is assumed. Thus the solid lines in fig. 2 represent calculated charge densities of the outer- shell orbits, which are compared to those of the non-relativistic calculations shown by dashed lines (Herman and Skillman 1963). The corresponding results of the relativistic and non-relativistic calculations for the eigenvalues of the 4f, 5d and 6s states of the neutral lanthanide atoms are shown in fig. 3 by the solid and dashed lines, respectively. Electronic configurations in the outer shells, which are used in calculations, are listed in table 3. It is remarkable in fig. 3 that magnitudes of the relativistic energy shift and

10 Y. 0 N U K I and A. HASEGAWA

Table 3

Electronic configuration in the outer shells of the neutral lanthanide atoms

Z Element Neutral atom Trivalent ion

4 f 5d 6s

57 La 4 f ° 5d I 6s ~ 4 f °

58 Ce 4 f z 6s 2 4 f l

59 Pr 4f 3 6s 2 4 f 2

60 Nd 4f 4 6s 2 4 f 3

61 Pm 4f s 6s 2 4 f 4

62 Sm 4f 6 6s 2 4 f 5

63 Eu 4 f 7 6s 2 4 f 6

64 Gd 4 f 7 5d 1 6s 2 4 f 7

65 Tb 4 f 9 6s 2 4 f 8

66 Dy 4 f l° 6s z 4 f 9

67 Ho 4 f 11 6s 2 4f 1°

68 Er 4 f 12 6s 2 4 f 11

69 T m 4f 13 6s 2 4f 12

70 Yb 4 f TM 6s 2 4 f 13

71 Lu 4 f TM 5d 1 6s 2 4f TM

the spin-orbit splitting in the 4f states are far larger than those in the 5d or 6s states, and increase monotonically as the lanthanide element changes from La to Lu. At the Gd atom having the 4f 7 configuration, a large energy dip of the 4f states is found in both relativistic and non-relativistic results. Such a large dip would not be found for the 4f 8 configuration. Therefore, the depth of the dip provides an approximate estimatign of the intra-atomic correlation energy of the 4f electrons in the lanthanide atoms, i.e. U ~ 400 mRyd (= 5 eV).

The relativistic energy shift and the spin--orbit splitting in the 4f states of the cerium atom are 200 mRyd and 31 mRyd, respectively. These energies are comparable to and/or larger than the width of typical 4f bands in the cerium compounds. The spin- orbit splitting in the 5d electrons of the cerium atom is 20mRyd in energy, which is not negligibly small either. Therefore, the relativistic effect should be taken into account in quantitative calculations of the energy band structures for the lanthanide compounds, and the relativistic energy band structure calculations should be carried out self-consistently because the relativistic effect on the 4f electrons is essentially indirect.

In various cerium compounds, the nearest-neighbor distance between the cerium atoms ace-ce ranges from 6 to 9 a.u. (Hill 1970), and its intermediate distance a c e - C e / 2 coincides roughly with the outer-shell region of the cerium atom. As seen in fig. 2, the wave function of the 4f electron decreases rapidly in the outer-shell region. The overlap between the wave functions of the 4f electrons in the neighboring cerium atoms is actually so small that they cannot be itinerant due to that alone. Nevertheless, the 4f electrons can be itinerant


in a crystal, but only if they hybridize strongly with the 6s, 5p or 5d electrons of the neighboring cerium atoms and/or the valence electrons of the constituent atoms. If this hybridization effect is not strong enough, the 4f electrons cannot be itinerant but will be localized at each cerium ion in the crystal.

It is now clear that the relativistic screening effect of the 6s electrons as well as the other s electrons tends to promote an itinerant nature of the 4f electrons in a crystal. It is difficult at present, however, to predict correctly in which cerium compounds the 4f electrons may be itinerant, because the strong correlations between the 4f electrons make it difficult to derive a quantitative criterion for the itinerancy of the 4f electrons theoretically.

2.2. Luttinger's theorem on the Fermi surface

The concept of the Fermi surface was introduced originally in the one-electron theory of metals in which the electron-electron interactions (correlations) are neglected. The Fermi surface represents a limit of the electronic momentum distribution in the ground state, and is defined as a constant energy surface in momentum space whose energy is equal to the Fermi energy. It divides momentum space sharply into two regions which the electrons occupy or do not occupy.

If a magnetic field is applied to the conduction electrons, the energy levels of the electrons converge to discrete energy levels called the Landau levels. The interval of the Landau levels is proportional to the magnitude of the magnetic field. As the magnetic field is increased, the Landau levels cross the Fermi level successively and cause various physical quantities to oscillate as a function of field. The de Haas-van Alphen effect is a typical example of such magnetic oscillatory phenomena (Shoenberg 1984).

In real metals, the conduction electrons interact with each other and therefore the Fermi surface cannot be defined so simply as in the one-electron theory. Instead of the one-electron energy, the one-particle excitation energy should be considered. In momentum space for such interacting electrons or quasi-particles, it is meaningful to define a constant-energy surface whose energy is equal to the chemical potential. Luttinger called such a constant-energy surface the true Fermi surface (Luttinger 1960, 1961). In the ground state, quasiparticles have a long lifetime on the true Fermi surface and the momentum distribution is discontinuous across it. Luttinger asserted that the volume of the true Fermi surface is equal to the volume enclosed by the Fermi surface in a non- interacting electron system. Thus the volume of the Fermi surface is independent of the interactions. He also showed that the true Fermi surface causes various magnetic oscillatory phenomena, just as the Fermi surface does in the one-electron theory. Even though the electron-electron interactions may change the topology of the Fermi surface, the volume of the Fermi surface is kept invariant. This is the essence of the Luttinger theorem on the Fermi surface. Therefore, the true Fermi surface is observed in measurements of the de Haas-van Alphen effect. In the following, we will call it simply the Fermi surface.


2.3. Relativistic band theory

Among many methods that were proposed for calculations of the electronic energy band structure in a given periodic potential, the augmented plane wave (APW) method (Slater 1937) and the Green function (KKR) method (Korringa 1947, Kohn and Rostoker 1954) were useful to produce quantitatively accurate results for simple metals, transition metals and their compounds, and these methods contributed much to the understanding of various physical properties of these materials (Dimmock 1971). In both methods, a spatial form of the potential is assumed in the so-called muffin-tin approximation, in which it is spherically symmetric within the sphere (the APW sphere) inscribed around each nucleus and is constant in the interstitial region between the spheres. Inside the APW sphere, the Bloch wave function is expanded in terms of the solutions of the Schr6dinger equation. This ensures high accuracy of the eigenvalues, but causes both methods to consume much computational time especially when applied to compounds with complex crystal structures having many atoms per primitive cell, because the eigenvalues should be found as zeros of a determinant with a large dimension.

To improve on this drawback in the APW and the KKR methods, linearized versions for these methods such as the LAPW method and the linearized muffin-tin orbital (LMTO) method were invented (Andersen 1975, Koelling and Arbman 1975). In these linearized methods, it is essential that the electron wave function behaves quite accurately as a linear function of energy around an energy appropriately chosen in the band so that the eigenvalues can be determined much faster by a usual matrix diagonalization technique. The relativistic effect is taken into account by perturbation theories, such as the Pauli approximation. These methods proved to work well in the understanding of systematic variations of many ground-state properties of a series of metals and compounds.

However, the Fermi surface depends sensitively on details of the E-k relation, and the determination of the Fermi surface demands a more precise calculation for the eigenvalues than that for the cohesive energy. Therefore, for studies of the Fermi surface, these l'inearized methods should be applied carefully. Errors originating from linearized approximations should be minimized. Nevertheless, the LAPW method is valuable for calculations of the electronic structure in lanthanide compounds with complex crystal structures, such as LaCu6.

For studies of the Fermi surface in the lanthanide compounds, it is necessary to develop a reliable theoretical method in which hybridization of the 4f electrons with other electrons as well as the relativistic effect can be taken into account quantitatively. For that purpose, the relativistic APW method proposed by Loucks (1967) provides a good starting basis. Loucks derived his original method from the Dirac one-electron equation, which is a natural extension of Slater's non-relativistic APW method (Slater 1937). It proved to be a powerful method comparable to a relativistic KKR method (Onodera and Okazaki 1966, Takada 1966). Loucks' method does not accocunt for the symmetrization of the wave functions by group theory, nor it is a self-consistent method. These shortcomings are serious limitations for calculations of the energy band structure in the lanthanide compounds.


To achieve symmetrization, a direct product of the space operator and the spin operator was constructed as a new operator, under which the variational expression of Loucks' method is kept invariant (Yamagami and Hasegawa 1990). By the projection operator technique, it is straightforward to derive a symmetrized form of the relativistic APW method, which covers both symmorphic and non-symmorphic space group.

Koelling (1969) proposed a similar method, but in his method he derived a symmetrized form by using a basis function of the Pauli-spinor type and the Foldy-Wouthusen transformation. An approach proposed by Yamagami and Hasegawa(1990) is more general and has wider applicability than his method because the relativistic effect can be taken into account both inside and outside the APW spheres consistently without using any approximations such as the Foldy-Wouthusen transformation. Koelling's method was not self-consistent.

Yamagami and Hasegawa carried out a self-consistent calculation of the energy band structure by solving the Kohn-Sham-Dirac one-electron equation by the density- functional theory in a local-density approximation (LDA). This self-consistent, symmetrized relativistic APW approach was applied to many lanthanide compounds and proved to give quite accurate results for the Fermi surface.

In LDA, the electron correlations are taken into account only by a mean field approximation which utilizes the correlation energy of the uniform electron gas. In the Ce compounds where the 4f electrons are believed to be itinerant in the ground state, such as in CeSn3, the topology of the Fermi surface can be described by the band structure calculated in LDA. However, the strong intra-atomic correlation effect between the 4f electrons should be considered for consistent explanations of the Fermi surface, the electronic specific heat coefficient and the cyclotron effective mass. Beyond LDA, there are two approaches by which the correlation effect between the 4f electrons is taken into account in an explicit way. One is p - f mixing theory and the other is renormalized band theory.

p - f mixing theory was first proposed for explaining complicated magnetic properties of the Ce pnictides (Kasuya et al. 1987). In this theory, the 5d and 6s electrons in the Ce atom and the valence electrons in the pnictide atom form usual bands just as calculated for the La pnictides in LDA. At each Ce atom, one 4f electron is localized and the 4f state is split by spin-orbit interaction. The 4f energy levels relative to the Fermi energy can be determined phenomenologically from the observed XPS spectrum. Hybridization of the 4f state with other states is then introduced in an LMTO scheme. There are no adjustable parameters in calculating the Fermi surface. It was found that the occupied 4f state lies far below the Fermi level, and weakly affects the Fermi surface. This p - f mixing theory explained well various magnetic properties of the Ce pnictides, especially experimental results for the de Haas-van Alphen effect in CeSb.

The Fermi surface of CeSb was thus calculated on the basis of p - f mixing theory, although it was not easy. This is because the Ce pnictides are semimetals and their energy band structures and Fermi surfaces are simple. In the usual Ce compounds where the 4f electrons are believed to be localized, it is difficult to carry out such calculations. Therefore, simplified calculations were carried out for such Ce compounds as CeA12

14 ¥. ()NUKI and A. HASEGAWA

(Guo 1990) and CeCu2Si2 (Harima and Yanase 1991a, 1992a) in which the 4f states are assumed to belong to the core states and the 4f bands are removed artificially if they appear in the conduction band.

For the antiferromagnetic compound NdB6 another simplified calculation was tried by Kubo et al. (1993). The antiferromagnetie band structure was first determined self- consistently with the standard KKR method by assuming that the 4f electrons are itinerant, and then the 4f bands were removed from the band structure obtained from the final potential. In these simplified calculations, the electron correlations are not taken into account.

The second theory beyond LDA is called renormalized band theory; this was applied to CeSn3 (Strange and Newns 1986) and CeRu2Si2 (Fulde 1991, Zwicknagl et al. 1990). Like p - f mixing theory, the correlation interactions between the 4f electrons are taken into account phenomenologically in the LMTO scheme. The set of phase shifts for the s, p and d states in the constituent atoms is given by a usual LDA calculation, and that for the 4f state in the Ce atom should be determined so as to include strong correlations. To calculate the electronic structure close to the Fermi energy, the values of the phase shifts and their derivatives at the Fermi energy are necessary. For CeRu2 Si2 Zwicknagl et al. (1990) determined the values of the phase shifts at the Fermi energy so that one 4f electron per Ce atom participates in forming the Fermi surface, and fitted their derivatives so that the density of states at the Fermi energy agrees quantitatively with the observed electronic specific heat constant y. Therefore, all necessary phase shifts are fixed and there are no adjustable parameters. Zwicknagl et al. (1990) explained the origins of the major observed dHvA branches and the magnitude of the cyclotron effective masses consistently.

In the following sections we outline the self-consistent, symmetrized relativistic APW approach.

2.3.1. Kohn-Sham-Dirac one-electron equation Here, we describe the framework of band theory in a local-density approximation (Hohenberg and Kohn 1964, Kohn and Sham 1965). The usual band theory is based on the Kohn-Sham one-electron equation. The wave function ~Pi and the eigenvalue Ei of an electron in the state i in a crystal is given as a solution of the equation,

(-A+v(r)+ f ~_rqdr2n(r') , +btxc[n(r)])~pi = Eil~i, (3)

where n(r) is the electron density. In the left-hand side of eq. (3), the first term is the kinetic energy, v(r) is the nuclear potential, the third term is a direct Coulomb potential, and ~×c[n(r)] is the exchange-correlation potential defined by

d(nExc(n)) (4) #xc(n) dn '


where Exc(n) is the exchange-correlation energy as a function of the density n in a homogeneous electron gas. The electron density in a crystal is calculated by

n(r) = ~-'~fi [~Pi(r)] 2 , (5) i

wherefi is the occupation number of state i. Therefore, eqs. (3) and (5) should be solved in a self-consistent way. The exchange-correlation energy of a homogeneous electron gas is used under the assumption that the electron density is a slowly varying function of space.

The exchange-correlation potential should be a complicated function of n(r) and many formulae were proposed for practical purposes. Here we show the formula proposed by Gunnarsson and Lundqvist (1976). This formula is frequently used in calculations for the Fermi surfaces which we shall explain in this chapter. It is expressed as a product of the exchange part and the correlation part as

#xc(n) = 13(n) #x(n), (6)

where #x(n) is the Kohn-Sham exchange potential, 1

#×[n(r)] - 2 [3zc2n(r)] 5 - - y ( 7 )

and 1 1.4

fi(n) = 1 + 0.0545rs In 1 + , (8) rs /

r3 ",1/3 where rs = t~svn) . Relativity affects the kinetic term and the exchange-correlation potential in the Kohn-

Sham equation. As investigated in detail for the uranium atom and the cerium atom, the relativistic effect on the exchange correlation potential is rather small and therefore we use #xc[n(r)] in a relativistic band structure calculation. The relativistic effect on the kinetic term is appreciably large and can be taken into account by adopting the Kohn-Sham- Dirac one-electron equation instead of eq. (3) as follows:

{ ap + fi + Io(r) + I J __2n(r') ' ' _'1 ]~_rqar + I#xc[n(r)] ~ ~Pi = WlPi, (9)

/ 3 = [ g 01 ] (1 is the 2 x 2 unit matrix), (11)

where W is the total energy of state i including the rest energy. In eq. (9), ~Pi is the four- component wave function. In a relativistic energy band theory, eqs. (9) and (5) should be solved in a self-consistent way.


Spatial forms of the electron density and the potential are determined in the muffin-tin approximation. Then, the wave function is expanded by the solutions of the Dirac equation inside the APW spheres and by the plane waves in the interstitial region. To determine the expansion coefficients and the eigenvalues, a variational principle is derived from eq. (9) as

i Wf+ii OtOd~2=j!i+iI¢'IH~dS-'2fspheres)(OI+OII)ta'/5(¢I-OII) dS, (13)

where regions I and II are the inside and the outside of the APW spheres, respectively, and /5 is the unit vector in the normal direction outward the APW spheres. In this variational principle, the surface integral performed on the APW spheres is introduced to ensure good eigenvalues for the composite trial wave functions.

2.3.2. Self-consistent, symmetrized relativistic APW approach In a relativistic APW approach, symmetrization with double space groups is necessary for the following reasons:

(1) The symmetry of the electronic states in a crystal can be identified. (2) The dimension of the matrix in the eigenvalue problem can be reduced and

its determinant behaves linearly as a function of energy in the vicinity of the eigenvalues. This result is important, because it becomes easy to determine the eigenvalues without loss of computational accuracy. Note that in a non- symmetrized form it behaves parabolically because of the double degeneracy due to spin.

(3) A self-consistent calculation can be carried out for compounds with a complicated crystal structure.

Here it is assumed that a crystal consists of different kinds of atoms, and the number of atoms of the sth kind in a primitive cell is ns. As for the shape of the one-electron potential and the electron density, the muffin-tin shape approximation is adopted. It is assumed that the space group is non-symmorphic. A non-symmorphic space group cannot be divided into translational and rotational parts, i.e., every rotation of the point group of the non-symmorphic space may be accompanied by a non-primitive translation, while a symmorphic space group can be divided neatly into translational and rotational parts. For example, CeNi has the non-symmorphic space group Cmcm, and CeSna the symmorphic space group Pm3m. For the application of the following formulae to the symmorphic space groups, the non-primitive translation can be set to be zero. In this section, we use atomic units in which h = 1, the rest mass of the free electron is m0 = ½ and the velocity of light is c = 274.072.

2.3.2.1. APW matrix elements in a symmetrized form. N sets of plane waves with spin are prepared first. Then, the Bloch function q)(k,r) is expanded in terms of symmetrized


plane waves which transform according to the vth column of the Xth extra representation F;~(Rj) of the sub-group of order g associated with wave vector k as

O(k,r) = E ~ ~ E UXv~)7"*~ W(pa, r). (14) a 3, v #

Here, t/J(p~,r) is the four-component plane wave with wave vector k~ a) and spin m = + l which is selected as the progenitor from the ath plane wave set, andp~ is an abbreviation for (k~ a), m). 7)xv~ is the full projection operator defined by

= - O ( R j ) , (15) g .

J

where l~ is the dimension of the extra representation X and the sum is taken over all elements of the single group. In eq. (15), the operator O(Rj) is defined by the direct product of the space operator O1 (Rj) and the spin operator O:(Rj),

o(Rj) = OI(Rj) O O2(Rj), (16)

where

o (Rj) = (Rjl,,(Rs)), (17) 0 02(Rj)= (D1/; (Rj) D1/2(Rj) ) , (18)

In eq. (17), v(Rj) is the non-primitive translation associated with Rj. The term DI/2(Rj) in eq. (18) is the spin representation of the full rotation group• The sum over # in eq. (14) is executed when linearly independent plane waves with the same symmetry are projected out. It is easy to show that the variational expression (13) is kept invariant under the operation O(Rj). Because of its similar symmetry property, we may use the four-component relativistic APW function.

By the theory of irreducible representation, it is possible to determine the eigenstates belonging to each extra representation separately: A variational calculation leads to a set of linear equations for the expansion coefficients which hold irrespective of v,

~ ~ rrZ(3) (19) A//at~3~, (k, E) '~v~' = 0, a = 1,2,. .. , N, /~ = 1, 2,. . . , n, 3 #'

with the matrix element

Adxau3~,(k, E) = E ~ exp [-iRjkl a, v(Rj)] x. 1/2 lj (n')m ' • F,,u (Rj) Dn,, (Rj) M (20) j n'

wherep3 (kl 3), n). In eq. (20) l j n' = M (m) represents the matrix element calculated between

the single relativistic APW functions with (k~a), m) and (k)3),n'), where k) 3)= Rjkl ~).

18 Y. ()NUKI and A. HASEGAWA

Therefore, the eigenvalues of the Xth irreducible representation at k are determined by the condition

det AdxauB~,(k, E) = 0. (21)

t;.~(a) For each eigenvalue, the expansion coefficients ~v , are determined by eq. (19) together with the normalization condition.

On account of the phase factor which appears in the matrix element of eq. (20), it is convenient to use the irreducible multiplier representation for non-symmorphic space groups instead of F ~ , (Rj), which is defined by

A~,~,(Rj) exp [ik . v(Rj)] ;~ = F~,(Rj) , (22)

because Rjk~ ~ ) - k is equal to a reciprocal lattice vector. Following a group theoretical prescription proposed by Sahni and Venkataraman (1970), we calculate the irreducible multiplier representations for the necessary sub-groups of both symmorphic and non- symmorphic double space groups.

Actually, the condition that the relativistic effect may be negligibly small in the interstitial region (i.e. hkj/mo <<c) holds fairly well in the energy band structure calculations for various lanthanide compounds. For computational purposes, it is practical to define the energy-independent components in the matrix elements for each representation as .Aau8~, , 13at~#,,, Cat~u,(s, l), and Dau~u,(s, l) and then rewrite eq. (20) in the form

Z A.tauS,,(k , E) = - ( E - x z +/3a~tt,

+ ~ ~ Z (l + 1)tl-t+l(as)} (23) [ Catcu,(s , l) {lrh(as) + s l

~ - I + 1 ( a , ) } ] , +Da~, ( s , l) {-~/l(as) +

where

~ : ( a ~ ) - - - cf(as) t¢ + 1 (24) g(a~) as

In eq. (23), V0 is the average potential in the interstitial region of space. In eq. (24), f (as) and g(a~) denote the small and large components of the electron wave function at the sphere radius as, respectively, which depend on E. They are obtained by solving the radial Kohn-Sham-Dirac equations for a given E,

d(cfr)dr - ( r - 1)~-frr - (E - Vs(r))gr, (25)

dgx _ c_ 2 (E - V~(r) + c2) c f x - (x + 1) g_yr, (26) dr r

where Vs(r) is the potential inside the s-type APW sphere consisting of the nuclear potential, the direct Coulomb potential and the exchange-correlation potential.


Here are the explicit expressions for the energy-independent components of the matrix elements in the symmetrized form that appear in eq. (23):

AX~.,e., = ~ exp [-i (~) - k). v(Rj)] A./(Rj) ~" D '/2.,.Rj) ]

× Or~c~ V _ 4 g g a s J l ( k V a~) exp [ikl~ ~). r~ ' ~U t'/s =

(27)

BL, e, ,, : ~ [k{ ~') . k~ ~'] exp [-i<~ ~,- k). v(Rj)] A~//<&) J

xO:/'Z(RJ)[ 6~a61J-E 4"ga~J'~')+exp[ik{~e)'f:J],z k a, .~ (~) ~

s ~V i=l

(28)

GL~ ~, (s, l) = E exp [-i ,(k! ~>J - k). v(Rj)] A z*./,.,p'o 'D v2̀D'.,n,..:, J

x [ ~ j , (k(l'~)a,) j, (~'~)a~) ~,=, exp like; '). 'r;] P, (k(, + (29)

: . '" D '/~ "" " x k <~)] D~.,~/(s, l) i~-~ ~ exp [-i(<~>-k) v(Rj)]A~*/(R,)(mlaln) , / . t . ; ) (k l + J . ] n t

[4JraZ " ,vq "'J / j , x [~-~j,(kl~)a,)j~(k~)a,) ~,=t exp [ikl~ ~). ~::]P' {~(~,.l-(~)~]

where

(30)

k/>:Rjk?), ~(°~) : k/) <+, i . | j . - - (31)

and r~ is the position vector of the ith atom of the sth kind, g2 is the primitive cell volume, is the Pauli matrix and jr(x), Pt(x) and P~(x) are the spherical Bessel function, the

Legendre polynomials and derivative of the Legendre polynomial, respectively. Moreover, the notation (m lal n') is defined by

(+½ I< ± ½) = ±e~, (±½ I< m ½) = ex T ie. (32)

where ex, ey and ez are the unit vectors in the x, y and z directions, respectively. The energy-independent components C~W~W (s, l) and D ~ u , (s, l) are also used to calculate the electron radial density function within the APW spheres.

2.3.2.2. Determination of eigenualues and eigenfunctions. The irreducible representations for the symmetry points, axes and planes of the Brillouin zone are classified into three types according to the Herring criterion (Herring 1937). These three types


are defined as (a), (b), and (c), in which the Herring criterion is equal to -1, 0 and 1, respectively.

In type (a), there is no degeneracy between irreducible representations, and the twofold degeneracy due to spin can be resolved by symmetrization. For each irreducible representation, the symmetrized APW determination behaves linearly as a function of energy in the vicinity of eigenstates, so that both eigenvalues and eigenfunctions can be determined easily.

In type (b), two different irreducible representations are degenerate. This type can be treated by merely calculating one of the two representations.

In type (c), the twofold degeneracy due to spin cannot be resolved by symmetrization. Both eigenvalues and eigenfunctions can be determined by using Soven's technique to overcome the problems of the double roots which result from the twofold degeneracy due to spin (Loucks 1967). If the subgroup contains the inversion, the following relations,

4 E) 4. Ada~/3u,(k , = ±Ad_a,_/3,,(k, E), (33)

4 E) and 4. hold between the symmetrized APW matrix elements A/tau~u, (k, Ad_at~_/3 u, (k, E) in which both wave vector and spin of the progenitors p~ and p~ are inverse, where the plus sign is applied if the progenitors have the same spin and the minus sign is applied if they have opposite spins. In such a case, it is possible to transform the matrix into a form suitable for Soven's technique. At general points of the Brillouin zone, calculations can be carried out by using the original, unsymmetrized relativistic APW method of Loucks (1967).

2.3.2.3. Electron density function. In order to carry out a self-consistent energy band calculation, it is necessary to calculate the electron density function associated with a symmetrized relativistic APW function. For the Bloch state (k ,)~) , the spherically averaged radial density function within the s-type APW sphere is given by

~r~Z(k, r) = 1 ~ [OZ2(s ' l) {l~t(r) + (1 + 1)~_,_l(r)} (34) ns I

Z s + Q2( , l) (~l(r) - ~-l- l(r)}],

where

1 T Tz(a)r r4(~):4 iS l), (35) a # fi ~'

Z S l r r4(a) • r)~(t3)~Z (~ Q2( , l )= ~ Z ~ Z Z l), (36) t-/ vl~ ur i c1 z~ apf3g'~.°,

a iz (3 W

= + (37) [g~:(as)as] 2

F E R M I S U R F A C E S O F I N T E R M E T A L L I C C O M P O U N D S 21

The normalization constant N z for the wave function belonging to the irreducible representation F ~ is written explicitly as

N z _ x+ ~ E { Nzc(s' l)[l~ +(l+ 1)~s,_,] +N~(s, l ) ( ~ - ~s_l_,)} - - N a

s l

(38)

where

NXa = E ~ E Z ~'ufr~(aT c'~,t~,'"a'(/3)AZc,#,/3u', (39) a # /3 g '

rrX(a)* rrX(/3)t'X tS l), (40) a ~t /3 tt '

N:(s, l) = ~ E E E tJvu" ~z(a)* r r,~(/3)~Zuvt ~, ua~,/3,, to,'° l), (41) a # /3 # '

:~ = fo a~ [/r(r) 2 +gr(r ) 2] r2dr [g~(aAaA 2 (42)

The component Ba#,/3#,x does not appear in the normalization constant. The ratio N~/N z is the probability amplitude in the interstitial region of the primitive cell, and the ratio of each term in the sum over s and l in eq. (38) to N x gives the probability amplitude partitioned according to the angular momentum l in the s-type APW sphere. These probability amplitudes are used to calculate the partial density of states. The spherically averaged radical density a,(r) within the s-type APW sphere is obtained by summing a)(k, r) over all occupied states as follows,

= s,coro(r)+ Wok :(k, r) n k

(43)

The first term on the right-hand side of eq. (43) represents the radial density of all the core electrons within the s-type APW sphere. In the second term on the right-hand side of eq. (43), the notation is changed and the Bloch states are identified by (n, k) instead of ()~, k), where n is a band index. This term represents the average of cry(k, r) with a weighting factor Wnk. A constant electron density in the region between the APW spheres is determined so that the unit cell is kept electrically neutral.

2.3.2.4. Self-cons&tent calculation. It is now possible to carry out a relativistic band structure calculation self-consistently. Following Mattheiss' method (Mattheiss 1964), a starting electron density for a crystal is constructed by superposing the self-consistent atomic electron densities, which are calculated for the neutral atoms using the method of Liberman et al. (1965). In calculations both for the atom and the crystal, the exchange


and correlation interactions of electrons are taken into account by the density functional theory in the local-density approximation. As for the charge densities of the core states in compotmds, a frozen-core approximation is adopted, i.e. the atomic charge densities of the core states are assumed to represent the core electrons in the compounds. In calculations of the energy band structure and the Fermi surface for CeSn3 (Hasegawa et al. 1990), for example, the atomic charge densities for Ce (the Xe core except for the 5p state) and for Sn (the Kr core plus the 4d state) were assumed to be frozen in CeSn3. The 5p state in the Ce atom should be included in the itinerant states and should be determined self-consistently together with other states in the outer shell states, because hybridization between them must be accounted for. A new crystal density function is calculated by eq. (43). A self-consistent calculation can be carried out in a manner similar to the ordinary non-relativistic band structure calculation (Mattheiss et al. 1968). In fig. 4, a flow chart is represented for a self-consistent energy band structure calculation by a symmetrized relativistic APW method in LDA.

2.4. Determination of the density of states, the Fermi surface and the cyclotron effective mass

To grasp the nature of the energy band structure visually, it is useful to make a drawing of the energy dispersion curves. Using a final potential of a self-consistent calculation, many eigenvalues are calculated for each band at symmetry points and along symmetry axes in the irreducible part of the Brillouin zone, and smooth energy dispersion curves are obtained by an interpolation scheme based on a eubic-spline method.

The density of states at the energy E per unit volume is related to the band structure by the well-known relation

2 j ' dS N(E) = (2z) 3 h-~vk' (44)

where vk is the absolute magnitude of velocity and the surface integral is performed over the constant-energy surface with energy E. Many eigenvalues should be calculated for each band at fine mesh points in the irreducible part of the Brillouin zone. If necessary, eigenvalues can be interpolated further at finer mesh points by an interpolation scheme based on a Fourier series expansion. The integration is performed by a tetrahedral method (Jepson and Anderson 1971, Rath and Freeman 1975). Each band can Contain two electrons per primitive cell in the Brillouin zone, and the total number of Bloch electrons determines the Fermi energy EF. It is given by

NBIoCh = N(E) dE. (45)

The density of states is also calculated for each band as a function of energy. The density of states at the energy E for the nth band is further partitioned according to the s-type APW sphere and the angular momentum I. Such partial density is defined by

2 [ Pn,(k),~ Nnl(E) - a a ( 4 6 )

(2jr)3 J v~


Solve the Kohn-Sham-

Dirac equation in the LDA.

O'in(i+ 1 )(r) =

No

Initial crystal charge density

Superpose tlae atomic charge

densities.

1 - f ) Oin(i)(r) + f Gout(i)(r)

I

Potential in the LDA I

I VT(r) = v(r) + VH(r) + gxc(r)

E = E + AE >~

Matrix ~lemen~

-~ ~o~,pp,(/,, E)

Eigenvalges

det Idf~c,p,,.(k g ) l = 0

L I ~¢W ¢tutrge densltv 1

IJout(i)(r)

Convergence te~t,

I O'out(il(r)- O'i.(i)(r) I < 5

O.in(i)(r)

~ Y e s

E-k curve

Density of states

Fermi surface

Cyclotron mass

Extra renresentation F t

Symmetrlze plane waves.

Fig. 4. A flow chart for a self-consistent energy band structure calculation by a symmetrized relativistic APW method in LDA. In each cycle of the iteration, the total electron potential VT(r ) is given by the sum of the nuclear potential v(r), the direct Coulomb potential VH(r ) and the exchange-correlation potential #xc(r). To construct a new input potential, the parameter f ( < 1) is introduced to optimize the convergence.

24 Y. 0NUKI and A. ttASEGAWA

where the probability amplitude P~t(k) is obtained by integrating an(k, r) from r = 0 to r = as. In particular, the number of electrons in the f state contained in the Ce APW sphere, nf, is given by

nf = Z fEF N~e,~=3(E) dE" (47) n

The electronic contribution to the specific heat of a metal at low temperature varies linearly with temperature, Ce~ = ~'b T, with the coefficient Yb given in one-electron theory by the density of states at EF as

= ½ 2k N(EF). (48)

Since the density of states on the free-electron model is proportional to the electron mass, this coefficient is usually expressed by a specific-heat effective mass or a thermal effective mass mtb, which is defined by

y_..bb = mtb , (49) 7o m0

where 70 and m0 are the free-electron values of the two constants. The interpolation scheme for each band is used to display a perspective view of the

Fermi surface and to calculate the extremal (maximum or minimum) cross-sectional area of the Fermi surface. It is also used to calculate a cyclotron effective mass mob which is defined for a given orbit on the Fermi surface by

zzh J --'v±dk (50) mcb =

where v± is the component of velocity normal to magnetic field and the integral is performed around the orbit. This formula can readily be transformed into

h 20S(kH) mcb- (51)

where S(kn) is the cross-sectional area of the Fermi surface which is perpendicular to field and kH is the wave number along the field direction. In dHvA experiments we can determine the cyclotron mass m2 at the extremal cross-sectional area, which is compared to the band mass mcb.

2.5. Mass enhancement factors

The experimental values for the low-temperature electronic specific heat coefficient ~, and equivalently the thermal effective mass mt are usually larger than the theoretical values of

FERMI SURFACES OF INTER_METALLIC COMPOUNDS 25

Yb and mtb which are determined by the band structure alone, as mentioned above. The mass enhancement factor 3, is defined by the ratio (Gschneidner and Ikeda 1983)

y _ m~' _ 1 + ~ . (52) ~b mtb

Origins for 2 are ascribed to the many-body effects which cannot be taken into account in the usual band theory. As the most probable origins, the electron-phonon interaction and the magnetic interaction are considered, and their contributions are denoted by 2p and 3,rn, respectively. Therefore, 3, is expressed as a sum of two contributions,

)~ = /~p n t- Am. (53)

The experimental cyclotron effective mass m c is also usually larger than the theoretical value mcb defined in eq. (51). Therefore, the enhancement factor for the cyclotron effective mass can be defined in the same way, such as

rn~' _ 1 + )~. (54) mcb

It should be noted, however, that the magnitude of this enhancement factor may be different from orbit to orbit on the Fermi surface. In sect. 4 we present values of Y/~'b and me~rob for many compounds, where mb is simply used instead of mcb.

Properties of the electron-phonon term ,~p in normal metals such as Pb, including its temperature dependence, were thoroughly studied and are well understood at present (Goy and Castaing 1973). Its magnitude is significantly smaller than 1. If it were large, it might cause lattice instability. In contrast to this small value of ~p, the magnetic contribution )~m can take a huge value in the heavy-electron compounds. For example, it amounts to more than 100 in CeCu6.

The magnetic contribution or the magnon enhancement mechanism Xm can be divided into two terms according to its origins. The first term occurs in many lanthanide compounds in which the 4f electrons are localized at lanthanide ions and their spin fluctuations enhance the effective mass of the conduction electrons via c - f interactions such as RKaKY interaction and the many-body Kondo effect, where c stands for conduction electrons and f for 4f electrons. A large ~ value, which is observed in CeBr, as shown in table 1, is an example of this term. In this cerium compound, however, the 4f electron affects the Fermi surface only weakly. The Fermi surface of CeB6 is quite similar to that of LAB6, although the value of ~m reaches 100. In this case, the y value of LaB6 is assumed to be the ]7 b value of CeB6. In PrB6 and N d B 6 , the 4f electrons are localized, but do not form a Kondo lattice. Therefore, only a small mass enhancement factor of Xm = 1-2 is observed in these lanthanide compounds. Nevertheless, this mass enhancement is larger than the mass enhancement due to the electron-phonon interaction mentioned above.


Apart from the electron-phonon case,/~m depends in some cases strongly on magnetic field as shown for Pr (Forgan 1981, Fulde and Jensen 1983). For the ferromagnetic paramagnon or spin waves, the effect of magnetic field is direct and reduces J.m strongly when the Zeeman energy exceeds the characteristic energy of the spin fluctuation. For the antiferromagnetic case, the effect is more complicated and in some cases, for example in CeB6, as we will see later, ~m increases with increasing field because of an induced magnon softening. However, when the Zeeman energy is much stronger than the characteristic energy of the magnetic fluctuation, ~,m decreases rather rapidly with increasing field.

Another magnetic contribution to ~-m manifests itself in the iron-series transition metals and their compounds. In these compounds, the 3d electrons are itinerant and their spins are fluctuating. Their magnetic properties stem predominantly from the spin fluctuations. In calculations of the band effective mass mb for these 3d electron compounds, a greater part of the contribution of the magnetic interaction can be taken into account, and thus the magnitude of ~-m is not very large. For example, MnSi is typical in this system, possessing a relatively large y value of 36 mJ/K 2 mol. In MnSi, ~m is found to be only about 4, although the conduction carriers are heavy electrons with the large cyclotron mass of 15m0 (Taillefer et al. 1986, Fawcett et al. 1970).

As will be explained in sect. 4, the 4f electrons in cerium compounds such as CeSn3 and CeNi, which belong to the valence-fluctuation regime, are itinerant in the ground state and contribute directly to the formation of the Fermi surfaces. Their Fermi surfaces can be well described by band theory. The enhancement factor in CeSn3 and CeNi is not large, less than 5, as in the 3d electrons of the iron-series transition metals.

3. Transverse magnetoresistance and de Haas-van Alphen effect

3.1. Transoerse magnetoresis tance

The high-field transverse magnetoresistance A p / p = [p(H) - p(0)]/p(O), in which the directions of magnetic field and current are perpendicular to each other, provides important information on the overall topology of the Fermi surface (Fawcett 1964). Under the high-field condition of ~ocr >> 1, it is possible to know whether the compound under investigation is a compensated metal with an equal carrier number of electrons and holes, ne = nh, or an uncompensated metal, nee nh, and whether or not open orbits exist. Here, co c = ell~roSe is the cyclotron frequency, r is the scattering lifetime, m S is the effective cyclotron mass and cocr/2~r means the number of the cyclotron motions performed by the carrier without being scattered. The characteristic features of the high-field magnetoresistance are summarized as follows: (1) when all cyclotron orbits are closed, (a) for the uncompensated metal the magnetoresistance saturates, A p / p ~ H °, and (b) for the compensated metal the magnetoresistance increases quadratically, A p / p ~ (wcz) 2. (2) When some of the cyclotron orbits are not closed but form open orbits, the magnetoresistance increases quadratically and depends on the current direction as


Ap/p ~ H2cos2c~, where a is the angle between the current direction and the open orbit direction in k-space. This is true regardless of the state of compensation.

If we count the number of valence electrons in a primitive cell, most of the lanthanide compounds are even in number, meaning that they are compensated metals. In this case the transverse magnetoresistance increases as H n (1 < n ~< 2) for a general direction of the field. Note that the integer n is not equal to 2 because the high-field condition is not fully satisfied in the real compounds. When the magnetoresistance saturates for a particular field direction, often a symmetrical direction, there exist some open orbits whose directions are parallel to a r x H , namely a = ~/2 in k-space.

Experimentally the current direction is fixed to a crystal symmetry axis of the sample and the sample is slowly rotated under constant magnetic field which is perpendicular to the current direction. The presence of open orbits is revealed by (a) spikes against a low background for the uncompensated metal and (b) dips against a large background for the compensated metal.

3.2. de Haas-van Alphen effect

Under a strong magnetic field the orbital motion of conduction electrons is quantized and forms Landau levels. Therefore various physical quantities show a periodic variation with H -1 since increasing field strength causes a sharp change in the free energy of the electron system when a Landau level crosses the Fermi level. In the three-dimensional system this sharp structure is observed at the extremal (maximum or minimum) cross-sectional area of the Fermi surface perpendicular to the field direction because the density of states also becomes extremal.

The magnetization or the magnetic susceptibility is the most common one of these physical quantities, and its periodic variation is called the de Haas-van Alphen (dHvA) effect (de Haas and van Alphen 1930, 1932). It provides one of the best tools for the investigation of Fermi surface properties such as the extremal cross-sectional area S, the cyclotron mass m c and the scattering lifetime r of metals (Shoenberg 1984). Sometimes other physical quantities are also measured; for example, torque, static strain, ultrasonic velocity, and magnetoresistance, etc. The last type of measurement is called the Shubnikov-de Haas effect.

The theoretical expression for the oscillatory component of magnetization Most due to the conduction electron was given by Lifshitz and Kosevich (1955). The dHvA experiments are usually conducted by the field modulation method. The detected signal or effective output voltage Vosc in the usual 2co-technique is proportional to Most and is given as follows:

2~crF V°sc = Z Arsin( T -b ~r), (55)

r

02 S -1/2 exp(_arm c TD/H) co (szgrm~ ~ (56) Ar ~ J2(x)TH -1/2 ~ ~ s \ 2m0 /


or

02 S -1/2 ~ J2(x) T m 1/2 exp [- rmZ(V + VD)m] z Ar 1-exp(-2arm~T/H) c o s \ 2m0 J ' (57)

2jr2ckB 2~Fh a - e ~ ' x - H2 , (58,59)

where h is the modulation field, J2(x) is the Bessel function, possessing a maximum at x=3.1, and r (r = 1, 2, . . . ) is a positive integer showing higher harmonics of the oscillation. The output voltage or the magnetization is periodic on 1/H and has a dHvA frequency F:

F = ---~-h S (60) 2~e

which is directly proportional to the extremal cross-sectional area S at zero field. The amplitude factor A is related to the thermal damping at finite temperatures T and the Landau level broadening TD which is caused by impurities, crystalline imperfections or strains. TD is called the Dingle temperature and is given by

T D = ~ h ~ -1, (61) 2JrkB

where r is the scattering lifetime of the carrier. For the fundamental oscillation (r = 1), we can determine the cyclotron mass m e from

the temperature dependence of the dHvA amplitude A(=A 1) in eq. (57), namely from the slope of a plot of In {A [1- exp(-2am~T/H)]/T} vs T at constant H and h by using a method of successive approximations, and we can obtain the Dingle temperature TD or the scattering lifetime r from the field dependence of the amplitude in eq. (56), namely from the slope of a plot of In [AH1/2sinh(am~ T/H)] vs H -1 at constant J2(x) and temperature.

The amplitudes of the higher harmonics (r ~> 2) become vanishingly small, and the fundamental one (r= 1) becomes dominant in the usual dHvA measurements. However, when the cyclotron mass is not large and the temperature becomes lower than 1 K, the higher harmonics become detectable. To distinguish the higher harmonics from the fundamental one, it is necessary to check carefully the magnitude, intensity and angular dependences of the dHvA frequencies and their cyclotron masses.

The quantity ]OzS/Ok~i ]-1/2 is the inverse square root of the curvature factor 02S/Ok~. The rapid change of the cross-sectional area around the extremal cross-sectional area along the field direction diminishes the dHvA amplitude for this extremal area.

The term cos(~grmS/2mo) is called the spin factor. When g = 2 (free-electron value) and m* =0.5m0, this term becomes zero for the fundamental oscillation (r= 1) and the dHvA oscillation vanishes for all values of magnetic field. This is called the zero spin- splitting situation in which the up and down spin contributions to the oscillation cancel


Magnetic Field

Fig. 5. Schematic picture of the change in the extremal cross-sectional areas depending on the up and down spin states. AF~ and AF 2 mean the different antiferromagnetic states, and H c is the critical field showing the metamagnetic transition. St, and S~ are the extremal areas for the up and down spin electrons, respectively, obtained from the dHvA measurements in the AF 2 region (Harima 1988).

LaSh 3

(a)

H//<III> (b) 0.SK

I r I

80 'Y,T i 90kOe

~7z-- Or

2,e L, ojhlll, 7,+2z! II

0 5 10 15x1070e

Fig. 6. dHvA oscillation and its FFT spectrum for LaSn 3 (Umehara et al. 1991a). The Greek letters in the FFT spectrum designate the various orbits.

out, and this can be useful for determining the g value. Note that in this situation the second harmonics for r = 2 should have a full amplitude.

When the extremal area changes linearly with increasing external field, the dHvA frequencies of the up and down spin electrons coincide, giving the extremal cross- sectional area for zero field mentioned above. Many lanthanide compounds show a magnetically ordered state at low temperatures. Conduction electrons in this system have different Zeeman and exchange energies, depending on the up and down spin electrons. For example, the antiferromagnetic AF~ state of these compounds often changes into a different antiferromagnetic AF2 state or into the field-induced ferromagnetic (paramagnetic) state. In this case, we usually get different Fermi surface areas for the up and down spin electrons, S T and St, when the field is increased above the critical field showing the metamagnetic transition He, as shown in fig. 5. The spin factor Sr becomes

y ' g r m e =c°S 2mo (62)

30 Y. (3NUKI and A. HASEGAWA

where Hex is defined by the exchange splitting energy Eex = ~BHex. In ferromagnetic compounds, it is possible to obtain different Fermi surface areas associated with the up and down spin electrons in zero field.

Simply thinking, the dHvA oscillation is detected when the high-field condition is almost satisfied; ~oer/2zr > 1 and the spacing between the Landau levels is larger than the thermal broadening kBT; hcoc > kBT. I f the magnetic field H is 100kOe or 10T and the carrier possesses a cyclotron mass of 10m0, the following conditions for the temperature and the scattering lifetime are required: T < 1.3 K and 7: > 3.6× 10 -11 s or TD < 0.03 K. A temperature of 0.4 K can be attained in the He3-cryostat (Windmiller and Ketterson 1968), and much lower temperatures are obtained in a dilution refrigerator (Reinders et al. 1987). Values of 77= 10-12-10 -11 s or TD=0.1-1 K are usual in samples.

The exact dHvA oscillation contains many dHvA frequencies Fi (i = 1, 2, 3, . . . ) or cross-sectional areas Si and becomes a sum of their contributions, which are analyzed by the fast Fourier transformation (FFT) method. The amplitude Ai corresponds to the amplitude in the FFT spectrum. Figure 6 shows the dHvA oscillation and its FFT spectrum for a field along the (111) direction of the cubic crystal LaSn3 at 0.5 K (Umehara et al. 1991a). From the FFT spectrum we can see many dHvA oscillations due to harmonics or sums and differences of the several dHvA frequencies.

4. Experimental results and comparisons with band calculations

4.1. Fermi surfaces in the simple cubic Brillouin zone

4.1.1. RB 6

The rare earth hexaborides RB 6 crystallize in the cubic (CaB 6 type) structure which possesses a CsCI type arrangement of R atoms and B6 octahedra. Figure 7 shows the crystal structure of RB6 and its simple cubic Brillouin zone. LaB6 is a reference non-f compound. CeB6 is a typical Kondo-lattice compound undergoing two magnetic ordering

(a)

I ()

(b)

Fig. 7. (a) RBt-cubic crystal structure. Large spheres without pattern and small spheres with pattern show the R atoms and the B atoms, respectively. (b) Brillouin zone of the simple cubic crystal lattice.


Table 4 Characteristic properties of the RB 6 compounds with a cubic crystal structure ~

31

Compound T N (K) n 7 ( m J/K2 tool) Fermi surface

LaB 6 Pauli para n e

CeB6 2.3 n~ TN = 3.2 K Kondo lattice

PrB6 7.0 ne

Ndt36 7.8 n~ = nh

2.6

250

three ellipsoids connected by necks

similar to LaBr, but spin-split

similar to LaBr, but spin-split

strongly altered by MBZ

Symbols: n~, number of electron carders; nh, number of hole carders; when no=nh the carders are compensated. MBZ, magnetic Brillouin zone.

transitions at the quadrupolar ordering temperature TQ = 3.2 K and at the Nrel temperature TN=2.3 K (Effantin et al. 1985, Komatsubara et al. 1983). Existence of quadrupolar ordering is due to the quartet F8 ground state in the 4flevels. PrB6 (TN = 7.0 K) and NdB6 (TN = 7.8 K) are typical localized 4f systems with magnetic ordering. Their characteristic properties are summarized in table 4.

The measurements of the dHvA effect in LaB6 (Suzuki et al. 1988, Ishizawa et al. 1977, 1980, Arko et al. 1976), shown in fig. 8, revealed that the Fermi surface consists of a set of three equivalent nearly spherical ellipsoids, denoted by ai (i = 1, 2 and 3), which

10 8

o~ {D

o}

~i0 7

>

10 5

i f ~ i i--~ i I i * I i ,

LaB6 i lZ { 1 0 0 } ¢ 3. {110}

1

6

I 80 0 30 60 90

<ii0> <i00> <iii> <ii0>

Field Angle (Degrees)

Fig. 8. Angular dependence of the dHvA frequency in LaB 6 (Ishizawa et al. 1977, 1980, Suzuki et al. 1988). The solid and dashed lines connecting the data are guidelines. The Greek letters designate the various orbits.


LaB6 R

(a)

(b) M

<i00> /<110> R

(e)

"q---------- ~"<i00> R

Fig. 9. (a) Cross-sections of the multiply connected ellipsoidal Fermi surfaces (Ishizawa et al. 1977). Co) Main three multiply connected ellipsoidal Fermi surfaces (Hasegawa and Yanase 1977b). (c) Twelve pocket Fermi surfaces in LaB 6 (Harima et al. 1988). The pocket Fermi surface is enlarged for visual convenience. The Greek letters designate the various orbits.

are connected by necks. This topology of the Fermi surface was constructed from the magnitude of the dHvA frequencies and the angle range where the dHvA branches a i were detected.

The energy band structure of LaB6 is characterized by the wide B 2s-2p bands which are split into the bonding and antibonding bands and by the La 5d bands which lie across the energy gap between the bonding and antibonding bands. This feature originates from a particular configuration of atoms in the CeB6 crystal structure. The six s states of the B atoms in an octahedron form d-like orbitals with F12 symmetry about the center of the octahedron, and the six p states of these B atoms also form d-like orbitals with both F12 and F25 symmetries about the same center (Longuet-Higgins and Roberts 1954). These d-like orbitals and the La 5d states have nearly equal energies, and therefore strong hybridization occurs between them. The strong hybridization causes a large wave-vector dependence of the d bands, and the Fermi surface is formed by one such d(eg) band (Hasegawa and Yanase 1977b). The Fermi surface of LaB6 is shown in figs. 9a,b. It consists of three equivalent electron sheets which are centered at the X point and are connected by small necks which intersect the E axes in the simple cubic Brillouin zone. The total number of carriers is almost equal to one electron per primitive cell. The electrons on the Fermi surface have dominantly La d character, and on the average the magnitude of their cyclotron effective masses is smaller than the free electron mass.


The neck orbit was not detected, however, in the above mentioned dHvA measurements done by Ishizawa et al. (1977) and Arko et al. (1976). Later, branches Pi (i = 1 . . . . . 6) shown in fig. 8 by open circles were detected by the torque method (Ishizawa et al. 1980) and were attributed to the necks because the angular dependence of branches Pi are consistent with the topologies of the necks. This Fermi surface of the neck is, however, thin and rather cylindrical, which is inconsistent with the short and thick neck constructed from the unobserved region of the ellipsoidal branches cti and also the results of band calculations. This puzzle was solved later by a combination of the improved ultrasonic dHvA measurements done by Suzuki et al. (1988) and the careful band calculations done by Harima et al. (1988). In fig. 9c twelve pocket Fermi surfaces calculated by Harima et al. are shown as an enlarged scale by a factor of ten. It was shown that branches p; are not due to the necks but due to the small and flat electron Fermi surfaces. The data shown as triangles in fig. 8 were obtained by the ultrasonic dHvA measurements (Suzuki et al. 1988). The complete observation of branches P3 and p5 is a clear evidence for existence of the small closed Fermi surfaces.

New band calculations done by Harima et al. were made by shifting the unoccupied La 4f levels upwards by an amount of 0.10 Ry, which leads to a new band which crosses the Fermi energy very slightly. Langford et al. (1990) also confirmed existence of the pocket Fermi surface by the LMTO band calculations. The neck orbit is, however, not detected experimentally because of the rapid variation of the cross-sectional area around the extremal neck orbit, implying a large curvature factor 02S/Ok~.

Similar Fermi surface topologies were obtained in CeB6 (0nuki et al. 1989a, Joss et al. 1987, 1989, Goto et al. 1988a, Suzuki et al. 1987, van Deursen et al. 1985) and PrB6 (Onuki et al. 1985b, 1989d, van Deursen et al. 1985), as shown in figs. I0 and 11, respectively. Judging from the values of branches ai for field along the (100) direction, the main Fermi surface is more spherical in CeB6 than in LaB6 and PrB6. The ratio of the maximum to minimum areas of the ellipsoidal Fermi surface is about 1.16 in CeB6, 1.24 in PrB6 and 1.27 in LAB6.

We also show in fig. 12 the cross-sectional area of the small and flat Fermi surface deduced from branch pi for RB6. It is approximated as an ellipsoidal Fermi surface. The Fermi wave vectors kFi (i = x, y and z) along the three principal axes are kvx = 0.012 (2~v/a), kFy = 0.023 (2st/a) and kvz = 0.0044 (2Jr/a) in LAB6.

In PrB6 two kinds of pockets Pi and pf as well as the ellipsoids a3 and a~ are found, as shown in fig. 11. The cross-sectional areas ofpi and pf are 118 and 28 times larger than in LAB6, respectively. The existence of two kinds of Fermi surfaces in PrB6 is explained by an exchange splitting of the up and down spin states of the conduction electrons as shown in fig. 5. This is due to a change of the antiferromagnetic spin structure at about 10kOe in PrB6 (Galera et al. 1992). The up and down spin states have different effective Fermi surface areas and cyclotron masses. For example, branches a3 and a~ in PrB6 have the values of 8.19x 10 70e (1.95mo) and 7.25x 10 70e (2.52m0) for field along the (100) direction, respectively.

A similar spin splitting of the Fermi surfaces is expected in CeB6 because the antiferromagnetic state of the so-called phase III changes into that of phase II

34 ¥. 0NUKI and A. HASEGAWA

10 8

%, O

107

106

<110>

I '

CeB6 {lOO}

0~i 0~ +4--

o

I

{11o}

L+-:~-o-~-o- + ~

~=-~-+~-o.__~_o~ . . . . . ~

I ' - -

~'Lx

- P3~, P4 ~P3 ~ D 5

-.e.-,a--',,~ o~ ~ s

I , , i , , I , , I ~ ,

30 0 30 60 90 <100> <111> <110>

F i e l d Angle (Degrees)

Fig. 10. Angular dependence of the dHvA frequency in CeB 6, Data shown by circles, crosses, squares and triangles are cited from ()nuki et al. (1989a), van Deursen et al. (1985), Joss et al. (1987, 1989) and Suzuki et al. (1987) and Goto et al. (1988a) Goto (1992), respectively. The solid lines connecting the data are guidelines. The Greek letters designate the various orbits.

o) O

>

I ' [ ~ ' I ' '

PrB8 (i00} ! ~ ~ o {Ii0}

108 ~__a~j~-~-~F~- 2 _~_~ _ .~ . . . . . .

" I

' p ,

/ , I , , , L I 4 , I , , ]

30 0 30 60 90 <i00> 


Fig. 11. Angular dependence of the dHvA frequency in PrB~ (Onuki et al. 1985b, 1989d). The solid and dashed lines connecting the data are guidelines. The Greek letters designate the various orbits.

LaB6 CeB6 PrB 6

O !

¢- 0.2 @rc/a~ p ' Fig. 12. Cross-sections of the pocket-Fermi surfaces in

LAB6, CeB~ and PrB 6. These electron pockets are fiat in character (()nuki et al. 1989a).

(quadrupolar ordering) at about 15 kOe. Goto (1992) confirmed that branches P6 and p~ shown in fig. 10 are due to two kinds of Fermi surfaces with different spin states. The Fermi surface of branch Pi in CeB6 accidentally possesses the same size as branch pf in PrB6.


Table 5 dHvA frequencies F and cyclotron masses m~ in RB 6 compounds (Ishizawa et al. !977, 1980, Onuki et al.

1989a,d, Goto 1992) a

RB 6 a 3 a~ y e p p ' F m~ F m~ F m~ F m~ F m~ F m~

LaB 6 7.89 0.64 3.22 0.85 0.49 0.0052 0.046

CeB 6 8.67 14-21 2.19 15.5 1.30 9.2 0.120 1.7-3.5 0.080 4.6 0.188 5.5

PrB 6 8.19 1.95 7.25 2.52 3.27 1.94 0.94 0.94 0.590 0.64 0.150 0.28 0.79 0.66

a c g hi F m~ F m~ F m~ F m*

NdB 6 9.90 2.00 3.44 2.43 1.27 1.47 0.95 1.08

F values in 107 Oe, m~ expressed in m 0.

Here, we note the occurrence of dHvA branches with frequencies of (1-2)x 10 70e in CeB6 and (3-4)x 10 70e in PrB6. These branches are not present in LAB6, and are probably produced by the small antiferromagnetic Brillouin zone boundaries in CeB6 and PrB6.

The cyclotron masses in LaBr, CeB6 and PrB6 are summarized in table 5. All masses in CeB6 are heavily renormalized by the many-body Kondo effect compared to those of LaB 6 and PrB6. The cyclotron masses in PrB6 are also three times larger than those in LAB6, which should be attributed to the usual electron-magnon interaction.

The cyclotron mass of branch a3 in CeB6 shows a striking variation as a function of magnetic field, as shown in fig. 13. Quite a different field dependence is observed in the electronic specific heat coefficient y (Mfiller et al. 1988), as shown also in fig. 13. It varies from 250mJ/K2mol in zero field to 50mJ/K2mol in 220kOe. Here, the masses shown by the solid line through the crosses in fig. 13 were estimated from the y value of CeB6 by using the relation ofmc(CeB6 ) = me(LaB6 ) [y(CeB6)/y(LaBr)], where mc(LaB6) = 0.6 lm0 for a3 and y (LaBr)= 2.6 mJ/K 2 tool. There exists a clear discrepancy between the results of two types of experiments. The reason for this is thought to be as follows. When one compares the Fermi surface of CeB6 to that of PrBr, one is led to believe that the observed a3-Fermi surface in CeB6 corresponds to branch a3 in PrB6. In PrB6, the mass of branch a~ is larger than that of branch a3. Therefore, it is natural to assume that branch a~ in CeB6 has also a larger mass and hence could not be observed experimentally. Therefore, the missing branch af is the main origin of the present discrepancy. We note that the field dependence of the cyclotron mass or the y- value was discussed briefly in sect. 2. The theoretical treatment for CeB6 was done by Wasserman et al. (1989).

The dHvA frequencies observed in NdB6 (Onuki et al. 1989d) are substantially different from those of LAB6, PrB6 and CeBr, as shown in fig. 14. One main reason for the discrepancy between the dHvA branches in NdB6 and in LaB 6 or PrB 6 seems to be the


i00

50

' I 7-- I '

CeB6 H//<I00>

0 0

+•+ p h a s e II

+ + + ++

1 0 0 2 0 0 3 0 0

Magnetic Field (kOe)

I

g

Fig. 13. Field dependence of the cyclotron mass of the a 3 orbit. The data are represented by circles (0nuki et al. 1989a), triangles (Joss et al. 1987, 1989) and a square (van Deursen et al. 1985). The cyclotron masses estimated from the low-temperature specific heat coefficients at various fields are shown by crosses

10 8

10 7

10 6 , I 30

<110>

{100} [ {110l • NdB6 /

• oooooOOO ~OOOoo OOoo o D . . . . . . . . . . . . . . . . . . . . .; . . . . . . . . . . . . . . . . . a

I o : ° °°g @'15 ° b

c ~ f8 ............ fld2 ~i~6o-o-o ° d~ i o o g o . q o o o o o ~o~.a, i hs ......... • I o o ~ % o o o o v _

::"<he _g_~x-,,~ ........... : - - - - - - ~ : ~ - ~ _ o 6 ~ ~ ~ ~ O O O o o o~

:o_~j I h l J 2;: ]

30 60 90 <100> <111> <110>


Fig. 14. Angular dependence of the dHvA frequency in NdB 6 (Onuki et al. 1989d). The solid and dotted

(Mfiller et al. 1988). The solid and dashed lines lines are the results of band calculations (Kubo et al. connecting the data are guidelines. 1993). The letters designate the various orbits.

large magnetic gaps in NdB 6 due to a larger number of the occupied 4f electrons in a new magnetic Brillouin zone.

Min and Jang (1991) and Kubo et al. (1993) calculated the Fermi surfaces both in the paramagnetic and antiferromagnetie states of NdB6 by the LMTO and KKR methods, respectively, treating the 4f electrons as the core electrons. The Fermi surface in the paramagnetic state o f NdB6 is similar to that o f LaB 6. On the other hand, the Fermi surface in the antiferromagnetic state, which was calculated by Kubo et al. (1993), can be roughly understood by the band-folding of the paramagnetic Fermi surface into a smaller tetragonal Brillouin zone based on the magnetic unit cell which contains the double chemical unit cells.

Figure 15a shows a multiply connected hole Fermi surface in band 27. A closed orbit centered at the M point on the M - X - F plane is denoted by branch c. This branch is equivalent to branch e in the paramagnetic state. Figure 15b shows two ellipsoidal electron Fermi surfaces centered at the R point and a multiply connected electron one centered at the F point in band 28. NdB6 in the antiferromagnetic state is thus a compensated metal, as opposed to the uncompensated metal LAB6, o r NdB6 in the paramagnetic state. Here, the electron Fermi surface o f NdB6 in the paramagnetic state is essentially a sphere with a hollow in the center.

The solid and dotted lines in fig. 14 represent the theoretical results based on the Fermi surface in fig. 15 (Kubo et al. 1993). Namely, the solid lines represent the field

NdB6

~ r


( A n t i f e r r o m a g n e t i e )

X F

[uollT e

Z A

z (a)

F

(band27)

37

/

[10

A

A (b)

M

A.._

[010]

. . . . . . 'on (band28)

Fig. 15. (a) Hole and (b) electron Fermi surfaces in the antiferromagnetic state of NdB 6 (Kubo et al. 1993). The letters designate the various orbits.

configuration of [110] to [100] in the (001) plane and [100] to [011] in the (0i l ) plane, while the dotted lines represent that of [011 ] to [001 ] in (100) and [001 ] to [ T 10] in (110). To explain the experimental results, it is necessary to consider three kinds of magnetic domains, whose tetragonal axes are directed along the three equivalent (100) axes. For example, the solid lines denoted by g and hi in fig. 14 correspond to orbits g and hi in fig. 15 for field along the [100] direction. On the other hand, orbit a cannot be closed for this field direction, but can be closed for field along the [001] direction. This orbit corresponds to branch a in fig. 14, as shown by a dotted line. Detected dHvA branches are thus explained by considering the three equivalent domains.

The cyclotron masses are in the range of I-2.4m0, roughly three times larger than those of LAB6. Mass enhancement due to the electron-magnon interaction in NdB 6 is comparable to that in PrB6, in contrast to extremely large enhancement in CeB6, as shown in table 5.

Magnetoresistance measurements were done for RB6. Reflecting the multiply connected Fermi surface, open orbits were observed for LAB6, PrB 6 and Ndl3 6 (Onuki et al. 1989d).


I () Fig. 16. CsC1 type cubic crystal structure.

CD 2

<>

0

<110>

LaAg

. o o o ° ° o

30 0 80 60 90 <i00> <iii> <ii0>


Fig. 17. Angular dependence of the dHvA frequency in LaAg (Niksch et al. 1987). The solid lines show the results of band calculations. The Greek letters designate the various orbits.

Table 6 Characteristic properties of LaAg and YZn with the CsCl-type cubic crystal structure

Compound T N (K) n 1, Fermi surface (mJ/K 2 mol)

LaAg Pauli para n~ = n h 9.9 ellipsoids YZn Pauli para n h multiply connected hole Fermi surface

4.1.2. LaAg and YZn LaAg and YZn are Pauli paramagnetic compounds with the CsC1 structure as shown in fig. 16. Their characteristic properties are listed in table 6.

Magnetoacoustic quantum oscillations were obtained for LaAg (Niksch et al. 1987). Two kinds o f ellipsoidal Fermi surfaces, denoted by a and fi, were observed, as shown in fig. 17. The solid lines are theoretical ones based on relativistic self-consistent Augmented Spherical Wave (ASW) calculations.

LaAg is a compensated metal. This is simply expected from the number o f valence electrons; La 3+ and Ag 1+ and the primitive cell contains one molecule of LaAg. Just as in LAB6, the La atoms make a simple cubic lattice, and therefore the La d(eg) band is expected to play an important role in determining the Fermi surface. Unlike the B atoms, however, the Ag atoms make a simple cubic lattice, and thus hybridization between the L a d band and the Ag sp bands cannot be so strong as the La d-B sp hybridization in LaB 6. The energy band structure of LaAg is rather similar to those of simple transition metals. The density of states as a function of energy has a sharp peak which originates from a flat part o f the La d(eg) band, and the Fermi level lies slightly below the sharp peak. Consequently the cyclotron effective masses are small in LaAg.


LaAg

(a) hole (b) electron

Fig. 18. (a) Hole and (b) electron Fermi surfaces in LaAg (Niksch et al. 1987). The Greek letters a and/3 designate the orbits.

Figure 18 shows theoretical Fermi surfaces calculated by Niksch et al. (1987). Branches a and fl correspond to small hole ellipsoids centered at the M point, possessing a dHvA frequency of 1.86x 107 Oe for field along the (110) direction and small electron ellipsoids centered at the X point, possessing a dHvA frequency of 7.20x 106 Oe for field along the (111) direction, respectively. A large hole Fermi surface centered at the F point and a large electron one centered at the R point were not observed experimentally, probably because of a resolution problem.

The conduction carriers are mainly due to the La 5d states, as mentioned above. However, the cyclotron masses are 0.92m0 for the small hole and 1.10m0 for the small electron, which are roughly twice as large as the corresponding band masses of 0,44m0 and 0.87m0, respectively. This is consistent with the ratio of the measured electronic specific heat coefficient y, 9.9 mJ/K 2 tool to the calculated one Yb, 5.1 mJ/K 2 mol (Hill et al. 1976). This large mass enhancement for LaAg is mainly due to electron-phonon interaction because the band Jahn-Teller effect is found in LaAg and also slightly due to hybridization of the La 4f electrons with the conduction 5d electrons.

dHvA experiments were done by Jan (1973) for YZn with the CsCl-type crystal structure. Two kinds of branches a and y were observed. Figure 19 shows the angular dependence of the dHvA frequency for branch y. The solid line in fig. 19 shows the results of APW band calculations done by Hasegawa and Yanase (1977a), which is based on the Xc~ method with an exchange parameter of 0.6.

Branch y is due to a multiply connected hole Fermi surface with the topology of intersecting cylinders directed along the FX direction in band 3, as shown in fig. 20, and branch a is due to a small electron-Fermi surface at the R point in band 4. In contrast to LaAg, YZn is an uncompensated metal with a hole character. This is simply expected from the number of valence electrons in a primitive cell; y3+ and Zn 2+. Compared to LaAg, YZn has one more conduction electron per primitive cell, and therefore the Fermi level approaches closely the sharp peak in the density of states which originates from a flat part of the Y 4d(eg) band (Hasegawa and Yanase 1977a). As a natural consequence, the electrons on the main Fermi surface (the y sheet) dominantly have the Y 4d character, and their cyclotron effective masses are larger than those in LaAg.


0.4

o

(100} {110}

Y

YZn

OO"

O

0 . 2 I ~ ~ , ~ I , , I , ,

30 30 60 90 <ii0> <i00> <iii> <Ii0>


R

Fig. 20. Intersecting cylindrical Fermi surfaces in band 3 ofYZn (Hasegawa and Yanase 1977a). The Greek letter }, designates the orbit.

Fig. 19. Angular dependence of the dHvA frequency in YZn (Jan 1973). The solid lines show the results of band calculations (Hasegawa and Yanase 1977a). The Greek letter 7 designates the orbit.

The cyclotron mass is 2.08m0 for 7 and 0.237m0 for a, compared to the band masses of 1.21m0 for 7 and 0.14m0 for a. The mass enhancement is relatively large, which is mainly due to electron-phonon interaction as in LaAg.

Magnetoresistance experiments (Sellmyer et al. 1975) confirmed that YZn is an uncompensated metal with a multiply connected Fermi surface which favors open orbits, at least, along the (110) direction. These results are consistent with the results of band calculations mentioned above.

4.1.3. RIn3 There are many RX3 compounds with the AuCu3 type cubic structure. Figure 21 shows the crystal structure of RX3 where the corner-sites are occupied by the R atoms and the face-centered sites are occupied by the X atoms. RIn3 and RSn3 are typical examples.

Celn3 is a well known Kondo-lattice compound showing antiferromagnetic ordering at 10K. The ordered moment 0.65/~B per cerium atom is comparable to the value 0.71 ~R expected from the F7 ground state (Lawrence and Shapiro 1980). Nevertheless, CeIn3 possesses a large electronic specific heat coefficient of 130 mJ/K 2 mol at low temperature, indicating a heavy-electron system (Nasu et al. 1971). Therefore Celn3 is considered to be in a similar situation as CeB6, possessing a low Kondo temperature and displaying magnetic order at low temperatures. The ground crystalline field state is, however, the F7 doublet and thus no quadrupolar ordering is expected. Prln3 is paramagnetic,

FERMI SURFACES OF INTERMETALLIC COMPOUNDS 4I

I )

Fig. 21. The AuCu 3 type cubic crystal structure of RIn 3. Large spheres without pattern and small spheres with pattern show the R atoms and the In atoms, respectively.

Table 7 Characteristic properties of the RIn 3 compounds with the AuCu3-type cubic crystal structure

RIn 3 T N (K) n y Fermi surface (mJ/K 2 mol)

Lain 3 Pauli para ne = nh 5.3-6.3

CeIn 3 10 n~ = n h 130 Kondo lattice

PrIn 3 singlet n e = n h 11.4 NdIn 3 5.9 ne = n h Stain 3 14.7, 15.2 ne=nh

(TQ=15.9K) Gdln 3 42 n¢ ~n h (?)

nearly spherical electron Fermi surface (band 7); complicated hole Fermi surface (band 6) similar to Lain 3 (branch d), but strongly altered by MBZ similar to Laln3 similar to Lain3, but affected by MBZ similar to Laln3, but strongly altered by MBZ

similar to LaIna, but affected by MBZ

possessing a singlet ground state; NdIn3 (TN=5 .9K) , Smln3 (TN=14.7 and 15.2K, T Q = 1 5 . 9 K ) and GdIn3 ( T N = 4 2 K ) are localized 4 f systems. Their characteristic propert ies are summarized in table 7.

As a proper reference for the RIn3 compounds, the electronic structure was investigated for Lain3 by various theoretical methods. An analysis o f the partial density o f states revealed that the Bloch states in the lowest three bands consist dominantly o f the In s state, and those in the upper part of the valence band consist mainly o f the In p and L a d states. The Fermi level lies in the vicinity o f a sharp peak in the density of states. The Fermi surface consists o f two sheets of bands 6 and 7 (Hasegawa 1982). The band 7 electron Fermi surface is essentially a sphere, which is centered at the R point and bulges slightly toward the M point and contains 0.38 electrons per primitive cell. The band 6 hole Fermi surface looks quite complex and contains the same number o f holes as electrons, because Lain3 has an even number o f Bloch electrons per primitive cell and thus is a compensated metal.

The angular dependence o f the dHvA frequency in Lain3 is shown in fig. 22 (Umehara et al. 1991b). The solid lines represent the results o f A P W band calculations (Kletowski et al. 1987, Kitazawa et al. 1985). Branch a originates from the band 7 electron Fermi surface, while the others originate from the band 6 hole Fermi surface, as shown in fig. 23.

42 Y. 0NUKI

10 8

o

(D

10 7

10 6

and A. HASEGAWA

__c d _ ~ g -- e c

~ ~ ~ d

eo~o~o~eeeoo~o_ ! o e k o e e¢ eoo

e e

h~_'

~ o eoee°o e ,

e~¢ooOee --

30 30 60 90

<ii0> <I00> <Iii> <ii0>


Fig. 22. Angular dependence of the dHvA frequency in Lain 3 (Umehara et al. 1991b). The solid lines represent the results of band calculations (Kletowski et al. 1987, Kitazawa et al. 1985, Hasegawa 1982). The letters designate the various orbits.

The latter Fermi surface consists of three kinds of major parts, which are centered at the F, R and X points. Among them, a Fermi surface centered at F, denoted by d, is electron in dispersion and is spherical in topology, bulges slightly along the (100) direction and connects with another part of the Fermi surface centered at R by the slender arm elongated along the (111) direction. The arm is denoted by j . The topology of Fermi surface is similar to that of Cu, although the volume is small compared to that of Cu.

Conduction electrons are mainly due to La 5d and In 5p electrons, as mentioned above. The cyclotron masses for branches a and d for field along the (100) direction are 0.57m0 and 0.40m0, respectively, which are almost the same as the band masses of 0.58mo and 0.53m0, respectively.

dHvA measurements in CeIn3 were done by Kurosawa et al. and others (Kurosawa et al. 1990, Satoh et al. 1992, Ebihara et al. 1993). The results are shown in fig. 24. Many dHvA branches are observed in the range of 4x 105 Oe to 3 x 107 Oe, which are highly different from those of Lain3 in the angular dependence.

Among them, a branch with the dHvA frequency of about 3x 107 Oe, denoted by d, is similar to branch d in Lain3, although this branch is observed in the whole angle region for CeIn3. Correspondingly, the arm orbit, denoted by j , is not observed in CeIn3. The branch d Fermi surface in CeIn3 is thus roughly spherical, possessing no arms. The angular dependence of the amplitude and the cyclotron mass for branch d is strange (Ebihara et al. 1993). As shown in fig. 25, the dHvA amplitude for branch d in CeIn3


f g R R k

. J

R h

( a )

F

(b) Fig. 23. (a) Hole and (b) electron Fermi surfaces in Lain 3 (Kletowski et al. 1987, Kitazawa et al. 1985, Hasegawa 1982). The stippled regions indicate the cross- sections of the hole Fermi surfaces in the 100 and 110 planes. The letters a, b, ..., designate the various orbits.

is strongly reduced in two angle regions where branch d in Lain3 is not observed by existence of arms. This is mainly due to the large cyclotron mass in these regions; for example, it is about 12m0 for field along the (110) direction, as shown in fig. 26, while it is rather light in the angular regions around (100} and (111). The broken line in fig. 25 shows the angular dependence of the dHvA amplitude under consideration of the reduction factor [sinh(ctm2T/H)] -1, roughly in good agreement with the experimental data. The strong angular dependence of the amplitude may be explained much better if we furthermore consider the curvature factor of this closed Fermi surface.

The cyclotron masses 2.02m0 for field along (100) and 2.88m0 along (111) in Celn3 are five to eight times larger than the corresponding values 0.40rn0 and 0.37m0 in Lain3, respectively. The detected largest mass is 20.7m0 for a branch with the frequency of 7.6x 106 Oe. This may be compared to the electronic specific beat coefficients of 130mJ/K 2 tool in CeIn3 and 5.3-6.3 mJ/K 2 mol in Lain3.

Here we note that CeIn3 is antiferromagnetic at the usual applied field of 150 kOe. Fermi surfaces in CeIn3 are thus strongly modified by the magnetic Brillouin zone boundaries. A spherical electron Fermi surface in band 7, denoted by a in Lain3, is not observed in CeIn3. This is most likely ascribed to the influence of the magnetic Brillouin zone boundaries because the renormalized mass for this orbit is not extremely large,


i0 7

108 i

10 6

{110} CeIn3

o ~ o ° o O O O oo o

30 0 80 60 90 <ii0> <i00> <iii> <ii0>

Field ~gle (Degrees)

Fig. 24. Angular dependence of the dHvA frequency in Celn 3 (Kurosawa et al. 1990, Satoh et al. 1992, Ebihara et al. 1993). The solid lines connecting the data are guidelines. The letter d designates the orbit.

about 10m0, following the relation m*(Celn3)= m*(Laln3)[7(Celn3)/7(Laln3)], where mc(Laln3) is about 0.5m0 for branch a, y (Celn3) is 130mJ/K2mol and y (Lain3) is 5.3-6.3 mJ/K 2 tool.

The conduction electrons with large masses in the heavy-electron system are believed to move slowly in the crystal compared to the usual carriers in the s and p electrons for a similar Fermi surface topology and mean free path. This is one of the fundamental understandings of the heavy-electron system. Ebihara et al. (1992b) experimentally confirmed that the product of the cyclotron mass and the inverse scattering lifetime or the Dingle temperature is constant by using two orbits of branch d in Celn3.

The relation between the effective mass m* and the scattering lifetime r for the conduction electrons in metals is defined as follows;

hkF = m'or; (63)

and

l = v v r , (64)

where the wave number kv is half of the caliper dimension of the cross-sectional area S of the Fermi surface, vF is the Fermi velocity and l is the mean free path. For example, the equation S = ;rkv applies to a simple circular area.


104 o

10 s

10 g

~q lo~ {100}I "i ' i10} :

10 o

i0-1 80 0 30 60 90

<ii0> <i00> <111> <110> Field Angle (Degrees)

15

i0

=o 5 o

~D

CeIn8 {100} } { 1 1 0 ~ ,

0 I , i , I , i 30 0 30 60 90

<ii0> <i00> <iii> <ii0> Field Angle (Degrees)

Fig. 26. Angular dependence ofthe cyclotron mass for branch d in CeI~ (Ebihara et N. 1993).

Fig. 25. Angular dependence of the dHvA amplitude for branch d in Celn~ at 0.5 K and 129 kOe (Ebihara et al. 1993). The solid line connecting the data is a guideline. The dashed line shows the angular dependence of the dHvA amplitude under consideration of the dHvA-reduction factor [sinh(am~T/H)] -~.

From eqs. (63) and (64) the following equation is obtained:

m* hkF r l

(65)

Thus m*/r is expected to be the same for two similar orbits with the same mean free path. When the effective mass m* is enhanced by a factor of (1 + ~) from spin fluctuations, eq. (65) indicates that r should also be enhanced by a factor of (1 +,1,). This occurs because a large mass is translated into a small velocity from eq. (64) so that the scattering lifetime becomes (1 +,t,) times larger than that obtained by eq. (64) if the mean free path is the same. In terms of the Dingle temperature, eq. (65) becomes

h2kF m*TD- 2JckBl" (66)

The effective mass m* is assumed to be the cyclotron mass m e in the dHvA experiments. Ebihara et al. (1992b) tested whether meT D is the same for similar orbits.

The above relation between the cyclotron mass and the Dingle temperature was applied to the heavy electrons in CeIn3. There are two orbits for branch d which possess the same dHvA frequency and therefore the same cross-sectional area of the Fermi surface but a different cyclotron mass, as mentioned above. Thus, hkv is the same for the two orbits. Moreover, the mean free path is considered to be the same because it is approximately equal to the average distance between impurities.


+~

102

~-.10

a I

71 I

Celn8 i l L i , ~ j i , ,

orbit d 3.15x1070e

x ~ H=70kOe

orbit D ~o~ ~2~44m0= '

3.29x107Oe H=129kOe m~=12mo %

0.5 1.0 Temperature (K)

I

.5

Fig. 27. Temperature dependence of the dHvA amplitude for orbits d and D in CeIn 3 (Ebihara et al. 1992b).

The dHvA frequency and cyclotron mass for field along the (111) direction in branch d are 3.15x 107 Oe and 2.44m0, respectively. The other orbit for field approximately along the (110) direction, which is now denoted by D, has 3.29x107 Oe and 12m0. Here the cyclotron masses were determined from the temperature dependence of the dHvA amplitude A, as shown in fig. 27.

For these two Orbits, fig. 28 shows a Dingle plot of In [AHmsinh(am~T/H)] vs H -]. The slope in fig. 28 gives the product of the cyclotron mass and the Dingle temperature. The slope for orbit d is almost the same as that for orbit D, indicating that the product of m~TD is constant for the two orbits. Orbit d possesses TD =0 .19K or l :=6.5x I0 -12 s, while TD=0.04K or ~:=3.0x10 -ll s for orbit D. We can thus conclude that the larger the mass becomes, the larger the scattering lifetime is such that the value of m c r - I or m~ TD is constant.

+~

orbit D -~g~.~^ o 3.29x1070e o% oo ~o~yg~,-~ 12m0 0.SK

1 L

Celn3

TD=0,04K

orbit d TD=0.19K 3.15 X 10 7 O e ~ ~ o ~ ' ~ ~ 2.44m0 0.5K

I _ _ I I I I I I q I

1.0 H-1 (xl0-5Oe-l)

Fig. 28. Dingle plot for orbits d and D in CeIn 3 (Ebihara et al. 1992b).

1.5

o) O

o~ i0 ~

gr~

N


i08

I06

<Ii0>

{100} {110} Prln3

id d

i

o

I J

30 0 30 60 9O <100> <111> <110>


Fig. 29. Angular dependence of the dHvA frequency in Prln 3 (Umehara et al. 1991c). The solid lines connecting the data are guidelines. The letters designate the various orbits.

Figure 29 shows the angular dependence of the dHvA frequency in PrIn3 (Umehara et al. 1991c). The common dHvA branches are denoted by the letters defined for Lain3. The Fermi surfaces of PrIn3, which has a singlet ground state, are similar to those of Lain3, although each cyclotron mass of PrIn3 is twice as large as the corresponding one for Lain3, as shown in table 8.

NdIn3 becomes antiferromagnetic below 5.9 K. The magnetization exhibits metamagnetic transitions at 76, 85 and 110kOe for field along the (100) direction, and at 73 and 90kOe for field along I110) (Czopnik et al. 1991). With increasing field, this compound goes from an antiferromagnetic to a paramagnetic state, passing through an intermediate magnetic state.

Umehara et al. (1992b) measured the dHvA effect in each magnetic state. The Fen'hi surfaces of NdIn3 in the paramagnetic (or field-induced ferromagnetic) state, which are obtained at higher fields than l l0kOe, are similar to those of Lain3, as shown in fig. 30a. Branches a and d are characteristic Fermi surfaces in bands 7 and 6 of Lain3, respectively. The main branch a consists of two closely separated frequencies, reflecting the up and down spin states of the electrons. We note that it is difficult in general to detect dHvA frequencies lower than 107 Oe at high fields.

However, in the antiferromagnetic state, there are many differences between the Fermi surfaces of NdIn3 and those of Lain3, as shown in fig. 30b. This is due to the magnetic Brillouin zone boundaries. This situation is similar to that of NdB6.


Table 8 dHvA frequencies and cyclotron masses a in RIn 3 compounds for field along the (100) direction (Umehara

et al. 1991b,c, 1992a,b, Satoh et al. 1992, Ebihara et al. 1992a)

RIn 3 a d b jb F m~ F m~ F m; F m~

Lain 3 7.47 0.57 2.78 0.40 6.07 0.69 0.330 0.49

Celn 3 2.93 2.02 3.30 ~ 12 ~

Prln 3 7.57 0.99 3.02 0.60 2.57 0.87

Ndln 3 (paramagnetic) 7.75 1.14 2.67 1.39 Ndln~ 8.09 1.05 3.17 0.80 (anfiferromagnetic) 1.70 0.69

Stain 3 7.81 ¢ 1.30 ~ 3.08 0.80 1.10 0.80

Gdln 3 6.63 0.61 3.07 0.49 1.64 0.52 1.11 0.31

1.38 0.26 0.096 0.17

0.76 c 20.7 c 0.079 c 4.8 c 0.051 c 1.5 c

1.28 0.36 0.27 0.68 1.20 0.91 1.29 0.60 0.49 0.60 0.26 0.42 0.22 0.30 0.19 0.31 0.95 0.24

0.857 0.32 0.261 0.17 0.193 0.16

0.128 0.28

0.12 0.31

0.096 0.29

a F values in 107 Oe, m~ expressed in m 0. b Field along the (111) direction.

c Field along the (110) direction.

According to the results of neutron experiments (Lethuillier et al. 1973), the magnetic unit cell possesses a tetragonal structure which contains double chemical unit cells. Therefore, the volume of the magnetic Brillouin zone becomes half the chemical one. Among the observed dHvA branches, the branch d Fermi surface remains in the antiferromagnetic state because it is fully contained in the tetragonal magnetic Brillouin

zone. Branch a is also observed in the antiferromagnetic state, although the dHvA amplitude

is strongly damped when the field is tilted by about 10 ° from (100) to (110 / in the

{100} and {110} planes, as shown in fig. 31. Umehara et al. (1992b) constructed the Fermi surface such that a nearly spherical Fermi surface in the paramagnefic state, which corresponds to the band 7 electron Fermi surface of Lain3, is changed into a multiply connected Fermi surface with necks, as shown in fig. 32. Note that no necks exist along the [001] and [00i] directions in the cubic notation. Therefore, cubic symmetry is broken in the antiferromagnetic state of Ndln3. This new Fermi surface in the antiferromagnetic state favors an open orbit along the [110] direction when field is directed along the

O

g

107


(a) Paramagnetic State

U I ! , i I ,

{100} I {110} NdI~3 I0 s

d o o

i

°°1

<ii0>

I0 ~

10 8

o

o ~

i0 7

I J , I L I z 10 6

30 30 60 90 <i00) <ii]> <110> <iI0~


(b) Antiferromagnetic State

{i00} I {110} NdIn3

d o o° d

~ ° o ~

I

30 0 30 60 90 <I00> <iii> <110>


Fig. 30. Angular dependence of the dHvA frequency in (a) paramagnetic and (b) antiferromagnetic states for Ndln 3 (Umehara et al. 1992b). The solid lines connecting the data are guidelines. The letters designate the various orbits.

[110] direction, which is confirmed in magnetoresistance experiments (Umehara et al. 1992b).

I f we follow the Fermi surface as shown in fig. 32, the branch a oscillation is not expected to be detectable for field along (110}; but it was experimentally observed even in the antiferromagnetic and intermediate magnetic states, although its amplitude is extremely small. This is because an electron can circulate around a closed orbit by breaking through the neck-Fermi surfaces. These necks, which are introduced by magnetic ordering, are broken through by the circulating electron in rather low field of 50 kOe.

The antiferromagnetic Fermi surface is thus reconstructed on the basis of the magnetic Brillouin zone. The same procedure mentioned above should be applied to the band 6 hole Fermi surfaces, probably producing small closed Fermi surfaces. They may possibly correspond to dHvA branches with frequencies of 1.5x 107 Oe and 5× 106 Oe as shown in fig. 30b.

The cyclotron mass of NdIn3 is twice that of Lain3. Differences of the cyclotron mass are small between the antiferromagnetic and paramagnetic states, as shown in table 8.

For Stain3, a large number of small spherical Fermi surfaces were also observed, which are not present in Lain3 (Ebihara et al. 1992a), as shown in fig. 33. Branches a and d in fig. 33 are similar to those of Lain3 in the magnitude of dHvA frequency. However,


: >

N

' ' T - - ~

30 - NdIna {1oo} 6 3 - 7 8 k O e

0.SK 20

10

0 " q ' - - ° r - ° l ~ ' ~ ' s '~

80 <110>

Io o I

o I i I {110}

o

o

i , I I i | f ~ r o n I

0 <I00>


30

Fig. 31. Angular dependence of the dHvA amplitude for branch a in the antiferromagnetie state of NdIn 3

i(

(a)

[ioo] t

: . ~ .~ .= . q . = z ~ . . :

i l? : 5 " 2 : 2 i l i ? i ~ ' ; 2 l ? ! ( b )

2 ! ? 2 ~ i l l l ~ - - [ 0 1 0 ]

i i i . 3 1 1 3 . , [ i ~ 1 : 1 1

Fig. 32. (a) Proposed electron Fermi surface for band 7; (b) cross-sections of this Fermi surface in

(Umehara et al. 1992b). The solid and dotted lines the R-M-X plane in the antiferromagnetic state of connecting the data are guidelines. NdIn 3 (Umehara et al. 1992b).

branch a for Smln3 is observed only around the (110) direction. The Fermi surfaces are probably modified in topology by the magnetic Brillouin zone boundaries. If we consider the spherical Fermi surface with arms or bumps along the [100], [100], [010] and [050] directions, the electron cannot circulate around (100) but can circulate around both (110) and (111). However, no signal is observed experimentally around (111>. Probably, the (111 ) direction is less detectable compared to (110), which originates from strong damping of the signal due to the curvature factor of the Fermi surface with arms or bumps.

Branch d is also supposed to correspond to branch d in Lain3, although the arms, denoted by j , are not present in Smln3. Its Fermi surface is probably nearly spherical as in Celn3, although the dHvA signal is not observed over the whole angular region.

The cyclotron masses of Smln3 are also roughly two or three times larger than those of Lain3, as shown in table 8.

Branches d and j are observed in the antiferromagnetic state of Gdln3, as shown in fig. 34 (Umehara et al. 1992a). This Fermi surface is probably contained in the magnetic Brillouin zone. As the magnetic structures of SmIn3 and Gdln3 are unknown, further analyses are not yet done.


i08

C )

i 0 7

1 0 6

<ii0>

1 l

{100}

' I ' I ¸ ~

{ii0} Smln3

o ~ o o o_~o_~o -o -~ ~ - o ~ - ~ o - - o ~ r ~ ~

/

(

30 0 30 60 0 <i00> <ii0>

Fie ld Angle (Degrees)

0) 0

10 8

107

10 6

<ii0>

{zoo} ' ' I ~ '

{ii0} @dln3

°o2

d d oo

- o ~ - - ~ - ~ - o ~ g ~ a ~ - a & ' o - g - o ~

. 0 . . ~ . ~ . ~ ~ ! ° 4 - 8 4 ° ~

° ~.~__~ I o04-/~.~-° o o~

I I i J J I I I

30 0 30 60 90

<i00> <iii> <ii0> Field Angle (Degrees)

Fig. 33. Angular dependence of the dHvA frequency in SmIn~ (Ebihara et al. 1992a). The solid lines connecting the data are guidelines. The letters designate the various orbits.

Fig. 34. Angular dependence of the dHvA frequency in GdIn 3 (Umehara et al. 1992a). The solid lines connecting the data are guidelines. The letters designate the various orbits.

The cyclotron masses for branches d and j in Gdln3 are almost the same as those of Lain3. We note that the dHvA branch with the frequency of 7.28 x 107 Oe in Gdln3, which is observed in a narrow region around ( 111 >, is the same frequency as branch a in Lain3. This branch possesses a relatively large mass of 1.70m0, which is three to four times larger than that of Lain3, 0.47m0 if it corresponds to branch a.

In powdered YbIn3, one dHvA branch of 4.50x 106 Oe is detected at high fields up to 30 T, suggesting that there exists a small spherical portion of the Fermi surface (Meyer et al. 1973).

The magnetoresistances of RIn3 (La, Ce and Nd) increase over a wide field region (Umehara et al. 1991b, 1992b, Satoh et al. 1992, Kurosawa et al. 1990). This result suggests that these compounds are compensated metals with an equal carrier number of electrons and holes. This is expected simply from the total number of valence electrons, 12 per primitive cell because of R 3+ and In 3+. However, the magnetoresistances in CeIn3 and Ndln3 saturate for fields along the characteristic field directions, indicating the existence of open orbits in these Fermi surfaces. For example, the multiply connected Fermi surface with necks in the antiferromagnetic state of NdIn3 favors an open orbit along


the (110) direction, as mentioned above. These behaviors are compared to those of Lain3 where the magnetoresistance increases over the whole angular region, indicating no open orbits. A different behavior of the magnetoresistance is observed in Gdln3, where the magnetoresistance saturates in all field directions in the {100} plane (Kletowski et al. 1985). For Gdln3, it is necessary to consider the Fermi surface in the antiferromagnetic state.

4.1.4. RSn3

CeSna at low temperature is thought to belong to the so-called valence-fluctuation regime with a Kondo temperature of about 200 K. Therefore, it is interesting to study the alloy system Ce(Inl_xLax)3, clarifying how the Kondo regime changes to the valence-fluctuating regime. Actually, an experimental work was reported (Benoit et al. 1985). There are some mysteries hidden in CeSn3 itself (Gschneidner et al. 1985). Some anomalies are attributed to off-stoichiometry effects and/or to the inclusion of other phases such as Ce2Sns, but many of the anomalies are not yet well understood. The characteristic properties of the RSn3 compounds are summarized in table 9.

Figure 35 shows the angular dependence of the dHvA frequency in LaSn3 (Settai et al. 1995, Umehara et al. 1991a, Johanson et al. 1981, 1983, Boulet et al. 1982). Main branches are two branches denoted by a and/3 which exist in the whole range of angles in the low frequency region, and three branches with high frequencies denoted by 71, Y2, and 73 centered at (111).

Compared to Lain3, LaSn3 has three electrons more per primitive cell, and hence the electronic structure of LaSn3 is that of an uncompensated metal having a Fermi surface which occupies half of the Brillouin zone (Hasegawa and Yamagami 1991, Hasegawa 1981, Koelling 1982). All sheets of the Fermi surface in Lain3 disappear in LaSn3. In LaSn3, band 8 yields a main sheet of the Fermi surface which looks like a composite sheet, and two small hole pockets lie at the F point in bands 7 and 8, as shown in fig. 36. The solid lines in fig. 35 are the results of band calculations done by Hasegawa and Yamagami(1991). A strong resemblance between the experimental and the theoretical angular dependences of the dHvA branches suggests that the experimental branches a and /3 may originate from the small hole Fermi surfaces in bands 7 and 8, respectively.

Hasegawa and Yamagami (1991) revealed that the composite sheet in band 8 actually consists of a large distorted hole sphere centered at the R point and a network which

Table 9 Characteristic properties of the RSn 3 compounds with the A u C u 3-type cubic crystal structure

RSn3 TN (K) n 7 Fermi surface (mJ/K 2 tool)

LaSh 3 Pauli para n h 11 distorted sphere with necks; and network (hole, band 8) CeSn 3 valence ne=nh 53 distorted sphere (hole, band 8); and complicated electron

fluctuation Fermi surface (band 9)


fl [ , r {loo}

10 8 6" 7,~ ao

,c~ i , / • O~ 1 0 7 : ~ , ~ , ~ < ~ ~ ~ , , ~> o ~ ~ ~

) A A j 0 J @ ~i

10 6 I , I , , , , I , ~,

30 0 30 <II0> <i00>

' ' ~ ( e )

{110} LaSh3 1 LaSna

(a) ho le e

- 6

~ (band 7) o

A~ A

I i i

60 90 <111> <110>

Fig. 35. Angular dependence of the dHvA frequency in LaSh 3 shown by circles (Umehara et al. 1991a) and triangles (Settai et al. 1995). The solid lines show the results of band calculations (Hasegawa and Yamagami 1991). The Greek letters designate the various orbits.

(b) ho l e (band 8)

ho le (band 8)

E

P

P

P

(d) ho le (band 8)

Fig. 36. Fermi surfaces of LaSn 3. (a) Small hole sphere centered at the F point in band 7; (b) small distorted hole sphere centered at the F point in band 8. The large hole surface in band 8 is shown in two separate parts: (c) large distorted sphere; (d) network (Hasegawa and Yamagami 1991). The Greek letters designate the various orbits.

surrounds the distorted hole sphere with many slender arms, as shown separately in figs. 36c, d, respectively. The distorted hole sphere contains about 0.6 holes per primitive cell and is connected with the network near the M point. Each connection part consists of a set of four thin necks. Complex structures of band 8 Fermi surface produce many dHvA branches, as shown in fig. 36c, d. The detected dHvA branches are thus well explained by the present band calculations.

Figure 37 shows the angular dependence of the dHvA frequency in CeSn3 (Umehara et al. 1990, Johanson et al. 1983). Some Fermi surface parts seem to be similar but other parts are considerably different from those of LaSn3, and the detected cyclotron masses are roughly five times larger than those in LaSn3, in agreement with the y values, as shown in tables 10 and 11.


CeSn3 i {loo} {11o}

I i° 10 8 a b ¢ ~ ~ e

:f

r °L ~ poo

105 i I , i I i ~ I , i I i l

30 0 30 60 90 (110> (100> (111> (110>

F ie ld ~ g l e (Degrees)

0

10 7

<

106

F

CeSn3

F F

(a)

P

F R

R

(b)

Fig. 37. Angular dependence of the dHvA frequency in R CeSn 3 (Umehara et al. 1990). The solid lines connecting the data are guidelines. The letters designate the various

orbits. R

Fig. 38. (a) Large hole Fermi surface in band 8; (b) large electron Fermi surface in band 9 of CeSn3 (Hasegawa et al. 1990). The letters designate the various orbits.

Table 10 Cyclotron masses and band masses in LaSn 3 (Umehara et al. 1991a, Hasegawa and Yamagami 1991) a

mass a /3 71 72 73 6 e ~ p (111) (111) (111) (111) (111) (110) (27 ° ) (100) (110)

m~ (too) 0,38 0.74 1.07 0.91 1.91 1.16 2.33 0.78 0.45

m b (m0) 0.16 0.42 0.67 0.42 0.67 1.2 1.6 0.69 0.40

m*dmu 2.4 1.8 1.6 2.2 2.9 1.0 1.5 1.1 1.1

a Note that the g value of 11 mJ/K 2 mol is roughly twice as large as the theoretical Yb value of 5.56 mJ/K 2 tool.


Table 11 Cyclotron masses m~ and their band masses m b in CeSn 3 (Umehara et ai. 1990, Hasegawa et al. 1990). Note

that the 7 value of 53 mJ/K 2 tool is roughly three times larger than the theoretical value of 15.4 mJ/K 2 mol

Mass a b (100) c (110) d (111) e f g (110) (100) (110) (111)

m~0) 4.15 3.83 2.72 6.30 6.25 4.07 mb~0) 2.1 1.7 0.9 1.7 2.3 2.3 3.6 1.4 2.1 m ~ b 2.4 4.3 1.6 2.7 2.7 1.9

Hasegawa et al. (1990) calculated the energy band structure of CeSn3 under the assumption that the 4f electron is itinerant. As shown in fig. 38, the calculated Fermi surfaces mainly consist of a large band 8 hole Fermi surface centered at R and a large band 9 electron surface centered at F. The origin of the analogy in Fermi surfaces between CeSn3 and LaSn3 is as follows. Namely, the large distorted spherical hole Fermi surface of band 8 in LaSn3 is similar to the band 8 hole Fermi surface in CeSn3. Small spherical hole Fermi surfaces in bands 7 and 8, denoted by a and/3 in LaSh3, are also present in CeSn3, corresponding to branches p and q, respectively in fig. 37, although their volumes of the Fermi surfaces in CeSn3 are smaller than those of LaSn3. The difference between LaSn3 and CeSn3 is ascribed to the large electron Fermi surface in CeSn3. Note that this Fermi surface has no occupied states along the (111) direction, which is different from the results of band calculations done by Koelling (1982) and the renormalized band calculations done by Strange and Newns (1986). Later, Norman and Koelling (1993) confirmed the validity of the electron Fermi surface calculated by Hasegawa and coworkers.

The solid lines in fig. 39 indicate the results of the band calculations done by Hasegawa et al. (1990). Branch a corresponds to the large hole Fermi surface, while the other main branches are due to the electron one. Both in the magnitude of the cross-sectional area and in the observed range of angle, the theoretical branches agree reasonably well with those of the experimental ones, supporting the validity of both the large hole and the large electron Fermi surfaces predicted by the calculations.

Here we note that branch a in fig. 39 disappears at angles in the vicinity of the (100) direction. The reason for the disappearance of branch a is due to the combined effect of the curvature factor and cyclotron mass, as shown in fig. 40. The hole Fermi surface is not a perfect sphere, but bulges appreciably towards the (100) direction. In the (111 ) direction, the orbit does not pass on any bulges. Therefore, as shown by the broken

line in fig. 40, 102S/Ok 2 [-,/2 has a sharp peak along ( I l l ) and becomes small along (100) and (110). The minimum value is about 1/20 of the maximum. Another possible origin is an increase of the cyclotron mass m* for branch a, because it becomes a maximum along (100) and a minimum along (111). Here we note that the probability amplitude of the 4f state averaged over the orbits perpendicular to the (100), (110) and (111) directions is found to be 70%, 65% and 60%, respectively. The intensity of the oscillation of the de Haas-van Alphen effect is thus damped by the factor [sinh(am2 T/H)] -1. The solid line


0

¢D

r~ .

{I00}

108 ~

< i07 , I ,

30 60 90 <Ii0> <i00> <iii> <ii0>


r~ 4 ~

4

4 ~

8 t I I ' ' ]

CeSn3 2

{I00} {ii0} ; J

' l I I

II

hi

/', -

LI

' \ i ~\

30 30 60 90 <ii0> <i00> <ii0>


Fig. 40. Angular dependence of the dHvA amplitude for branch a (Hasegawa et al. 1990). The dashed curve shows the curvature factor 102S/02kr, I -'/2, and the

Fig. 39. Angular dependence of the high dHvA solid curve includes another factor [sinh(a m*e T/H)] -I" frequency in CeSn3 (Umehara et al. 1990). The solid [02S/Ok~l -'/2. Data are for T -0 .5 K and H = 150kOe. lines show the results of band calculations (Hasegawa The circles are the experimental results (Umehara et al. 1990). The letters designate the various orbits, et al. 1990 ).

<L \ <L

<3

40

30

20

i0

I ' I ' ' I ' ' I ' '

LaSn3 } J//<ll0>

30 0 0 30 60 90 Field Angle (Degraes)

40

3O

Q .

\ Q

<3

2O

10

i i i i I - i

(b)

LaSn3 J//<100 > 0.5K

I I ~ I E I I I

/ /

HH4.5 °

~ ~ H f f < 100,

50 I00 150 Magnetic Field (kOe)

Fig. 41. (a) Angular and (b) field dependencies of the magnetoresistance in LaSn 3 (Umehara et al. 1991a). Open orbits occur in the stippled region in (a). The solid lines connecting the data are guidelines.


in fig. 40 shows the angular dependence of the curvature factor multiplied by this factor which is calculated for branch a by assuming that T=0.5K and H = 150kOe. We see that this combined damping factor qualitatively explains the experimental result for the intensity of branch a.

The large hole Fermi surface in band 8 contains 0.44 holes per primitive cell, and the large electron one in band 9 contains the compensating number of electrons. The number of holes and electrons contained in other small Fermi surfaces is fairly small, in total about 0.1 per cell. Every carrier possesses larger masses than the corresponding band masses. The ratio of the cyclotron mass m e to the band mass m2/mb for each branch is in the range of 2 to 4, as shown in table 11. This is consistent with the ratio of y to Yb, 3.4.

The magnetoresistance is also useful to determine the character of the 4f electrons in CeSn3. Figure 41 shows the angular and field dependences of the magnetoresistance in LaSna (Umehara et al. 1991a). The sharp dips and spikes around the (100) direction indicate that the (100) direction is a singular field direction and the spikes mean open orbits, resulting from the uncompensated nature of LaSh3. This is simply expected from the total number of valence electrons, 15 for La 3+ and Sn 4+. These open orbits are explained well by the results of band calculations done by Hasegawa and Yamagami (1991). Figure 42 is a typical example of the (100) open orbits running on the large Fermi surface in band 8. Magnetic field is at 4.5 ° from the (100) direction on the { 100} plane.

On the other hand, the magnetoresistance of CeSn3 in fig. 43 increases in the all field directions (Umehara et al. 1990), indicating compensated carriers and the absence of open orbits in CeSn3, which may be compared to the uncompensated state of LaSn3. These results indicate that Ce is tetravalent, Ce 4+, confirming the itinerant nature of the 4f electron.

The results of magnetoresistances for LaSn3 and CeSn3 are consistent with the results of the band calculations mentioned above (Hasegawa and Yamagami 1991, Hasegawa et al. 1990). The multiply connected band 8 Fermi surface in LaSn3 favors the experimentally observed open orbits. All of the Fermi surfaces in CeSn3 are closed ones, in good agreement with the compensated metal of CeSn3 without open orbits.

It is remarkable that the itinerant 4fband model fits the dHvA results so well. From the viewpoint of the energy band structure we summarize the f-electron behaviors of LaSn3 and CeSn3. In LaSn3, band 8 forms a large distorted hole sphere around the R point, and each of bands 7 and 8 forms a small hole sheet at the F point. These characteristic features of the energy band structure in the vicinity of the Fermi level (EF) are shown schematically in figs. 44a, b. The center of the unoccupied 4f bands is located at about 0.2 Ryd. above EF. The energy band structure around the R point in band 8 is similar to the nearly-free-electron band and the Fermi surface of band 8 is quite insensitive to the location of the 4f bands (E4f). In contrast, however, since the Bloch states at the F point in bands 7, 8 and 9, denoted as F 7 and F~, consist dominantly of the Sn 5p states and have the same symmetry as in the 4f bands, they can hybridize strongly with the 4f states. Hence, the position of their energy levels depends sensitively on the location of the 4f bands. The size of the small hole sheets is apt to vary easily by a change of the location of the 4f bands.


d

LaSn3

(

~ t , . - t-0.07~.0.997,01 open orbits

Fig. 42. (100) open orbits running on the large hole Fermi surface in band 8 of LaSn 3 (Hasegawa and Yarnagami 1991). Magnetic field is applied at an angle of 4.5 ° from the (100) direction on the {100} plane. The center of this figure is located at (0.6, 0.5, 0.5)(2n:/a). The hatched regions show the unoccupied electron states.

50 ~ I , , , , ,-

I J/ /<lO0> 1

40 I°'l 5K

20 !

• !

10

It i''' ' ' -

, 150k0e

30 0 0 30 60 90

<Ii0> <i00> <i00> <iii> <ii0>


Fig. 43. Angular dependence of the magnetoresistance in CeSn 3 (Umehara et al. 1990). The solid lines connecting the data are guidelines.

(a) (b)

-1

E4f

r s,r-- -.,%%

EF / ' 1

1

E4f

8 -- t a

. / F ~ -

./- F7- F8-

: 'q-~ 7

T R S Z F A

Fig. 44. Schematic representations of the relationship between the energy band structures (bands 7, 8, 9) for LaSn 3 and CeSn 3. Solid curves show the energy bands, and solid lines show the Fermi level (EF) and the center of the f bands (E4r) for LaSn 3, and dashed curves and lines show those for CeSn 3. (a) Energy band scheme around the R point; (b) energy band scheme around the F point.


Based on the itinerant-electron model for the 4f electrons, CeSn3 has one more Bloch electron per primitive cell. As electrons are added to the 4f bands, the 4f bands shift downwards and the Fermi level rises. In contrast to a small change in the band 8 large hole sphere shown in fig. 44a, bands 7, 8 and 9 around the F point are modified drastically, as shown in fig. 44b. The F~ state shifts down to just above EF, and the two small hole surfaces diminish considerably. Band 9 around the F point also sinks so deeply, i.e., the I'~ state shifts toward the same position of the F 8 state, that it can form an electron sheet around the F point which is dominant enough to compensate the large hole sphere around the R point. Only a slight rising of the Fermi level is necessary. Therefore, the large hole sheet contracts a little, and is separated completely from the network. The energy band structure for CeSn3 thus obtained is shown by broken curves in figs. 44a, b. This is a simple explanation for the fact that CeSn3 has an isolated, distorted hole sphere in band 8 which looks quite similar to the distorted hole sphere in band 8 in LaSn3. In spite of the resemblance between these hole sheets, the Bloch states on the large hole sheet in CeSn3 have a large probability of 4f components, about 60% on the average. A distinct difference between LaSn3 and CeSn3 is the existence of a large electron sheet in band 9 in CeSn3 which appears to compensate the large hole sheet in band 8.

4.2. Fermi surfaces in the bcc Brillouin zone

4.2.1. RX Rare earth monopnictides RX possess the NaC1 type crystal structure. The primitive cell contains one molecule of RX. Figure 45 shows the crystal structure and its Brillouin zone. Especially the CeX compounds, in which X stands for N, P, As, Sb and Bi, have attracted a particular interest because of various anomalous magnetic and transport properties (Kasuya et al. 1987). LaX is expected to be a semimetal with a small and equal number of electrons and holes. A similar semimetallic character is observed in CeX, except CeN. CeX is a Kondo-latfice compound, having anomalous magnetic properties at low temperatures. Even though the carrier number is small, the Kondo effect is strong and the

kz

(

t~ (a) A ~ (b)

Fig. 45. (a) NaC1 type cubic crystal structure of the RX compounds. Spheres with and without pattern show the X and R atoms, respectively; (b) Brillouin zone of the face-centered cubic crystal lattice.


Table 12 Characteristic properties of the RX compounds

Compound T N (K) n 7 Fermi Surface (mJ/K 2 mol)

LaSb Pauli pa ra no=nh 0.80

CeSb 16.5 n~ = nh Kondo lattice

PrSb singlet no = n h SmSb 2.1 n~ = n~ GdSb 27 no = n h LaBi Pauli para ne = nh CeBi 25 n~ = nh

Kondo lattice CeAs 7-8 n e = n~ YbAs 0.5 n~ = n~

20

0.95 20

200

three ellipsoidal electron Fermi surfaces (band 4) and compensated two spherical hole Fermi surfaces (band 2 and 3). n~=0.014mo1-1 similar to LaSb but spin-split

similar to LaSb similar to LaSb similar to LaSb similar to LaSb similar to LaBi

similar to LaSb, but n~ =0.001 mo1-1 similar to LaSb

), value is large, about 20 mJ/K 2 mol for both CeBi and CeSb. The characteristic properties o f RX compounds are summarized in table 12.

The angular dependence of the dHvA frequency was clearly observed in LaSb (Settai et al. 1993, Kasuya et al. 1987, Kitazawa et al. 1983). It is expected from a simple consideration o f the valencies of constituent atoms that LaSb may be an insulator, but in reality there is a slight overlapping between the Sb 5p valence bands and the La 5d conduction bands. Thus LaSb becomes a semimetal. Although a self-consistent relativistic calculation in LDA actually yielded a good fit with the experimental results, it was found that a better fit can be achieved by shifting the La 5d bands and the unoccupied 4fbands upwards relative to the Sb 5p valence bands (Hasegawa 1985). It was also found that a correct Fermi surface can be obtained for LaSb by a non-self-consistent calculation with a full Slater exchange potential. Results o f band calculations thus obtained are shown by solid lines in fig. 46, which are compared with the experimental dHvA results (Settai

et al. 1993). In later calculations due to an LMTO method performed by Sakai et al. (1985) and

Kasuya et al. (1987), the relative positions o f the Sn 5p bands and the La 5d bands were adjusted artificially so as to reach a proper overlap between them, and the 4 f bands were shifted upward to a level suggested by a BIS experiment. The results of their calculations are the same as those shown in fig. 46. There is, however, an obvious shortcoming which is inherent in LDA; the overlap between the valence and conduction bands is too deep. Such a shortcoming manifests itself most seriously in small Fermi surfaces of semimetals. Most o f this may be removed by taking the self-interaction correction into account.

The Fermi surface consists of three kinds o f sheet (Hasegawa 1985), as shown in fig. 47. Band 2 forms a small and nearly spherical hole Fermi surface centered at the F point,


151 I ,

x

o)

5q

I - 7

{100} [110}

o, o o

] i - - l - - - i i I 30 o 30

LaSb

(

60 90 <11o) <100) <111) <110)

F i e l d A n g l e ( D e g r e e s )

Fig. 46. Angular dependence of the dHvA frequency in LaSb (Settai et al. 1993). The solid lines show the results of band calculations (Hasegawa 1985). The Greek letters designate the various orbits.

Fig. 47. Fermi surfaces of LaSb (Hasegawa 1985): (a) hole Fermi surface in band 2, centered at F; (b) hole Fermi surface in band 3, centered at F and the three electron Fermi surfaces in band 4, centered a tX.

(b)

denoted by ft. Band 3 also forms a hole Fermi surface centered at the F point, denoted by fiq It is slightly stretched into the (100) direction. On the other hand, band 4 consists of three equivalent, nearly ellipsoidal electron Fermi surfaces centered at the X point, denoted by ai (i = 1, 2 and 3).

LaSb is thus a semimetal. Namely, the top of the valence band with the dominant Sb 5p character is located at F. The bottom of the conduction band with mostly La 5d character is located at X. They slightly overlap. The narrow 4f bands lie a few eV above the Fermi level, and thus the mixing of the 4f states into the valence band states is not large. The cyclotron masses are thus small; 0.14m0 for branch a3, 0.15m0 for branch fl and 0.49m0 for branch fl~ for field along (100) direction (Settai et al. 1993).

LaBi is also a semimetal. The Fermi surface is quite similar to that of LaSb (Kitazawa 1982). The cyclotron masses are in the range of 0.18m0 to 0.36m0. The experimental electronic specific heat coefficients of LaSb and LaBi are 0.80 and 0.95 mJ/K 2 tool, respectively. This is in good agreement with the calculated values, 0.50 and 0.85 mJ/K 2 mol (Hasegawa 1985, Sakai et al. 1985).

62

70

6O ~D

0

?2 50 g

40

I

(o10)

Y. 0NUKI and A, HASEGAWA

30 i 30

[101]

I I [ t l l l l l [

CeSb

F(~

v S~t~)

I L I I I I t l l f

30 60 90 [001] [111] [110]


r /3

< >

I I i I i

I I I I I I I I I

36 38 40 42 Magnetic Field (kOe)

Fig. 49. dHvA oscillation on the high- and low- field sides of the magnetic transition from the S' to F phases in CeSb (Crabtree et al. 1987).

Fig. 48. Angular dependence of the transition field between the S' and F phases in CeSb (Crabtree et al. 1987).

CeSb and CeBi, which show anomalously large magnetic anisotropy and a very complex antiferromagnetic phase diagram called "devil's staircase" (Rossat-Mignod et al. 1985), belong to a Kondo-lattice system with a small carrier number. Even though the cubic 1"7 state isthe ground state in the paramagnetic state, anisotropy in the ordered state is very strong.

CeSb exhibits at least 15 magnetic phases as a function of temperature and magnetic field. The low-temperature phases consist of stacks of ferromagnetically aligned (001) planes with magnetization parallel (T) or antiparallel (+) to field along the [001] direction; S2(TT$+Ti"+), S'(TT$) and F(Ti"T). The ordered state thus shows an Ising- like character with ferromagnetic ordering within (001) or z-plane, while the nearly full moment of Jz = 5/2 is oriented along the [001] or z-axis with 4f(Fs) character. These interesting properties are explained by the p - f mixing model (Takahashi and Kasuya 1985). Because of the strong p - f mixing between the 4f(F8) and Sb 5p states at the F point, the 4f(Fs) state becomes more stable than the 4f(F7) state at low temperatures in the ferromagnetic ordered state. This feature is strongly enhanced by the non-linear effect due to the small Fermi energy. Here the 4f(F7) state mixes rather weakly with the electrons in the Ce 5d conduction band.

The strong magnetic anisotropy leads to domain effects in the presence of a field. In the absence of fields, the magnetic moment has an equal probability of pointing along any of the three crystallographically equivalent (100) directions. In field the magnetic energy is lowered if the moment chooses to point along the <100 / direction closest to the applied field direction, resulting in a single domain sample.


Figure 48 shows the transition field between S I and F phases as a function of angle in the (010) and (510) planes (Crabtree et al. 1987). Domain effects are evident in the sharp cusp in the transition field occurring at [111]. For field directions between [001] and [111] in the (510) plane and between [001] and [101] in the (010) plane, the favored moment direction is [001]. However for directions between [111] and [110] in the (110) plane, the favored direction switches to either [010] or [100]. The cusp at [l 11] reflects this switch in the magnetic domain. The strong magnetic anisotropy can also be seen in the shape of the transition field. The solid line in fig. 48 is the form Hc/cosO where 0 is the angle between the field and the closest (100) type direction. The excellent fit of this curve to the transition field implies that for an arbitrary direction the transition occurs whenever the component of field along the closest (100) direction equals Ho. This behavior is expected if the moment is pinned along the closest (100) direction.

Figure 49 shows the dHvA oscillation on the high and low-field sides of the magnetic transition from S r to F (Crabtree et al. 1987). The Fermi surface changes significantly between these two phases. The low-dHvA frequency oscillations with large amplitude in the high-field region are abruptly replaced by the higher-dHvA frequency oscillations with smaller amplitude in the low-field region.

dHvA studies in the F phase were reported first by Kitazawa et al. (1983); more complete studies in the two phases o fS ~ and F phases were done by Aoki and coworkers (Aoki et al. 1985, 199l, Crabtree et al. 1987). Figures 50 and 51 show the angular dependence of the dHvA frequency in the S ~ and F phases, respectively.

In fig. 51, the solid lines show the results of band calculations done by Kasuya and coworkers (Kasuya et al. 1987, Sakai et al. 1985). The band structure calculations were carried out for a ferromagnetic state by an LMTO method. To represent the Sb 5p bands and the Ce 5d bands, potential parameters in the LMTO method were determined so as to reproduce the Fermi surface of LaSb properly. The CeSb 4f state with Jz = 5/2 was located at 1 eV below the Fermi level so as to fit the photoemission spectra (Hillebrecht et al. 1985). One of the 4f electrons is localized at this level. Hence, there are no adjustable parameters in calculations of the Fermi surface for CeSb. The 4f electrons cause ferromagnetism, and affect the Fermi surface, especially the small hole sheets at the F point through the 5p-4f hybridization effect. As shown fig. 51, the agreement between the experimental data and the theoretical results is surprisingly good, supporting validity of the p- f mixing model. Due to ferromagnetic ordering, two hole bands split into four different hole bands, named fit,/32,/33 and/34. On the other hand, the electron bands at X are split by the 5d-4f intra-atomic exchange interaction. The different sizes of the three electron ellipsoids explain the separation in the dHvA branches ai, as shown in fig. 52 (Crabtree et al. 1987). The smaller ellipsoid whose axis is along the moment direction of the [001] axis gives rise to branch a3, while the larger ellipsoids produce branches a1 and a2. The cusp in branch ai at [111] is due to the domain switching effect. As mentioned above, when field is directed from [111] to [110] in (110), the favored magnetic moment switches from [001] to either [010] or [100]. Figures 51 and 52 are tentatively illustrated as the [100] moment. Therefore, branch al corresponds to the smaller ellipsoid. Here all branches et i are experimentally split into the up and down electron states.


09

Fx.

>

9 , 0 I ' 1 ' I I '

I

I (ii0) CeSb (010) I S' (¢¢¢)

0 I , , I , I ,__

30 0 30 60 [101] [001] [111]


9O [110]

9 , 0 1 ' I ' I ' l '

(010) (i i0)

F(t'1't') I

o , ~ o° o oX . . . . o - 80O0o°O~ °° o

i 0 - o ~ a~/ -

2

0 30 0 30 60 90

[i01] [001] [111] [110]


Fig. 51. Angular dependence of the dHvA frequency Fig. 50. Angular dependence of the dHvA frequency in the F phase of CeSb (Aoki et al. 1991, 1985). in the S' phase of CeSb (Aoki et al. 1985). The solid The solid lines show the results of band calculations lines connecting the data are guidelines. The Greek (Kasuya et al. 1987, Sakai et al. 1985). The Greek letters designate the various orbits, letters designate the various orbits.

HI[O01 ] [001].

[IO0] [100] [110]

Fig. 52. Ellipsoidal Fermi surfaces of CeSb for the magnetic moment in the [001] and [100] directions (Crabtree et al. 1987).

According to the p - f mixing model, branch/34 is the most important band. In earlier experiments, however, branch/34 was not observed. This fact caused some investigators to doubt the strong p - f mixing model and to apply a weak p - f mixing model (Norman and Koell ing 1986). Later, branch f 1 4 w a s observed by acoustic and usual dHvA measurements (Aoki et al. 1991, Kasuya et al. 1987). Generally thinking, it may be difficult to detect branch/34 by the usual dHvA experiments because the small amplitude of FFT spectrum


Table 13 Cyclotron masses m~ for the field along (100) in the RX compounds (Settai et al. 1993, Aoki et al. 1985, Goto

et al. 1993, Ozeki et al. 1991, Tanaka et al. 1993, Takeda 1992, Takeda et al. 1993)

Compound a 3 al, az 3 [Y

LaSb 0.14 0.15

CeSb 0.23 0.94 0.50 (/3 0

0.82 0.97 (./32)

PrSb 0.19

SmSb 0.21

0.28

GdSb 0.24

CeAs 0.35

YbAs 0.18

0.82 0.26

0.60 0.27

0.52 0.23

0.47

0.49

0.89 (/33) (/34)

0.40

0.74

0.64

for branch/34 with its large mass is masked by the huge amplitudes of higher harmonics for the other branches with small masses. The difficulty in observing branch/34 is thus ascribed to its large mass. The mass enhancement in CeSb is quite large, more than twenty. However, the cyclotron masses in CeSb, except branch/34, are not large, as shown in table 13. They are in the range of 0.3m0 to 0.9m0 mass enhancement factor of two or three (Kitazawa et al. 1988, Aoki et al. 1985). Therefore the mass &branch/34 should be large, it is estimated to be about 10m0. Unfortunately, it has not yet been clearly determined by experiments.

We mention dHvA measurements in other RX compounds, dHvA measurements on CeBi were made by Kasuya et al. (1987). The result is not perfect, but the observed branches ai, [31 and/32 agree very well with the results of band calculations.

dHvA measurements were also done for PrSb, SmSb and GdSb (Goto et al. 1993, Ozeki et al. 1991, Tanaka et al. 1993). Figures 53-55 show the angular dependence of the dHvA frequency in PrSb, SmSb and GdSb, respectively. The Fermi surfaces obtained are similar to that of LaSb. For the antiferromagnetic compound SmSb, the dimensions of the Fermi surfaces are the same in both paramagnetic and antiferromagnetic states. The cyclotron masses in the paramagnetic (antiferromagnetic) states are 0.21m0 (0.28m0) for branches a3, 0.82m0 (0.60m0) for branch al and a2, 0.26m0 (0.27 m0) for branch/3, and 0.74m0 (0.64rn0) for branch y for field along the (100) direction, which are 1.5-2 times larger than those of LaSb.

Shubnikov-de Haas oscillations were detected in CeAs (Kwon et al. 1991, Takeda et al. 1993). For a good stoichiometric sample of CeAs, the carrier number is one order of magnitude smaller than that of CeSb. Branches ai and 3 were observed, although branch/31 due to a hole Fermi surface in band 3 was not observed. The topology of the Fermi surface is similar to that of LaSb, although the volume is small compared to LaSb, as shown in fig. 56.


o

o o)

r+,

<

15

10

0

<ii0>

PrSb I

{100} i {110}

30 0 80 60 90

<i00> <Ii0>


Fig. 53. Angular dependence of the dHvA frequency in PrSb (Goto et al. 1993). The solid lines connecting the data are guidelines. The Greek letters designate the various orbits.

2 0 I ~ ' 1 ' I '

{100} {110} SmSb

& . b i \ / '

N s

I 0 I , I ~ I , I ,

30 0 30 60 90 <110> <100> <111> <110>

F ie ld Angle (Degrees)

Fig. 54. Angular dependence of the dHvA frequency in SmSb (Ozeki et al. 1991, Tanaka et al. 1993). The solid lines connecting the data are guidelines. The Greek letters designate the various orbits.

2 0 ! ' I ' I ~ I ' •

* / + 1o i+ ' w ! \ I

2 + / !

O/a I I

0 I , i ~ I , [ ,

30 0 30 60 90 <110> <100> <111> <110>


Fig. 55. Angular dependence of the dHvA frequency in GdSb (Goto et al. 1993). The solid lines connecting the data are guidelines. The Greek letters designate the various orbits.


5

x

~4 r,-.

 <100> <111> <110>


O

o

x

rz~

< 1 >

1 0

Fig. 56. Angular dependence of the dHvA frequency in CeAs (Kwon et al. 1991, Takeda et al. 1993). The 0 solid lines connecting the data are guidelines. The < 110 > Greek letters designate the various orbits.

r ' ' p ' V-

{100} {110} VbAs

OL~

I , , { , t ,

30 0 30 60 90 <100> <111> <110>


Fig. 57. Angular dependence of the dHvA frequency in YbAs (Takeda et al. 1990, Yakeda 1992), The solid lines connecting the data are guidelines, The Greek letters designate the various orbits.

dHvA measurements were also done for YbAs, as shown in fig. 57 (Takeda et al. 1990, Takeda 1992). It is an interesting compound in the sense that it is a Kondo-lattice compound which competes strongly with magnetic fluctuations. At low temperatures of 0.6 K, it orders antiferromagnetically. The dHvA signals were observed both above and below the N6el temperature, without a change of the dHvA frequency but with a decrease of the dHvA amplitude below the N6el temperature. The Fermi surface of YbAs is similar to that of LaSb. The ~ value is estimated at the extremely large value of 200 mJ/K 2 mol (Suzuki 1993).

4.2.2. RA/2 The RA12 rare earth compounds possess the cubic Laves-phase structure, which is shown in fig. 58. CeAI2 provides a good example of a Kondo-lattice system with the F7 ground state and an incommensurate sinusoidally modulated antiferromagnetic structure below 3.8K (Barbara et al. 1979), as shown in table 14.

Figure 59 shows the angular dependence of the dHvA frequency in LaA12 (Seitz and Legeler 1979, Reichelt and Winzer 1978). These dHvA branches are well explained by the results of APW band calculations by Hasegawa and Yanase (1980a), as shown by solid lines in fig. 59. The La atoms in fig. 58 form a diamond sublattice, and the tetrahedra of the A1 atoms occupy vacant comers in the La sublattice. Owing to this closely packed crystal structure, the electronic structure is characterized by strong hybridization between the La 5d and the A1 3p bands (Hasegawa and Y~anase 1980a). In the vicinity of the Fermi level, the 4f components in the Bloch states are small, less than 3% only. The Fermi surface consists of various sheets distributed in bands 8, 9 and 10.

68

Fig. 58. The RAI2 compounds with the cubic Laves phase crystal structure. Spheres with and without pattern show the A1 atoms and the R atoms, respectively.

Fig. 59. Angular dependence of the dHvA frequency in LaA12 (Seitz and Legeler 1979). The solid lines are the results of band calculations (Hasegawa and Yanase 1980a). The Greek letters designate the various orbits.

Y. 0NUKI and A. HASEGAWA

O

10 ~ c~ CD

10 c

109

{100 }

108

~ o ~ 38 ° 0 0 oO

o O O ° o o ~ o o o o

10 s ~ 30

<110>

I 30 60 90

<100> <111> <110> F i e l d a n g l e (Degrees)

Table 14 Characteristic properties of the RA12 compounds

Compound TN (K) n y Fermi surface (mJ/K 2 tool)

YA1 z Pauli para ne = nh 5.4

LaA12 Pauli para no = nh 11 CeAI 2 3.8 n e = n h 135

Kondo lattice

sphere (electron, band 10); and a "jungle-gym" Fermi surface (hole, band 9)

similar to YAlz similar to LaA12, but spin-split

A main spherical branch ~ is due to a band 10 electron Fermi surface which is a sphere

centered at the F point but has bumps in the (100 / direction, as show in fig. 60. The other branches are ascribed to the multiply connected hole Fermi surface associated with band 9. The latter "jungle-gym"-Fermi surface favors the (100> and <110) open orbits, consistent

with magnetoresistance results (Reichelt and Winzer 1978). LaA12 is thus a compensated metal. This is simply understood because the primitive cell contains two molecules of

LaA12. The cyclotron mass is in the range of 1.7m0 to 0.2m0, as shown in table 15. dHvA experiments and band calculations were carried out for YA12 by Seitz (1978)

and Hasegawa and Yanase (1980b), respectively. Although the data are limited only in the


LaAI 2

(a) (b)

69

Fig. 60. (a) Electron Fermi surface in band 10; (b) hole Fermi surface in band 9 of LaAI 2 (Hasegawa and Yanase 1980a). The Greek letters designate the various orbits.

Table 15 dHvA frequencies F, cyclotron masses rn~ and band masses rn b in the RA12 compounds a

Compound ~(110) e(111) F m~ m b F m~ m b

LaA12 7.23 1.68 0.94 0.362 0.23 CeA12 7.61 16.2 0.318 1.1

6.98 15.0

0.19

" F values in 107 Oe, m* expressed in mo; mb expressed in m 0. References: Seitz and Legeler (1979), Hasegawa and Yanase (1980a), Reinders and Springford (1989).

{ 100} plane, the Fermi surface o f YA12 is similar to LaAlz. A small difference between YAI2 and LaA12 is found in the band 9 hole Fermi surface.

Figure 61 shows the typical dHvA oscillation for field tilted 45 ° from the (100) direction in the { 110} plane o f CeA12 (Reinders and Springford 1989). The metamagnetic transition from the antiferromagnetic to field-induced ferromagnetic (or paramagnetic) state occurs at 52.7 kOe at this orientation. One dHvA frequency of 3.10 x 106 Oe denoted by e is observed in the antiferromagnetic state. The same frequency is also seen above the transition, changing its amplitude to a huge value.

The angular dependence o f the dHvA frequency in CeA12 is shown in fig. 62 (Reinders and Springford 1989, Lonzarich 1988). The dHvA branches of CeAl2 are similar to those o f LaAl2. The electron branch ~ is clearly split into up and down spin branches due to the ferromagnetic exchange interaction. The exchange splitting energy defined by eq. (62) is estimated to be 10meV.

These spin-split ~ branches are explained by LMTO band calculations (Guo 1990) which treat the 4 f electron as a spin-polarized core state. The dHvA branch with the frequency of 1.3x 108 Oe, centered at <111>, was assigned from a band 9 hole Fermi surface.


bO

r ~

CeAl2

Hc

50 100 Magnetic Field (k0e)

Fig. 61. dHvA oscillation taken with the field oriented 45 ° from (100) in the {110} plane of CeA12 (Reinders and Springford 1989). The dHvA oscillations are seen above and slightly below the magnetic phase transition, which occurs at 52.7 kOe at this field orientation.

10 9

10 8 ,

O

107

r ~ .

>

lO 6

Fig. 62. Angular dependence of the dHvA frequency 105 I in CeA12 (Reinders and Springford 1989, Lonzarich 30 1988). The Greek letters designate the various <ii0> orbits.

I ' ' I I

{100} {110} CeAl2

~ 8 - " J ~ '~-on~~-~-o . .~~ . . . . . . o oo

L ~(+)

J I

e(+) j6(~)

I I

, i , I , l

0 30 60 <100> <111>


i

9O <110>

The measured cyclotron masses in CeAla are 1. lm0 for branch e and 16m0 for branch ~. The enhancement factor for the m c value of LaAlz is seen to vary and falls between 5 and 10. Here, the y value of CeA12 at low temperatures (Bredl et al. 1978) is 135 mJ/K 2 mol, while that of LaAI2 is 11 mJ/K 2 tool (Hungsberg and Gschneidner 1972). Therefore, the enhancements of m S and y in CeA12 over their values in LaAI: are of comparable magnitudes.

4.3. Fermi surfaces in the hexagonal Brillouin zone

4.3.1. RGa2 RGa2 compounds crystallize in the simple hexagonal A1B2-type structure. The primitive cell contains one molecule of RGa2. Figure 63 shows the crystal structure of RGa2 and its hexagonal Brillouin zone. Among them, CeGa2 is a highly anisotropie ferromagnet with the easy axis in the basal plane. The magnetic phase diagram is not simple, indicating the ferromagnetic state below 8.4 K and two or three complicated antiferromagnetic states in the temperature region between 8.4 K and 11.4 K (Jerjini et al. 1988, Takahashi et al. 1988). From resistivity data and other magnetic properties, it is concluded that CeGa2 is not a Kondo lattice compound but a usual f-localized one. SmGa2 is also an f-localized compound with a N6el temperature of 20K. We summarize in table 16 the characteristic properties of RGa2 (Umehara et al. 1992c, Tang and Gschneidner 1989, Tang 1989, Dijkrnan 1982).

We show in figs. 64 and 65 the angular dependences of dHvA frequency in LaGa2 (Sakamoto et al. 1990) and CeGa2 (Umehara et al. 1991d, 1992c), respectively. The dHvA


kz

71

(b)

Fig. 63. (a) The hexagonal A1B 2 type crystal structure of the RGa 2 compounds. Spheres with and without pattern show the Ga atoms and the R atoms, respectively; (b) Brillouin zone of the body-centered tetragonal crystal lattice for c/a > v'~.

Table 16 Characteristic properties of the RGa 2 compounds

Compotmd T N (K) T c (K) n 7 (mJ/K 2 mo O Fermi surface

LaGa2 Pauli n h 4.1-5.6 para

CeGa2 8.4 11.4 nh SmGa~ 20 n h

8.9-9.1

two kinds of ellipsolidal hole Fermi surfaces (bands 3 and 4) and a multiply connected hole Fermi stu-face (band 5). similar to LaGa2, but spin-split similar to LaGa2, but affected by MBZ

branches in CeGa2 are similar to those o f LaGa2, although all branches in CeGa2 are split into the up and down spin states of the electrons due to the ferromagnetic exchange interaction. The exchange energy is estimated to be about l 7 meV from the spin factor.

Branches a and/3 correspond to the ellipsoidal Fermi surfaces of revolution along the c-axis (FA direction). We note that the branch denoted by /3 actually consists o f two separated branches in LaGa2. Its topology has dumb bell characteristics. It is not easy to clarify the topologies o f branches 7, e and 6 from the present data.

The magnetoresistance was measured for CeGa2 (Umehara et al. 1991d, 1992c). The magnetoresistance increases in a wide angle range, with a H 13-1'8 dependence. When field is applied along the [1010] direction, the magnetoresistance saturates. It was concluded that CeGa2 possesses open orbits in a wide range o f angles, namely, in the basal plane and arotmd the [0001 ] direction.

Owing to the simple hexagonal crystal structure with one molecule per primitive cell belonging to the symmorphie space group (P6/mmm), LaGa2 is a compound like LaSb for which the energy band structure can be calculated most easily i f the one-electron potential

72 Y. O N U K I a n d A. H A S E G A W A

108_ ' ' I ' ' I ' ' ' ' ! ' ' t / ' I ' '

- ~ L a G a 2 " " ' - - J ', 6

I

o "~

5 . . . . . - i " -

F A F M F K F A

1061 , , I ~ , I , ~ I ~ , I ~ , I , , I , , I 90 60 30 0 0 30 60 9 0

[0001] [10i0] [1150] [ 0 0 0 1 ]


] 0 8 ~ ' 1 ' ' 1 ' ' ' ' ' ' 1 ~ ' 1 ' '

d C e G a 2 6

107

F A F M F ' K F A

90 60 30 0 0 30 6 0 90

[0001] [10i0] [1150] [0001] Field Angle (Degrees)

Fig. 64. A n g u l a r dependence o f the dHvA frequency in LaGa 2 (Sakamoto et al. 1990). The solid lines connecting the data are guidelines. The dashed lines show the results o f band calculations for band 5

( H a r i m a and Yanase 1991b). The Greek letters designate the various orbits.

Fig. 65. Angular dependence o f the dHvA frequency in CeGa 2 (Umehara et al. 1991d). The solid lines connecting the data are guidelines. The Greek letters designate the various orbits.

is constructed appropriately. Nevertheless, its Fermi surface proved to possess a sheet with a fairly complicated topology. Harima and Yanase (1991b) performed LAPW band calculations for LaGa2. An ellipsoidal hole Fermi surfaces exist in bands 3 and 4, centered at the A point, which correspond to branches a and fi, respectively. A mukiply connected hole Fermi surface, which favors the open orbits, exists in band 5, as shown in fig. 66. The broken lines in fig. 64 are the results of band calculations for band 5. The band 5 Fermi surface consists of twelve multiply connected arms which stretch from A to K, possessing a hollow in the center F. Detected branches 7, 6 and e are ascribed to this Fermi surface.

The cyclotron mass of LaGa2 is in the range of 0.15m0 to 1.83m0, which is similar to that of CeGa2, 0.32m0 to 1.44m0. The masses of branches a and fi in CeGa2 are twice as large as those of LaGa2. On the other hand, the masses of the other branches in CeGa2 are almost the same as those in LaGa2. The mass enhancement is anisotropic, depending on the band, as shown in table 17. Here we note the 7 value of CeGa2. The 7 value determined at temperatures lower than the magnetic ordering temperature is about 9 mJ/K 2 mol (Umehara et al. 1992c, Dijkman 1982), while Tang and Gschneidner (1989) estimated it as 32.6 mJ/K 2 mol from the paramagnetic state. Gsehneidner (1993) suggests


[0001]

H

[ ioio] [1120]

Fig. 66. Multiply connected hole Fermi surface in band 5 of LaG% (Harima and Yanase 1991b). The Greek letters designate the various orbits.

10 8

0

o

i07

, i t i i , i I ' i ! i i , 4 1 , , i

s.~a~2 ~ ° 1

E T

FA i061, , ,

90 G0 [oooi ]

FM FK FA

30 0 0 30 60 90

[10i0] [1120] [0001] Field AngLe (Degrees)

Fig. 67. Angular dependence of the dHvA frequency in SmGa2 (Sakamoto et al. 1990, 1992). The solid lines connecting the data are guidelines. The Greek letters designate the various orbits.

Table 17 dHvA frequencies F and their cyclotron masses m~ a in the RGa 2 compounds for the field along [0001] except

in branches 0, r/, V for the field along [100] (Sakarnoto et al. 1990, 1992, Umehara et al. 1991d)

RG~ 0 q 6 y e 3 a * F m~ F * F * F * F * F * F m e m e m c m e m e m e

LaG% 71.7 1.83 37.6 1.30 18.3 0.94 4.98 0.27 2.21 0.15

4.50 0.25

CeGa 2 66.0 1.42 33.0 1.41 18.0 1.33 4.00 0.41 1.88 0.32

64.0 16.0 1.28 3.75 0.44

SmG~ 2 128.3 2.5 77.15 1.6 28.85 1.2 4.96 0.25 2.28 0.11

a F values in 106 Oe, m~ expressed in m 0.

tha t b o t h v a l u e s a r e co r r ec t . T h a t is, o n o r d e r i n g , t h e d e n s i t y o f s ta tes at t he F e r m i e n e r g y

is r e d u c e d b y a f a c t o r o f a b o u t 3.5 in CeGa2 .

S m G a 2 is an a n t i f e r r o m a g n e t . T h e e - a x i s c o r r e s p o n d s to an e a s y ax i s a n d m e t a m a g n e t i c

t r a n s i t i o n s o c c u r at 13, 32 .5 , 35, 36.5 k O e a n d m o s t l ike ly at h i g h e r f ie lds . F i g u r e 67


shows the angular dependence of the dHvA frequency (Sakamoto et al. 1990, 1992) . Branches a and/3 are split into the up and down spin states of the electrons. The splitting energies are 10meV at fields of 17kOe to 27kOe and 26meV at fields of 45kOe to 60kOe. The cyclotron mass in SmGa2 is in the range of 0.1m0 to 2.5m0, the same magnitude as in CeGa2. The mass enhancements of CeGa2 and SmGa2 are due to the usual electron-magnon interaction.

4.4. Fermi surfaces in the tetragonal Brillouin zone

4.4.1. RRu2Si2 and RRu2Ge2 RRu2(Si, Ge)2 compounds possess the tetragonal ThCrzSi2-type crystal structure with one molecule per primitive cell. Figure 68 shows the crystal structure and its tetragonal Brillouin zone. LaRuzSi2 or LaRu2Ge2 is a non-4f reference compound. CeRu2Si2 is thought to be a non-magnetic Kondo-lattice compound. Reflecting a rather low value of Kondo temperature of about 20 K, the electronic specific heat coefficient y is large: 350mJ/K 2 mol (Besnus et al. 1985). CeRuzGe2 is not a Kondo lattice compound but an f-localized ferromagnetic compound with a Curie temperature of 8 K, similar to CeGa2, as shown in tables 1 and 18.

Figures 69 and 70 show the angular dependence of the dHvA frequencies in LaRu2Si2 (Onuki et al. 1992) and LaRu2Ge2 (Fukuhara et al. 1993). The detected branches are simple in their angular dependences. Branch a is the main one. This Fermi surface is assumed to be an ellipsoid of revolution shrunk along the [001] direction. The volume of the Fermi surface becomes 1.3 x 1024 cm -3 for LaRu2Si2, which is about half of the volume of the Brillouin zone. Here, the volume of the Brillouin zone is (2Jr/a)2(4Jr/c) of 2.912x1024cm-3 if we use the lattice parameters a=4 .215A and c=9 .930A for

ElOOlli [001] kz

l r ~ . . . . . . . . . . . . . . . . . . . ' I

(a) kx (b)

J 010 ] , ~ 2 ~

Fig. 68. (a) Body-centered tetragonal ThCr2Si z type crystal structure. Spheres without pattern, with simple cross pattern and with complex pattern show the Th, Cr and Si atoms, respectively; (b) Brillouin zone of the body-centered tetragonal crystal lattice for c/a > v/2. The rectangular parallelepiped which is equivalent to the Brillouin zone is indicated by the dashed lines.


Table 18 Characteristic properties of the RRu2Si 2 and RRuzGe 2 compounds

75

Compound T¢ (K) n 7 ( m J/K2 tool) Fermi surface

LaRuzSi 2 Pauli para n~, 6.5

CeRuzSi z valence fluctuation n¢ = n h 350

LaRuzGe 2 Pauli para nh

CeRuzGe 2 8 n h 20

large hole Fermi surface (band 14)

large hole Fermi surface (band 14); and a multiply connected electron Fermi surface (band 15) with open orbits

similar to LaRuzSi 2

similar to LaRu2Si 2

' ' I ' ' I ' ' -

Ru2Si2

I 10 8

o

o)

~ I ~ , I ,

90 [ 001 ]

O~

' e e o e o o o o ~

o o s m ~ e o e o

I r ]

60 30 0 30 [ 1 0 0 ] [110]


Fig. 69. Angular dependence of the dHvA frequency in LaRuzSi 2 (Onuki et al. 1992). The solid lines are the results of band calculations (Yamagami and Hasegawa 1992). The Greek letters designate the various orbits.

1o 8

g

107

' I i ' r

LaRu2Ge~

o o

o o I #i o ~ o _ j ~ _ ~ o ~ ~

90 60 30 0 30

[001] [100l [ n 0 ] Field Angle (Degrees)

Fig. 70. Angular dependence of the dHvA frequency in LaRu2Ge 2 (Fukuhara et al. 1993). The solid lines connecting the data are guidelines. The Greek letters designate the various orbits.

LaRu2Si2 in calculation. The other branches fib /32 and [33 also originate from small ellipsoids, similar to rugby balls in topology.

The cyclotron masses for these branches are in the range of 0.5mo-2.4mo, as shown in table 19.

It was revealed by a relativistic APW calculation (Yamagami and Hasegawa 1992) that the main Fermi surface of LaRu2Si2 is a large closed hole sheet which is centered at the Z point in band 14. It is essentially a sphere but highly distorted. Although its volume is


Table 19 Cyclotron masses for the field along [100]

Compound a fll f12 f13 ~4 m~ m b m~ m b m~ m b m~ m b m~ m b

LaRu2Si z 1.44 1.20 0.84 0.85 0.53 0.58 0.52 2.37 b 2.59 b 0.67 b 0.40 b 0.55 b 0.30 b 0.51 b

0.47 LaRu2Ge 2 1.95 0.76 0.43 0.43 0.63 CeRuzGe 2 5.6 1.5 0.87 0.85 2.3

0.97 b 1.5 b 0.62 b 1.9 b

5.7 1.5 0.81 0.84 1.5 0.97 b 1.5 b 0.62 b 1.1 b

m~

CeRu2Si 2 ~ 120 2.3 1.8 19.7 20 12.3 2.6 b 1.0 b

References: 0nuki (1993), Aoki et al. (1992), Onuki et al. (1992), Fukuhara et al. (1993), King and Lonzarich (1991), Lonzarich (1988).

b Values for the field along [001]. c Field along [100] for ~;, along [110] otherwise.

nearly equal to ha l f o f the Bril louin zone, it has an extraordinarily large cross-sectional area in the (001) plane which exceeds the size o f the Bril louin zone itself. The Fermi surface is a flat el l ipsoid with steep concave and convex curvatures as shown in fig. 71. The solid lines in fig. 69 are the results of band calculations. Additionally, three rugby balls are present in bands 11, 12 and 13 centered at Z, which correspond to/33,/32 and/31, respectively. Branch/34 s e e m s to be an orbit circulating along the tube of the doughnut in a band 15 electron Fermi surface. The calculated )'b value is 6.95 mJ/K 2 mol for LaRu2Si2, which is nearly the same as the experimental y value of 6.5 mJ/K 2 mol. Therefore the band masses are the same as those o f the experimental cyclotron masses, as shown in

table 19. The field dependence o f magnetoresistance for LaRu2Si2 shows a saturated behavior

for the whole angle region, indicating that LaRu2Si2 (LaRu2Ge2) is an uncompensated metal and possesses no open orbits ((3nuki et al. 1992). This is simply expected because the primitive cell contains one molecule of LaRu2Si2 and the La ion is trivalent, La 3÷, which is consistent with the results o f band calculations.

The dHvA data for the ferromagnetic compound CeRu2Ge2 in fig. 72 (King and Lonzarich 1991) are similar to those of LaRu2Ge2 or LaRu2Si2, although every branch is split into the up and down spin states. The cyclotron masses for branch a is 5 .6 - 5.7m0 which is roughly three to four times larger than 1.95m0 of LaRu2Ge2 or 1.44m0 of LaRu2Si2, as shown in table 19. We note that branch a is not detected around [001] in LaRu2Ge2 and CeRu2Ge2. This is mainly due to a resolution problem because the

FERMI SURFACES OF INTERMETALL1C COMPOUNDS 77

LaRu2Si 2

band 11 band 12 band 13 ~ ~ ~h01e /~3 /~ ~, centered at Z

band 14

hole centered at Z band 15

electron centered at F

Fig. 71. Fermi surfaces of LaRu2Si 2 (Yamagami and Hasegawa 1992). The Greek letters designate the various orbits.

dHvA signal for field along [001] is strongly reduced by both the curvature factor and the cyclotron mass compared to the signal around [100] in LaRu2Si2.

Figure 73 shows the angular dependence of the dHvA frequency in CeRu2Si2 (0nuki 1993, Aoki et al. 1992, Onuki et al. 1992, Lonzarich 1988). Two kinds of rugby balls denoted by 7 and/3 are present, which are similar to branches/31 and/32 of LaRu2Si2, respectively. On the other hand, branches to, e and a are not present in LaRu2Si2. The cyclotron masses are of the order of the free-electron mass for branches )' and/3, while the other branches possess extremely large values, 120m0 for branch tp, 20too for branch to, 19.7m0 for branch e and 12.3m0 for branch a, as shown in table 19.

Under the assumption that the 4f electrons are itinerant, Zwicknagl et al. (1990) carried out band structure calculations for CeRuzSi2 by a relativistic LMTO method both with the LDA and the RB theory, and showed that the Fermi surface consists of four closed hole sheets centered at the Z point and one complicated multiply-connected electron sheet. Under the same assumption, Yamagami and Hasegawa (1993) also calculated an energy band structure for CeRuzSi2 by a relativistic APW method with LDA. In fig. 73, the calculated results for the dHvA frequencies by Yamagami and Hasegawa (1993) are shown by solid lines which are compared to the experimental results. The theoretical


io 8

c )

107

90

[ 001 ]

CeRuiGe~

i

60 30 0 30

[100] [110] Field Angle (Degrees)

108

• ~ 107

I [ '

90 60 30 0 30 [001] [100] [110]


Fig. 72. Angular dependence of the dHvA frequency in CeRuzGe 2 (King and Lonzarich 1991). The solid lines connecting the data are guidelines. The Greek letters designate the various orbits.

Fig. 73. Angular dependence of the dHvA frequency in CeRu2Si 2 (Onuki 1993, Aoki et al. 1992, Onuki et al. 1992, Lonzarieh 1988). The solid lines are the results of band calculations (Yamagami and Hasegawa 1993). The letters designate the various orbits.

Fermi surface sheets which were used to calculate the dHvA frequencies in fig. 73 are shown in fig. 74. The Fermi surfaces proposed by Zwicknagl et al. (1990) and Yamagami and Hasegawa (1993) actually look similar to each other. In calculations of the former, adjustable parameters were used to fit the theoretical dHvA frequencies to the observed ones, while no such phenomenological procedure was employed in calculations of the latter. Therefore, we discuss the origins of dHvA branches on the basis of the Fermi surfaces calculated by Yamagami and Hasegawa.

The hole Fermi surfaces in CeRu2Si2, centered at Z, are similar to those of LaRu2Si2. The large hole Fermi surface denoted by a in figs. 73 and 74 corresponds to branch t/t, although it is observed in a limited angle region. The cyclotron mass of ~ is extremely large. The band mass is theoretically calculated as 1.93m0 for field along the [100] direction and as 4.12m0 for [001] (Yamagami and Hasegawa 1993). The experimental mass of 120m0 is about 60 times larger than the band mass. The cyclotron mass is thus estimated as 260m0 for [001]. This extraordinarily large mass is consistent with the large 7 value and also the prediction of the renormalized band structure calculations (Zwicknagl et al. 1990), which gives a mass exceeding 200m0 for [001]. Branches/3, y, to, e and a most likely correspond to hole bands 12 (denoted by c) and 13 (b), band 15 electron orbits j , h and k, respectively.

FERMI SURFACES OF INTERMETALLIC COMPOLrNDS

CeRu~Si~ (b) electron (band15)

(a) hole (centered at Z) bandll bandl2 bandlS

bandl4

centered at Z

79

centered

at X

Fig. 74. Fermi surfaces of CeRu2Si 2 (Yamagami and Hasegawa 1992). The letters designate the various orbits.

The magnetoresistance of CeRu2Si2 is also useful to determine the nature of the 4f electrons as in CeSn3. In figs. 75 and 76a we show the angular dependence of the magnetoresistanee zlp/p = [p(H)- p(0)]/19(0) under constant fields and in fig. 76b the field dependence of the magnetoresistanee for currents along [110] and [001], respectively. The magnetoresistance shows a sharp peak at the critical field Hc of 75 kOe for field along the [001] (c-axis) direction. This corresponds to the metamagnetic transition.

We will now discuss the magnetoresistances at lower fields than the critical field. In the configuration of J [I [110] and/-/[1 [001], the magnetoresistance Ap/p follows a Hl'7-dependence below 65kOe, while in the configuration of J II [110], H II [1t0] it saturates with increasing fields, reflecting a Shubnikov-de Haas oscillation with the dHvA frequency of 2.8x105Oe. The angular dependence of magnetoresistance under field of 65kOe shows a maximum and a minimum at H II [001] and H II [110], respectively. Moreover, when the direction of field is rotated from the [100] direction to [110] direction for current along the [001] direction, the magnetoresistance increases over the whole field direction, typically showing a Hl8-dependence in the J [I [001] and / /I t [110] configuration as shown in fig. 76b. These results indicate that CeRu2Si2 in the ground state is a compensated metal with an equal carrier number of electrons and holes and that open orbits exist along the J x H direction, namely [001 ] (c-axis) direction. The open orbits originate from the multiply connected electron Fermi surface mentioned above.

80

q ~

\ Q

<1

' I (a)

CeRu2Si2

J//[ilO] 0.5K

Y. ONUKI and A. HASEGAWA

q~ \ Q

. , o o t -

i I J , , I , , I , , ,

0 30 60 90 [001] [110]


J

A /150kOe ~ l

(b) ]

CeRu28i~ /

J / / I l l 0 ] H//[IIO]

l i l l ] l l l i l i 1 1 1 50 100 150

Magnetic Fie ld (kOe)

Fig. 75. (a) Angular and (b) field dependences of the magnetoresistance for the current along [110] in CeRuzSi2 (Onuki et al. 1992).

\ Q

<~

1.5

0.5

{ a ) l ~ J i i J i i i i J

CeRu2Si2

J//[001] H=150kOe 0.5K

_ i i i i i i i i ~ i i

0 45 [loo] [11o]


~ 0

1 , , , , i , , , , i , , , ,

(b)

CeRu2Si2 / 1 J//[OOl] H/ / [ l l0 ] o, 5K

/

0 50 100 150 Magnetic Field (kOe)

Fig. 76. (a) Angular and (b) field dependences of the magnetoresistance for the current along [001] in CeRu2Si z (Onuki et al. 1992).


We note that the magnetoresistance under field of 65 kOe approximately follows the angular dependence of A p / p = a cos20 + b cos20, where 0 means the field angle between the field and open orbit directions, and a and b are constant but are functions of H. This angular dependence is expected for a compensated metal with open orbits. If the metamagnetic behavior is not present in this compound, we expect a similar angular dependence even under field of 150 kOe. Here, a sharp peak reflected in the angular dependence of the magnetoresistance at 150 kOe at 0 = 60 °, as shown in fig. 75a, corresponds to the metamagnetic transition. It follows a 75kOe/cos0-dependence. Therefore the transition occurs whenever the component of field along the [001 ] direction equals 75 kOe and thus it becomes 150 kOe at 0 = 60 °.

As mentioned above, LaRu2Si2 is an uncompensated metal, while CeRu2Si2 is expected to be a compensated metal from the results of magnetoresistance. As the primitive cell contains one molecule of LaRu2Si2 or CeRu2Si2, we can conclude that the Ce ion becomes tetravalent, namely implying an itinerant 4f-electron character. Therefore, the situation is similar to the relationship between LaSn3 and CeSn3.

According to the inelastic neutron-scattering experiments on CeRu2 Si2, the ground state originates from two low-temperature contributions: on-site interactions (Kondo) and inter- site interactions (antiferromagnetic correlations). The inter-site contribution is drastically reduced or suppressed at H >> Hc (Rossat-Mignod et al. 1988). Correspondingly the low- temperature specific heat coefficient of 350mJ/K2mol is reduced to 80mJ/K2mol at 200kOe (van der Meulen et al. 1991). There remains a possibility that the main Fermi surfaces with a dominant 4f component disappear in topology when field crosses the critical field. This is open to future studies.

4.4.2. CeCu2Si2

dHvA oscillations have been observed in the typical Kondo lattice compound CeCu2Si2 (Hunt et al. 1990, Springford 1991), having the same crystal structure as CeRu2Si2. Superconductivity and very weak antiferromagnetic order coexist in this material below 0.7 K. The characteristic properties of CeCu2Si2 are shown in table 1.

Figure 77 shows the angular dependence of the dHvA frequency. Although only part of the Fermi surfaces is observed, the detected carriers possess relatively large masses of 5m0 for field along the a-axis. Judging from the large value of the electronic specific heat coefficient, 1000 mJ/K 2 mol, carriers with much larger masses should exist in this material.

Band calculations were made for CeCu2Si2 by Sticht et al. (1986), using a Kondo-lattice ansatz for the cerium 4f state and LDA potential parameters. Harima and Yanase (1991 a, 1992a) also calculated the energy band structure for LaCu2Si2 and CeCu2Si2. As regards the observed part of Fermi surface, the calculated Fermi surface of LaCu2Si2 seems to fit the experimental results of CeCu2Si2 better than the itinerant f-electron Fermi surface for CeCu2Si2. Figure 78 shows the multiply connected Fermi surface in band 19 for LaRu2Si2 which corresponds to the observed dHvA branches. The 4f electrons in CeCu2Si2 are thus most likely localized and do not affect the Fermi surface significantly. Precise experiments are necessary to clarify the real situation.


o

o

o

I f T-- I

o/ CeCu2Si2 ]

0 30 60 90 c-axis a


LaCu2Si 2

Fig. 78. Multiply connected Fermi surfaces in band 19 of LaCu2Si2 (Harima and Yanase 1991a, 1992a).

Fig. 77. Angular dependence of the dHvA frequency of CeCuzSi z (Hunt et al. 1990). The solid lines connecting the data are guidelines.

4.5. Fermi surface in the orthorhombic Brillouin zone

4.5.1. RNi

RNi crystallizes in an orthorhombic structure. Figure 79 shows the CrB crystal structure and its Brillouin zone. The primitive cell contains two molecules of RNi. CeNi can be characterized as a valence-fluctuating compound, similar to CeSn3. Its Kondo temperature

kz

( a ) I D~ "' , r ' > j -] i ,1,. ! I I

""-, i ° _LJ "x I

Fig. 79. (a) c-base centered orthorhombic CrB type-crystal structure. Spheres with and without pattern show the B atoms and the Cr atoms, respectively. (b) Brillouin zone of the e-base centered orthorhombic crystal lattice for a < b. The rectangular parallelepiped which is equivalent to the Brillouin zone is shown by the dashed lines.


Table 20 Characteristic properties of the RNi compounds

83

Compound T~ (K) n g Fermi surface (mJ/K 2 tool)

LaNi CeNi PrNi

Pauli para n¢ = n h 5.0 valence fluctuation n¢ = nh 65-85

20 n~ = nh

multiply connected Fermi surfaces with open orbits multiply connected Fermi surfaces with open orbits similar to LaNi but should be spin-split

\ q~ <1

10

(a) LaNi J//e-axis 150k0e / / ~ , ~ o . s K "

, \ <

~ . ~ ° ~ - ° H//b-axi s

0 I I , , I , I , r

-30 0 30 60 90


\ q

120

4t

, , l l l l l t l l * l l

(b) / LaNi / H//b-axis J f f e - a x i s / 0.5K

° ~

~ ° l t l ] l ; l l ] l l l l

50 100 150

Magnetic Field (k0e)

Fig. 80. Angular and field dependencies of the magnetoresistance in LaNi (Onuki et aI. 1989b). The solid lines connecting the data are guidelines.

\

~2

, ' , ' , i . , i , , , , '

(a) CeNi o j ~ ' ~ ' ~ o ~ . J / /e-axis ~ . ~ - ' ~ 150kOe 0.5K g/

\ / \ Q2

H/ /a-axis b

0 ' ' ' ' ' ' ' 0 -30 0 30 60 90 120


I l l l l t l - - l t l t l l l

(b) °2 CeNi Hffb-axi s / JHe-axis / 0.5K /

~ ' l l i l t l i i l r l l _ L . j

50 100 150 Magnetic Field (k0e)

Fig. 81. Angular and field dependencies of the magnetoresistance in CeNi (Onuki et al. 1989b). The solid lines connecting the data are guidelines.

is about 150 K (Gignoux et al. 1983). PrNi is an f-localized anisotropic fer romagnet with an easy axis a long the c-axis, which orders at Te = 20 K. The characteristic properties o f RNi are summar ized in table 20.

Figures 80 and 8t show the typical angular and field dependences o f the t ransverse magnetores is tanee in LaNi and CeNi, respectively (Maezawa et al. 1989, Onuki et al.


108

o 0

107

IL'I '' ]

10 8 , , I , , I , r

[i00] [010] a-axis b


[001] O

10 8

0

0~

10 ~ <

CeNi

mm~

o m m m e) m

[zoo] a-axis

J

O ®

, q [ r , I r E _

[OLO] [ooz] b e


Fig. 82. Angular dependence of the dHvA frequency in LaNi (Maezawa et al. 1989). The solid lines represent the results of band calculations (Yamagami and Hasegawa 1991). The Greek letters designate the various orbits.

Fig. 83. Angular dependence of the dHvA frequency in CeNi (Onuki et al. 1989b). The solid lines represent the results of band calculations (Yamagami and Hasegawa 1991). The letters designate the various orbits.

1989b). The magnetoresistance of CeNi is found to be almost the same as in LaNi. The magnetoresistance of LaNi at 75kOe is similar to that in CeNi at 150kOe, regarding its shape as well as its magnitude. In other planes the behavior between LaNi and CeNi is also similar. The magnetoresistance increases with increasing field over a wide angle region, except for several particular configurations of field and current. These behaviors suggest that LaNi and CeNi are compensated metals with similar Fermi surfaces. The open orbits exist along the b- and c-axes.

Figures 82 and 83 show the angular dependence of dHvA frequency in LaNi and CeNi, respectively (Maezawa et al. 1989, Onuki et al. 1989b). The two branches a (4.10 x 107 Oe) and /3 (1.40 x107 Oe) for field along the b-axis in LaNi may correspond to those a (3.60x 107 Oe) and c (1.25x 107 Oe) in CeNi, although the angular region for these branches are different in both compounds. However, two other branches, indicated as f and h, are observed along the b-axis in CeNi, which are not present in LaNi. From these experimental results, Onuki and coworkers concluded that the Fermi surface of CeNi is similar to that of LaNi.

The cyclotron masses of branches a and c in CeNi are 10.3mo and 8.91m0, respectively. The masses of branches a and /3 in LaNi are 1.73m0 and 0.93m0, respectively. The

e


e

a LaNi I~

85

CeNi

T

J z

(b)

Fig. 84. (a) Hole Fermi surfaces in band 19; (b) electron Fermi surfaces in band 20 of LaNi, respectively (Yamagami and Hasegawa 1991). The Greek letters designate the various orbits.

(a)

b

(a)

T

,v (b)

I

Fig. 85. (a) Hole Fermi surfaces in band 20; (b) electron Fermi surfaces in band 21 of CeNi, respectively (Yamagami and Hasegawa 1991). The letters a, c, h, . . . , designate the various orbits.

cyclotron masses of CeNi are about ten times larger than those of LaNi. This is roughly consistent with the electronic specific heat coefficient. It is 65 or 85 mJ/K 2 tool in CeNi, while it is only 5mJ/K 2 mol in LaNi (Gignoux et al. 1983, Isikawa et al. 1987).

Yamagami and Hasegawa (1991) calculated the energy band structures of LaNi and CeNi by the relativistic APW method. The solid curves in figs. 82 and 83 are theoretical results. The experimentally observed branches are almost in agreement with the calculated ones. Here the f electron in CeNi is treated as an itinerant electron. The origins of the branches for LaNi and CeNi are shown in figs. 84 and 85, respectively. The Fermi surfaces in bands 19 and 20 in LaNi refer to hole and electron, respectively. In CeNi bands 20 and 21 refer to hole and electron, respectively. Both compounds are compensated metals with an equal carrier number of electrons and holes and possess multiply connected Fermi surfaces which favor the experimentally observed open orbits along the b- and c-axes for both compounds. The fact that LaNi and CeNi have almost the same dHvA frequency


Table 21 dHvA frequencies F, cyclotron masses rn~ and band masses m b in the RNi compounds for the field along the

[010] direction (b-axis) a

Compound a #

F m~ m b F m: m b

LaNi 4.10 1.73 1.04 1.40 0.93 0.50

CeNi 3.60 (a) 10.3 (a) 2.62 (a) 1.25 (c) 8.91 (c) 3.68 (c)

0.658 (f) 3.06 (0 0.91 (f)

0.215 (h) 2.58 (tl) 0.98 (11)

PrNi 4.30 2.2 1.30 1.06

a F values in 107 Oe, rn~ expressed in m 0. References: 0nuki et al. (1989b), Maezawa et al. (1989, 1992), Yamagami and Hasegawa (1991).

for field along the b-axis is accidental because the topologies of the Fermi surfaces are different between LaNi and CeNi. Since the main dHvA branches are explained by the present band calculations, the 4f electron in CeNi is considered to form an itinerant 4f band in the same way as in CeSn3.

Every carrier possesses larger masses than the corresponding band masses, as shown in table 21. The ratio of the cyclotron mass m~* to the band mass mb is in the range of 3-4, which is roughly consistent with the ratio of Y/Yb, 4.6-6.0.

dHvA experiments on the anisotropic ferromagnet PrNi (Tc = 20 K) show that the Fermi surface seems to be roughly similar to that of LaNi (Maezawa et al. 1992), as shown in fig. 86. The results ofmagnetoresistance are also almost similar to those of LaNi, although

1 0 8

1 0 7

PrNi

1 0 6 , , , , , , , , ~ , , ~ , , ,

b c

[i00] [010] [001]


Fig. 86. Angular dependence of the dHvA frequency in PrNi (Maezawa et al. 1992). The solid lines connecting the data are guidelines. The Greek letters designate the various orbits.


open orbits exist only along the b-axis in PrNi. The cyclotron mass is also comparable to that of LaNi, as shown in table 21.

The dHvA study in LaNi and CeNi provides an important lesson. When the number of Ce atoms is even per primitive cell, the band structures of the La and Ce compounds can be similar even in the itinerant 4f band model. Also the transverse magnetoresistance has similar characteristics. Careful band calculations and precise experimental studies are essential.

4.5.2. RCu2 The crystal structure of RCu2 is orthorhombic (Larson and Cromer 1961) as shown in fig. 87. The primitive cell contains two molecules of RCu2. This structure can be thought of as a distorted hexagonal A1B2 structure because the orthorhombic b-axis approximately corresponds to the hexagonal c-axis and the relation c ~ v ~ a holds. In fact, only LaCu2 possesses the hexagonal A1B2 structure. Therefore, instead of LaCu2, YCu2 becomes a non-f reference material for RCu2. CeCu2 can be classified as an antiferromagnetic Kondo-lattice substance with the Nrel temperature TN = 3.4 K (Onuki et al. 1990a, 1985a, Gratz et al. 1985). Below TN, the magnetization of CeCu2 shows a metamagnetic behavior around 17 kOe when magnetic field is applied along the a-axis. The magnetic susceptibility and magnetization show a large anisotropy at low temperatures, reflecting the orthorhombic structure. SmCu2 is an f-localized antiferromagnet with Nrel temperature of 21.7 K, as shown in table 22.

Figure 88 shows the angular dependence of the dHvA frequency in YCu2 (Settai et al. 1990, 1992, Onuki et al. 1989c). About twenty branches are observed in YCu2. Many cylindrical arms are detected, showing a nearly 1/cos0 behavior of the angular dependence. Here 0 is the angle between the direction of the cylinder axis and the field direction. We note that the cylinder axes of branches a and 6 do not coincide with the symmetry axes. They deviate by 15 ° and 4 ° from the b-axis in the plane perpendicular to the a-axis (a-plane). Branches/3 and g also deviate by 40 ° in the b-plane and by I0 ° in the a-plane from the c-axis, respectively. Theoretically, three closed Fermi surfaces are

C

1 b

~ a Fig. 87. Orthorhombic crystal structure of RCu 2. Large and small spheres show the R atoms and the Cu atoms, respectively.


Table 22 Characteristic properties of the RCu2 compounds

Compound T N (K) n 7 (mJ/K ~ mol) Fermi surface

YCu 2 Pauli para ne =nh 6.7 multiply connected Fermi surfaces

CeCu 2 3.5 ne = n h 82

Kondo lattice

SmCuz 21.7 nc = nh

present in bands 30, 31 and 33. They correspond to branches ~, 0 and ~/, respectively, which are nearly ellipsoidal Fermi surfaces elongated along the b-axis.

The conduction carriers due to branches a and 6 are thought to play an important role in the band Jahn-Teller effect of the C44 and C66 modes from the results of the acoustic dHvA measurements (Settai et al. 1992).

The magnetoresistance was measured for YCu2 (Onuki et al. 1989c). The magnetoresistance increases with increasing field over a wide angle range, following H 1'1-1-4. This behavior indicates that YCu2 is a compensated metal. However, the magnetoresistance saturates only when field is directed along the a-axis with current along the b- and c- axes. Therefore, open orbits exist along the b- and c-axes. These results suggest that the Fermi surface is multiply connected.

IO s YCu~

o i.o o ~ 1 0 7 . , o

b c a b


Fig. 88. Angular dependence of the dHvA frequency shown by squares (0nuki et al. 1989c) and by circles, diamonds and triangles (Settai et al. 1990, 1992) in YCu 2. The solid lines connecting the data are guidelines. The Greek letters designate the various orbits.


YCu2

1st . . . .

X

b,

X ~ n + ~ hole

X

(a)

X SIst hole c X

,)

b

X

32nd electron

X

(c)

X

X 33rd electron

<d)

a

Fig. 89. Hole and electron Fermi surfaces in YCu/: (a) hole in band 30; (b) hole in band 31; (c) electron in band 32; (d) electron in band 33. The solid lines show the first Brillouin zone (Harima and Yanase 1992b). The thick solid lines correspond to the observed orbits.

The LAPW band calculations were done by Harima and coworkers (Harima and Yanase 1992b, Harima et al. 1990a). The origin of the dHvA branches are shown in fig. 89. YCu2 is a compensated metal, Band 30 consists of small hole ellipsoids. Band 31 consists of ellipsoidal hole Fermi surfaces centered at the W point and a multiply connected Fermi surface, stretching in the a-plane. The latter Fermi surface favors the presence of open orbits along the b- and c-axes. Band 32 is also a multiply connected electron Fermi surface, which favors open orbits along the b-axis. Finally, band 33 consists of small electron-ellipsoids centered at the F point. These results are consistent with the results of magnetoresistance measurements (Onuki et al. 1989c). The fact that the minima of branches are off-symmetrical is due to the non-cubic crystal structure.

On the other hand, as shown in fig. 90, about ten kinds of dHvA branches are observed around the a-axis in CeCu2, whereas only one branch is detected around the c-axis (Settai et al. 1990, 1992, Satoh et al. 1990). As the dHvA experiments were done above 60 kOe, this compound is in the paramagnetic (or field-induced ferromagnetic) state for the field along the a-axis. On the other hand, it is antiferromagnetic in the a-plane. In general, the

90

10 8

O

o

107

Y. ()NUKI and A. HASEGAWA

, , , , i i , , , , , i r , , , - i , , , , , j , ,

CeCu2 ° I

106 . . . . . . . . . . . . . . . o, L, . . . . . . , Fig. 90. Angular dependence of the dHvA frequency in CeC½ (Satoh et al. 1990). The solid lines H / / b - a x i s e a connecting the data are guidelines. The Greek letters

F i e l d Angle (Degrees) designate the various orbits.

detectable number of dHvA branches is small in the antiferromagnetic state due to the magnetic Brillouin zone boundaries, as seen in CeA12 and Celn3.

When we compare the Fermi surfaces of CeCu2 to those of the reference material YCu2, it is difficult to say whether they are similar or not because too many branches are thought not to be observed in CeCu2. The effective cyclotron masses in CeCu2 range from 0.5m0 to 5.3m0, and are larger than those in YCu2, 0.1-0.7m0. This mass enhancement is roughly consistent with that of the low-temperature specific heat coefficient ratio. Namely, the y value of CeCu2 is 82 mJ/K 2 mol but is reduced to 50 mJ/K 2 mol at 80 kOe (Bredl 1987), while it is 6.7mJ/K 2 mol in YCu2 (Luong et al. 1985).

Magnetoresistance measurements were done for SmCu2, indicating that it is a compensated metal with open orbits, at least, along the b-axis (Maezawa et al. 1986). Shubnikov-de Haas oscillations were observed in the magnetoresistance. The detected dHvA frequencies are in the range of (0.68-1.25)x 106 Oe.

4.5.3. RCu6 The f electrons in RCu6 (R = Ce, Pr, Nd and Sm) show a variety of magnetic behaviors. C e C u 6 is a typical non-magnetic Kondo-lattice compound with a Kondo temperature of about 4 K (Onuki and Komatsubara 1987a). PrCu6 is a nuclear cooling material with a singlet ground state (Takayanagi et al. 1988). NdCu6 (TN =6.1 K) is a metamagnetic compound with four discontinuous steps in the magnetization curve (Takayanagi et al. 1991, Onuki et al. 1986), and SmCu6 (TN = 9.6 K) shows a Van Vleck susceptibility due to


Table 23 Characteristic properties of the RCu6 compounds

91

Compound T N (K>) n y (mJIK 2 mol) Fermi surface

LaCu6 Paul/para n e = n h 8.0

CeCu 6 Kondo lattice ? 1600

PrCu6 singlet n e = n h 16

NdCu 6 6.1 n~ = n h

SmCu6 9.6 ne ~ nh(?)

four complicated Fermi surfaces

similar to LaCu6(? )

similar to LaCu 6

similar to LaCu 6

strongly altered by MBZ

O

b\ , a .

Fig. 91. Orthorhombic CeCu 6 type crystal structure. Large and small spheres show the Ce atoms and the Cu atoms, respectively.

10 8

~ 1 0 7

o~

N 10 6

i _O~

u2 - "*-i'~"~" : 62 - ~_ .d . I , 1 / / G o

e I 7..' L-72

I

1 0 5 ~ , ,a~_s~_-7-3 t~.J J , , , c_ Hl/b-axis e a b


Fig. 92. Angular dependence of the dHvA frequency in LaCu 6 (Onuki et al. 1987b, 1991b). The solid lines connecting the data are guidelines. The Greek letters designate the various orbits.

the Sm 3+ ion (Onuki et al. 1990b). The characteristic properties of R C u 6 are summarized in table 23.

The RCu6 compounds possess the monoclinic structure at low temperatures, which is a slight modification of the orthorhombic CeCu6 structure. For example, the orthorhombic structure of CeCu6 with a = 8.105 A, b = 5.105 A and c = 10.159 A at room temperature, as shown in fig. 91, changes into the monoelinic one with a=5.080,~, b = 10.121 A, c=8.067A and /3=91.36 ° at 65K (Asano et al. 1986). The structural transition temperature is roughly 200 K. This transition is associated with a complete softening of the transverse elastic constant C66 (Suzuki et al. 1985). Here, a, b, c and Y (= 90 °) in the


1 0 8 - ~ - ~ I J ' I ' ' ' ' I ' T I , ,

~io 7

lO ~

10 ~ H//b-axis

I C e C u 6

t-" 1 ~ , L . , , ~ . . . . ~ , ,

* " ~ --'7:,,'" °. "'°°. ° "'" °

~o,,, I

~ ° ] . . ° ° O ~ o ***° * ° o * oo*° • . - £ o i . ° * ° ° ° ° - ° °

I °: - : ' ° ? ' " °° . . . . ? ° : "

[ *

I t I I I I I I I I i I I i I i J I I I i i I ~ i

C a b


10 i

~10 '

i0 c

10 5 H//b-axis

, r , i , , , i , , , , i ,

PrCu6

-6~ ~ J ~ 4- .--~,~r .~--~__.__-

. ~ , f o

7

- ° " i -

, ~ ° ° l . . . . o !

I I I I I I I i i i i i i i ! i i i i i i i

e a b

Field M~gle (Degrees)

Fig. 94. Angular dependence of the dHvA frequency Fig, 93. Angular dependence of the dHvA frequency in PrCu 6 (Onuki et al. 1987b). The solid lines in CeCu 6 (Springford 1991, Chapman et al. 1990a). connecting the data are guidelines. The Greek letters The solid lines connecting the data are guidelines, designate the various orbits.

orthorhombic notation are converted into c, a, b and/3, respectively, in the monoclinic one. As the crystal distortion is small, we use the orthorhombic notation. The primitive cell contains four molecules of RCu6.

Figures 92-96 show the angular dependence of the dHvA frequency in RCu6 where R represents La, Ce, Pr, Nd and Sm (Onuki et al. 1987b, 1990b, 1991b, Springford 1991, Chapman et al. 1990a, Springford and Reinders 1988, Endoh et al. 1987). The band calculations for LaCu6 made by Harima et al. (1990b) show a lot of extremal cross- sections. The observed signals in LaCu6 are really quite numerous but they represent only a part of the signals expected from the band calculations. However, the main observed signals do correspond to results of band calculations. In the same sense, the signals in PrCu6 and NdCu6 seem to correspond to the band calculations. The common dHvA branches are denoted by Greek letters. The detected dHvA branches are many in number, concentrating at the symmetry axes. The largest branch is a which consists of two or three branches with the largest dHvA frequencies of about 2x 107 Oe.

The Fermi surface of SmCu6 is quite different from that of LaCu6, probably reflecting the small magnetic Brillouin zone boundaries. In CeCu6, w e find both similar but also different branches along the c-axis, compared to NdCu6 or LaCu6.

As mentioned above, Harima et al. (1990b) calculated the band structure of LaCu6 with the orthorhombic structure by an LAPW method. The Cu-3d band and La-4f band are


108 . . . . . . . . . . . . . . . . . . . . . . . . 107

I , c~ NdCu6 1

o ~ "-~- ~ ----~ o ~

. . . . o . 7 1 f . . . . . . . . i . . . . . . . . ', . . . . . . . . 10 5

t t / / b -ax i s e a b Field Angle (Degrees)

Fig. 95. Angular dependence of the dHvA frequency in NdCu 6 ((3nuid et al. 1991b). The solid lines connecting the data are guidelines. The Greek letters designate the various orbits.

r SmCu6

x2;2U '. ° L

/ y.o.o J

104 , , [ i , I . . . . I ~ , , I i , i ,

I-I//b-axi s a Field Angle (Degrees)

Fig. 96. Angular dependence of the dHvA frequency in SmCu 6 (Endoh et al. 1987, Onuki et al. 1990b). The solid lines connecting the data are guidelines.

well localized and are separated from the Fermi level. The conduction bands are mainly due to the 4s components of Cu. We show in fig. 97 the calculated Fermi surfaces. As the non-cubic unit cell contains four molecules of LaCu6, about 1200 basis functions for each point are needed especially for 120 d-bands due to the 24 Cu atoms. LaCu6 is a compensated metal with hole Fermi surfaces in bands 149 and 150, and electron Fermi surfaces in bands 151 and 152. The theoretical Fermi surfaces are many in number and are characterized as corrugated Fermi surfaces with concave and convex curvatures, elongated along the c-axis. From the magnitudes and angular dependences of the extremal orbits, most of the experimental dHvA branches can be identified, as shown in fig. 97. The largest orbit, which is a belly orbit on a "catcher mitt" due to the band 151 electron, corresponds to branch a. The theoretical dHvA frequency of 2.06 × 107 Oe in the direction along the b-axis is in good agreement with the experimental value of about 2x 107 Oe.

The calculated electronic specific heat coefficient of 6.2 mJ/K 2 tool is almost the same as the experimental value of 8 mJ/K 2 mol for LaCu6. The detected masses are thus small and fall into the range of 0.076m0 to 2.50m0, reflecting the main 4s components of Cu. Branch a is the main Fermi surface, which possess the cyclotron mass of 1.89m0.

On the other hand, the cyclotron masses of PrCu6 and CeCu6 are twice and forty times larger than that of LaCu6, respectively. No mass enhancement is found in NdCu6 and SmCu6, as shown in fig. 98. Here, the electronic specific heat coefficients of PrCu6 and


LaCu 6 149th ho le R 151st electron

(a)

R R , l ~ f l ' t h h n l o e !~ 152nd electron e

] b~

R R

Fig. 97. Hole and electron Fermi surfaces in LaCu 6 (Harima et al. 1990b): (a) hole band 149; (b) hole band 150; (c) electron band 151; (d) electron band 152. The thick solid lines correspond to the observed orbits.

CeCu6 at zero external field are 16 and 1600 mJ/K 2 mol, respectively. These values may be compared to 8 mJ/K 2 mol of LaCu6 (Satoh et al. 1989, Takayanagi et al. 1988).

The large mass due to the Kondo-lattice character of CeCu6 seems to be strongly reduced by magnetic field. The specific heat coefficient y at low temperatures strongly depends on the magnitude and direction of the field (Satoh et al. 1989, Amato et al. 1987). Experimental results obtained by Amato and coworkers for field along the c-axis, which is the most sensitive direction, indicate a metamagnetic transition at about 20 kOe. Note that the field effect is weak along the a- and b-axes, which are the hard axes. For the highest applied field of 75 kOe, which almost corresponds to the initial field for the dHvA measurement, the ], value is reduced to 500 mJ/K 2 mol, which is larger than the g value of LaCu6 by a factor of 63. This value is roughly consistent with the cyclotron mass enhancement ratio of 40.

The field dependence of the cyclotron mass was studied by Chapman et al. (1990b) for field along the c-axis. The mass of 1 lm0 measured at 41 kOe is reduced to 6.0m0 at 106 kOe for dHvA branch of 1.2 x 106 Oe. For another branch of 1.03 x 107 Oe, 34.6m0 at 103 kOe is also reduced to 29.6m0 at 122 kOe. These results are shown in fig. 99. Here, a zero-field cyclotron mass was assumed for which the ratio m*(H)/m*(O) fits with the field dependence of y(H). Because of the limited range of the field, it is difficult to establish


i00

10

R

0.1

LaCu6 o CeCu 6 o PrCu6

NdCu6 SmCu6

H//c-ax±s

i , . . . . " 1 i ~ , ~ , , i I

O O

/ : °

0.01 ~ r ~,..i , ,~ ..... i . . . . . . . . i . . . . . 104 105 106 107 108

dHvA Frequency (Oe)

Fig. 98. Cyclotron masses vs dHvA frequencies in RCH 6 (Onuki et al. 1988). The solid straight lines are guidelines.

1 ' ' I ' ' ~ ' ' ' - -

~ ' CeCu 6

~ ~- 0.5

D

o +

t

0 [ . . . . . ~ . . . . I . . . . 0 100

Magnetie Field (kOe)

Fig. 99. Field dependence of the normalized cyclotron masses m*(H)/m*(O) (Chapman et al. 1990a) and the specific heat coefficients y(H)/y(0) (Amato et al. 1987). The cyclotron masses at zero field are estimated as m*(0)=20m0 for a dHvA frequency F=l.20xl06Oe (open circles) and m*(0) = 120m 0 for F = 1.034x 107 Oe (squares). The results of specific heat coefficients are denoted by crosses, and the solid line is a guideline.

whether both field dependences are the same or not. Note that the field effect on the cyclotron mass for the hard axes has to be weak, in order to be consistent for y(H).

Chapman et al. (1990b) concluded that the Fermi surface o f CeCu6 is not well described by LMTO band calculations performed within the local density approximations, in which the f electrons are included as either band or core states. Other kinds o f band calculations and more experimental dHvA data, in particular around the b-axis, are desirable.

5. Conclusions

Many lanthanide compounds are clarified in Fermi surface properties. Most o f them are light lanthanide compounds. They most l ikely order antiferromagnetically and the 4 f electrons are localized. Therefore, the Fermi surface in the antiferromagnetically ordered state should be similar to that of the corresponding non-4f La compound. The presence o f f electrons, however, alters the Fermi surface through the f-electron contribution to the crystal potential and through the introduction of magnetic Bril louin zone boundaries. On the other hand, 4f electrons are delocalized, representing an itinerant character, in some compounds such as CeSn3, CeNi and most likely CeRu2Si2. The many-


body Kondo effect strongly enhances the effective mass in the Ce (or Yb) Kondo-lattice compounds.

We summarize the Fermi surface properties of the lanthanide compounds: (1) As the 4f bands in Y and La compounds are located far above the Fermi level, their

contribution to the conduction electrons is less than 10%. For example, the conduction electrons are mainly La 5d electrons in LAB6, while they are Cu 4s electrons in LaCu6. The magnetoresistance and dHvA data are in good agreement with the results of band calculations for the compounds with the cubic, hexagonal and tetragonal structures. However, even in the cubic case, the spin-orbit interaction is essential to correctly calculate the energy bands and Fermi surfaces, as shown in LaSn3. As for LaNi, YCu2 and LaCu6 with the orthorhombic crystal structure, the characteristic topology of the Fermi surface such as open orbits for LaNi is also explained by the results of band calculations.

(2) Many dHvA measurements were performed in Ce compounds. The 4f-localized compounds such as CeGa2 and CeRu2Ge2, which do not show the many-body Kondo effect, are similar to the corresponding La compounds in topology of the Fermi surface. The detected cyclotron mass is not large, comparable to those of the other lanthanide magnetic compounds.

For the compounds belonging to the valence-fluctuation regime, such as CeSn3 and CeNi, the dHvA data can be fitted very well by the results of band calculations based on the itinerant 4f model. The mass enhancement is fairly homogeneous for each orbit and not very large, less than 5, because the 4f band mass is already fairly large. Even in CeRu2Si2, the 4f electrons are most likely itinerant in the ground state. A main Fermi surface with the dominant 4f component is observed by the dHvA experiments, possessing the large cyclotron mass of 120m0 for field along the [100] direction. The mass enhancement is anisotropic for each Fermi surface in CeRuzSi2.

The 4f character in CeSn3 and CeRu2Si2 can be determined by magnetoresistance measurements because the primitive cell contains one molecule and the valence electrons are odd in number for LaSn3 and LaRu2Si2. If the 4f electron is itinerant, the valence electrons are even in number for CeSn3 and CeRu2Si> This difference can be clearly distinguished by the magnetoresistance. The experimental results are as follows. The magnetoresistance in LaSn3 and LaRu2 Si2 saturates over a wide angle region, representing uncompensated metals. The magnetoresistance in CeSn3 and CeRu2Si2 increases over a wide angle region. This result shows that CeSn3 and CeRuzSi2 are compensated metals. Therefore, it is concluded that the 4f electron is itinerant in CeSn3 and CeRu2Si2 in the ground state.

For the compounds belonging to the Kondo regime, the dHvA data can be explained by putting one 4f state below the Fermi energy and the other unoccupied 4f bands above the Fermi energy. Therefore the Fermi surface is essentially similar to that of the La compound, as well as to those of the well localized 4f systems. The mass enhancement factor for the conduction electrons in the Kondo regime is quite large, of the order of 10 to 100 which becomes anisotropic in the some compounds such as in CeSb.


The large cyclotron mass of 80m0 is detected in the non-magnetic Kondo-lattice compound CeCu6. It is, however, not clear whether the 4f-electron character of CeCu6 is itinerant or localized.

(3) The 4f electron character of Yb compounds is supposed to be similar to that of Ce compounds. The dHvA measurements for Yb compounds are small in number. The Fermi surface of YbAs with magnetic ordering is similar to that of LaSb.

(4) Fermi surfaces of Pr compounds with the singlet ground state such as PrIn3, PrSb and PrCu6 are almost the same as those of the corresponding the La compounds, although their cyclotron masses are twice as large as those of La compounds. Even in the antiferromagnetically ordered Pr compounds such as PrB6, most of the dHvA branches are roughly similar to those of La compounds, while some dHvA branches are not present in the La compounds. They are probably produced by the antiferromagnetic Brillouin zone boundaries. The cyclotron mass of PrB6 is roughly three times larger than that of LAB6. The Fermi surface in the ferromagnetic compound PrNi is similar to that of LaNi, although the directions of open orbits are a little different between them.

(5) The magnetic energy gaps associated with the magnetic ordering are small enough and thus the electrons undergoing cyclotron motions can break through these energy gaps and circulate on orbits of the paramagnetic Fermi surface as in Pr compounds, even if the magnetic field is not strong. The occurrence of this effect becomes more difficult as the number of f electrons increases. The electrons follow the orbits on the antiferromagnetic Fermi surfaces in Nd, Sm and Gd compounds. Typical examples are shown in NdIn3 and NdB 6. For example, the paramagnetic (or field-induced ferromagnetic) Fermi surface of NdIn3 is almost the same as that of Lain3. A nearly spherical Fermi surface in the paramagnetic state, which corresponds to the band 7 electron Fermi surface of Lain3, is changed in the antiferromagnetic state into a multiply connected one with necks. On the other hand, if a Fermi surface is small and is located at the center of the Brillouin zone, it remains in the antiferromagnetic state because it is contained in the magnetic Brillouin zone. Branch d in Lain3 is most likely observed in the magnetic RIn3 compounds. The small Fermi surfaces of the monopnictides, RX, also are not changed by the magnetic Brillouin zone.

Mass enhancement due to the electron-magnon interaction in magnetically ordered compounds is large compared to the one due to the electron-phonon interaction. The mass enhancement factor is in the range of 1-2.

(6) Sm compounds have interesting magnetic behaviors, dHvA measurements have been performed on some compounds such as SmIn3, SmSb, SmGa2, and SmCu6. They are, however, not valence-fluctuation compounds but f-localized ones. Therefore, the situation is similar to the Nd system. Fermi surface studies for valence-fluctuating Sm compounds are open to future studies.

(7) We found that the band theory worked fairly well for studies of the electronic structures in various lanthanide compounds. The energy band structures and the Fermi surfaces were clarified for many La compounds, and the theoretical results were used as a good starting point for understanding of the electronic structures of the Ce and other light lanthanide compounds, in which the 4f electrons are believed to be localized. Moreover,


the band theory could provide clear evidence that the 4f electrons in some Ce compounds, especially CeSn3, belonging to the valence-fluctuation regime, are itinerant in the ground state, and contribute directly to the formation of the Fermi surface. The agreement between theory and experiment is as good as that attained for the 3d electron system in the iron series transition metals, as far as the topology of the Fermi surface is concerned.

(8) Some drawbacks of the band theory are apparent. The disagreement between theory and experiment becomes larger when it is applied to the complicated crystal structures, like in LaNi, CeNi, YCu2 and LaCu6. Even in the La compounds with cubic crystal structures, some of the dHvA frequency branches cannot be explained well quantitatively, especially in the low-frequency region. The theory can certainly be improved by taking into account non-muffin-tin shape corrections via a full-potential scheme, and some disagreements may be removed for these La and Ce compounds. It seems to us, however, that a treatment of the exchange-correlation interactions is more serious, and it is essential to improve the theory so as to go beyond LDA. Such an improvement should be carried out in a new framework of band theory in which the exchange interaction is taken into account explicitly with the screening effect.

(9) As for an appropriate band theory for the localized 4f-electron system, an attractive approach based on the p- f mixing model was proposed, and was applied to CeSb. A future problem is to refine the approach so as to carry out quantitative calculations in a self-consistent way. The anomalously large enhancement factors for the cyclotron effective masses and the y values observed in the Ce compounds cannot be explained by band structure alone. Quantitative analysis of the mass enhancement factor is a problem challenging to many-body theory. There is still much room for improvement for a complete understanding of the electronic structures of lanthanide compounds.

Acknowledgement

We are very grateful to T. Kasuya, O. Sakai, K. Ueda, A. Yanase, H. Harima, H. Yamagami, Y. Kubo, T. Komatsubara, T. Suzuki, T. Goto, K. Satoh, H. Aoki, H. Sato, I. Umehara, I. Sakamoto, K. Maezawa, M. Springford and G. Crabtree for helpful discussions, and to T. Yamazald for typing the manuscript.

References

Amato, A., D. Jaccard, J. Flouquet, E Lapierre, J.L.

Tholence, R.A. Fisher, S.E. Lacy, J.A. Olsen and

N.E. Phillips, 1987, J. Low Temp. Phys. 68, 371.

Andersen, O.K., 1975, Phys. Rev. B 12, 3060.

Anderson, P.W., 1961, Phys. Rev. 124, 41.

Aoki, H., G.W. Crabtree, W. Joss and E Hulliger, 1985,

J. Magn. & Magn. Mater. 52, 389.

Aoki, H., G.W. Crabtree, W. Joss and E Hulliger, 1991, J. Magn. & Magn. Mater. 97, 169.

Aoki, H., S. Uji, A.K. Albessard and Y. 0nuld, 1992, J. Phys. Soc. 61, 3457.

Arko, A.J., G.W. Crabtree, D. Karim, EM. Mtieller, L.R. Windmiller, J.B. Ketterson and Z. Fisk, 1976, Phys. Rev. B 13, 5240.

Asano, H., M. Umino, Y. ()nuki, T. Komatsubara, E


Izumi and N. Watanabe, 1986, J. Phys. Soc. Jpn. 55, 454.

Barbara, B., M.E Rossignol, J.X. Boucherle, J. Schweizer and J.L. Buevoz, 1979, J. Appl. Phys. 50, 2300.

Benoit, A., J.X. Boucherle, J. Flouquet, J. Sakurai and J. Schweizer, 1985, J. Magn. & Magn. Mater. 47&48, 149.

Besnus, M.J., J.P. Kappler, P. Lehmann and A. Meyer, 1985, Solid State Commun. 55, 779.

Boulet, R.M., J.-P. Jan and H.L. Skriver, 1982, J. Phys. F 12, 293.

Brandt, N.B., and VV Moshchalkov, 1984, Adv. Phys. 33, 373.

Bredl, C.D., 1987, L Magn. & Magn. Mater. 63&64, 355.

Bredl, C.D., E Steglich and K.D. Schotte, 1978, Z. Phys. B 29, 327.

Buschow, K.H.J., H.J. van Daal, EE. Maranzana and EB. van Aken, 1971, Phys. Rev. 3, 1662.

Callaway, J., and N.H. March, 1984, Solid State Phys. 38, 135.

Chapman, S.B., M. Hunt, E Meeson, RH.P. Reinders, M. Springford and M. Norman, 1990a, J. Phys.: Condens. Matter 2, 8123.

Chapman, S.B., M. Hunt, R Meeson and M. Springford, 1990b, Physica B 163, 361.

Crabtree, G.W., H. Aoki, W. Joss and E Hulliger, 1987, in: Theoretical and Experimental Aspects of Valence Fluctuations and Heavy Fermions, eds L.C. Gupta and S.K. Malik (Plenum Press, New York), p. 197.

Czopnik, A., J. Kowalewski and M. Hackemer, 1991, Phys. Status Solidi a 127, 243.

de Haas, W.J., and P.M. van Alphen, 1930, Leiden Comm. 208d, 212a.

de Haas, W.J., and RM. van Alphen, 1932, Leiden Comm. 220d.

Dijkrnan, W.H., 1982, Thesis (University of Amster- dam).

Dimmock, J.O., 1971, in: Solid State Physics, Vol. 26, eds. H. Ehrenreich, E Seitz and D. Tttrnbull (Academic Press, New York) p. 103.

Ebihara, T., I. Umehara, A.K. Albessard, Yr. Fujimaki, K. Satoh, Y. Onuki, B. Liu and M. Kasuya, 1992a, L Phys. Soc. Jpn. 61, 2104.

Ebihara, T., I. Umehara, A.K. Albessard, K. Satoh and Y. 0nuki, 1992b, J. Phys. Soc. Jpn. 61, 1472.

Ebihara, T., I. Umehara, A.K. Albessard, K. Satoh and Y. Onuki, 1993, Physica B 186-188, 123.

Effantin, J.M., J. Rossat-Mignod, R Burlet, H. Bartholin, S. Kunii and T. Kasuya, 1985, J. Magn. & Magn. Mater. 47&48, 145.

Endoh, D., T. Goto, T. Suzuki, T. Fujimura, Y. 0nuki and T. Komatsubara, 1987, J. Phys. Soc. Jpn. 56, 4489.

Falicov, L.M., W. Hanke and M.B. Maple, 1981, Valence Fluctuations in Solids (North-Holland, Amsterdam).

Fawcett, E., 1964, Adv. Phys. 13, 139. Fawcett, E., J.E Maita and J.H. Wernick, 1970, Int. J.

Magn. 1, 29. Forgan, G.M., 1981, Physica 107 B, 65. Fukuhara, T., K. Maezawa and J. Sakurai, 1993,

Physica B 186-188, 143. Fulde, P., 1991, Electron Correlations in Molecules

and Solids (Springer, New York). Fulde, P., and J. Jensen, 1983, Phys. Rev. B 27, 4085. Galer~ R.M., E Morin, S. Kunii and T. Kasuya, 1992,

J. Magn. & Magn. Mater. 104-107, 336. Gignoux, D., E Givord, R. Lemaire and E Tasset,

1983, J. Less-Common Met. 94, 165. Goto, T., 1992, private communication. Goto, T., T. Suzuki, Y. Ohe, S. Sakatsume, S. Kunii,

32 Fujimura and T. Kasuya, 1988a, J. Phys. Soc. Jpn. 57, 2885.

Goto, T., H. Matsui, R. Settai and S. Sakatsume, 1993, Physica B 186--188, 107.

Goy, P., and B. Castaing, 1973, Phys. Rev. B 7, 4409. Gratz, E., E. Bauer, B. Barbara, S. Zemirli, E Steglich,

C.D. Bredl and W. Lieke, 1985, J. Phys. F 15, 1975. Gschneidner Jr, K.A., 1993, private commun. Gschneidner Jr, K.A., and K. Ikeda, 1983, J. Magn.

& Magn. Mater. 31-34, 265. Gschneidner Jr, K.A., S.K. Dhar, R.J. Stierman, T.-

W.E. Tsang and O.D. McMasters, 1985, J. Magn. & Magn. Mater. 47&48, 51.

Gunnarsson, O., and B.I. Lundqvist, 1976, Phys. Rev. B 13, 4274.

Guo, G.Y., 1990, Physica B 165&166, 335. Harima, H., 1988, Thesis (Tohoku University). Harima, H., and A. Yanase, 1991a, J. Phys. Soc. Jpn.

60, 21. Harima, H., and A. Yanase, 1991b, J. Phys. Soc. Jpn.

60, 2718. Harima, H., and A. Yanase, 1992a, J. Magn. & Magn.

Mater. 108, 145. Harima, H., and A. Yanase, 1992b, J. Phys. Soc. Jpn.

61,602. Harima, H., O. Sakai, T. Kasuya and A. Yanase, 1988,

Solid State Commun. 66, 603.


Hailma, H., S. Miyahara and A. Yanase, 1990a, Physica B 163, 205; 1990.

Hailma, H., A. Yanase and A. Hasegawa, 1990b, J. Phys. Soc. Jpn. 59, 4054.

Hasegawa, A., 1981, J. Phys. Soc. Jpn. 50, 3313. Hasegawa, A., 1982, in: Crystalline Electric Field

Effects in f-Electron Magnetism, eds. R.E Guetin, W, Suski and Z. Zolnierek (Plenum, New York) p. 201.

Hasegawa, A., 1985, J. Phys. Soc. Jpn. 54, 677. Hasegawa, A., and H. Yamagami, 1991, J. Phys. Soc.

Jpn. 60, 1654. Hasegawa, A., and A. Yanase, 1977a, J. Phys. F 7,

1229. Hasegawa, A., and A. Yanase, 1977b, J. Phys. F 7,

1245. Hasegawa, A., and A. Yanase, 1980a, J. Phys. F 10,

847. Hasegawa, A., and A. Yanase, 1980b, J. Phys. F 10,

2207. Hasegawa, A., H. Yamagami and H. Johbettoh, 1990,

J. Phys. Soc. Jpn. 59, 2457. Herman, E, and S. Skillman, 1963, Atomic Structure

Calculations (Prentice-Hall, Englewood Cliffs, NJ).

Herring, C., 1937, Phys. Rev. 52, 361. Hill, H.H., 1970, in: Plutonium 1970 and other

Aetinides, ed. W.N. Minder (Metal Soc. AIME, New York) p. 2.

Hill, R.W., J. Cosier and D.A. Hukin, 1976, J. Phys. F 6, 1731.

Hillebrecht, EU., W. Gudat, N. M~rtensson, D.D. Sarma and M. Campagna, 1985, J. Magn. & Magn. Mater. 47&48, 221.

Hohenberg, P., and W. Kohn, 1964, Phys Rev. B 136, 864.

Hungsberg, R.E., and K.A. Gschneidner Jr, 1972, J. Phys. & Chem. Solids 33, 401.

Hunt, M., P. Meeson, E-A. Probst, P.H.P. Reinders, M. Springford, W. Assmus and W. Sun, 1990, Physica B 165&166, 323.

Ishii, T., K. Soda, K. Naito, T. Miyahara, H. Kato, S. Sato, T. Moil, M. Taniguchi, A. Kakizaki, Y. (3nuki and T. Komatsubara, 1987, Phys. Scr. 35, 603.

lshizawa, Y., T. Tanaka, E. Bannai and S. Kawai, 1977, J. Phys. Soc. Jpn. 42, 112.

Ishizawa, Y., H. Nozaki, T. Tanaka and T. Nakajima, 1980, J. Phys. Soc. Jpn. 48, 1439.

Isikawa, Y., K. Mori, T. Mizushima, A. Fujii, H. Takeda and K. Sato, 1987, J. Magn. & Magn. Mater. 70, 385.

Jan, J.-P., 1973, Phys. Rev. B 8, 3590. Jayaraman, A., V. Narayanamurti, E. Bucher and R.G.

Maines, 1970, Phys. Rev. Lett. 25, 1430. Jepson, J., and O.K. Anderson, 1971, Solid State

Commun. 9, 1763. Jerjini, M., M. Bonnet, P. Burlet, G. Lapertot, L

Rossat-Mignod, J.Y. Henry and D. Gignoux, 1988, J. Magn. & Magn. Mater. 76&77, 405.

Johanson, W.R., G.W. Crabtree, A.S. Edelstein and O.D. McMasters, 1981, Phys. Rev. Lett. 46, 504.

Johanson, W.R., G.W. Crabtree, A.S. Edelstein and O.D. McMasters, 1983, J. Magn. & Magn. Mater. 31-34, 377.

Joss, W., J.M. van Ruitenbeek, G.W. Crabtree, J.L. Tholence, A.J.E van Deursen and Z. Fisk, 1987, Phys. Rev. Lett. 59, 1609.

Joss, W., J.M. van Ruitenbeek, G.W. Crabtree, J.L. Tholence, A.J.P. van Deursen and Z. Fisk, 1989, J. Phys. C 8, 747.

Kadowaki, K., and S.B. Woods, 1986, Solid State Commun. 58, 507.

Kasaya, M., J.M. Tarascon and J. Etourneau, 1980, Solid State Commun. 33, 1005.

Kasuya, T., 1956, Prog. Theor. Phys. 16, 45. Kasuya, T., O. Sakai, J. Tanaka, H. Kitazawa and T.

Suzuki, 1987, J. Magn. & Magn. Mater. 63&64, 9.

King, C.A., and G.G. Lonzarich, 1991, Physica B 171, 161.

Kitazawa, H., 1982, Thesis (Tohoku University). Kitazawa, H., T. Suzuki, M. Sera, I. Oguro, A. Yanase,

A. Hasegawa and T. Kasuya, 1983, J. Magn. & Magn. Mater. 31-34, 421.

Kitazawa, H., Q.Z. Gao, H. Shida, T. Suzuki, A. Hasegawa and T. Kasuya, 1985, J. Magn. & Magn. Mater, 52, 286.

Kitazawa, H., Y.S. Kwon, A. Oyamada, N. Takeda, H. Suzuki, S. Sakatsume, T. Satoh, T. Suzuki and T. Kasuya, 1988, J. Magn. & Magn. Mater. 76&77, 40.

Kletowski, Z., N. Iliew and B. Stalinski, 1985, Physica 130 B, 84.

Kletowski, Z., M. Glinski and A. Hasegawa, 1987, J. Phys. F 17, 993.

Koelling, D.D., 1969, Phys. Rev. 188, 1049. Koelling, D.D., 1982, Solid State Commun. 43, 247. Koelling, D.D., and G.O. Arbman, 1975, J. Phys. F 5,

2041. Koelling, D.D., B.D. Dunlap and G.W. Crabtree, 1985,

Phys. Rev. B 31, 1966.


Kohn, W., and R. Rostoker, 1954, Phys. Rev. 94, 1111.

Kohn, W., and L.J. Sham, 1965, Phys. Rev. A 140, 1133.

Komatsubara, T., N. Sato, S. Kunii, I. Oguro, Y. Fun~awa, Y. Onuki and T. Kusuya, 1983, J. Magn. & Magn. Mater. 31-34, 368.

Kondo, J., 1964, Prog. Theor. Phys. 32, 37. Korringa, J., 1947, Physica 13, 392. Kubo, Y., A. Asano, H. Harima and A. Yanase, 1993,

J. Phys. Soc. Jpn. 62, 205. Kurosawa, Y., I. Umehara, M. Kikuchi, N. Nagai, K.

Satoh and Y. 0nuki, 1990, J. Phys. Soc. Jpn. 59, 1545.

Kwon, Y.S., T. Suzuki and T. Kasuya, 1991, Physiea B 169, 497.

Langford, H.D., W.M. Temmerman and G.A. Gehring, 1990, J. Phys. Condens. Matter. 2, 559.

Larson, A.C., and D.T. Cromer, 1961, Acta Crystal- logr. 14, 73.

Lawrence, J.M., and S.M. Shapiro, 1980, Phys. Rev. B 22, 4379.

Lethuillier, R, J. Pierre, G. Fillion and B. Barbara, 1973, Phys. Status Solidi 15, 613.

Liberman, D., J.T. Waber and D.T. Cromer, 1965, Phys. Rev. 137, A27.

Lifshitz, I.M., and R.M. Kosevich, 1955, Zh. Eksp. Teor. Fiz. 29, 730 [1956, Soy. Phys.-JETP 2, 636].

Longuet-Higgins, H.C., and M. de V. Roberts, 1954, Proc. R. Soc. 224, 336.

Lonzarich, G.G., 1988, J. Magn. & Magn. Mater. 76&77, 1.

Loucks, T.L., 1967, Augmented Plane Wave Method (Benjamin, New York).

Luong, N.H., J.J.M. Franse and T.D. Hien, 1985, J. Magn. & Magn. Mater. 50, 153.

Luttlnger, J.M., 1960, Phys. Rev. 119, 1153. Luttinger, J.M., 1961, Phys. Rev. 121, 1251. Maezawa, K., S. Wakabayashi, Y. Isikawa, K. Sato,

Y. ()nuki and T. Komatsubara, 1986, J. Phys. Soc. Jpn. 55, 4135.

Maezawa, K., T. Kato, Y. Isikawa, K. Sato, I. Umehara, Y. Kurosawa and Y. Onuki, I989, J. Phys. Soe. Jpn. 58, 4098.

Maezawa, K., T. Kato, Y. Isikawa and K. Sato, 1992, J. Magn. & Magn. Mater. 104-107, 1365.

Mattheiss, L.E, 1964, Phys. Rev. 133, A1399. Mattheiss, L.E, J.H. Wood and A.C. Switendiek, 1968,

in: Methods in Computational Physics, Vol. 8, eds. S. Fembach and M. Rotenberg (Academic Press, New York) p. 63.

Meyer, R.T.W., L.W. Roeland, ER. de Boer and J.C.R Klaasse, 1973, Solid State Commun. 12, 923.

Min, B.I., and Y.-R. Jang, 1991, Phys. Rev. B 44, 13270.

Mfiller, T., W. Joss, J.M. van Ruitenbeek, U. Welp and R Wyder, 1988, J. Magn. & Magn. Mater. 76&77, 35.

Nasu, S., A.M. Van Diepen, HM. Neumann and R.S. Craig, 1971, J. Phys. & Chem. Solids 32, 2773.

Niksch, M., B. Lfithi and J. Ktibler, 1987, Z. Phys. B 68, 291.

Norman, M.R., and D.D. Koelling, 1986, Phys. Rev. 33, 6730.

Norman, M.R., and D.D. Koelling, 1993, in: Handbook on the Physics and Chemistry of Rare Earths, Vol. 17, eds K.A. Gsehneidner Jr., L. Eyring, G.H. Lander and G.R. Choppin (North-Holland, Amsterdam) p. 1.

Onodera, Y., and M. Okazaki, 1966, J. Phys. Soc. Jpn. 21, 1273.

Onuki, Y., 1993, Physica B, to be published. Onuki, Y., and T. Komatsubara, 1987a, J. Magn. &

Magn. Mater. 63&64, 281. 0nuki, Y., Y. Machii, Y. Shimizu, T. Komatsubara and

T. Fujita, 1985a, Jr. Phys. Soc. Jpn. 54, 3562. Onuki, Y., M. Nishihara, M. Sato and T. Komatsubara,

1985b, J. Magn. & Magn. Mater. 52, 317. 0nuki, Y., K. Ina, M. Nishihara, T. Komatsubara, S.

Takayanagi, K. Kameda and N. Wada, 1986, J. Phys. Soe. Jpn. 55, 1818.

Onuki, Y., A. Umezawa, W.K. Kwok, G.W. Crabtree, M. Nishihara, T. Komatsubara, K. Maezawa and S. Wakabayashi, 1987b, Jap. J. Appl. Phys. 26, 509.

0nuki, Y., Y. Kurosawa, T. Omi, T. Komatsubara, R. Yoshizaki, H. Ikeda, K. Maezawa, S. Wakabayashi, A. Umezawa, W.K. Kwok and G.W. Crabtree, 1988, J. Magn. & Magn. Mater. 76&77, 37.

Onuki, Y., T. Komatsubara, RH.E Reinders and M. Springford, 1989a, J. Phys. Soc. Jpn. 58, 3698.

0nuki, Y., Y. Kurosawa, K. Maezawa, I. Umehara, Y. Isikawa and K. Sato, 1989b, J. Phys. Soc. Jpn. 58, 3705.

0nuki, Y., T. Omi, Y. Kurosawa, K. Satoh and T. Komatsubara, 1989c, J. Phys. Soc. Jpn. 58, 4552.

0nuki, Y., A. Umezawa, W.K. Kwok, G.W. Crabtree, M. Nishihara, T. Yamazaki, T. Omi and T. Komatsubara, 1989d, Phys. Rev. B 40, 11195.

Onuki, Y., A. Fukada, I. Ukon, I. Umehara, K. Satoh and Y. Kurosawa, 1990a, Physica B 163, 600.

Onuki, Y., A. Umezawa, W.K. Kwok, G.W. Crabtree, M. Nishihara, K. Ina, T. Yamazaki, T. Omi, T.


Komatsubara, K. Maezawa, S. Wakabayashi, S. Takayanagi and N. Wada, 1990b, Phys. Rev. B 41, 568.

Onuki, Y., T. Goto and T. Kasuya, 1991a, in: Materials Science and Technology, Vol. 3A, ed. K.H.J. Buschow (VCH, Weinheim) oh. 7, p. 545.

0nuki, Y., I. Umehara, N. Nagai, Y. Kurosawa and K. Satoh, 1991b, J. Phys. Soc. Jpn. 60, 1022.

Onuki, Y., I. Umehara, A.K. Albessard, T. Ebihara and K. Satoh, 1992, J. Phys. Soc. Jpn. 61, 960.

Ozeki, S., Y.S. Kwon, Y. Haga, T. Suzuki, G. Kido and T. Kasuya, 1991, Physica B 169, 499.

Parks, R.D., 1977, Valence Instabilities and Related Narrow-Band Phenomena (Plenum Press, New York).

Rath, J., and A.J. Freeman, 1975, Phys. Rev. B 11, 2109.

Reichelt, J., and K. Winzer, 1978, Phys. Status Solidi b 89, 489.

Reinders, EH.P., and M. Springford, 1989, J. Magn. & Magn. Mater. 79, 295.

Reinders, P.H.P., M. Springford, E Hilton, N. Kerley and N. Killoran, 1987, Cryogenics 27, 689.

Rossat-Mignod, J., J.M. Effantin, P. Burlet, T. Chattopadhyay, L.P. Regnault, H. Bartholin, C. Vettier, O. Vogt, D. Ravot and J.C. Achard, 1985, J. Magn. & Magn. Mater. 52, 111.

Rossat-Mignod, J., L.P. Regnault, J.L. Jacoud, C. Vettier, P. Lejay, J. Flouquet, E. Walker, D. Jaccard and A. Amato, 1988, J. Magn. & Magn. Mater. 76&77, 376.

Ruderman, M.A., and C. Kittel, 1954, Plays. Rev. 96, 99.

Sahni, V.C., and G. Venkataraman, 1970, J. Phys.: Condens. Matter 11, 199.

Sakai, O., M. Takeshige, H. Harima, K. Otaki and T. Kasuya, 1985, J. Magn. & Magn. Mater. 52, 18.

Sakamoto, I., T. Miura, K. Miyoshi and H. Sato, 1990, Physica B 165&166, 339.

Sakamoto, I., T. Miura, H. Satoh, T. Miyamoto, I. Shiozaki, I. Oguro and S. Maruno, 1992, J. Magn. & Magn. Mater. 108, 125.

Satoh, K., T. Fujita, Y. Maeno, Y. (3nuki and T. Komatsubara, 1989, J. Phys. Soc. Jpn. 58, 1012.

Satoh, K., I. Umehara, Y. Kurosawa and Y. ()nuki, 1990, Physica B 165&166, 329.

Satoh, K., I. Umehara, N. Nagai, Y. Onuki, I. Sakamoto, M. Hunt, P. Meeson, E-A. Probst and M. Springford, 1992, J. Magn. & Magn. Mater. 104-107, 1411.

Seitz, E., 1978, J. Phys. F 8, L189.

Seitz, E., and B. Legeler, 1979, J. Phys. Colloq. C 5, suppl. 5, 40, 76.

Sellmyer, D.J., ER. Szofran and J.W. Weymouth, 1975, J. Low Temp. Phys. 18, 85.

Settai, R., H. Natsui, Y. Ohe, T. Goto, T. Fujimura, Y. ()nuki, E Iga and M. Kasaya, 1990, J. Magn. & Magn. Mater. 90&91,446.

Settai, R., T. Goto and Y. 0nuki, 1992, J. Phys. Soc. Jpn. 61,609.

Settai, R., T. Goto, S. Sakatsume, Y.S. Kwon, T. Suzuki and T. Kasuya, 1993, Physica B 186--188, 176.

Settai, R., T. Goto and Y. ()nuki, 1995, unpublished. Shoenberg, D., 1984, Magnetic Oscillations in Metals

(Cambridge University Press, Cambridge). Slater, J.C., 1937, Phys. Rev. 51,846. Springford, M., 1991, Physica B 171, 151. Springford, M., and P.H.P. Reinders, 1988, J. Magn.

& Magn. Mater. 76&77, 11. Steglich, E, J. Aarts, C.D. Bredl, W Lieke, D.

Meschede, W. Franz and H. Schafer, 1980, J. Magn. & Magn. Mater. 15-18, 889.

Sticht, J., N. d'Ambrumenil and J. Kfibler, 1986, Z. Phys. B 65, 149.

Strange, D., and D.M. Newns, 1986, J. Phys. F 16, 335.

Sugiyama, K., F. Iga, M. Kasaya, T. Kasuya and M. Date, 1988, J. Phys. Soc. Jpn. 57, 3946.

Sumiyama, A., Y. Oda, H. Nagano, Y. 0nuki, K. Shibutani and T. Komatsubara, 1986, J. Phys. Soc. Jpn. 55, 1294.

Suzuki, T., 1993, Physica B 186-188, 347. Suzuki, T., T. Goto, A. Tamaki, T. Fujimura, Y. (3nuki

and T. Komatsubara, 1985, J. Phys. Soc. Jpn. 54, 2367.

Suzuki, T., T. Goto, S. Sakatsume, A. Tamaki, S. Kunii and T. Kasuya, 1987, Jap. J. Appl. Phys. 26, 511.

Suzuki, T., T. Goto, Y. Ohe, T. Fujimura and S. Kunii, 1988, J. Phys. C 8, 799.

Taillefer, L., G.G. Lonzarich and P. Strange, 1986, J. Magn. & Magn. Mater. 54-57, 957.

Takada, S., 1966, Prog. Theor. Phys. Suppl. 36, 224. Takahashi, H., and T. Kasuya, 1985, J. Phys. C 18,

2697, 2709, 2721, 2731, 2745, 2755. Takahashi, M., H. Tanaka, T. Satoh, M. Kohgi, Y.

Ishikawa, T. Miura and H. Takei, 1988, J. Phys. Soc. Jpn. 57, 1377.

Takayanagi, S., N. Wada, T. Watanabe, Y. 0nuki and T. Komatsubara, 1988, J. Phys. Soc. Jpn. 57, 3552.

Takayanagi, S., N. Wada, Y. Onuki and T. Komatsub- ara, 1991, J. Phys. Soc. Jpn. 60, 975.

Takeda, N., 1992, Thesis (Tohoku University).


Takeda, N., M. Kagawa, K. Tanaka, A. Oyamada, N. Sato, S. Sakatsume, 1". Suzuki and T. Komatsubara, 1990, J. Magn. & Magn. Mater. 90&91,425.

Takeda, N., Y.S. Kwon, Y. Haga, N. Sato, T. Suzuki and T. Komatsubara, 1993, Physica B 186-188, 153.

Tanaka, K., N. Takeda, Y.S. Kwon, N. Sato, T. Suzuki and T. Komatsubara, 1993, Physica B 186-188, 150.

Tang, J., 1989, PhD Thesis (Iowa State University). Tang, J., and K.A. Gschneidner Jr, 1989, J. Less-

Common Met. 149, 341. Umehara, I., Y. Kurosawa, N. Nagai, M. Kikuchi, K.

Sato and Y. Onuki, 1990, J. Phys. Soc. Jpn. 59, 2848.

Umehara, I., N. Soc. Jpn. 60,




Umehara, I., T. Satoh and Y. 19.

Nagai and Y. 0nuki, 1991a, J. Phys. 1294. Nagai and Y. Onuki, 1991b, J. Phys. 591. Nagai and Y. 0nuki, 1991c, J. Phys. 3150. Nagai and Y. Onuki, 1991d, J. Phys. 1464. Ebihara, N. Nagai, Y. Fujimaki, K. 0nuki, 1992a, J. Phys. Soc. Jpn. 61,

Umehara, I., T. Ebihara, N. Nagai, K. Satoh, Y. Fujimaki and Y. Onuki, 1992b, J. Phys. Soc. Jpn. 61, 1633.

Umehara, I., N. Nagai, A. Fukada, K. Satoh, Y. Fujimaki and Y. 0nuki, 1992c, J. Magn. & Magn. Mater. 104-107, 1407.

van der Meulen, H.E, A. de Visser, J.JM. Franse, T.T.J.M. Berendschot, J.A.AJ. Perenboom, H. van Kempen, A. Lacerda, R Lejay and J. Flouquet, 1991, Phys. Rev. B 44, 814.

van Deursen, A.J.E, R.E. Pols, A.R. de Vroomen and Z. Fisk, 1985, J. Less-Common Met. 111,331.

Wasserman, A., M. Springford and A.C. Hewson, 1989, J. Phys. Condens Matter. 1, 2669.

Wilson, K.G., 1975, Rev. Mod. Phys. 47, 773. Windmiller, L.R., and LB. Ketterson, 1968, Rev. Sci.

Instrum. 39, 1672. Yamada, K., K. Yosida and K. Hanzawa, 1984, Prog.

Theor. Phys. 71, 450. Yamagami, H., and A. Hasegawa, 1990, J. Phys. Soc.

Jpn. 59, 2426. Yamagami, H., and A. Hasegawa, 1991, J. Phys. Soc.



Jpn. 62, 592. Yosida, K., 1957, Phys. Rev. 106, 893. Zwicknagl, G., E. Rtmge and N.E. Christensen, 1990,

Physica B 163 97.

Handbook on the Physics and Chemistry of Rare Earths Vol. 20 edited by K.A. Gschneidner, Jr. and L. Eyring © 1995 Elsevier Science B.V.. All rights reserved

Chapter 136

THE INTRICATE WORLD OF RARE EARTH THIN FILMS: Metals, Alloys, Intermetallics, Chemical compounds, . . .

M. G A S G N I E R

Centre National de la Recherche Scientifique, Laboratoire de Chimie Mdtallurgique et Spectroscopic des Terms Rares,

UPR 209 CNRS Bellevue, 1, place A. Briand, 92195 Meudon Cedex, France

Co~e~s

Symbols, abbreviations and units 108 1. Introduction 108 2. Rare earth metals 111

2.1. Introductory remarks 111 2.2. Valence changes in rare earths: from

vapor to solid state 111 2.2.1. Introduction 111 2.2.2. R atomic vapor 112 2.2.3. R clusters and surface

characterizations 114 2.2.4. R sub-, mono-, and multi-layers

on oriented crystals t 15 2.2.4.1. Samarium 115 2.2.4.2. Ytterbium 116

2.2.4.2.1. The Yb/Ni system 116 2.2.4.2.2. The Yb/A1 system 116 2.2.4.2.3. The Yb/Mo system 117

2.3. Crystallographic properties 118 2.3.1. Introduction 118 2.3.2. Epitaxial crystal growth 118

2.3.2.1. R/W systems 118 2.3.2.2. R/Re systems 119 2.3.2.3. R/V systems 119

2.4. Electrical properties 120 2.4.1. Crystalline films 120 2.4.2. Amorphous samples 121

2.5. Magnetic properties 122 2.5.1. Crystalline state 122

2.5.1.1. Thin oriented and polycrystalline R films on oriented substrates 122

2.5.1.1.1. W (110) substrates 122 2.5.1.1.2. Fe (100) substrates 124

105

2.5.1.t.3. Cu (100) and Ni (111) substrates 124

2.5.1.2. Polycrystalline films 124 2.5.1.2.1. Ferromagnetic order

at R surface 124 2.5.1.2.2. Ferromagnetic films 125 2.5.1.2.3. Multilayer

(Er, Tm/Lu),-type films 125

2.5.1.2.4. Theoretical models 125 2.5.2. Amorphous films 125 2.5.3. Magnetic domain structures 126

2.6. Optical properties 126 2.6.1. Very low energy range (below

7eV) 126 2.6.1.1. Scandium films and

single crystals 126 2.6.1.2. Yttrium 127 2.6.1.3. Europium, gadolinium,

terbium, dysprosium, holmium, erbium, thulium and ytterbium 127

2.6.2. Low energy range (7-70eV) 128 2.6.2.1. Scandium films and

single crystals 128 2.6.2.2. Yttrium 128 2.6.2.3. Lanthanum and cerium 129 2.6.2.4. Gadolinium, dysprosium,

thulium, and lutetium 129 2.6.2.5. Samarium 130 2.6.2.6. Europium and ytterbium 130 Medium energy range (70- 600 eV) 130

2.6.3.

106 M. GASGNIER

2.6.3.1. Scandium and yttrium 130 2.6.3.2. Lanthanum 130 2.6.3.3. Cerium 131 2.6.3.4. Gadolinium, thulium and

lutetium 131 2.6.3.5. Ytterbium 131

2.6.4. High energy range (beyond 800 eV) 131

2.7. Applications relative to metallic films and foils 132 2.7.1. The piezoresistance response of

Yb foils 132 2.7.2. Diffusion barriers: Sm and Yb

metal interfaces 132 2.7.3. Tunnel junctions: Yb/oxide/p-

InAs 133 2.7.4. Magnetic devices 133

2.8. Metallic or contaminated films or fine particles? Remarks about the fcc phase 133

2.9. Formation and properties of the rare earth hydrides 135 2.9.1. Formation of the hydrides 135

2.9.1.1. Contamination of thin R films 135

2.9.1.2. Residual hydrogen 135 2.9.1.3. Reaction of R elements

with water vapor 137 2.9.2. Physical characteristics 137

2.9.2.1. Electric resistance and resistivity 137

2.9.2.2. Work function 140 2.9.2.3. Surface magnetization 140

2.10. Rare earth deuteride and tritide 140 2.10.1. Bulk materials 140

2.10.1.1. Introduction 140 2.10.1.2. Gettering 140

2.10.2. Thin films 141 2.10.2.1. Scandium and yttrium 141 2.10.2.2. Erbium 141

2.11. Formation of the rare earth nitrides 142 2.12. Reactivity with CO, CQ and CnH .

gases 143 2.12.1. Rare earth/CO and C,H n

interactions 143 2.12.2. Lanthanide/CQ reactions 144

3. Metallic R-alloys 144 3.1. Permanent magnets 144

3.1.1. Introduction 144 3.1.2. [R(Pr, Nd),R'(Dy)]xFeyBz alloys 145

3.1.2.1. Magnetic properties 145 3.1.2.1.1. Thick and thin films 145

3.1.2.1.2. Multilayers and modulated films 146

3.1.2.1.3. Magnetic domains 147 3.1.2.2. Hydrogen treatments 148 3.1.2.3. Microstructural

properties 150 3.1.2.4. Other compounds:

RFe(N or C) 151 3.1.2.5. NdH Fe4B 4 152 3.1.2.6. AI, Cr, Mn, Ga, Nb,

Zr, Cu and W addition effects 152

3.1.2.6.1. AI addition 152 3.1.2.6.2. Cr and Mn additions 153 3.1.2.6.3. Ga addition 153 3.1.2.6.4. Nb addition 153 3.1.2.6.5. Zr addition 153 3.1.2.6.6. Si addition 153 3.1.2.6.7. W addition 155

3.1.2.7. Applications 155 3.1.3. RTiFe(Co) alloys (R=Sm, Nd,

Dy) 155 3.1.3.1. (Sm, Nd)TiFe magnets 155 3.1.3.2. (Sin, Dy)TiCo magnets 155

3.1.4. Smx(Co, M)y substituted alloys (M=Fe, Cu and Zr) 156

3.1.5. RCo(B) amorphous films 156 3.1.5.1. Sm~Col0o_x alloys 156 3.1.5.2. Amorphous NdCoB

magnetic thin films 157 3.1.5.3. Applications 157

3.2. (TM/R)n modulated and multilayered films. (R = Y, La, Ce, Nd, Gd, Tb, Dy; TM=Fe, Co, Ni) 157 3.2.1. fie/R), films 157

3.2.1.1. (Fe/Y),, 157 3.2.1.2. (Fe/La), layers 158 3.2.1.3. (Fe/Nd), and (Fe/Dy),

films 158 3.2.1.4. (Fe/Gd), films 159 3.2.1.5. (Fe/Tb), films 160 3.2.1.6. (Fe/Nd, Er, Tm), films 161 (Co/R), films 162 3.2.2.1. (Co/(Pr, Nd)), films 162 3.2.2.2. (Co/Gd), films 162 3.2.2.3. (Co/Tb), films 164 3.2.2.4. (Co/Dy), films 164

3.2.3. (Ni/R), films 165 3.2.3.1. (Ni/Ce), layers 165 3.2.3.2. (Ni/Dy), layers 165

3.2.4. Other multilayer systems 165

3.2.2.

THE INTRICATE WORLD OF RARE EARTH TH1N FILMS 107

3.2.4.1. YCo/(Nd, Gd, Er)Co/YCo sandwiches

3.2.4.2. (TbFe/Ni-Fe-Mo) bilayer films

3.2.4.3. (PtMnSb/TbFe) bilayer films

3.2.4.4. (Fe/TbFe) bilayers 3.2.4.5. (Zr-Fe/TbFe)~

amorphous multilayers 3.2.4.6. (ZnS/GdFe) multilayers 3.2.4.7. (TbFe/SiO), muttilayers 3.2.4.8. Insulating/magneto-

optic/insulating systems 3.2.4.8.1. Si3N 4 3.2.4.8.2. SiO2/GdTbFe 3.2.4.8.3. Dielectric/Nd-Dy-

Fe~2o-Ti/Si3 N 4 - A1N on plastic

3.2.4.9. Amorphous (TbxFel_x/A1203)n multilayers

3.2.5. Formation of sandwiched layers: R(Dy, Tb) ions implanted in Fe and Ni films. Structure and magnetic properties

3.3. R-Fe,Co/hydrogen and other gaseous contaminants: changes in magnetic properties

3.4. RNi 5 and RC% as hydrogen storage films 3.4.1. LaNi 5 alloy

3.4.1.1. Hydrogen absorption - Crystalline states

3.4.1.2. Electric resistivity 3.4.1.3. Hydrogen separation and

permeation 3.4.2. Other RNi 5 alloys 3.4.3. RC% alloy (R = La, Sm) 3.4.4. Remark

3.5. Polytypic structures 3.5.1. Ferromagnetic samarium-nickel

alloys 3.5.2. Samarium-cobalt alloys 3.5.3. Rare earth trialuminides

3.6. R-noble metal alloys 3.6.1. The R-Cu system

3.6.1.1. Amorphous R-Cu films (R = Y, Tb, Dy)

3.6.1.1.1. CUxYI_ ~ 3.6.1.1.2. Dy-Cu and Tb-Cu 3.6.1.1.3. Cu addition to Tb-

Fe-Co

3.6.1.2. Crystalline R-Cu films 165 (R =Y, Ce, Dy, Ho, Er

and Yb) 178 165 3.6.1.2.1. (Cu/Y), 178

3.6.1.2.2. Ce/Cu interface 178 165 3.6.1.2.3. Cu-Dy, Cu-Ho, Cu- 166 Er 179

3.6.1.2.4. Yb/Cu 179 I66 3.6.1.3. R-Cu samples as 166 precursors for synthesis 166 catalysts 179

3.6.1.4. Ion-beam mixing 180 166 3.6.2. The R-Au system 180 166 3.6.2.1. Amorphous GdAu and 166 GdFeAu films 180

3.6.2.2. Crystalline films 180 3.7. R-Pd alloys (R=Ce, Eu, Er, Yb) 18I

166 3.7.1. Valence change in R-Pd alloys 181 3.7.1.1. Ce-Pd amorphous

crystalline samples. 166 Comparison to other

materials 18 I 3.7.1.2. Eu and Yb-Pd

amorphous specimens 182 167 3.7.2. Rx-Pdy crystallographic

properties 182 3.8. Superconducting materials 184

167 3.9. Miscellaneous R-M alloy films and thin crystals 185

169 3.9.1. Y, La-Pb multilayer samples 185 169 3.9.2. Transport properties in U-R films

(R = ad, Yb) 185 169 3.9.3. Quasicrystal Co-Er alloys 185 170 4. Metalloid R-compounds 186

4.1. Rare-earth chalcogenide and bismuth 171 systems 186 172 4.1.1. RAs films (R=Tb, Dy, Er, Yb 172 and Lu) 186 172 4.1.1.1. ErAs, ErxScl_xAs and 172 ErP, As~_ x specimens 186

4.1.1.2. YbAs films 187 173 4.1.1.3. Yb-As2S 3 films 187 174 4.1.2. RSb films (R=Sm, Tm, Yb) 188 177 4.1.3. RBi films (R=Gd) 188 177 4.2. Pb(Eu, Yb)(Te, Se, S) thin films 188 177 4.2.1. Lead--europium films 188

4.2.2. Lead-ytterbium films 190 177 5. Conclusion 190 177 References 190 178

178

108 M. GASGNIER

Symbols, abbreviations and traits

AES Auger electron spectttm MBE bee body centered cubic M s dhcp double hexagonal close packed Pa Eg energy gap R e-beam electron beam RBS e-gun electron gun rf EDP electron diffraction pattern RHEED EDX energy dispersive X-rays SQUID EELS electron energy loss spectrum ESR electron spin resonance STEM fcc face centered cubic H c coercive force or coercivity T hcp hexagonal close packed Tc HREM high resolution electron microscopy TCR kAm -1 12.5 Oe (1 kOe=80kAm -1) TEM K u uniaxial magnetic anisotropy (uniaxial TM

perpendicular energy) UPS L Langmuir (deposit at XAS

10 -6 Torr s = 1.33 x 10 -4 Pa s) XPS LEED low-energy electron diffraction XRD

molecular beam epitaxy saturation magnetization 133.33 Torr rare earth elements Rutherford backscattering radio frequency (sputtering) reflection high-energy electron diffraction superconducting quantum interference device scanning transmission electron microscope Tesla (10 kGauss) superconducting transition temperature temperature coefficient of resistance transmission electron microscope transition metal ultraviolet photoemission spectroscopy X-ray absorption spectroscopy X-ray photoemission spectroscopy X-ray diffraction pattern

1. Introduction

During the last decade numerous papers have reviewed and commented the main physical and chemical properties o f the rare earth elements. Eyring (1979), Gasgnier (1980, 1989) and Boulesteix (1982, 1984) have reported the main characteristics o f the sesquioxides (R2 03) and o f the intermediate oxides (ROx, with R = Ce, Pr and Tb, and 1.5 ~<x ~ 2). Netzer and Bertel (1982) and Netzer and Matthew (1987) have provided much informations relative to the surface reaction (adsorption), valence and electronic states and catalysis properties o f rare earth metal alloy, hydride and oxide as thin samples. The characteristics o f rare earth compounds (sulfides, silicides, borides, . . . ) have been reviewed by Gasgnier (1989). Eschenfelder (1980a, 1980b), Gasgnier (1982), Buschow et al. (1982) and Busehow (1984) have presented a large number o f results on the rare earth-3d transition metal alloys as amorphous or crystallized thin and bulk materials. The properties of permanent magnets, superconductors (other than those o f the new high-To ceramics) and magnetic multilayers have been reviewed by Burzo and Kirchmayr (1989), Coey (1991) and Gasgnier (1991).

Before investigating the results given in the literature, one must emphasize three main problems which seem to be always in competition. Indeed, and in spite of the numerous reliable experimental results and theoretical studies published by several research groups,

THE INTRICATE WORLD OF RARE EARTH THIN FILMS !09

"strange" and "extraordinary" new properties are always being reported now and again in different articles.

The first problem is relative to the oxidation state, and we should like to exclaim: "poor rare earth valency!". So, recently, Savrin et al. (1988) have reported an tmexpected series of oxides as Pr2Os, Nd205 and Nd6Oll. However, a careful survey of the published X- ray diffraction patterns shows that these "compounds" correspond to Pr(OH)3, Nd(OH)3 and C-Nd203 respectively. The misappreciation of the oxidation states of the R elements is hardly understandable. Indeeed, the authors claim that the Pr and Nd oxidation states correspond to the electronic 4f3(6s 2) and 4f4(6s 2) structures, respectively, and therefore they conclude that these elements have a +5 valence, includingf electrons in the valence band. Such electronic configurations are known to be related to the neutral atoms, but in the elemental metallic state the basic configuration becomes 4fn(5d16s 2) except for Eu and Yb which retain the 4fn(6s 2) configurations (n = 7 or 14). To explain the valences of the R elements, one must recall the works of D.A. Johnson (1969, 1977) who has studied the stability of the RC12 compounds with respect to the disproportionation reaction:

3RC12(s) + R(s) --+ 2RC13(s).

The dichlorides are stable if the change in free energy is positive. The following order for the relative reducibility of the lanthanides has been deduced: Eu, Yb, Sin, Tm, Dy, Nd, Ho, Er, Pr, Tb, Ce, Gd and La. In this way, one can remember the useful classification of the R elements:

Eu

Yb, Sm, Tm

La to Lu (incl. Sc + Y)

Ce, Pr, Tb

Ce, Pr, Tb

pure +2 (EuO)

+2 with S, Se, Te (very unstable with 02)

+3 (R203)

+4 (Ro2)

+3 --+ +4 (ROx) Under standard conditions of temperature and pressure it is not possible to obtain other oxides.

The second problem concerns the reactivity of the lanthanides. Numerous research groups have demonstrated that they are excellent getters for hydrogen and that they can absorb (OH)- radicals. But such properties often remain misappreciated, and numerous physical and chemical results and interpretations are then hidden or altered. Indeed, the hydrides or the hydroxides can be formed as chemical compounds either at the surface of a sample or at grain boundaries. This getter effect is strongly enhanced in the case of thin films which are characterized by a large surface/volume ratio. Besides, in the case of multilayer sequences, the interface between two different materials must be carefully studied. Two phenomena can occur concurrently: one is relative to the cation and/or anion diffusion and the other to the possible formation of chemical compounds and alloys. So, in the case ofW/C/W/C.. , as a stacking sequence, the formation of a WxCyOz compound (0.5-1 nm thick) has been observed at ambient temperature (Gasgnier et al. 1983). In the same way, the formation of passivation thin films, even if their thickness does not exceed

110 M. GASGNIER

some 10nm, becomes a "poison" for some physical measurements. A rapid calculation, in the case of a film with a thickness of about 100nm, demontrates that about 10% of the total thickness is far from the "ideal" metallic material. Therefore, many times it is difficult to neglect the formation of thin contamination films at the interfaces.

The last problem is relative to the crystallographic phases. They are often deduced from electron diffraction patterns (EDP's). Various phenomena which occurred in the course of the study of thin samples are sometimes badly known, or else the patterns can be misinterpreted and the indexation becomes wholly wrong. Recently Z. Li et al. (1988) have claimed to the formation of new polymorphic erbium oxide phases. These were in fact the well-known ErH2, C- and B-Er203 compounds (Gasgnier 1980, 1990). Other misinterpretations result from decided opinions on chemical reactivity, phase transitions, compound formation (as Lu(OH)4 for example) (Gasgnier 1991) . . . and/or on disorder between two crystallographic phases. The rare earth series display basic chemical and physical properties which are now well established. Moreover, the new micro- (and even nano-) analysis apparatus should be used in a systematic way to insure accurate determination of the specific properties of the materials.

Another remark must be made: it is appropriate that authors should report all the pertinent references in their articles, but many times this is not the case. So, it is often observed that compounds like SmO (this one is something of a "myth" for numerous authors) and Sm20 (Eick et al. 1956, Ellinger and Zachariasen 1953) are always taken into account. However a later paper of Felmlee and Eyring (1968), which demonstrated that these compounds are actually SmNl_xOx and SmH2, respectively, is never listed. As an example, one can mention the results of Tkach et al. (1980) who claim to the formation of SmO (with a fcc parameter as a = 0.502 nm) instead of the SmNl_xOx compound. In the same way one can add that these authors have "deduced a new Sm-hcp metallic phase", which is in fact the dhcp phase (Gasgnier 1980) which seems fully unknown to them. A second example is also noteworthy: Curzon and Chlebeck (1972, 1973) had, at first, claimed that rare metal films crystallized as a new fcc phase. However, later on (see Gasgnier 1980 for accurate comments) they agreed to have been confused and concluded that this phase was in fact the rare earth dihydride. These authors have published a large number of papers which refer to the dihydride films, but others only reference the first articles. So the following questions can be put: "Why is the gettering action of R elements for hydrogen neglected and/or ignored by some research groups? Is it to fit some theoretical results?" In conclusion one can notice that the second example overlaps the three problems discussed in this Introduction. These remarks allow us to understand why some properties of rare earth elements have always been the subject of hard polemics and debates.

Therefore, our purpose is to demonstrate that the physical and chemical properties of rare earth metallic and rare earth alloy thin films or single-crystals must be cautiously analyzed. Particularly, the lack of crystallographic spectra (X-ray or electron diffraction), of chemical analyses (absorbed or adsorbed gases, surface contamination, impurities,... ), of structural investigations (grain size, defects . . . . ) for example, is truly detrimental to precise characterization of the materials. In this way one can claim that numerous

THE INTRICATE WORLD OF RARE EARTH THIN FILMS 111

polemics become unfruitful because the arguments of the different authors are often strictly not convincing.

2. Rare earth meta ls

2.1. Introductory remarks

For about twenty years the problem of the purity of rare earth metals either as thin films, or thin particles, or thinned materials is a matter of fact. These metals are quite sensitive to various gaseous contaminants. So, processes like vacuum deposition, annealing, aging, and thinning treatments either under vacuum or at ambient atmosphere, must be carried out very cautiously. Consequently the possible formation of chemical compounds and/or surface or volume contamination might be proven. So, one can point out that the experiments of Onsgaard et al. (1979), Onsgaard and Ignatiev (1982) and Tougaard and Ignatiev (1981) have shown that the (10.0) and (00.1) single crystal surfaces of scandium exhibit segregation of impurities like S, C1, C and O. After heating (between 813 and 1213 K) and/or krypton ion bombardment a clean Sc surface has been obtained, as demonstrated by the Auger spectra. Another example is from SIMS measurements by Reichl and Gaukler (1986). At the surface of a Y evaporated film the following species have been observed: YH +, YHO +, YO-, YO] and Y203. It is unlikely that the presence of such poisons, and also that of composite materials (e.g. metal + hydride and/or oxide) are always verified, and thereby the physical and chemical properties are changed compared to the ones of the pure bulk metal.

2.2. Valence changes in rare earths: from vapor to solid state

2.2.1. Introduction

The problem of mixed-valence behavior which is sensitive to particle size has been studied for Sm, Tm and Yb metals. A review paper by Connerade and Karnatak (1990) points out, for vapors and clusters, the main calculations and interpretations which have been done to explain this property. The authors report numerous XAS results which demonstrate experimentally the valence change with cluster size.

Netzer and Bertel (1982) have given numerous results relative to the mechanism of surface oxidation. A theoretical approach of valence fluctuations has been done by B. Johansson (1979) and Rosengren and Johansson (1982 and refs. therein). The latter is a review paper which allows to have a good understanding of the main results and hypotheses published up to this date. Before discussing the results, one must add the following remarks. The first was made by B. Johansson (1979): "This means that experimental results, obtained from a surface-sensitive technique, must be carefully analyzed before a specific structure of the spectrum can be said to originate from the bulk or the surface, respectively". The second one is that the divalent state of Tm has not been convincingly demonstrated up to this date.

112 M. GASGNIER

2.2.2. R atomic vapor

The problem of the electronic (or ionic) configurations for the three different states of the R elements: vapor, metal and oxide, has been described in detail by Gsehneidner (1971), Gschneidner and Daane (1988), Gschneidner et al. (1990), and Beaudry and Gsehneidner (1978). In the gaseous state two types of configuration are encountered:

(1) 4fn(5d16s 2) for La, Ce, Gd and Lu [Sc with 3da4s 2, and Y with 4d15s 2 must be added]. This is the normal configuration whieh leads to a difficult reducibility of the elements (see D.A. Johnson 1969, 1977).

(2) 4fn+d(6s 2) which is the most common configuration for Pr--+ Eu and Tb ~ Yb. In the metallic state the configuration change leads to the following electronic states: (1) 4fn(5d16s2), i.e., the normal trivalent state for Sc, Y, La --+ Sm, Gd ~ Tm and Lu. (2) 4fn(6s 2) for Eu and Yb, i.e., the divalent state and the more reducible metals of

the R series (see D.A. Johnson 1969, 1977). The first experimental absorption spectra have been reported by Materlik et al. (1983b).

The LIII (2p --+ 5d transition) absorption edges of Ce, Sm, Gd and Er as vapors and metals are compared. From previous works (Materlik et al. 1983a), it is asserted that Sm and Gd to Lu metals exhibit similar white lines well described by the ground-state potential and that no major redistribution of the valence electrons occurs. (The authors demonstrated that the white line and the near-edge structure can be well described by a single-particle band-structure calculation.) In the case of metallic vapor of Ce and Gd the Lni edges almost coincide with those of the metal. In contrast, for Sm, and Er, the peak of the white line is shifted towards higher energies by about 8 eV. In the same way the LI spectra give identical results (shift of about 5 eV). The authors conclude that a configuration change occurs for Sm and Er (4f6--* 4f 5 and 4f~2--~ 4f 11, respectively) upon solidification.

Blancard et al. (1989, 1990a,b), Sarpal et al. (1991) and Connerade and Karnatak (1990) have carried out accurate experiments to establish the valence of Sm and Tm vapors. The Mw-v (3d--+ 4f transitions) edges recorded by XAS show that Sm and Tm atoms have characteristics of the +2 valence state. This is well demonstrated by a remarkable evolution in the spectra as one changes from the atomic vapor to matrix-

. . . . . . i b . . . . . . i b~ . . . . . i b 3 . . . . . .

1 i ~ i u

Fig. 1. The evolution of valence (by adding 2 to IAnl) with cluster concentration for Sm (solid squares) and Tm (open squares). (The term cluster size relates to the average number of atoms in the first coordination cell, as revealed by EXAFS.) (By courtesy of Drs. R.C. Karnatak and J.M. Esteva, Univ. Paris-Sud, LURE, Orsay, France).


Tm CLUSTERS NIv ,.~

:%. : ". ;. SOLID

. . . . __1 ....--. " v . . . . . . . _ _ / "x . ," ' - ~(~/Tm) = 8o:1

_ _ _ _ . j . . . . . " . ,;" X._,." "< R'(Ar/Tm)=221:l

/ " .

:' " R'(Ar/Tm) = 3346:1

"" "" " ". R(Ar/Tm)=5085:1 . , . , ~ ' . , ' v~ ' : , : . . . . " , . , . , ~ , :

4 5 5 1 4 6 0 1 4 6 5 1 4 7 0

a Photon Energy (eV)

M v Samarium

M IV

1060 1070 1080 1090 1100 1110 1120

b PHOTON ENERGY(eV)

Fig. 2. (a) The 3d (Mv) spectrum of Tm showing the evolution from the vapor to the solid via intermediate concentrations of trapped clusters for Tm in At. (b) The 3d (Mw_v) spectra of Sm: comparison between the (1) vapor and (2) condensed phases. (By courtesy of Drs. R.C. Karnatak and J.M. Esteva).

isolated atoms, clusters and solids. In the case of atomic Sm vapor, it is observed that the 3d spectrum is close to that of SINS. It is concluded (figs. 1-3) that the localized

am

, i

= S m 2 + Mv ::

• , MIv

L~]~ ~'~ Vaponr (1300°K) / ~

SmS(lO0) ( 2 9 3 o K ~

: %

: ".."" r=2300:1 (10°K). '~ , " " " " " . . . . ' " " ' : "

1070 1090 1110

Photon Energy (eV)

Fig. 3. Comparison between the 3d spectra of Sm vapor, SInS solid and Sm in clusters for two different concentrations ~ (argon to samarium ratio). Notice that at very low concentrations muttiplets are present. (By courtesy of Drs. R.C. Karnatak and J.M. Esteva).

114 M. GASGNIER

excited states possess properties similar to those in the solid. The spectra are interpreted according to the multiconfigurational Dirac-Fock calculations.

2.2.3. R clusters and surface characterizations

Mason et al. (1981) have studied Sm clusters prepared by vapor deposition onto amorphous carbon. XPS and UPS data show that Sm is primarily divalent in the smallest particle sizes. The trivalent state appears as the size increases and becomes the dominant state for the bulk metal. For Sm, Nd and Pr clusters isolated in matrices of Ne, Ar and Kr (freezing at 5 K), Niemann et al. (1986, 1987) and Liibcke et al. (1986) show, from the Lm edge spectra, that for Sm a valence transition occurs at 1% metal concentration (from +2.0 to +2.6) with a critical cluster size of 13 atoms. For clusters consisting of more than 20 atoms the average valence approaches +3. For Pr and Nd a complete valence change occurs within an atomic concentration range of 0.10-0.25% metal content, and clusters containing more than 5 atoms are totally trivalent. Chorkendorff et al. (1983) have studied AES and energy-loss spectra of Yb vapors. It is demonstrated that the N4,sN6,7N6,7 Auger transition can be interpreted by using an independent particle description. Experimental and calculated results agree reasonably between them. The 16.10 eV metal-vapor Auger energy shift can be explained by a thermochemical model. The relative energies and intensities of the individual Auger lines are found to be essentially the same for the vapor and the solid phases. The quasiatomic rather than the band-like model allows to describe correctly the solid-state spectra. Brrchignac et al. (1991) have studied the generation of Sm, Eu and Yb metal clusters by means of the gas-aggregation technique. They draw attention to the transfer of a 4f-localized electron to the 5d-delocalized orbital as cluster size increases, and second to the interplay between the electronic structure of the clusters and their stability. As a function of temperature (4.2-10 K) the mass spectra exhibit different nucleation conditions. It is suggested that a rapid cooling favors icosahedral clusters structures (see also Rayane et al. (1989) in the case of Sm clusters), whereas smooth cluster growth induces the R bulk structure. The authors conclude that it is not straigthforward to correlate cluster stabilities and electronic structures.

The experiments of Blancard et al. (1989, 1990a,b) and Connerade and Kamatak (1990) show clearly that Sm and Tm clusters imbedded in an Ar matrix (10K) exhibit a +2 valence for very low dilutions (figs. 1-3). Two main conclusions arise from these results: First, surface divalency in metallic Tm occurs only on rough surfaces where the atoms have reduced coordination numbers, as observed by Domke et al. (1986) for Tm sputtered films (100nm thick) deposited onto copper substrates at 300 or 13 K. Second, the previous interpretation of Thole et al. (1985) for Sm is not consistent with the new results. Indeed, the Hartree-Fock calculation cannot explain transitions from the Sm 4f 6 ground state and the observed 3d-4f multiplet structure for Sm atoms and small clusters at low teperature. So, multiconfigurational Dirac-Fock calculations (unsealed "ab initio" calculations) have been performed to understand the 3d-4f spectra. It is also concluded that for Sm clusters the divalence is found to stabilize for a coordination of 8-10,


whereas it is only 6-7 for Tm. The latter result has been determined in the case of rough surfaces by Domke et al. (1986). They report from photoemission measurements that films deposited onto smooth surfaces are purely divalent, whereas in the case of a rough surface small divalent components (low-coordinated atoms) are well observed.

Previously B. Johansson (1979), L.I. Johansson et al. (1981), Lang et al. (1981), Kaindl et al. (1983) and Gerken et al. (1985) concluded that, whatever the substrates, thin Tm films stay trivalent. A systematic study of the lanthanide series from Ce to Lu has been carried out by Gerken et al. (1982, 1985) and Kammerer et al. (1982), who report XPS and 100 eV phonon energy spectra to investigate the surface core level shifts. The 4f emission from the surface layer atoms and the bulk atoms exhibits clearly separated structures with different binding energies. For Sm they conclude to a well-defined surface divalent state. One must point out the work of Strasser (1988) who has studied the 4d core electron and valence excitations by EELS. It is shown that Sm is divalent at the surface and trivalent in the bulk. Wieliczka and Olson (1990) have observed, for Sm (2-200 nm)/Cu bilayers, a heterogeneous mixed valence state in Sm. From energy distribution curves it is concluded that the surface layer is completely divalent, with the underlying layers being trivalent. The divalent intensities recorded increase with the initial stages of Cu diffusion throughout the Sm film. The anomalous diffusion indicates that the Cu distorts the Sm lattice to an extent which allows for a trivalent to divalent transformation. It is also demonstrated that no Cu-Sm alloys are formed.

One can conclude, first that for Sm the divalent and mixed-valence characteristic surfaces have been well recognized (Wertheim and Creeelius 1978, J.W. Allen et al. 1978, 1980, Gerken et al. 1982, 1985, den Boer et al. 1988); and second that this character is only observed in Tm for some particular cases (vapor, clusters, and films deposited onto rough surfaces).

2.2.4. R sub-, mono-, and multi-layers on oriented crystals

2.2.4.1. Samarium. F~ildt and Myers (1983, 1984a,b, 1985, 1986) and F~ildt et al. (1988) have studied the mixed-valence state of Sm onto A1 [(001) and (111)]-, Cu (001)- and Pd (001)-oriented single-crystals. From LEED and XPS (3d5/2 spectra) measurements it is shown that isolated Sm atoms adsorbed onto A1 (111) have an intermediate valence of+2.40. For a Sm monolayer the valence reaches +3. On A1 (001) and Cu (001) surfaces the valence states of one monolyer are 2.95 and 2.70 respectively. The mixed valence is homogeneous for Sm onto Cu (001). Surprisingly a weak component [Sm on A1 (001)] has been interpreted to be associated with a Sm 4+ valence state, which is not possible of course (see the Introduction and Connerade and Karnatak 1990). In the case of Pd (001) substrates XPS shows that Sm exhibits a completely +3 state, similar to A1 [(001) and (111)] substrates. The valence decreases with coverage and saturates at the value 2.75, that might be due to charge transfer between adsorbate and substrate.

On the contrary, Andersen et al. (1988) report, from XPS study of Sm on a Cu (100) single-crystal surface, that the mixed valence of Sm is of a heterogeneous nature. This suggests that such a conclusion also applies to A1 [(111) and (100)] surfaces. This is

116 M. GASGNIER

also supported by Wieliczka and Olson (1990). The heterogeneity results from a divalent surface layer and a trivalent intermetallic compound. However, according to Jaffey et al. (1989), the observation of mixed valence associated with a single overlayer structure as found for the SrrdCu (111) system, indicates that a homogeneous mixed valence can exist. But, at other coverages, and after annealing, more than one phase will form, (SmCu and SmCus) and heterogeneous mixed valence will be observed. These authors assert that valency variations may have consequences for both the energy and intensity of the Auger transitions. A correlation between LEED intensity and Auger intensity ratio during Sm uptake at 300K is reported. A scheme of the structures observed in LEED after annealing is given.

Andersen et al. (1988) explain the results of Ffildt andMyers (1983, 1984b, 1986) by the fact that Sm and Cu or AI form intermetallic compounds. Stenborg and Bauer (1987a) also discuss these results in terms of the average coverage and not of atomic distribution. They observe that Sm has a pronounced tendency to form islands on Mo (110) surfaces. They conclude, from low EELS measurements, that changes in the electronic structrure do occur as a function of coverage but these cannot be interpreted unambiguously in terms of a valency change. In the case of Sm monolayers deposited onto Mo (110) substrates, Stenborg and Bauer (1987a, 1988) have observed, from EELS measurements, that the two volume plasmon losses are respectively attributed to divalent and trivalent Sm.

2.2.4.2. Ytterbium. 2.2.4.2.1. The Yb/Ni system. Heterogeneous mixed-valence and compound formation in ordered Yb/Ni (100) and (110) overlayers have been studied by Chorkendorff et al. (1985a,b), Andersen et al. (1987) and Nilsson et al. (1987, 1988). From various spectroscopic analyses the authors report structural investigations for films grown at 300K or at 673 K. The results demonstrate the importance of surface compound formation. It is concluded that, at 300 K the interface exhibits a simple layer-by-layer growth, whereas at 673 K three types of coverage are observed: at low coverages Yb is found to be absorbed on the Ni surface (hexagonal overlayer incommensurate with the Ni (100) surface); at higher Yb coverages (less than a full monolayer) there is formation of a surface intermetallic compound; and with further deposition a three-dimensional crystallographic system growth (formation of the compound). As a function of the temperature treatments it is demonstrated that Yb changes valency from +2 to +3 in the bulk, whereas a stable divalent layer remains at the interface. Lastly, XPS measurements show that the 5p level resonates strongly at 181 eV as a consequence of the 4d-4f giant resonance. 2.2.4.2.2. The Yb/AI system. Spectroscopic and structural investigations of Yb/A1 (110) and Yb/A1 (100) interfaces have been studied by Chorkendorff et al. (1985a), Nyholm et al. (1984), Onsgaard and Ellegaard (1984), Onsgaard et al. (1984), Tibbetts and Egelhoff (1980), and Egelhoff and Tibbetts (1980). In the case of the Yb/A1 (110) system it is concluded that Yb in Yb-A1 alloys forms homogeneous-mixed-valence compounds, and that island growth and/or diffusion play an important role. It is also found that Yb persists in a divalent state at the surface independently of the concentrations. Two compounds as


YbAI2 and YbA13 can be formed. For the Yb/A1 (100) system it has been found that the pure Yb surface layers exhibit only the valence two, whereas a mixed-valent state (YbA13) begins after heating above 423 K. Further annealing above 623 K causes the Yb to revert to the divalent state. In the case of single crystals Kaindl et al. (1982, 1983) report that YbA12 has a mean valence of 2.4 and that the two surface layers are divalent.

~055

<£

20.50

045 <~

> LJ

cz 0.40 LaJ LLJ

i i

-CLOSEPAEKED~ "~ e _- • FROM CRYSTAL DATA •F •

,/ Yb / Mo(110)

~ ( 1 0 x 2 )

10 1L5 2~0 a DEPOSITION TlME(min)

25

@ @too~]l © @

i [1~ol

Fig. 4. (a) Coverage as deduced from a LEED pattern as a function of deposition time: crosses, n x 2 structure; solid circles, hexagonal structure. (b) Model of the 10x2 structure (letters a~t). One half of the unit mesh is shown with the correct relative size of Yb and Mo atoms. (By courtesy of Prof. E. Bauer, Physikalisches Institut, Univ. Clausthal, 3392 Clausthal-Zellerfeld, Germany).

2.2.4.2.3. The Yb/Mo system. Stenborg and Bauer (1987a,b, 1988) and Stenborg et al. (1990) have studied the adsorption of Yb onto Mo (110) crystals. It is deduced from LEED and different spectroscopic measurements that the number of nearest neighbors may be changed from 0 to 12 going from a two-dimensional gas of individual atoms (one- dimensional system), to a two-dimensional condensate with adjustable density and finally to a metallic multilayer system. This permits one to link dimensionality and electronic structure. From LEED patterns, the "LEED coverages" are obtained by assuming that cell sites in the adsorbate lattice are occupied. The nx2 and 10x2 structures are observed for a "coverage" from 0.40 to 0.45, and then the hexagonal structure is formed (fig. 4a). The coexistence range of the two structures is small. Different possible models of the 10x2 structures are shown in fig. 4b. The authors conclude that intermixing with the substrate does not occur in the submonolayer range. Some results are given in terms of the comparison &the 4fphotoelectron spectra relative to one Yb monolayer and to a thick film: differences in line widths for various temperatures are caused only by vibrational (of phonon) broadening. From EELS data the volume plasmon loss at 9.40 eV shows that Yb is divalent in agreement with the results of Colliex et al. (1976) and Onsgaard and Chorkendorff (1986).

118 M. GASGNIER

2.3. Crystallographic properties

2.3.1. Introduction Since about ten years few new data have been reported about the rare earth phase diagrams (Gasgnier 1980). One can only mention the case of cerium for which some new transitions have been observed at high pressure and high temperature (Gschneidner 1985).

Among the broad literature which deals with rare earth metals, as thin films, few of them exhibit clear XRD and/or EDP results. One can notice, for instance, that the patterns exhibited by O. Nakamura et al. (1988) and Hauser (1985) define pure Gd and Tb thin films respectively. However, W.D. Schneider et al. (1983) assert that their Yb films crystallize in the metallic (hop + fcc) phases without XRD proof. Likewise Kosak et al. (1987) do not report crystallographic data in the case of Sc thin films. One should only admit that the films are purely metallic as claimed by some authors (R.E Miller et al. (1979) for instance). However, that is not always the case: Dudfis et al. (1985) have proved from XRD, that the Dy and DyH2 phases can coexist. Moreover, the formation of the sesquioxide cannot be rejected. Mahmoud and el Mandouh (1987) did not find any evidence for the formation ofSc203 from XRD measurements on thick Sc films (see sect. 2.8).

Remark: In the field of structural investigations one must mention the work of Kuzmenko et al. (1972, 1976, 1980, 1984a,b, 1986a,b) and Kuzmenko and Melnikov (1982, 1988) who have studied the amorphous ~ crystalline transition in Yb films. It is observed to occur under particular experimental conditions: application of a perpendicular magnetic field, a flow of helium gas, an oblique deposition; and a short current pulse. The most important parameter is the thickness of the sample. The transition is explained in terms of avalanche (shock) crystallization. However no XRD or EDP data are exhibited and the crystalline phases of the metal (Ice or hcp) are not defined. One must notice that Haussler and Bauman (1980) using a parallel (to the surface) magnetic field do not observe this transition at 4.2 K.

2.3.2. Epitaxial crystal growth 2.3.2.1. R/W systems. Melmed et al. (1984) and Ciszewski and Mehned (1984a-c) have studied surface diffusion of Sin, Eu, Gd and Dy on tungsten by means of field emission microscopy. The crystalline layers have been grown by vapor deposition onto either W emitters or (001)-oriented W single crystal. Optimum growth is studied as a function of the temperature (between 730 K for Eu and 1200 K for Dy). The nucleation sites and the commonly epitaxial relationships are well defined by various field electron micrographs. The epitaxial relationship most commonly observed is (00.1) R (Sm, Gd, Dy) [I (011) W and (110) Eu [I (110) W. Reshentnikova and Yuldasheva (1979) have studied the emission areas of Dy, Ho and Er deposited onto a point single crystal of W.

The adsorption of Gd, Dy and Sc on the (112) surface of a W single crystal has been studied by EM. Gonchar et al. (1987) and Gorodetskii and Shevlyakov (1980), respectively. Various kinds of structure growth have been observed as a function of the ratio of the density of adatoms to the surface density of W atoms. They also found a

THE INTRICATE WORLD OF RARE EARTH THIN FILMS t 19

large difference in the initial heats of adsorption of Gd (close to that of La) and of Dy. V.V. Gonchar et al. (1985) report the atomic structure of submonolayer films fo La absorbed on the (001) or (111) faces of W. The authors have constructed a phase diagram demonstrating the evolution from first-kind phase transitions to the hexagonal structures. [It is also shown that films grow on (011) Cr surface exhibit rather isotropic structures, whereas for (011) W and Nb surfaces they present anisotropic structures. Such differences are discussed in terms of the electronic properties of the three different systems as interactions of adatoms through d-electrons of the substrate.] Gorodetskii and Martynyuk (1989) report that the threshold potential methods allow to detect Sc on polycrystalline W surface, in amounts as small as about 5% of a monolayer.

Other work has been carried out by Mittsev and Mukhuchev (1982, 1983) who investigate the lifetime dependence of Cs adatoms on film thickness of Tm and Sm monolayers deposited onto W substrates. The adsorption of Cs atoms yields data on the growth mechanism of R films on W surfaces. It is assumed first that the binding energy of Sm atoms decreases weakly in the transition from a two-layer film to a three-layer one, and second that the growth of a Tm crystalline phase occurs on the surface of the first layer of atoms and that the concentration in the second layer required for the starting of the growth is low. It is also observed that the lifetime of Cs atoms presents a nonmonotic variation. The surface-coverage dependences of the heat of adsorption and lifetime of Tm atoms on a (100) face of W have been studied by Burmistrova et al. (1983). They conclude that theory and experiment are satisfactory in agreement and that the lifetime is strongly influenced by binary and ternary collisions in the adsorbed film.

2.3.2.2. R/Re systems. Melmed et al. (1984, 1987) have investigated the epitaxial growth from the vapor of Eu/Re systems by means of the field emission microscopy. They assume that besides the classical bcc phase, a metastable fce phase can form. However the latter, consisting of very small crystallites, is metastable. In the case of lanthanum films on a (1010) face of rhenium, Lozovyi et al. (1984 and refs. therein), show that there is a correlation between the surface-density dependence of the heat of adsorption and structural changes. They compare the results with those obtained for other substrates such as (112) W and Mo (Lozovyi et al. 1982).

2.3.2.3. R/V systems. From RHEED measurements Homma et al. (1987a,b), and Yang et al. (1988) have shown that Ce (111) and Dy (00.1) single crystals deposited by MBE onto V (ll0)-oriented films ( -100nm thick), present structural changes as a function of the thickness (from 0.3 up to 15 nm). The surface reconstruction patterns allow to define how these patterns are correlated to the in- and out-of-plane crystal structures. It is observed that the in-plane lattice constant of Dy is approximately 4% expanded relative to the bulk one in the case of 0.4-5 nm thick films. The epitaxy is such that the (11.0) Dy axis is found to be parallel to the (110) V axis. The same orientation is reported for the Gd/Nb system (Kwo et al. 1986).

120 M. GASGNIER

5O0

450

4OO

350

3O0 B d

250 ! 200

150

100

50 0

G

® q)

BULK

500 I000 !500 2000

Thickness ,

Fig. 5. Dependence of resistivity p on the thickness of Y films deposited at 5 x 10 -7 Torr. (By courtesy of Prof. A.E. Curzon, Physics Dept., Simon Fraser Univ., Bumaby, Canada).

2.4. Electrical properties

2.4.1. Crystalline films Curzon and Singh (1979) report anomalous resistivity behavior of yttrium thin films as a function of the thickness (fig. 5). The results are explained in terms of faint contamination (H2, 02) and of defect scattering. So, the results of Kosak et al. (1987), Loboda and Protsenko (1981a,b), Loboda et al. (1980, 1982) and Protsenko (1988), relative to Sc thin layers, must be examined with much wariness (see sect. 2.8).

The temperature and thickness dependence of the electric resistivity of Sin, Dy and Tm thin films (25-370 nm thick) was measured between 4.2 and 300 K by Dud~is and Fehrr (1984, 1987), Dud~is et al. (1985, 1986, 1987a-d, 1990), and J~inos et al. (1987). For Dy films the Nrel temperature and the residual resistivity ratio increase both as thickness increases. The thickness dependence of the spin-disorder resistivity is reported in fig. 6. In the case of Tm samples it is observed that the Nrel temperature increases (from 49 to 54K) and spin-disorder resistivity decreases (from 35 to 10~tff2m) as thickness increases (fig. 7). Such results, and correlations with the crystalline orientations (basal plane of crystallites parallel or perpendicular to the substrate surface) correct the errors made by other investigators (see Gasgnier 1980). On the other hand the resistance ratio as a function of the temperature exhibits different kinds of curves as the thickness varies as measured for Tm films (fig. 8). Different magnetic transitions have been also observed. One can conclude that numerous kinds of anomalies were caused by hydrogen in solution in the metallic matric, in agreement with Dud~is (1991), and also by structure


~- 60 E

E p j-, 5O

40

BULK

t-

I m I

0 iO0 200 300 t[nm]

Fig. 6. Thickness dependence of the spin-disorder resistivity of thin DX films. (By courtesy of Dr. J. Dud~s, Technical Univ., Kosice, Czechoslovakia).

60

5O

BULK

/BULK \

4O -g

%

20

10

I I I

tO0 20O 3OO tInml

Fig. 7. Thickness dependence of N~el temperature T N and spin-disorder resistivity Pm of Trn thin films (By courtesy of Dr. J. Dudfis).

. 3 -12

5

3 2

I I I m I

0 100 200 300 T[K]

Fig. 8. Resistance ratio R]R4. 2 as a function of temperature for 4 Tm films: (1) 16nm thick; (2) 89nm, (3) 189nm; (4) 364nm. (By courtesy of Dr. J. Dud~s).

defects and internal stress. Such parameters, and above all the hydrogen contaminat ion are either omit ted or taken into account separately. Therefore the interpretat ions are often

in d i sagreement with each other.

2.4.2. Amorphous samples K u z m e n k o and Meln ikov (1982) and Kuzmenko et al. (1986b) have shown that on heat ing amorphous Yb films the electric resistivity falls abrupt ly at 15 K, corresponding to the

122 M. GASGNIER

amorphous --~ crystalline transition. When the sample reaches a critical thickness the resistance also decreases rapidly (Kuzmenko et al. 1984a). In another paper Kuzmenko et al. (1984b) report that amorphous Yb films exhibit a positive magnetostriction which decreases sharply with increasing temperature. They conclude that a superconducting transition may occur at low temperature.

2.5. Magnetic properties

2.5.1. Crystalline state 2.5.1.1. Thin oriented and polycrystalline R films on oriented substrates. 2.5.1.1.1. W (110) substrates. Structural magnetic and electronic excitations of epitaxial ferromagnetic Gd (00.1) films deposited onto W (110) clean single crystals have been studied by Weller and Alvarado (1985, 1986, 1988), Weller and Sarma (1986) and Weller et al. (1985a-c). Such substrates provide high surface mobility of adsorbate atoms, and no Gd-W compounds are formed even at 723 K. The growth habit and the surface geometry are generally characterized by AES and LEED for film thicknesses from 0 up to 100 nm. Spin-polarized LEED and magneto-optic Kerr effect allow to demonstrate the existence of a surface-enhanced magnetic order. Clean Gd surfaces are found to order magnetically at temperatures up to 22K above the bulk Curie point (293 K). However this surface temperature falls to the bulk one when the Gd surface is contaminated by 02, H2, CO or CO2 (even under a vacuum of about 10 -8 Pa). Therefore, as also reported by Kolaczkiewicz and Bauer (1986), extreme care must be taken to clean the substrate and the evaporant. The main results given by Weller and Alvarado (1985, 1986, 1988) are as follows. First, the 4f spins of the surface are not ferrimagnetieally coupled to the bulk moments. Second, films grown onto substrates heated at 723 K exhibit a remanent surface magnetization at 200 K. Third, the 4fT(5d6s) 3 --~ 4f8(5d6s) 2 interband transition has been detected. This 4f ~ 5d mechanism has been previouly investigated by Mauri and Landolt (1981) in the case of polycrystalline films and Reihl and Himpsel (1982) for (00.1) films by means of spin-polarized photoemission. Mauri and Landolt (1981) claim that the transition is a strong quasielastic one-electron transition from the 4f 8 state into conduction states (resonant scattering mechanism), while Reihl and Himpsel (1982) explain the data by taking into account the Gd band structure and/or escape cone rules.

On another part, Farle and Baberschke (1987) and Baberschke et al. (1987), from ESR studies, claim that the ferromagnetic ordering temperature is a function of the nearest- neighbor coordinations. For N = 12 they obtain the bulk Curie point; for N = 9, as a semi- infinite system, the surface Curie temperature is 22 K higher; and for N = 6, as a single monolayer, this temperature is 22 K lower. Such results allow one to detect a fraction of a Gd monolayer on a metal surface in the paramagnetic state. However, the Ising model of phase transitions in ultrathin films reported by Aguilera-Granja and Mor~n-L6pez (1990) fails to explain such results.

The theoretical determination of antiferromagnetic coupling and surface state for Gd (00.1) has been studied by Wu and Freeman (1991). It is shown that the surface Gd

THE INTRICATE WORLD OF RARE EARTH THIN FILMS ]23

co ' I ' ' I ' ' I ' ' I ' I ' ' |

f Tb (O001)/W (IlO)

20 -

z _o 15--

_N

~ 10- - d z ft.

TCbTNb

12o 15o 18o 21o 240 270 300

TEMPERATURE (K)

Fig. 9. Electron spin polarization P (%) of the topmost surface layer of 5 nm-thin Tb (00.1)/W (110) films as

a fimction of temperature. (By courtesy of Dr. C. Rau, Dept. Physics, Rice Univ., Houston, TX, USA).

layer expands outwardly by 6% and is coupled antiferromagnetically with the underlying ferromagnetic bulk. The existence of this surface state has been established by D. Li et al. (1991) for 2-4 Gd monolayers (0.6-1 nm) onto W (110) substrates. This indicates the spatial locality of the surface state. It is added that this surface state can be correlated with the development of the Gd bulk band structure which occurs with increasing film thickness as Gd films grow. Salas and Mirabal-Garcia (1989, 1990a) have studied another parameter as the Hopkinson temperature. The "Hopkinson maximum" is the local maximum which the initial magnetic susceptibility presents just below the Curie point (~3 K). The authors claim that Weller and Alvarado (1988) have observed this maximum. But it cannot be detected whether the samples are contaminated. From other works, relative to "butterfly" susceptibility measurements, Salas and Mirabal-Garcia (1990b) concluded to the incoherent character of the magnetization processes at low field in the vicinity of the Hopkinson temperature.

Farle et al. (1985, 1989) have investigated the uniaxial magnetic anisotropy of monolayers and a 8 nm thick epitaxial Gd layer near the Curie point. For monolayers the magnetization is aligned normal to the surface and is up to 10 times larger than the bulk anisotropy. In zero external field, magnetization lies completely in the surface plane.

In the case of Tb (00.1) films (5 um thick) epitaxially and homogeneously grown onto W (110) crystals, Rau and Jin (1988) and Rau et al. (1990) find that at the topmost surface layer a long-ranged ferromagnetic order exists up to a surface Curie temperature of 250 K (above the Curie and Nrel points, 220 and 228 K respectively). The results are shown in fig. 9 for electron spin polarization (% as a function of the temperature). Moreover a short-range ferromagnetic order at Tb surfaces extends up to 300 K.

124 M. GASGNIER

2.5.1.1.2. Fe (100) substrates. Taborelli et al. (1986a,b) and Landolt et al. (1986) have studied the magnetic coupling of a very thin Gd adlayer on a Fe (100) surface. They conclude that individual Gd atoms chemisorbed on Fe strongly couple antiferromagnetically to the substrate. A Gd monolayer induces a Gd-Fe surface Curie temperature near 800 K (far from those of Gd and Fe, -1040K). A film with a thickness of 3 nm (12 Gd atomic layers) is found to order magnetically below the Curie point (Gd-Gd coupling), with an opposite magnetization to the Fe substrate. Spin-polarized AES allows one to investigate the 4d core-hole transitions. Carbone and Kisker (1987) have used spin-resolved photoemission to study the electronic structure of the ferrimagnetic Gd/Fe interface. They observe for the first time a high Gd 4f-electron polarization for Gd films up to one monolayer thickness. The main effect of the Gd adsorption on the Fe derived valence bands is a depolarization. For thicker films (3.5 nm) the 4f polarization is small. In the case of Nd and Dy atoms adsorbed onto Fe surfaces, Carbone et al. (1990) have invoked Hund's rule to demonstrate that the Dy moment is antiparallel to the Fe moment, whereas the Nd moment is parallel to the Fe moment. 2.5.1.1.3. Cu (100) and Ni (111) substrates. LaGraffe et al. (1989a-c) and Dowben et al. (1989) have investigated the magnetic properties of Gd/Cu (100) systems. It is shown that Gd (1-6 monolayers) exhibits a local magnetization component along the surface that decreases for thicker overlayers. The 5d exchange splitting changes from 1.1 to 0.6 eV as thickness increases. From 170 up to 340 K there is little or no interdiffusion; that occurs only at higher temperature (above 370 K). Using valence-band emission it is observed that the binding energies of both the Cu 3d and the state symmetry of the 5p3/2 and 5d levels of Gd have been determined. It is concluded that a number of many-electron processes occur, which makes photoemission of R overlayers particularly complex and substantially alters the photoemission cross-section.

LaGraffe et al. (1990a) report that the Tb/Ni (111) system exhibits a magnetic ordering of the Tb overlayers as measured from the Tb 5p3/2 branching ratio. This ordering increases, reversibly, at temperatures well below the Curie point. The Tb magnetization axis is widely in-plane for very thick films, whereas it is found normal to the film for the Gd/Cu (100) system. In the Gd/Ni (111) system LaGraffe et al. (1990b) observed a pronounced interdiffusion of Ni at tempera~res as low as 150K. Such a phenomenon is equivalent to that noted previously for the Yb/Ni (111) interface (LaGraffe et al. 1985, 1988).

2.5.1.2. Polycrystalline films. 2.5.1.2.1. Ferromagnetic order at R surface. Rau (1982, 1983) and Rau and Eichner (1981a,b, 1986) have shown that 500nm thick Gd films, deposited onto various substrates, show evidence for ferromagnetic order at the surface. From electron-spin polarization measurements they observe an almost linear variation of the electron-spin polarization between 160 and 315K (polarization = 0). It is found that the surface Curie temperature (310K) is far above that of the bulk (293 K). This indicates uniaxial anisotropic magnetic exchange interactions at the topmost surface of the film. Such results are in agreement with those of Weller et al. (1985c).


Cerri et al. (1983) report first that the spin polarization of photoelectron decreases linearly between 20 and 300 K and that this parameter strongly deviates from the bulk magnetization. As hydrogen influences the magnetism of Gd, the authors observe that a submonolayer of hydrogen strongly reduces the spin polarization at 20 K, from 70% for the clean surface to 45% and 30% for 0.5LH2 and 1.0LH2, respectively. 2.5.1.2.2. Ferromagnetic films. The magnetic properties or rf sputtered Gd films have been studied by O. Nakamura et al. (1988). They report that the variations of the estimated Curie temperature (from 273 to 293 K, i.e., below the bulk value) of films (900 nm thick) annealed up to 830K, are correlated with the relaxation of lattice imperfections. The Curie point of 273 K is measured for unannealed films. However it is noted, first that after annealing the lattice constants of the hep structure become smaller than those of the bulk; second, that at interfaces the oxygen content increases; and third, that the hydrogen amount is not known (see Cerri et al. 1983). Ferromagnetic Gd foils for transient field experiments have been prepared by Maier-Komor (1989). It is observed that samples either contaminated by hydrogen, or grown onto substrates (overall Ta substrates) heated at 700 K have no or poor magnetic quality. To obtain good ferromagnetic foils a refrigerator cryopump is used. Bachurin et al. (1981) in the case of sputtered Gd films, observe the ferromagnetic --+ paramagnetic transition near 300 K. Such a result is observed from temperature dependence of the relative sputtering coefficient of Gd: at the Curie point this parameter increases by 10-15% in the course of the annealing from 233 up to 323 K. It is observed that in the case of Dy films no transition occurs. 2.5.1.2.3. Multilayer (Er, Tm/Lu)n-typefilms. Coherent multilayers have been synthetized by sputtering by Lowe et al. (1985). Coherence has been determined from XDP for film thicknesses between 0.8 and 1.8 ~tm. Lowe et al. observed suppression of the antiferromagnetie-ferromagnetic transition temperature and a decrease of the Nrel temperature with decreasing modulation thickness. These phenomena have not been elucidated. It is also observed that magnetic interactions between Tm layers separated by Lu layers is small compared to the interactions within the Tm layers. 2.5.1.2.4. Theoretical models. Few new papers have appeared on this subject. Urbaniak- Kucharczyk (1986, 1988) has studied the magnetic contribution to electric resistivity in thin Gd films. The numerical results show the resistivity dependence on the film thickness (as monoatomic layers) and the surface properties. The surface deformation of helimagnetic order in Dy, Ho and Tb0.9Ho0.1 films with a thickness of 10-25 atomic (00.1) planes has been investigated by Zajac (1977).

2.5.2. Amorphous films Hauser (1985) has established that a spin-glass transition occurs in disordered Tb films (0.27-1.50 ~tm thick). The spin-glass interaction depends strongly on the degree of disorder of the films as shown by the wide variation of the spin-glass freezing temperature and by anomalies in the susceptibility versus temperature curves. However, above the spin- glass freezing temperature there is no sign of ferromagnetism, and films deposited at 77 K do not exhibit any significant spontaneous magnetization. One notes that surface samples,

126 M. GASGNIER

after exposure to air, are considered to have transformed to TbO2. But no crystallographic or spectrographic proofs were given to support such an assertion.

2.5.3. Magnetic domain structures The magnetic domain structures of Gd and Tb single crystals, between 77 and 293 K, have been studied by Comer and Saad (1977), Comer et al. (1978, 1980) and R.L. Smith et al. (1980a,b). The conventional Bitter wet colloid technique was used for the Curie temperature observations and a dry colloid method (carried out by evaporation of Fe on the sample) for the low-temperature experiments. Various kinds of domains are observed as a function of the applied magnetic fields, of the crystallographic planes (a, b or c axes) and of the temperature. Some are clearly identified as parallel ferromagnetic domains with well-defined contrast, other ones are complex and difficult to interpret. Particularly, some patterns observed at 77 K exhibit, in the basal plane (00.1), a network of domains with hexagonal symmetry (Comer and Saad 1977, Comer et al. 1978). However, later on, this configuration was never observed. Chapman et al. (1981) have studied by Lorentz microscopy the domain structures of thinned Tb single crystals. The samples have been observed in a range of temperatures between 150 and 230K, i.e. in the range of the magnetic transitions of Tb. By heating and cooling, the configuration of the magnetic domains (parallel spaced 180 ° domain walls) seems to be well linked to these transitions: the paramagnetic --+ helical antiferromagnetic transition at 230K and a ferromagnetic transition at 220 K.

2.6. Optical properties

2.6.1. ~ r y low energy range (below 7 eV) The results reported by numerous research groups show broad differences. In fact, as noticed previously (Gasgnier 1980) only a few papers deal with contamination of the films (see, for instance, R.E Miller et al. 1979, Krizek and Taylor 1975, and Apostolov et al. 1983).

2.6.1.1. Scandium films and single crystals. The optical properties of single-crystal and thin hcp Sc samples have been performed from 0.20 to 5.50 eV by Weaver and Olson (1977a,b) who notice that there are close likenesses of the electronic properties of Sc, ¥, and heavy lanthanides. Sigrist et al. (1987) report the main optical characteristics (reflectivity, real and imaginary parts of the dielectric function, electron energy loss function) carried out for vacuum measured freshly deposited and air exposed films. These parameters are compared to those obtained for a single crystal at 4.2 K (Weaver and Olson 1977a,b). Some slight discrepancies appeared between the results, but it is asserted that the four structures observed below 5.50 eV are assigned to pure Sc metal. On another part, Tougaard and Ignatiev (1981), from EELS studies, report that Sc (00.1) single crystals exhibit a peak at 5.80eV and a strong shoulder at 4.00eV; these are interpreted as excitation of valence band electrons. Onsgaard et al. (1980) using reflection energy-loss

THE INTRICATE WORLD OF RARE EARTH THIN FILMS i27

spectra observed two structures for Sc (00. l) single crystals. They are located at 2.30 and 5.50 eV and are interpreted as interband transitions. Lastly, it is difficult to analyze the results of Mahmoud and el Mandouh (1987) because their films are highly contaminated.

2.6.1.2. Yttrium. Weaver and Olson (1977a) notice remarkable resemblance of the electronic properties of Sc and Y as single crystals and films (Weaver and Olson 1977b, Weaver and Lynch 1973). In the case of thin films, Apostolov et al. (1983) take care to note that hydrogenation and oxidation can play an important role in the energy range above 3 eV. They observe four direct optical transitions between 1.60 and 3.10 eV, in good agreement with electron band structure calculations.

2.6.1.3. Europium, gadolinium, terbium, dysprosium, holmium, erbium, thulium and ytterbium. Apostolov et al. (1981) have studied the transmission spectra of Tb films deposited at 77K onto glass substrates over the energy range 1.60-3.10eV. During evaporation and measurements the pressure was around 10 -6 Pa. A direct evidence for seven optical transitions is explained in terms of electron band structure calculations. The magnetic ordering effects in the transmission spectra of ferromagnetic Tb are also discussed.

The optical conductivity, established by polarimetry, for Tb, Dy and Ho films has been reported by Ahmed-Mokhtar et al. (1982) over the energy range 0.50-5.00 eV at different temperatures (from 30 to 300 K). The results are compared to those given by Krizek and Taylor (1975) carried out by ellipsometry. It is evident that wide differences appear, and that it is difficult to fit the results. However, Ahmed-Mokhtar et al. (1982) report that for Tb, changes in the magnetic state are observed below 1.50 eV which give rise to an optical resonance (effective s - f exchange energy); while for Dy such changes have little influence on the optical properties; and for Ho unexplained anomalies occur in the conductivity and the refraction indices. One must add that the thickness of the films does not exceed some 30 nm, and under these conditions probably contaminations occur, but they are never taken into account. Reflectance, dielectric constants, optical conductivity and interband transitions of Gd and Dy films have been studied by Quemerais et al. (1981) between 2 and 30eV. The authors compare their results to those reported previously. Between 2 and 10 eV they conclude that the principal interband transitions are p-+ d, and d-+ p with a slight participation from s ~ p.

The thermally modulated reflectance of Gd, Tb and Dy films (100 ~m thick) has been measured by R.E Miller et al. (1979), over the range 1.45-3.20 eV, at 315 and 97K. The experimental procedure (evaporation under a vacuum of 10 -8 Pa) excludes the formation of the hydride and the oxide (Rahrnan Khan and Miller 1979). At 97K, pronounced structure develops: 1.60, 2.00 and 2.80 eV for Gd; 1.70 eV for Tb; and 2.20 eV for Dy. They noted that thermoreflectance anomalies occur at the ferromagnetic Curie point of Gd and the N~e! points of Tb and Dy. The structures are interpreted according to different hypotheses and compared to those of Krizek and Taylor (1975). For Tm films evaporated under a vacuum of 10 -7 Pa, Onsgaard et al. 0983) report EELS measurements at low energy range. At 4.50 eV they observe an intense peak attributed to a valence band to

128 M. GASGNIER

conduction band transition. Idczak and Zukowska (1981) give some optical properties (reflection factor, refractive index) of thick (~350um) thermally evaporated Yb films. They found that the optical constants increase monotically with increasing wavelength of the light.

Bauer and Kolaczkiewicz (1985) have investigated by low EELS the edge structures of Eu, Gd and Tb single-crystal films or atomically dispersed layers adsorbed on W (110) and W (112) surfaces. Several few intense structures and a sharp dominant loss peak at about 4 eV have been recorded. The latter has been attributed to spin exchange excitation of the 4f level. A comparison to XPS results led to a re-consideration of the interpretation of the 4f XPS binding energies.

2.6.2. Low energy range (7-70eV) 2.6.2.1. Scandium films and single crystals. In the case of clean single crystals Tougaard and Ignatiev (1981) and Onsgaard et al. (1980) report from EELS experiments that the surface and volume plasma are located at about 8 and 12 eV respectively. (The bulk plasmon corresponds to the collective excitation of the conduction electrons). Other experiments carried out with thin films yield higher energy values for the volume plasmon: 14.00 eV (Brousseau-Lahaye et al. 1975); 13.50 eV (Frandon et al. 1980), and 12.90 eV (Cukier et al. 1980). The calculated value is reported to be equal to 12.90 eV; it seems clear that the discrepancy proceeds from the purity of the films. (The bulk plasmon is shifted towards higher energies for hydrided and oxidized films as demonstrated by Colliex et al. (1976) and Onsgaard et al. (1980).) At higher energies, Tougaard and Ignatiev (1981) and Onsgaard et al. (1980) report for excitations of 3p (M2-3 threshold) and 3s electrons to empty states in the valence band, and collective excitations of "inner" 3p electrons the following values: 29-31 eV, 54 eV and 42.50 eV, respectively. The M2-3 threshold has been located at similar values by Brousseau-Lahaye et al. (1975) and Frandon et al. (1980), whereas Cukier et al. (1980) report a higher energy: 38 eV. The real and imaginary parts of the dielectric constant and the absorption coefficient have been reported by Brousseau-Lahaye et al. (1975) and Frandon et al. (1980).

In the case of Sc films exposed to air, Sigrist et al. (1987) observed in the vacuum ultraviolet region several structures located at 7.60, 10.30 and 21.00eV. These authors discuss such peaks according to the formation of a thin transparent surface oxide layer. In this way, it is not possible to assign the peaks at 7.60 and 10.30eV to the metal or to the oxide layer. However, the peak at 21.00eV, observed also by Frandon et al. (1980) and Cukier et al. (1980) for Sc203 thin films, is related to this oxide layer.

2.6.2.2. Yttrium. Chee et al. (1979) have studied the optical behavior of Y films (200 nm thick) in ultrahigh vacuum. They report the refractive index and extinction coefficient, the reflectance, the real and imaginary parts of the dielectric constant and the volume and surface loss functions as a function of the photon energy. They observe that oxidation (or hydrogenation?) and nitrogen gas (as admitted deliberately in the vacuum chamber) can strongly affect the optical properties. The results are compared to those of Weaver


and Olson (1977b), and it is concluded that there is no resemblance between them: the interband transition at 7.00 eV, the surface plasmon at 9.40 eV and the volume plasmon at 11.80 eV reported by Chee et al. (1979) do not correspond to the values given by Weaver and Olson (1977b) as: 7.70 eV, 11.50 eV and 12.50 eV respectively. Other researchers report the following values for the volume plasmon: 12.50 eV (Brousseau-Lahaye et al. 1975), 12.80eV (Frandon et al. 1980); 13.00eV (Cukier et al. 1980). (The calculated value is 11.20 eV.) At higher energies the 1'42-3 threshold has been recorded at 36.00eV (Cukier et al. 1980) and 35.00eV (Brousseau-Lahaye et al. 1975, Frandon et al. 1980). The real and imaginary parts of the dielectric constant and the absorption coefficient as a function of the energy have been deduced by the latter authors.

2.6.2.3. Lanthanum and cerium. Cukier et al. (1980) have reported on LaF3 thin films studied by EELS, that the volume plasmon of La is located at about 12eV. The 02-3 threshold (5p electron excitations) occurs at 22-23 eV. Miyahara et al. (1982) assert that the absorption spectra of metallic La and Ce films present two maxima close to 10 eV and 25 eV. The authors compare their results to those published previously and discuss the origins of small structures in terms of intrinsic properties or of contamination of the samples. The higher energy peaks are linked to the 5p--+ 5d transition.

2.6.2.4. Gadolinium, dysprosium, thulium, and lutetium. The positions of volume plasmon energy of Gd and Dy (calculated and experimental) reported by Quemerais et al. (1981) differ from those given in other works. Their calculated values of 11.20 and ll.40eV, and 12.10 and 12.20eV as measured for Gd and Dy, respectively, are lower than the values reported by Colliex et al. (1976) and Cukier et al. (1980). This indicates that the samples of Quemerais et al. (1981), evaporated under a vacuum of 10-6pa, are purer. In the same way the volume plasmon energy (~11 eV) given by Miyahara et al. (1982) reflects a nearly pure metallic state. The peak relative to the 5p electron excitations is located at 33-35 eV according to the above-mentioned authors. However, different interpretations have been given to explain this edge. So, Quemerais et al. (1981) show that the shake-up structure comes from a 5p hole and a 4f open shell coupling, whereas Murgai et al. (1988) from photoemission measurements, report that the 5p-5d intershell interaction results in an enhancement of the 5d emission (at 32 eV) above the 5p3/2 and 5pl/2 core level thresholds at 21 and 27 eV respectively. The 02-3 threshold has been observed by Cukier et al. (1980) and Miyahara et al. (1982) between 20 and 30eV; this one is more intensive for GdF3 and DyF3 than for LaF3, due to the presence of the 4f electrons. For Tm films evaporated at a pressure below 10 -7 Pa, Onsgaard et al. (1983) observe four main peaks, located at 8.90 eV (surface plasmon), 12.50 eV (bulk plasmon), 40.50 eV (5p ~ 5d transition) and 57.00 eV (5s ~ conduction band transition). One must note that the higher volume plasmon value given by Colliex et al. (1976) is surely caused by contamination of the film. (The calculated value is estimated at ~11.90 eV.)

In the case of clean Lu (00.1) single crystals, surface plasmon (9.80 eV), bulk plasmon (13.20eV), 02-3 threshold (30-33 eV) and 5p--+ds transition (43.30eV) have been recorded by Onsgaard et al. (1980). The bulk plasmon value is in agreement with the

130 M. GASGNIER

theoretically expected values and the results of Colliex et al. (1976). (One must add that lutetium films are less sensitive to contaminants than those of other R elements). Onsgaard et al. (1980) notice that the Lu 5p ~ 5d strong resonant transition is similar to the Sc 3p --~ 3d one. Such a result has been also suggested by Murgai et al. (1988) in the case of Gd thin films, and appears to occur in all R elements possessing d character in the valence band.

2.6.2.5. Samarium. The ultraviolet absorption spectrum of Sm thin films exhibits three peaks at 9.00, 16.00 and 30.00eV (Miyahara et al. 1982). The origin of the second one has not been assigned. (However it might be linked to that for the bulk plasmon of the hydride.)

Remark: The Sm203 bulk plasmon is located at 15.20 eV (Gasgnier and Brown 1983), and that relative to SmH2 is located at higher energy (Colliex et al. 1976).

On their part den Boer et al. (1988) observe that Sm monolayers deposited onto Nb substrates are initially purely divalent. The photoemission spectrum exhibits two peaks at about 5 eV and 25 eV, which are characteristic of the Sm 2÷ valency state. One hour after deposition and exposition to oxygen, the spectrum fully changes and two peaks (at about 10 and 20 eV) are observed, which are related to mixed-valent or trivalent Sm. One must notice that after exposition to 02 the volume plasmon peak is shifted towards higher energy (~14 eV). The 5p --~ 5d resonance has been measured, and it is evidently sensitive to the occupancy of the Sm 5d state.

2.6.2.6. Europium and ytterbium. The 5p--* 5d transition (5p3/2-5pl/2 peaks) for Eu and Yb has been studied from photoelectron energy distribution curves by G. Rossi (1987), G. Rossi and Barski (1985, 1986), G. Rossi et al. (1984, 1985) and Yeh et al. (1984). As a preliminary remark one must note that, first, Yb films (~50 nm) are considered to be purely fcc, and second, possible contaminations are never taken into account. However, the main results indicate that strong 5p hole --* 5d electron interactions occur in the electron emission processes. The two metals show the same resonance effect above the threshold of the 5p multiplet. Miyahara et al. (1982) for Eu thin films observe the presence of small structures near the onset of the 5p absorption. These are discussed in terms of EuO contamination.

2.6.3. Medium energy range (70-600 eV) 2.6.3.1. Scandium and yttrium. Frandon et al. (1980) have recorded the L2-3 edge (2p electron excitations) of Sc at about 405 eV, and the M4-5 (3d electrons) and M2-3 (3p electons) edges of Y at 155 and 300 eV. The spin-orbit splitting of the 2p levels in Sc is measured to be about 5 eV, while for Y the spin--orbit splitting of the 3d electrons (2 eV) is not observed.

2.6.3.2. Lanthanum. Moser et al. (1984) have compared the N4-5 edge (excitation of the 4f3/2 and 4f5/2 electrons) recorded by EELS and XPS. The former exhibits a rich


collection of structures extending from 97 up to 140 eV (large electrostatic coupling between the 4d and 4f shells in the final 4d94f 1 state). The intensity of these multiple structures varies as a function of the primary electron energy; i.e., the intensity increases with decreasing excitation energy. This is due to dipole-forbidden transitions. From LaF3 thin films, Cukier et al. (1980), locate the N4-5 edge at about l l 9 e V

2.6.3.3. Cerium. For cerium films crystallized as the y-phase (fcc), L.I. Johansson et al. (1978) report a giant enhancement of the valence-band photoemission intensity. The photoemission peak is located at 120eV. The effect is interpreted as being due to autoionizafion decay following the 4d ~ 4f transitions.

2.6.3.4. Gadolinium, thulium and lutetium. 4d-+ 4f resonant photoemission and Auger spectra of Gd have been carried out by Gerken et al. (1980, 1981). Several multiplet structures are observed close to the main photoemission peak located at 148 eV Some Auger structures are identified as due to the direct recombination of 4d94f 8 states with the 4f and valence electrons, whereas for photoemission they are identified as originating from excited quintet configurations of the 4f 6 state reached by the Auger decay of the resonantly excited 4d94f 8 configurations.

For Tm this 4d-4f resonance has been investigated by Egelhoff et al. (1981). With quite good resolution the authors observe a shoulder at 172 eV and a peak at 177 eV in the photoelectron spectra. The autoionization resonance is explained according to a decay channel processes. Onsgaard et al. (1983) observe two structures at 170 and 178 eV and notice that theoretical calculations lead to an energy splitting equal to 11 eV. For Lu, Onsgaard et al. (1980) report that the 4d5/2 and 4d3/2 transitions occur at 203 and 215 eV respectively. The energy separation reflects the spin--orbit splitting.

2.6.3.5. Ytterbium. Another kind of experiment has been reported by Hecht et al. (1984). They investigate the 4f5/2 and 4f7/2 photoemission peaks which can be resolved into two pairs of doublets at a kinetic energy of 100eV. They conclude that the doublet results from surface and bulk emission. The former is interpreted as an intrinsic binding energy shift and is not due to a contaminant as claimed previously by Alvarado et al. (1980). Different models are discussed to describe this result.

2.6.4. High energy range (beyond 800 eV) From XPS measurements the 2pl/2, 2p3/2 and 3d3/2, 3d5/2 doublets of Sc and Y have been recorded at 850-855 eV and 1090-1098 eV, respectively, by Reichl and Gaukler (1986, 1988).

The major part of these studies has been carried out for La thin films by Kanski and Nilsson (1979), Kanski and Wendin (1981), Esteva et al. (1983a,b) and Moser et al. (1984); they were extended to Ce and Gd by Esteva et al. (1983a,b). The 3d---~4f (3d5/2 and 3d3/2 main lines or M4-5 threshold) spectra have been recorded by various experimental methods: XAS, XPS, electron-excited-Auger (and stimulated-X-ray)

132 M. GASGNIER

appearance and EELS. One of the most interesting results looks at the disagreement of 2-3 eV in the energies between XPS and XAS (Esteva et al. 1983a). Such a discrepancy is discussed in terms of strongly localized valence electrons. In the same way, Moser et al. (1984) notice that EELS and XPS exhibit a similar shift which is interpreted as an indication for the breakdown of dipole selection rules in EELS when the excitation threshold is approached (Matthew et al. 1983). Esteva et al. (1983b) have shown that the multiplet structures of La and Gd are only detected over a limit thickness of about 30 urn.

Remark: The M4-5 thresholds of the R elements have been studied by EELS and XAS, by the way of the sesquioxides, intermediate oxides and dioxides (Ce, Pr and Tb). (Colliex et al. 1985, Manoubi et al. 1990, Gasgnier et al. 1989.)

2.7. Applications relative to metallic films and foils

2.7.1. The piezoresistance response of Yb foils To measure the amplitude of the pressure induced inside a material submitted to a shock wave, it is possible to use the piezoresistivity response of metals (as ytterbium) or alloys (as manganin). In the ease of Yb numerous studies have been done by Y.M. Gupta (1983a,b), S.C. Gupta and Gupta (1985), Chen et al. (1984), Brat and Gnpta (1986), Grady and Ginsberg (1977), S.A. Miller (1988), Aidun (1986) and Bosca et al. (1981). The metal is used either as a thin deposited film or a foil (50 ~tm thick). Although the laboratory results promised to be very interesting for the fabrication of gauges, it is noteworthy that to our knowledge no patent was taken out. It seems that several parameters restrict industrial application: formation of the dihydride (YbH2), coexistence of the hcp and fce phases (Bosca et al. 1981), stress measurements below 200 Pa, difficulty to interpret lateral measurements, resistance change for parallel and perpendicular measurements (S.C. Gupta and Gupta 1985). The whole of these results show that simple analyses are not adequate and, therefore, further developments are required (Y.M. Gupta, 1983a). One can add that the lack of crystallographic data and chemical analyses is truly prejudicial to interpret the results. In this way, numerous authors do not refer to the high-pressure crystallographic transition of ytterbium.

2.7.2. Diffusion barriers: Sm and Yb metal interfaces It has been shown that ytterbium (and also samarium) have a unique reactive behavior on mercury-cadmium-telluride surfaces, due to the large rare earth affinity for both Hg and Te. They act as effective diffusion barriers at the interface between HgCdTe and prototypical reactive metals (A1, In or Cr). Ytterbium was found to prevent A1-Te reaction, and to reduce the Al-induced mercury depletion of the substrates, and the outdiffusion of Te. The results of Raisanen et al. (1988), Wall et al. (1987, 1988) and Franciosi et al. (1988) show that the diffusion barrier effect is the result of the superior thermodynamic stability of the HgCdTe/Yb reaction products at the interface.


2.7,3. Tunnel junctions: Yb/oxide/p-InAs In order to obtain devices with negative differential conductance, Kunze and Kowalsky (1988) have used ytterbium as a film gate, The low work function of Yb compared to the electron affinity of InAs increases the surface field. And, the low resistive tunnel junction serves as ohmic contact to the inversion layer.

2.7.4. Magnetic deuices A Japanese patent (K. Takeda et al. 1989) mentions the use of polycrystalline Gd film (with a lower Curie temperature than a single crystal) after annealing treatments, as heat- sensing switches or thin film inductance devices.

2.8. Metallic or contaminated films or fine particles? Remarks about the fcc phase

Once again one must draw attention to the high reactivity of rare earth metal, as thin films, with gases as H2, 1-120, 02, CO, CO2, CnHn, N2, . . . . In this way the purpose of this section is to indicate that a lot of results published by several research groups, seem to be doubtful. One may refer to a paper of Curzon (1984) who demonstrates, by means of a quadrupole gas analyzer, that the films are at first hydrided and not oxidized (see sect. 2.9).

The first series of results concerns the electrical properties of three R elements (Y, Sm and Yb) reported by Ashrit and Angadi (1980a, b, 1981, 1982, 1983), Ashrit et al. (1980, 1984) and Angadi and Ashrit (1981a--c, 1983a,b). The main purpose of these papers was to study the electric resistivity, the temperature coefficient of the resistance (TCR) and the thermoelectric power of films deposited trader a poor vacuum of about 10-3-10-4pa. The variations of these parameters were studied as a function of the thickness, annealing, aging, substrate temperature, deposition rate and pressure in the vacuum chamber. Since the authors do not report any XRD or EDP they cannot define the crystallographic structure of their films. The results relative to electric resistivity were analyzed using the Fucks-Sondheimer and Mayadar-Shatzkes theories, i.e., in terms of pure metallic films. One must notice that these authors sometimes mention that possible contamination by hydrogen is possible (Angadi and Ashrit 1983a, Ashrit and Angadi 1982). Rajora and Curzon (1984) have commented on the whole of these results and demonstrated that the variations of resistivity, by whatever the characterization method, are clearly due to hydride formation in the films, with the additional possibility of oxygen contamination. They conclude: "it is certain that the films studied were composite films (metal+hydride) thus agreement between theory and experiment is fortuitous".

The next series is concerned with fine particles. Yamaguchi (1982a-d) has studied the crystallographic properties of tribophysically pulverised R-metals (Gd, Tb and Dy). This author observed a strange hcp +-~ fcc martensitic transformation for Gd and Tb small particles (about 100 nm in size), but not for Dy small grains (about 5 nm in size). Moreover the cubic particles of Gd are not attracted to a magnet, whereas coarser grains

134 M. GASGNIER

having the hexagonal structure are ferromagnetic. The interplanar spacings reported in various tables do not correspond to those of the metal. In this way Curzon (1982) and Curzon and Gasgnier (1985) have shown that the fcc structure may be due either to R203 or RH2 chemical compounds. Exactly in the same way Chizhov et al. (1982) and previously Morozov et al. (1975, 1976) and Kostygov et al. (1977) report the presence of the fcc phase in very small particles (25-40 nm in size) for Gd, Tb and Ho materials. From XRD Chizhov et al. (1982) show that, as the grain size decreases, two fcc structures are formed. As demonstrated by Singh and Curzon (1982) it is clear that the first one is due to the dihydride and the second one to the sesquioxide (for holmium the lattice parameter is 0.529 urn, i.e., exactly half the value of that for the bcc C-Ho203). In addition, Chizhov et al. (1982) observe that the magnetic properties undergo a drastic change for small particles (below 100nm) in that no magnetic ordering is observed down to the helium temperature and they become no longer ferromagnetic. Singh and Curzon (1982) notice that the magnetic ordering disappears for hydrided particles and conclude that: "the results must be interpreted in terms of contaminants rather than in terms of new size dependent forms of the R metals" (see also sect. 2.9.1.1 for other details).

Some other papers report the formation of the fcc metallic phase for the R elements. In a first paper Kozlovskii et al. (1981) disclaimed the formation of the Gd dihydride compound, but later on (Kozlovskii 1989) asserted the contrary; Parmigiani (1982) reports a strange lattice contraction for Yb and Eu films and does not link this change to hydridization of the metals; McMinn et al. (1990) claim, in the case of rio thin films, that the fcc structure is a non-equilibrium metallic phase. Hussain and A1-Bassam (1979) and Hussain (1980, 1981) report that electrical properties of Gd thin films are closely linked to microstructural changes. Particularly the authors observe that a granular to porous and to continuous crystalline change corresponds to the fcc to hcp crystallographic change. The resistivity curves and EDP show that the films are hydrided (the vacuum deposition carried out under 10 -4 Pa).

To conclude, and in order to introduce the next section, relative to rare earth hydride compounds, one must point out the work of Loboda et al. (1980), Loboda and Protsenko (1981a,b) and Loboda et al. (1982). These authors have studied the structure and electric resistance of scandium films (30 up to 280nm) deposited under a vacuum of 10 - 3 -

10 .4 Pa. Loboda et al. (1980) claim that the chemical transformations, observed inside a TEM, lead to the formation of ScH2 and Sc203. They report a good agreeement for the lattice parameters. Then, Loboda and Protsenko (1981a) disclaim such an assertion, and assign the fcc lattice to a pure metallic phase. In a following paper Loboda and Protsenko (1981b) come back to their first assertion and claim the formation of the ScH2 compound. Lastly, Loboda et al. (1982) do not discuss the electric resistivity in terms of chemical contamination, but as a function of the defect ratio, thickness and grain size. This is an exceptional change of ideas which demonstrates how it is sometimes difficult to give sterling conclusions without carrying out experiments which lead to a focused network of results.


2.9. Formation and properties of the rw~e earth hydrides

2.9.1. Formation of the hydrides 2.9.1.1. Contamination of thin R films. Contamination of R thin films is too much important to be neglected. Under various experimental procedures the formation of the dihydride (RH2) can readily occur. It is now well-established that thinner films (10- 40 nm thick) consist mainly of hydride, whereas for thicker layers (40-80 nm) there is coexistence of the metal and hydride. Curzon (1984) has tentatively explained why R films are so contaminated. When the R metal is evaporated, hydrogen is generated at the filament and/or the crucible. Another H2 source is due to the reduction of water at the vapor source, and this one cannot be eliminated unless I-t20 is removed from the system. So, hydrogen is difficult to remove efficiently by diffusion pumps, and during metal condensation it is easily absorbed. Therefore, the thinner films consist mainly of hydride, whereas in thicker layers only the surface would be affected. The surface substrate can also act as a contaminant. The experiments of Curzon (1984) have been carried out with 17120 and D20, and it is shown that erbium, at the evaporation source, reduces water to produce H2 and D2. Such an article is very important because it demonstrates, without ambiguity, the high power "getter" effect of R for hydrogen. In this way, the new phases such as the new fcc metal structure, the strange RxOy compositions, the new chemical compounds,... (of which the lattice parameters are close to the one of the bulk hydrides), reported by different research groups, cannot be taken into account.

In this way, Gschneidner (1980, 1992) has clarified the problem of the purity of R metals. It is shown, first, that H, O, C, N and F are usual contaminants for commercial samples, and, second, that physical properties (magnetic, low-temperature capacity, electronic, thermal, . . . ) are often flawed by such impurities. Therefore these samples must be carefully outgassed before making films. However, it is difficult to completely eliminate the hydrogen inside the vacuum chamber. Whatever the deposition mode during evaporation, numerous parts of the equipment (crucible, target, walls of the chamber, . . . ) are more or less heated. They outgas various gases including water vapor which is dissociated by the rare earth to form the hydride. In this way one must mention the conclusion given by Surplice and Kandasamy (1982): "The experiments show that Er, Yb and Sc films prepared in ultra high vacuum will sorb H2 readily at room temperature".

2.9.1.2. Residual hydrogen. Rahman Khan (1977, 1978, 1981, 1984, 1987a,b) and Rahman Khan and Miller (1979) show that the formation of RH2 is strongly dependent of the residual gases in the vacuum chamber and of the adsorbed gases within the substrate. The results are given for Gd, Tb, Ho and Er thin films. The gettering action of Gd is reported in figure 10. From the curve it is seen that effective gettering happens within 45 seconds, and then saturates. On heating in He there is formation of RH3. In the same way Curzon and Singh (1979, 1981a,b) have studied the formation of the hydrides for Y, Ce, Pr and Nd samples. They observe the formation of various compounds like C- and A-Nd203, CeO2 and also C-Ce203. However, one must notice that in the case of Ce, two fcc structures (al ~ 0.543 nm and a2 ~ 0.555 nm) have been formed. This is explained

136 M. GASGNIER

5 x 10_5

¢ 0 I'-

Z -- 5 x l O - 6 bJ

¢0 o') bJ n--

5 x l O -7 i I | w

0 I 0 2 0 5 0 4 0 5 0

T I M E IN SECONDS

!

6 0

>

Fig. 10. The gettering action of Gd (formation of GdH 2 in the early stages of the evaporation). (By courtesy of Dr. M.S. Rah- man Khan, Dep. Appl. Phys., Univ. of Rajshahi, Rajshahi, Bangladesh).

in terms of metastable solid solutions of y-Ce and Cell2. In the case of Y layers these authors add that it is difficult to form the YH3 compound even under exposure to 2670 Pa of hydrogen. Kozlovskii (1989) reports that under sputtering deposition in Ne, Ar and Kr gases, there is formation of the GdH2 and DyH2 compounds.

The hydrogen absorption rate of thin R films has been studied by Eley and Needham (1984), Wulz and Fromm (1986a), Varkanova and Morozova (1984), Zhavoronkova and Peshkov (1978, 1979), and Zhavoronkova and Boeva (1989). The former authors have drawn particular attention to interstitial H2 and to catalytic activity of the dihydride films for the H2 +D2 ~ 2HD reaction. Calorimetric measurements of the interaction of H2 with R (Ce, Gd, Dy, Er, Tm, Yb and Lu) films (20-50nm thick) have been carried out by Smutek and Cern~, (1985) and Boeva et al. (1986). They conclude that the heats of H2 dissolution and RH2 formation become closer to each other as the temperature decreases. They demonstrated that, at 295 K, Ce, Dy, Er, Tm and Lu give heats of dihydride formation values 6-14% lower than those calculated from the data at high temperature. Only Gd (which has an anomalously high specific heat) does not present a significant difference. One can also notice that the effect of oxygen preadsorption layers strongly influences the H2 absorption. So, Wulz and Fromm (1986a) have determined that, in the case of La films, a thickness of 20 monolayers of oxygen at the layer surface drastically reduces the H2 reaction. Hosoda et al. (1988) add that 02 precoverage has less effect than H20 precoverage. Kawahata et al. (1990) compare the rate of the H2 adsorption on La and Ni films.

Kumar et al. (1984a,b) have investigated the chemisorption of H2 upon clean La and Yb polycrystalline bulk materials. Time-of-flight analyses, surface recoiling of adsorbate atoms, XPS and UPS measurements show clearly the evolution of the recorded spectra upon exposure of the metals to H2. It is observed that LaH2 is formed in the outermost sufaee layer at 50L H2 exposure. However, the top layers (~2 nm) are not saturated for ~2000L exposure.


AES and EELS methods have been used by Bracconi et al. (1987, 1988) and Bracconi and Laesser (1987, 1988) to compare the electronic structures of Y and Nd metal films to those of their hydrides (YH2, PrH2 and PrH3). As reported by Colliex et al. (1976), EELS reveals that the volume plasmon of Pr and PrH2 are shifted. Also special attention is given to 02 contamination.

2.9.1.3. Reaction of R elements with water vapor. The problem of the reaction of the R elements with water vapor is very important (Dexpert-Ghys et al. 1975, Curzon 1984). H.K. Smith et al. (1980) and Oesterreicher et al. (1979) have demonstrated that the water- splitting process generates the formation of the dihydride according to the reaction:

2R + 2H20(g) - + 2RH2 + 02.

Kumar et al. (1984b) observed that during initial H20 exposure upon La specimens, both oxide and hydride are formed, which is followed by hydroxide formation at >35L exposures. Gimzewski et al. (1979) observe, from XPS experiments, that reaction of Sc with water at 293 K gives initially the oxide (Sc203), and above ~50L the hydroxide. However, at 80 K only hydroxide and chemisorbed water are produced, which is in contrast to the behavior of the lanthanides. But, since no experiments show the plasmon energy loss spectra (below 50 eV) the possible formation of the dihydride is not observed (see Gimzewski et al. 1977 and Gasgnier 1980).

2.9.2. Physical characteristics 2.9.2.1. Electric resistance and resistivity. From the results reported by Curzon and Singh (1979, 1981a,b) it appears that the electric resistance of RH2 films (R = Pr, Nd and Y) is complex. As a function of thickness, temperature, H2 partial pressure, and aging, the variations of resistance differ from one element to the other with a nearly similar but not systematic identical appearance. For Y thin layers, the complex variation of the electric resistance as a function of time at constant H2 pressure is shown in fig. 11. The resistivity curves, for Y, YH2 and YH3, as a function of temperature are given in fig. 12. Rahrnan Khan (1981, 1984, 1987a) has shown that the formation of the trihydride involved a rapid fall in conductivity and a negative value of the TCR. This indicates that the metallic dihydrides have become converted to semiconducting trihydrides. This transition has been also observed by Curzon and Singh (1979, 1981a,b) in the course of over hydrogenation of their samples (under H2 pressures of 2670 Pa). The increasing in resistivity for ScH2 thin films has been observed by Loboda et al. (1980) and Loboda and Protsenko (1981b).

Rahman Khan (1977, 1987b) explains the variation of resistivity with temperature and thickness in terms of structural phase changes. It is observed that the temperature dependence of the resistance and TCR values indicate metallic conduction characteristics of the hydrides. The thickness dependence of resistivity of HoH2 films (7-90 rim) at 293 and 77K is given in fig. 13. Surplice and Kandasamy (1982), Kandasamy and Surplice (1981, 1982, 1985) have studied H-Sc, H E r and H-Yb systems and deduced phase boundaries from changes of film resistance with atomic ratio H/R. The slow variation of

138 M. GASGNIER

18

16

14

12

I0

8

B

T i m e • rains

Fig. 11. The effect of 20 Torr of H 2 at 293 K on the electric resistance of a 180 nm Y film. At point A hydrogen is admitted to the system: an ordered phase develops and the resistance drops. At point B the hydrogen is pumped away and the resistance remains constant up to point C. (By courtesy of Prof. A.E. Cnrzon).

9O

70 . . . ~ - ~ " ~ p n - c m

60 ~

5O

T 4°

2O iJ~l-cm

10

r , , , I , , , , I , , , i I , , , , I

I00 150 200 250 300 T°K-~

Fig. 12. A plot of resistivity versus T for films containing predominantly Y (circles), YH 2 (squares) and YH 3 (triangles). (By courtesy of Prof. A.E. Curzon).


2 0 0

I 150

< IO0

I-- > V- ff)

50 bJ

R o o m t e m p e r a t u r e

o . . . . . o f 7 7 K

~ _ - - ~ . . e . . . . " _ _ B u l k

I 0 0 2 0 3 0 4 .00 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0

T H I C K N E S S , .~

Fig. 13. Thickness dependence of resistivity of HoH z films (7-90nm). (By courtesy of Dr. M.S. Rah- man Khan).

10 9

10 8

10 7.

10 ~-

a-_

10 ~'.

I0~

1

1o 7 ]

100

d 7 ~ / xz /

V..~,

Fig. 14. Change of resistance with atomic ratio r = H/Yb. Solid and dashed curves are for films that were hydrided slowly and quickly, respectively. (After Surplice and Kandasamy 1982.)

resistivity in RH2 indicates that most of the modifications of the conduction band occur in the mixed phase; this could be due to the R-RH2 structural transformation between the metal and the metal + dihydride phases. In the case of H-Yb system, in which the hydride is a poor conductor, the solubility limit (the position of the first phase boundary) has been estimated. Changes of resistance with atomic ratio are reported in fig. 14.

140 M. GASGNIER

2.9.2.2. Work function. The changes in work function in the course of hydrogenation have been determined for Sc and Er thin films by Miiller and Surplice (1977) and Kandasamy and Surplice (1985). As for the electric resistance they correlate the variations with changes of phase in the R/H system. In a general manner, first, small doses of H2 reduce the work function to about 0.!0 eV below the value for the clean metal; second, larger doses increase it to about 0.20 eV above this value; and third, further doses quickly raise the work function to a maximum of about 0.55 eV above the one of the clean metal. The results relative to the metallic phase can be interpreted as changes of surface potential; but for the other phases they depend on changes of the Fermi level of the H/R system as well as on the surface potential. Moreover these results are compared to those obtained for other metal hydrides (La, Ta, Ti, U, Pd, Nb and Zr). Similar observations have been reported by Eley and Needham (1984) for Gd films.

2.9.2.3. Surface magnetization. Cerri et al. (1983) have studied the spin-polarized emission of clean and hydrided (submonolayer coverages) polycrystalline Gd thin films. At 20 K, hydrogen coverage (chemisorption) drastically reduces the spin polarization from 70% (clean surface) to 45% (N0.5L H2) and 30% (~I.0L H2). With increasing temperature the polarization decreases linearly, up to 130K, then rises to a maximum near 200K, and finally decreases again. Extrapolation of the linear part of the curves shows that chemisorbed hydrogen strongly reduces the ordering temperature and induces a canted or disordered spin structure at the Gd surface. This experiment is a sensitive monitor of hydrogen contamination.

2.10. Rare earth deuteride and tritide

2.10.1. Bulk materials 2.10.1.1. Introduction. As a short introduction, one must emphasize the latest results of Adachi et a1.(1992) who report the possibility of "cold fusion" using the system D2- LaNis. This has been deduced from analysis of H2 in gases resulting from D2 absorption with an LaNi5 ingot at 100-300 K under a pressure of ~5x 105 Pa. Such an assertion calls for new experiments and will certainly be the subject of new polemics.

2.10.1.2. Gettering. Maienschein (1978) has reported that cerium is one of the best chemical getters which can be used to scavenge tritium from inert gases. Indeed, this metal, as well as Sc, Y and Er, has low dissociation pressures for temperatures between 298 and 523 K. Maienschein assumes that dissociation of the tritium molecule to two tritium atoms and diffusion of tritium atoms through the solid tritide (due to the flaking and spalling effects of the material during tritiding) are both rapid. As cerium hydrides are stable and exhibit plateau regions, it is also assumed that the gas-phase mass transfer is the controlling step in the gettering process.

Hubberstey et al. (1976) have used yttrium sponge as a getter for hydrogen isotope removal from liquid lithium. The rate of gettering is remarkably rapid at 673K. Hydrogen isotope concentration in Li can be reduced from 1.00 to less than 0.05 tool%


x (x = H or D). Such a result should be extrapolated to lithium-tritide solutions. In the same way Buxbaum (1982) have used yttrium for the separation of tritium from the liquid lithium breeder-blanket of a fusion reactor.

2.10.2. Thin films 2.10.2.1. Scandium and yttrium. Malinowski (1981)has shown, from AES spectra, that the so-called LMV peak of Sc might be a useful indicator of film deuterium content. Indeed, he reports a linear dependence of the Sc LMV peak height on the deuterium content of the film (100nm thick). This is observed as a function of the fractional decomposition of the film such as

S c D 2 ----r ScD0.5 --+ Scmetal (a t 673 K).

One must notice that films were contaminated by C and O (from evaporator), and S (from Mo substrates).

Cowgill (1979) has studied dynamic deuteron implant effects (at 40keV) using Sc targets (previous experiments gave results at 200keV, see Cowgill (1977)). The experimental system is useful for studying D2 retention and mobility in materials under deuteron bombardment. Isotopic hydrogen exchange has been observed dynamically at 413 K. It is also shown that oxygen implants deplete the target of D2 within the implant range due to the formation of ScaO3. Cowgill (1981) has used the same technique for measuring D2 diffusion in films. He notices that no significantly different behavior is observed for films of different thicknesses (0.5-5.5 ~tm), the diffusion being identical to the one observed in bulk samples.

Singleton and Yannopoulos (1975) have used Sc and Y films (500-1200 nm thick) for fabrication of radioactive electron emitters (tritriated electron sources). The stability of the sources in flow gas streams increases from Ti to Y to Sc. Once again, it is shown that the surface contamination has a profound influence on both the loading and loss of tritium in the films. Bacon et al. (1984) have manufactured SoD2 and ScDT thin film targets (10-50gm) for neutron protection inside an intense neutron source for use in cancer therapy. The films must not be heated at temperatures over 723 K to maintain their chemical stability.

2.10.2.2. Erbium. Thin ErD2 or ErT2 films are used for neutron generator targets (or tubes), for high-intensity rotating target neutron sources, for radiotherapy, and for high- intensity neutron sources for cancer research.

Provo (1979) has studied the hydriding process for the following system: Er (400- 600nm thiek)/Cr (100-500nm thick)/Cu (substrate). He determines that to achieve an E r D 2 / T 2 occhider film gas-to-metal atomic ratio of 1.7, a minimum of 150nm of Cr underlay is required for an in situ hydriding process, whereas such a minimum is 300 nm for an air-exposed hydriding process. The formation of oxides at each interface and the interfacial metal loss (diffusion) at the Er/Cr edge can limit the optimum hydriding process. Another characteristic of ErT2 films has been studied by Mitchell and Patrick

142 M. GASGNIER

(1981) and Mitchell and Provo (1985). They report the temperature dependence and irregularities of helium release rates from EfT2 films. Some fragmented results had been reported previously by Beavis (1980), Beavis and Kass (1977) and Kass (1977). Mitchell and Patrick (1981) give details on He release fraction as a function of aging and of temperature. The samples are aged over very long periods (70-2587 days), either maintained at different temperatures (from 77 to 500K) or sometimes annealed in the course of aging. The main results indicate first that large changes in He release rates follow immediately upon temperature changes and second that the accelerated release process is reversible. Then, Mitchell and Provo (1985) observe that nonuniformity of the release is greatest for samples undergoing the transition into accelerated release, which occurs when the oecluders (EFT2 films, 0.5-2 ~tm thick) approach the maximum quantities of helium that they can retain. It is concluded that the variability in He release rates might be due to a bursting activity: 3He is released in bursts of at least 109 atoms; this release is also stimulated by vibrating or flexing the film substrates.

Holloway et al. (1978) and Antepenko and Holloway (1980) have studied the degradation of ErD2 and ErT3 films, ranging in areal density from 0.012 to 0.534 mg/cm 2, and deposited by e-beam onto Mo substrates. It is shown that the total unavailable metal for the nonannealed films, if converted to total oxide, would be 11.5 nm. For in situ hydrided films this thickness does not excess 5 nm. It has been also determined that 0.01 mg/cm 2 of Er is not hydrided for films that were e-beam deposited and in situ hydrided. Lastly samples subjected to vacuum annealing at 773 K (1 h) exhibit a total nonhydrided metal quantity of ~0.02 mg/cm 2, therefore a total surface oxide level of 16.5 nm.

2.11. Formation of the rare earth nitrides

The formation of pure rare earth nitrides is often difficult to carried out, because the presence of oxygen can lead to the formation of oxynitrides. However under certain experimental conditions it is possible to form pure nitrides.

One of these procedures consists of carrying out the interaction of nitrogen with continuously renewed films of rare earth metals as reported by Varkanova and Nazarov (1977), Varkanova and Morozova (1981), Varkanova (1982) and Varkanova et al. (1982). These studies have been done for Sc, Y, Sm, Gd, Er and Yb metals. The absorption of nitrogen has been investigated as a function either of the rate of condensation of the metals, or of the temperature (between 298 and 473 K), and/or of the nitrogen pressure (between 10 -6 and 5x 10-4pa). The most important study is relative to the sticking coefficient of nitrogen against the various parameters above-mentioned. In a general manner, the functions obey linear, increasing or decreasing, laws. Two kinds of composition have been observed. For scandium in the gas-excess regions it forms a single- phase nitride system (ScN0.9, fec with a = 0.453 rim). In the metal-excess region there is a mixture of two phases: one relative to the metal and the other to the nitride. Varkanova (1982) has also established, as a first approximation, that the changes in the sticking coefficient are due to the heat of sublimation of the metal: higher heat of sublimation


leads to higher sticking. The nitrogen absorption of rare earths is always compared to that of titanium which seems to be similar.

Another technique has been carried out by Ma et al. (1987): thin films (150nm thick) are deposited onto Si or NaC1 substrates, and then irradiated at high dose with nitrogen ions (2-5×1017N+cm-2). In the case of gadolinium there is, at lower doses (2 × 1017N+cm-2), formation of a compound of which the crystallographic parameters do not exactly correspond to the lattice standard value of GdN due, probably, to a deficiency in nitrogen content. In the same way, XRD indicates that the gadolinium lattice is also not correct. This is possibly due to a metastable structure of gadolinium supersaturated with nitrogen. At higher doses the GdN compound becomes predominant and the interplanar spacings are close to the standard values. However, one must remark that the correct XRD interplanar spacings show clearly that the "so-called" Gd (110) line (with a low intensity) with a spacing value of 0.187 um is in fact the (220) line of GdH2. In this way the formation of a new metastable compound seems less probable. The presence of hydrogen throughout the starting material is once again not surprising (the authors do not give their vacuum evaporation parameters).

2.12. Reaetioity with CO, C02 and CnHn gases

2.12.1. Rare earth~CO and CnHn interactions

In an earlier chapter of this Handbook series, Netzer and Bertel (1982) have reviewed work carried out in order to study the reaction of rare earth metal surface with carbon monoxide. Affrossman (1981) has studied the reactions of CO with clean scandium film. He reports, from XPS experiments, that this metal dissociates CO to form a carbide and sorbed oxygen. The behavior of scandium shows strong similarities with that of tungsten. In the same way methanol and ethanol dissociate to leave oxygen preferentially at the Sc surface at low exposures and to form carbides at higher doses. In this case, there is formation ofa "~-CO" type layer. Cern~ and Pientka (1987) and Cern~, and Smutek (1990) for thin Dy films (150 nm) report, from calorimetric experiments (heat measurements), that CO dissociates on the metal surface (see also Surplice and Brearley 1978). This is followed by rapid penetration of the oxygen atoms (formation of the oxide), while the carbon atoms remain on the surface and cause a gradual blocking. They do not observe the formation of carbides. Moreover, it is determined that the rate of heat production is fairly high, but lower than with hydrogen at the same H/Dy ratios (Boeva et al. 1986).

From mass spectrometry studies Curzon (1984) reports that the reduction of CO, inside the vacuum chamber, leads to the formation of CH4 (and consequently of CH3, CH2 and CH). The results indicate that the CH4 (and also H2) arises from the reduction of the CO (and also H20, which reacts with CO). That is another way to explain the formation of hydrides with rare earth thin films. The adsorption of C3H6, C2H2 and CH4 on clean polyerystalline Dy films at 295K has been studied by Cern~ and Smutek (1990). The experiments suggest that at low doses, the gases are completely dissociated into C and H atoms. The bonding of these atoms to Dy is assumed to be equivalent to that which

144 M. GASGNIER

occurs in chemisorption of CO. That leads to a surface-blocking effect of the formed species, and Dy films possess a higher chemisorption capacity for C2H2 than for C3H6.

2.12.2. Lanthanide/C02 reactions

Little research has been carried out to study lanthanide/CO2 reactions (see Netzer and Bertel 1982). Mehrhoff (1980) has studied the gettering of CO2 by erbium thin films deposited onto Mo substrate discs heated at about 700 K. The reaction begins near 570 K in an abrupt manner (no reaction is detected with Mo). Mehrhoff (1980) also reports isothermal measurements, ratios of CO2 pumped by the films at various temperatures (from 890 to 1185 K), sticking coefficients versus exposure to CO2, and monolayers of CO2 absorbed as a function of the temperature. It is also shown that there is formation of CO near 770 K, that could be due to the interaction of CO2 and erbium metal. Arakawa et al. (1988) have reported the dissociation of CO2 on some rare earth (Pr, Nd, Sm, Dy and Er) films (1 ~tm thick). The oxidation of the metal is investigated by measurement of the resistivity of the films. Under CO2 atmosphere the resistivity increases strongly: for Dy, at 603 K, it is 14 times that at 298 K. Above 823 K the films have insulating properties due to the metal --+ sesquioxide transformation. For praseodymium the resistivity behaviour is fully different, which is possibly due to the formation of a non-stoichiometric oxide.

3. Metallic R-alloys

Metallic R-alloys are now being studied increasingly in order to obtain numerous manufactured products. However, as for pure metallic thin films, the cross-shaped problem is the contamination by atmospheric gases. This is a dramatic feature, not always pointed out by numerous research groups, and it can be on the contrary a benefit in the case of hydrogen storage materials like RNi5 or RCos.

3.1. Permanent magnets

3.1.1. Introduction Numerous papers have been published on these permanent magnet materials; we cannot list all of them in this chapter (see Burzo and Kirchmayr 1989 and Gasgnier 1991 for example). A publication of the Gorham Advanced Materials Institute (May 10, 1991) showed that the global permanent magnet market was clearly influenced by the increasing NdFeB sales ($2.7 billion or 12.652 metric tons, therefore 17% of the market), and by the continued penetration of RCo alloys (11% of the market).

One of the most important problems relative to the synthesis of these materials remains the formation of new phases and structural inhomogeneities inside the matrices. From XRD after heat treatment at 740K of NdFeB melt-spun ribbons, Strzeszewski et al. (1990) have pointed out four phases: Nd, Nd203, and two (Nd, Fe)O iron-rich phases (with tetragonal and hexagonal structures, 70 at.% and 85 at.% Fe, respectively). TEM imaging showed that such phases were present as spherical groins. As different kinds of


phases can be formed, it follows that the magnetic properties can be different from one sample to the other. The aim of this section is to report the new experiments and results obtained since about 1987.

3.1.2. [R(Pr, Nd),R' (Dy)]xFeyBz alloys In a previous paper (Gasgnier 1991) we have shown that, since 1984, the research and development on these materials was growing more and more. Thus, there are a lot of recent papers which give details on new experimental methods and unusual synthesis treatments.

3.1.2.1. Magnetic properties. 3.1.2.1.1. Thick and thin films. Sputtering deposition methods of R-TM permanent magnet films (SmCos, Sm2(Co, Fe, Zr)17, Sm-Yi-Fe and Nd2Fel4B) which exhibit high intrinsic coercive forces, large remanent moment values, and special anisotropies have been studied by Cadieu (1988). In the case of thick crystallized Nd2FeI4B films (thickness 0.8-3.2 ~xm), Cadieu claims that, as a function of the sputtering rates, it is possible to synthetize in-plane or perpendicular easy direction of magnetization. So, at deposition rates <0.18 nrn/s the films are easier to magnetize perpendicularly to the plane. Such specimens possess higher remanent magnetization (~1 T) than in-plane magnetic films (~0.6 T). An XRD trace (between 10 and 18 °) shows only the presence of the reflections relative to the tetragonal structure (a = 0.880 nm and c = 1.218 nm) &the Nd2Fe14B alloy.

The crystallization behavior of rf sputtered amorphous films (4 and 8 ~tm thick) have been studied by Homburg et al. (1990) and Gu et al. (1990). The films when annealed at 886 K begin to crystallize and are fully crystallized at 1023 K as the NdzFe14B phase. At 1123 K a small amount of (x-Fe was observed. At a slow sputtering rate deposition and after annealing at 1023 K, an unknown phase was formed. Such a sample exhibited a higher coercivity (>1256kAm-1). The sputtered and annealed (up to 823K) films are magnetically soft with a low coercivity (<800kAm-1). The former present an in- plane magnetization suggesting the existence of anisotropy. After annealing above the crystallization temperature, a hard magnetic phase is formed. The coereivity reaches a maximum at 1023 K and then decreases rapidly (due possibly to the formation of large grains containing many domains). SEM observations show that films deposited at a rate of 0.8 nm/s have a dense packed structure (block-like grains with a laminar substructure) whereas films sputtered at a rate of >l.5nm/s exhibit a columnar structure with voids between the columns. The latter possess an effective vertical anisotropy. It is concluded that grain size and orientation are the most important factors determining the coercivity. Other parameters are the degree of isolation between grains and the density of faults which increases with the sputtering rate.

For the thinnest amorphous films (100nm) deposited by triode sputtering onto substrates maintained at 293 and 77K, and then annealed upto 773 K, Alameda et al. (1990) show that the in-plane magnetic (induced) anisotropy, measured at the glass-film interface, increases at low temperature and falls to low values after annealing. The same

146 M. GASGNIER

result is valid for Ku. The authors give a clear correlation between the behaviors of these macroscopic and microscopic anisotropies (i.e. the product of the magnitude of local anisotropy and the volume where the principal axes of these anisotropies are correlated). 3.1.2.1.2. Multilayers and modulated films. Aylesworth et al. (1988, 1989) report the properties of Nd17(Fe0.9Co0.1)76B7/Fe or Ag sputtered multilayer specimens deposited onto mica or tantalum substrates at different temperatures (between 293 and 993 K). The individual layer thicknesses are 10-50urn for the alloy and 0.5-20 nm for the Fe or Ag, the total thickness being 1 ~tm. After annealing at 873 K, XRD reveals first the formation of the Nd2Fe17 and AgNd alloys, and second the presence of a contaminant labelled as "NdO" with a fcc structrue (a0 ~ 0.510 nm). One must point out that this compound does not exist. Moreover, although the measured interplanar spacings (0.288 and 0.250urn for the two first diffraction lines) are consistent with a fee lattice (dm/d2oo = 1.15), they have been indexed as a bcc structure, i.e., according to the (110) and (200) planes (dllo/d2oo = 1.415). In fact, the value of the fcc lattice parameter corresponds to that of NdNxOy which is formed after moderate annealing of R thin films (Gasgnier et al. 1976). This compound cannot be confused with NdH2, NdN, or C- and A-Nd203. The authors observe that the "NdO" contaminant diminishes in amount when the mica substrate is covered by an Fe layer (50nm) and disappears completely if a Ta substrate is used. However, in the case of (ProrNd)2Fe14B/Ta cosputtered multilayers this contaminant coexists with the Nd2Fe14B and Fe2Ta alloys (Aylesworth et al. 1991). But, in the case of Pr2Fe14B/Pr or Ta multilayers this contaminant is not observed (Aylesworth et al. 1990, 1991). Multilayers which are contaminated have larger coercivity, lower magnetization and are more randomly aligned than clean films prepared under similar conditions. The grain orientations and the anisotropies strongly depend on the substrate material and the in- situ applied magnetic field. So, non-multilayer samples deposited onto mica tend to have larger Ku than similar films deposited onto Ta. Moreover a magnetic field (104 kA m -1) applied parallel to the film plane during Nd2(FeCo)14B formation, produced films with in-plane anisotropy. For these samples, after annealing between 723 and 873 K, He can reach values as 800kAm -I at 293 K. Variations of Hc versus maximum applied field (NdFeB/Fe samples), temperature (PrFeB/Pr samples) and nominal Ta thickness ((Pr or Nd)FeB/Ta samples) are shown in figs. 15, 16 and 17, respectively.

Martinez et al. (1988a,b) have investigated Nda6Fe68B6 or Nd12FesoB6/Fe92B8 compositionally modulated films with a modulation length varying between 0.34 to 5.47 um for the Nd-rich alloy, and a thicker Fe-rich layer (200 urn). At helium temperature and as a function of the applied magnetic fields (perpendicular or parallel to the substrate), the magnetization increases as these fields increase. From hysteresis loops it is shown that the spin-wave modes (collective excitations) depend on both the thickness and the modulation of the multilayers (geometry of the samples). The perpendicular magnetization values decrease as the modulation lengths increase. This phenomenon may be attributed to the increase of the number of paramagnetic Fe atoms, as deduced from Mtssbauer spectra which show an increase of the paramagnetic doublet contribution with increasing modulation length. From these spectra it is shown that both the hyperfine fields and the easy magnetization magnitude are not correlated.


8 ° C3 c£

:£o

I 1 i I

perpendicular

T=2OOK X ~ f l ~ I ~ 1 1 1 ~

210 410 610 810 Hma × (kOe)

Fig. 15. Coercivity versus maximarn applied field at T=200K for a NdFeB (20nm)/Fe(0.5nm) sample. The result indicates that magnetization reversal in the easy direction is controlled by a domain-wall pinning mechanism. (By courtesy of Dr. D. Sellmyer, Behlen Lab. of Physics, Univ. Nebraska, Lincoln, NB, USA).

O tO

(U C)

3~

' I ' 1

• - - zoo ~: 40 ~, ",,,%,.',,, + - - 200 ~: lo ~ \ " , ~ A - - iO0 $,: I0 A x - - I lam

0 100 200 300

T e m p e r a t u r e (K )

18

-$- O 9

O -r

NFB(200 A):Ta(X A) ' r a n d o m ~

/ NFB(200 A):Ta(X A) 'aligned'

PFB(200 A):Ta(X A)

0 , , I J ~ , , I , ~ , , l , ~ l , , , ~ l , ~ , , l J , , ,

0 5 10 15 20 25 30 35 X

Fig, 17. Coercivity versus nominal Ta thickness with the field applied perpendicular to the film for "aligned" PrFeB (20nm)/Fe (xnm) and "aligned" and "randomized" NdFeB (20nm)/Ta (xnm) films (By courtesy of Dr. D. Sellmyer).

Fig. 16. Summary of coercivity versus temperature data with the field applied perpendicular to PrFeB film plane. (By courtesy of Dr. D. Sellmyer).

3.1.2.1.3. Magnetic domains. In a general manner magnetic domains are observed either by means o f Lorentz electron microscopy investigations (thin specimens) or by decorative methods (thick samples). In the first case, Bras et al. (1988a,b, 1990) have improved the suitable conditions to investigate magnetic domain nucleation, domain wall motion, domain size and wall energy in highly uniaxial magnetocrystall ine anisotropy materials. This technique is available by using the magnetic field o f the standard objective lens

148 M. GASGNIER

which induces magnetic structure variations and by optimizing the grain orientation (i.e., a small angle between the anisotropy axis and the normal to the foil). The "optimal orientation" is obtained by means of a rotating specimen holder. This allows separate study of small grains and their interactions. In the case of a thinned Nd2Fe14B ribbon the authors have determined from the unusual Foucault mode images the wall width, the diameter of bubbles near stripe domains (70-100nm) and their stability, the global grain magnetization which permits one to deduce that the reversal domain nucleation arises under the influence of a demagnetizing field, and the neighbouring grain influence (abrupt change in the grain magnetization). Examples of strip domains obtained by 200 kV Foucault images are shown in figure 18.

In another set of experiments Griitter et al. (1988, 1990a,b) have used magnetic force microscopy (Heinzelmann et al. 1987) to study Nda4FeglB5 materials having optimum magnetic properties. This allows them to observe magnetic domains in air, and to achieve a high lateral magnetic resolution (<10 nm). The authors notice that Lorentz microscopy images look similar to those obtained by this technique; They observe the formation of polyhedral-shaped domains (600-700 nm in size) and of double-peak structures separated by less than 10 nm. But a conclusive interpretation has not been given up to now. In the same way, domain walls are observed as being very sharp due to efficient pinning of which the exact nature remains unclear.

3.1.2.2. Hydrogen treatments. To produce coercive powders for the processing of permanent magnets McGuiness et al. (1986, 1989a,b, 1990a,b) have used hydrogen. In a first route they have produced N16Fe76B8 and Nd14.sDyl.sFe76B7 alloys by a hydrogen decrepitation or attritor/jet milling. The former induces larger magnetic parameters, e.g., the coercivity is 1040kAm -1 and 1600kAm -1 for NdFeB and NdDyFeB, instead of 720 kA m -1 for a sample prepared by attritor milling. This coercivity is achieved for an average grain size of <14 ~tm (for larger grain sizes the value of He decreases). To avoid excessive grain growth the sintering temperature must be reduced to below 1313 K for a 1 h sinter. In addition, a Nd-rich phase has been observed at grain boundaries, and the NdFe4B4 phase is also detected. This research group has used another treatment as an effective processing route to produce polymer-bonded magnets. These are made by a hydrogenation=disproportionation-desorption process which leads to the production of fine-grained homogeneous isotropic materials which exhibit appreciable coercivities (604-1040kAm-1). The optimum temperature was found to be 1058K. Thermal treatment strongly affect, here again, the grain size, and therefore the magnetic properties. This process leads to roughly spherical grain powders (~500 gm in diameter), whereas hydrogen decrepitation leads to flake-like powders with a great proportion of fine debris. From Ndl6Fe76B8 and Nd2.1FelaB materials, heated at -1073 K, and then quickly cooled in hydrogen to 298 K, the formation of different crystallographic structures has been observed. These have been indexed from XRD as a-Fe (bcc, a = 0.287 rim), NdHx (fcc, a=0.546nm), Fe2B (ferromagnet tetragonal with a=0.511nm and c=0.425nm) and NdFe4B4. The formation of the hydrided variant NdEFelaBHz7 has also been observed (MeGuiness et al. 1989b). The authors conclude, first, that disproportionation takes place


Fig. 18. 200 kV Foucault images of strip domains due to demagnetizing field relative to Nd2Fe14B monocrystals. (a, b) Opposite domain contrasts due to change of sign of the angle between lens field and anisotropy axis. (c) Softening contrast due to the decrease of the magnetization component (the electron beam deviation becomes weak for low angles). (d) No domain contrast (angle close to 0°). (By courtesy of Drs. J. Bras et al., Lab. Physique du Solide, Univ. R Sabatier, Toulouse, France).

150 M. GASGNIER

during the production of the high-coercivity powder (for the sample not subjected to a vacuum annealing treatment), and second, that the development of this high coercivity can be ascribed to the reforming of crystals of Nd2Fel4B and the establishment of a fine optimum grain size.

3.1.2.3. Microstructuralproperties. As discussed earlier (Gasgnier 1991) disorder seems to rule over the nature of the various mierostructural phases which are formed either during synthesis or in the course of the preparation of the samples for TEM investigations. For example Hole et al. (1990) noticed that the phases are different according to the mode &preparation: ion erosion or electropolishing. Ramesh et al. (1987) observed for a (Nd, Pr, Ce)2Fe14B thinned alloy, the formation of a fee phase (a = 0.524 nm) and of a bee one (a-0.290nm). They conclude, on the basis of results published in 1961(!), that the former is a "NdO" phase wich contains some dissolved Fe, and that the latter is a ion-milling artifact. Such structures are observed at the grain-boundaries. Fidler (1987) and Fidler and Tawara (1988) for electropolished and ion-milled NdlsFeyTB8 specimens report the formation of the following structures: Nd2Fel4B, NdFe4B4, four Nd-rieh compounds located at grain boundaries, and a-Fe precipitates. One of the Nd- rich phases, NdzFeB3, has been recognized within the phase diagram. Other ones also identified are: A-Nd203, NdC12, Nd chlorate and Nd(OH)2C1. Such contaminations are very prejudicial to magnetic properties, more especially the Nd-ehlorine phases which contain a high density of dislocations. The problem of the Nd-rich phases has also been studied by Tang et al. (1988) who report the formation of a fee structure (a -- 0.510 nm) as do Aylesworth et al. (1989, 1990). From Auger spectra, Tang et al. (1988) conclude that this phase is a Nd-Fe-B-O quaternary liquid phase. These authors observe another Nd-rich phase with a dhep structure (a=0.365 nm and c = 1.180nm) which is that of Nd metal. Hole et al. (1990) observe also at grain-boundaries the formation of such Nd-rich phase with Fe and B additions. They identify, from Auger spectra, the presence of a-Fe mierocrystallites and Nd203 and B203 inclusions. They conclude that during annealing the quantity of hard magnetic phase increases due to the reaction of Fe excess with the Nd- rich phase; on fast cooling, precipitation of ct-Fe could contribute to magnetic hardening.

Iwamura et al. (1990) observe a grain-boundary phase with a tetragonal structure (a=0.512nm and c=0.800nm) in NdzFe14B ribbons (45-100~tm thick) with high H¢ (1840 kAm-1). It is metastable and decomposes into "fee Nd" and NdHFe4B4 on heating at 963 K. On the contrary, G.X. Huang et al. (1990) claim that their Nd13.sFes1.75B4.75 melt-spun thinned ribbons are single phase which explains their high coercivity. After annealing at 573 K an unknown intergranular grain-bonndary phase is formed. Koestler et al. (1989), from TEM observations and EDX microanalyses, have deduced that the grain-boundary fee phase was Nd75Fe25. The a0 parameter (a0 ~ 0.560 nm) is however incompatible with any of the NdFe (O?) known structures, but it could possibly be linked to a [Nd(Fe)]203 bcc compound. Indeed the C-Nd203 compound with ac = 1.116 nm (i.e. a0 × 2) can be confused with a fee compound. In this way, the weak (211) reflection does not appear in EDP, and only the (222), (400), (440), (622) and (444) reflections are observed.


In the case of Co-substituted Ndls(Fel-xCox)77B8 samples, Koestler et al. (1989) report the formation of two fcc phases. The first one is defined as Nd(Fe, Co)2 with a fcc structure (a=0.730nm). The second has a fcc lattice (a=0.540nm) and composition Nd20(Ndl-xCox)80. The authors claim that this phase is close to that of Nd6Fe23 (fee, a = 1.210nm), but there are few correlations between the lattice parameters. They have not observed the Ndl.lFenB4 compound. Yamamoto et al. (1987) for NdlsFe77-xCoxB8 (x = 0-77) and Nd24Fe58Co10B8 materials observed the following NdCo alloys: 1:3, 2:7, 5:19, 1:5, 1:2, 7:3, and 3:1; and the Ndl.I(Fe, Co)aB4, Nd(Fe, Co)2 and Nd3(Fe0.sCo0.5) intermetallics. The Nd(Fe, Co)2 phase may be formed peritectically and acts as a nucleation site of reversed domains. In the case of the Nd24Fe58Co10B8 sample the Nd2(Fe, Co)14B, Nd-rich and B-rich phases are not observed. Strzeszewski et al. (1988) have studied rf sputtered Nd16.5(Fe0.9Co0.1)76.sB7 films (1-2 gm thick). XRD reveals the coexistence of the 2:14:1 hard phase with the fcc (a = 0.512 nm) phase. The amorphous- crystalline transition is observed at 878 K. Thin samples observed by TEM show the coexistence of ct-Fe and an amorphous phase. After annealing up to 1003 K Nd203 is formed. To prevent oxidation and obtain the hard magnetic phase, the films must be covered with a thin gold layer (20 nm). Lorentz microscopy reveals the presence of various domains predominantly parallel to the film plane.

Cochet-Muchy and Paidassi (1988) have studied the problem of the effects of oxygen for different solidification conditions of NdlsFe77B8 samples. For as-cast materials they observe the following phases: Nd2Fe~4B, ct-Fe, NdL1FeaB4, Nd-rich phase, C-Nd203, Nd(OH)3, Nd82.sFe2.5Ox (as do Ramesh et al. (1987)), and Nd55Fe25020 or Nd7Fe55031. One must also point out the Auger analysis results of Jaswal et al. (1988) who report for different R2Fel4B (R = Y, Nd, Gd) materials, that the surfaces present a high degree of oxidation after exposure to the atmosphere. Reduction of these oxides is achieved by heating in the presence of H2 or CO (C, S and N as contaminants are also detected).

In conclusion one must point out that the synthesis of Nd2Fel4B pure hard magnet films has not been achieved. The formation of various phases, often labeled with chemical formulae which are not known to exist, is observed as a function of the thermal treatments, the purity of the starting materials, the contamination by various gases . . . . The most likely contaminant seems to be oxygen. However, numerous authors do not know the chemical properties of the transition metals and deduce new metallic or oxide compounds either from the value of the lattice parameters of from "tentative" identifications. So, Aylesworth et al. (1991) for Pr2Fel4B (20nm)/Pr (4rim) multilayers claim the formation of a "PRO" oxide (as for "NdO", Aylesworth et al. (1989)). One must also notice that these phases are generally located at grain boundaries, or are present as small particles, or are observed as amorphous states. This problem is also encountered in the new high-Te superconductors: it is very difficult, during synthetization, to avoid the formation of isolated phases; they always affect the physical properties of the superconductors as well as the supermagnets.

3.1.2.4. Other compounds: RFe(N or C). Recently, new types of compounds have been prepared. Sellmyer (1991) has studied the magneto-optic properties of R2Fel7Nx (x ~ 4) alloys as thin films. Such a material crystallizes according to a rhombohedral structure.

152 M. GASGNIER

In the solid state, Jaswal et al. (1991) have studied the structural parameters and the magnetic moments of (Nd, Y, Lu)2FeI7 and (Nd, Y, Lu)2Fel7Nx alloys. They observe, for instance, a significant increase in Curie temperature upon nitrogenation. Coene et al. (1990) have investigated the magnetic and crystallographic properties of Y2FetTCx (0 ~<x ~< 16) compounds. As a function of the increasing carbon content they observe a structural change from the hexagonal Th2Nil7 type to the rhombohedral Th2Zn17 type. Near the phase transition there appears a partial disordering of the lattice leading to an X-ray pattern which has CaCus-type base reflections. EDP also reveals such a disorder. It is observed that the lattice constants increase as the C content increases. The crystallographic properties are reported in terms of stacking sequences.

3.1.2.5. Ndl.IFe4B4. The Ndl.IFe4B4 (B-rich) compound, observed by different authors mentioned above, has been studied in detail by Zhao et al. (1989a-d). They have demonstrated from EDP and TEM observations that thinned materials are tetragonal (a=0.711 nm and c = 0.389 nm) with an incommensurate structure in the c direction of the tetragonal lattice (Zhao et al. 1989a,b). The specimens are highly planar-faulted. Refinements of the results have led to the conclusion that, in fact, this compound exhibits the characteristics of infinitely adaptive structures (Zhao et al. 1989c,d). Several different superstructures have been observed, which coexist throughout the matrices and may be related to local fluctuations of the composition. In the case of Co-substituted samples the crystal structures are built up of an interpenetrated Nd-substructure and a (Fe, Co)- B-substructure. Similar results have been reported for Cel.IFe4B4 alloys by L. Li et al. (1990).

3.1.2.6. AI, Cr, Mn, Ga, Nb, Zr, Cu and W addition effects. 3.1.2.6.1. AI addition. For NdlsFe66Co10BsAll magnets, Yamamoto et al. (1987) have observed that the Ndx(Fe, Co)y Laves phases become unstable with A1 addition, decomposing into the Nd3(Fe, Co) (non-magnetic) and Nd(Fe, Co)3 (magnetic) alloys. The former is supposed to be peritectically formed around Nd2(Fe, Co)24B grains to magnetically separate each grain and suppress domain walls in the matrix. Therefore, A1 addition increases coercivity but weakens intrinsic magnetic properties (Rodewald and Fernengel 1988); consequently the improvement must be due to microstructural changes.

Such an increase of He has been measured by G. Schneider (1988), Grieb et al. (1989), Knoch et al. (1989a,b, 1990a,b) and Fidler et al. (1989) for A1, A1N or A1203 additions. For instance, the maximum recorded Hc value can reach 1400kAm -1 after annealing at 873 K of a Nd2FeT1B6A12.3 material. The as-sintered material has a coercivity of 800kAm -1, and an undoped material exhibited a He value of 60kAm -1. The microstructural properties studied by EDX and EDP vary from one sample to another: probably due to a contaminant whether or not it has been detected. According to Fidler et al. (1989) and Knoch et al. (1990b) five different structures have been recognized:

(1) fce (a = 0.520 nm) labeled "~'-Nd" (Nd-rich); (2) rhombohedral, as NdsFe3B6; (3) Laves phase, as Nd(Fe, A1)2 (low A1 content, stable up to 873 K);


(4) hexagonal (a=0.380nm and c= 0.600 nm), as Nd203; (5) hexagonal (a=0.390nm and c=0.610nm), as "(zI-Nd ''. (Other phases, such as NdsFe2(B, O)x, Nd36Fe63Alx (2.5 ~<x ~< 5), Nd33Fe67Alx (7

<x <25), have also been detected, by EDX experiments). One must remark that "(~- and ~-Nd" do not exist in the phase diagram. The first one (hexagonal) is observed upon A1203 addition and it is characterized by a low Fe content (4.5 at.%). Its parameters, close to those of A-Nd203, are possibly slightly enlarged by the presence of Fe atoms in the Nd203 lattice. The second (ice with 7 at.% Fe) remains fully unknown, and cannot be compared to the fcc/3-La structure (Fidler et al. 1989). From these results the above- mentioned authors find a correlation between the microstructure of their materials and the wetting behavior of the liquid at the sintering temperature. Particularly it is responsible for the separation of the Nd2Fe14B grains by a nonmagnetic phase which would suppress the magnetic interaction between the grains. Therefore enhancement of He results from a higher contiguity of the intergranular region and from the suppression of the nucleation sites for reversed domains (surface hardening of hard magnetic grains). 3.1.2.6.2. Cr and Mn additions. Rodewald and Fernengel (1988) have observed that Cr additions (up to 5%) increase Hc, do not change the anisotropy field and facilitate numerous magnetic parameters (particularly the nucleation of reversed domains). On the contrary, Mn addition decreases He. 3.1.2.6.3. Ga addition. Fidler et al. (1990) and Knoch et al. (1990a) report that Ga additions enhance He. So, for a NdlsFe61-xCo17BTGax material for x--O, 1.7 and 4.24, He has been measured as 584, 1308 and 1456 kAm -1 respectively. Various phases such as NdCo2, Nd(Co, Fe)3, Nd(Co, Fe)4 B4, Nd(Ga, Fe, Co), Nd(Ga, Fe, Co)2 and Nd-rich (hexagonal) have been detected as intergranular compounds. The hard phase showed the presence of domain walls (Lorentz microscopy). In the bulk state Grrssinger et al. (1990) reported a large number of magnetic properties for the Nd(Fe0.9-xB0.08Gax)5.5 materials. 3.1.2.6.4. Nb addition. The magnetic properties and the microstructure of Nb-containing (Nd, Dy)FeB materials are reported by Parker et al. (1987a,b). As Nb content increases the He values are enhanced (1040kAm -1 without Nb and 1280kAm -1 with Nb). Four phases, other than the hard magnetic one, have been detected: NdFe4B4, Nd-rich (at grain boundaries, as small coherent precipitates) Fe2Nb (as large inclusions) and (x-Fe. The presence of these precipitates would increase H e in sintering and melt-spun samples. Allibert (1989) for NdlnNblFe78B7 alloys observed, as a function of the annealing temperature, the formation of different alloys and compounds: Nb3Fe3B4, and Nd-rich at 1273 K; Ndl.IFe4B4, Nd-rich (containing chlorine), pure Nd and Nd2FeB3 (as needles) at 873 K (figs. 19a,b). It is noted that under equilibrium conditions Nb does not dissolve in the Nd2FeI4B phase and cannot alter its intrinsic properties. 3.1.2.6.5. Zr addition. Identical conclusions have been reported for Zr-containing alloys by Allibert (1989). At 1273 K, three phases have been detected: Nd2Fe14B (without Zr), ZrB2 (as needles) and Nd-rieh (fig. 19c). As for Nb, it is concluded that the influence of Zr on NdFeB magnets is typically a microstructural effect. 3.1.2.6.6. Si addition. The interaction between ion-plasma sprayed NdxFe93-xSi2B5 films and Cu substrates has been studied by Linetski et al. (1990). The layers (40-70 ~tm thick)

154 M. GASGNIER

N b 3 F e 3 B 4

N d 2 F e l 4 B

Nd r i c h p h a s e

Ndl+eFe4B 4

Nd2FeI4B

Y

Nd

X

Nd2FeI4B

ZrB 2

Nd rich phase

Fig. 19. (a,b) Microstructures and chemical compounds in the Nd14NblFe78B7 samples annealed (a) at 1273K for 30h and Co) at 873K for 800h. (The Y phase contains chlorine and the X needles are close to the Nd2FeB 3 composition). (c) Microstructure and chemical compounds of a Ndj4Zr1Fe78B 7 sample annealed at 873 K for 800h. (By courtesy of Dr. C.H. Allibert, Lab. Thermodynamique et Physico-Chimie M&allurgie INPG, St. Martin d'H~res, France).


have a low Hc due to the formation of Nd-Cu phases. FiNer (1987) reports that under production conditions a large amount of Si is found and that Si atoms replace Fe atoms within the Nd2FeI4B grains. 3.1.2.6.7. Waddition. Bulk Nd~3Dy9Fe72-xCosWxB8 alloys (x = 0--1.0) have been studied by Rodewald and Schrey (1990). At 1373 K only 0.5-0.6 at.% W is dissolved, whereas at 1123 K the solubility drops to 0.4 at.%. For thinned samples TEM observations reveal the formation of rod-shaped particles (100-600 nm in diameter, 1-3 ~tm in length) relative to the orthorhombic WFeB compounds. Hc can reach 1360 kA m -1 for sintered magnets annealed at 803 K (x = 0.2 at.% W). The coercivity is determined by nucleation of reversed domains.

3.1.2.7. Applications. To our knowledge few patents (see also Gasgnier 1991) have been taken out in the field of thin films during the last years. Yamashita et al. (1988) have prepared NdxFexoo-xBy films (x = 13-27; y = 3-17) formed by sputtering under well- defined experimental conditions. The patent is concerned with preparing perpendicular magnetic films.

3.1.3. RTiFe(Co) alloys (R=Sm, Nd, Dy) 3.1.3.1. (Sm, Nd)TiFe magnets. The works ofKamprath et al. (1988a, b, 1990), Liu et al. (1988) and Cadieu (1988) deal with the synthesis of a (SmYiFe) phase with a high in- plane intrinsic Hc, e.g. 2800 kA m -1 at 293 K (4640 kA m -1 at 5 K). (No corresponding hard phase has been observed for the (NdTiFe) system.) The composition of this alloy has been assigned to be Sm(Ti, Fe)ll. As for SmxCoy sputtered films, the magnetic properties depend upon the experimental procedures. However, if such properties are of a high quality, it seems that the crystalline characteristics of this system are very difficult to define. Kamprath et al. (1988a) report that the magnetically hard phase coexisted with Sm2Fe17, (Sm+Ti)Fe5 and Sm(Ti, Fe)12 alloys, and assigned to the Sm(Ti, Fe)11 phase a tetragonal structure (a = 0.839 nm and c = 1.230 nm). In a second paper (Kamprath et al. 1990) this phase became hexagonal (a = 0.876 nm and c = 2.562 nm). Other alloys, such as SrnFe3, Sm2Fe7 and Sm(Fe, Ti)2, have been also observed. The last one is indexed from XRD to have a tetragonal structure (a = 0.709 nm and c = 0.781 nm). Demczyk and Cheng (1990) report in the case of ion-beam milled ingots, that convergent e-beam diffraction and EDP allow them to show that the SmTiFell structure is tetragonal (space group: I4/mmm) with a=0.830nm and c=0.475nm. (Stadelmaier et al. 1987, reported, from XRD, these parameters as a=0.857nm and c=0.476nm). EDX spectra (Demczyk and Cheng 1990, Cheng et al. 1988) showed that the stoichiometry of the magnetic alloy is close to 1:1:11.

3.1.3.2. (Sm, Dy)TiCo magnets. In the case of RTiCol~ alloys, Demczyk and Cheng (1990) and Cheng et al. (1990) have shown the presence of 1:12 and 2:17 phase mixtures. Convergent e-beam diffraction showed that the Sm2Fel7 phase is rhombohedral (space group: R3m) (a = 0.841 nm and c = 1.211 nm referred to the hexagonal axes). In the case

156 M. GASGNIER

of DyTiColl a hexagonal 2:17 form (space group: P63/mmc) was found (a=0.796nm and c = 0.795 nm).

Therefore, the crystallographic problems are not yet clearly resolved. This results assuredly from the great difficulty to synthesize pure stoichiometric alloys. So, the samples are constituted by the coexistence of several phases which are formed either in the course of the deposition of the materials, or during annealing, or yet within the amorphous--crystalline transition. This assertion can be illustrated by the results obtained by Sahashi et al. (1983) on Sm(Co, Cu, Fe, Ti)7 magnets, which crystallize in three polymorphic phases as Th2N17 (stabilized by Fe), Th2Nil7 (ordered states) and TbCu7 (stabilized by Cu and Ti). The hard magnetic properties depend, according to these authors, on the TbCuT-type phase stability.

3.1.4. Smx(Co, M)y substituted alloys (M=Fe, Cu and Zr) Cadieu (1988) and Cadieu et al. (1989, 1990) have synthesized SmCos, Sm2(Co, Fe, Zr) l 7

and Sm(Co, Fe, Cu, Zr)7 based sputtered films (2-10 ~tm thick). Such materials can exhibit an in-plane (static) energy product of 15-30 MGOe. The authors have demonstrated that this parameter strongly depends mainly on the texture of the films. In this case the c- axes of the crystallites lie in the film plane. Such a configuration can be obtained by strictly following the experimental procedures: sputtering, rare gas pressures, substrate temperature, substrate materials, applied magnetic field during sputter deposition and crystallization as a result. SmCo5 films with a (110) texture possess a substantially greater intrinsic He (1120 kA m -1) than (200)-oriented layers. Moreover, a lesser degree of in- film-plane anisotropy was observed in films directly crystallized than for films crystallized from an amorphous deposit.

In the case of substituted Co films Cadieu et al. (1989, 1990) have obtained a high static energy product of 30 MGOe for specimens deposited onto sapphire substrate precoated with A1203, and sputtered with a two-component Ar + 25% Xe sputtering gas. From XRD the authors conclude that the 2:17 H phase allows the magnetization to remain in the film plane (for the 2:17 R phase it does not). The layer must not have any a columnar growth pattern during deposition, because this introduces porosity and lowers the effective magnetization values. Lastly as a function of the sputter conditions, the Sm content can vary (films could be richer or deficient in Sm when compared to the target) and this can also change the magnetic properties of the films.

3.1.5. RCo(B) amorphous films 3.1.5.1. SmxCo~oo-x alloys. It now seems established that the main magnetic properties of these materials depend on the cation content. That is what is observed by Numata et al. (1988) and Lii et al. (1983) who discuss the origin of the anisotropy (see also Buschow 1984, Gasgnier 1982). It is shown that among the amorphous SmxCol00-x (9~<x~<44) magnetron sputtered films deposited onto substrates held at 313-413K, perpendicular magnetization is observed for a composition range of 18 ~< x ~< 26 and for a narrow range of substrate temperatures of 333-363 K. In this region, the anisotropy is

THE INTRICATE WORLD OF RARE EARTH THIN FILMS ! 57

positive and possibly due to a microstructure mechanism. Between 363 and 413 K the anisotropy is negative. It is concluded that no correlation occurs between stress-induced and growth-induced anisotropy and uniaxial anisotropy. Fang et al. (1988) report on the thermomagnetic effect of films subjected to high magnetic fields at low temperature. The results are discussed in terms of Sm moments to the magnetization.

3.1.5.2. Amorphous NdCoB magnetic thinfilms. Amorphous NdCoB magnetic thin films have been studied by Ratajczak et al. (1989, 1990a,b) and Ratajczak and G6sciafiska (1990). The amorphous layers (14-100 nm thick) are deposited by flash evaporation onto substrates cooled with liquid nitrogen. The starting material is a NdzCo14B compound. Some films are covered with a SiO protective layer. EDP reveals the amorphous or poorly- crystallized character of the films. It is unlikely that chemical microanalyses have been carried out. The authors report on the influence of annealing (from 523 K to 623 K) on saturation magnetization, Hall resistivity, spontaneous Hall coefficient (these three parameters decrease as T increases), and kinetics of structural relaxation. They notice that film thickness plays an important role in saturation magnetization and coercive field measured in the easy direction.

3.1.5.3. Applications. Thin (Sm, Pr, Ce, Nd, Y)Co65-85 ferromagnetic films have been manufactured by Harada et al. (1988) useful for recording materials and miniature motors. Miyamoto and Tazaki (1985) have fabricated magnetic discs, cards or tapes with Sml-xCox films deposited by coevaporation onto polyimide substrates.

3.2. (TM/R)n modulated and multilayered films. (R = Y, La, Ce, Nd, Gd, Tb, Dy; TM= Fe, Co, Ni)

3.2.1. (Fe/R)n films 3.2. l. 1. (Fe/Y),. By means of e-gun evaporation Badia et al. (1990) have investigated the magnetic properties of various Y(~3.8 nm thick)/Fe (1.3-4.7 nm thick) modulated films. By using a SQUID magnetometer they observed that Ms (at constant high applied field) decreases as the substrate temperature increases (from 0 to 200 K) and increases as the iron layer thickness increases. It is also shown that remanence and Hc are both small, and that the magnetization is in-plane. M6ssbauer spectra revealed different magnetic structure relative to each sample (i.e. the number of the Y-Fe sequences). It is concluded that both polarization of the Fe layers by the diffused Y atoms and the surface roughness are to be considered as a source for the random anisotropy.

From a dual e-beam gun system, Morishita et al. (1986, 1987) and Kajiura et al. (1987) observe that various kinds of sequences lead to various magnetic behaviors. For Fe thickness less than 0.6 nm magnetization disappears and an amorphous alloy forms; for thickness between 0.6 and 1.2 nm the iron magnetization is reduced; and for thickness more than 1.2. nm the iron bulk property is re-established.

158 M. GASGNIER

3.2.1.2. (Fe/La)n layers. Ferrater et al. (1990) have investigated the approach to Ms and thermal demagnetizing processes for several (Fe/La)n modulated films (300 nm thick). It is shown that Ms at 4.2 K is lower than for (Y/Fe)n films (except for larger Fe thicknesses) and that magnetization decreases as the temperature increases. Moreover, it is asserted that the La/Fe interfaceis constituted by mixing of Fe in the La which contributes to a small paramagnetic state, and that as a consequence of the interplay between the ferromagnetic layers and the Fe-La interfaces, the moments freeze over a wide range of temperatures in a spin glass-like state with a great deal of short-range ferromagnetic order.

3.2.1.3. (Fe/Nd)n and (Fe/Dy)n films. These two systems are often compared for magnetization measurements. In order to have a clear idea of the magnetic properties one must point out a short paper by White (1990) who discusses the results of studies relative to the alignment of R moments opposite to Fe moments. Indeed, Yoden et al. (1988), Hosoito et al. (1988a,b, 1989), Mibu et al. (1989, 1990) and Shinjo et al. (1989a,b) find that Dy moments align antiparallel to Fe moments, whereas Nd moments align parallel to Fe moments. This might lead one to conclude that there is an antiferromagnetic exchange interaction for Fe-Dy, whereas the F e N d exchange interaction should be ferromagnetic. According to White (1990), who invokes Hund's rule, the exchange interaction in both cases is, in fact, antiferromagnetic (see also Carbone et al. 1990). The main results given by ¥oden et al. (1988), Hosoito et al. (1988a,b, 1989), Mibu et al. (1989) and Shinjo et al. (1989a,b) do indicate that, as a function of the temperature, the magnetization changes direction, from in-plane at high temperature to perpendicular at low temperature. The magnetic properties are discussed as a function of the Dy and Fe thicknesses. For instance, with decreasing thickness of the Dy layer (below 3 nm), Ku of the Fe layer becomes dominant, which probably originates from the magnetic coupling of the Fe/Dy interface. In the case of thin Dy layers (below 2 nm) the Fe films are amorphous with a magnetic transition at about 270 K, close to that of the bulk amorphous Fe. In the case of Fe/Nd samples a gradual spin reorientation takes place which is discussed as a function of the Nd moment. The experiments have been carried out from neutron diffraction, MSssbauer, and SQUID magnetometer measurements. XRD clearly shows the crystallographic changes of the samples, prepared with a dual e-gun system, according to the thickness of the Nd layer: the dhcp phase of Nd metal and the bcc phase of Fe are well-resolved.

Sellmyer and Shah (1987), Tiwald et al. (1988a,b), Shan et al. (1988) and Shan and Sellmyer (1988, 1990) have investigated the structural, magnetic and magneto-optic properties of (Fe/Nd, Dy)n layers (300 nm thick) prepared by a multiple-gun system. The main results show that Ku depends on the thicknesses of the Nd, Dy or Fe layers. The origin of the parameter is discussed in terms of high density of R-Fe pairs oriented perpendicular to the films. The authors report on a great number of magnetic properties as a function of the thicknesses of the R and Fe layers: magnetization, volume anisotropy energy (which is found to be larger than that of crystalline Fe), coercive field, and also magneto-optic properties such as Kerr rotation and real part of the dielectric constant. XRD indicates that a 4 nm Fe/5.6 nm Dy film has a crystalline structure, whereas a 1.5 nm Fe/1.4 nm Dy film


is badly crystallized. The indexation of the XRD patterns would allow one to conclude that the c~-Fe and Dy phases coexist (Shan and Sellmyer 1988). For (Fe/Nd), layers Sellmyer and Shah 1987 report that the samples are well crystallized for stacking layers 10 nm thick and nearly amorphous for stackings 2 nm thick. This is unlikely: in the first case an accurate re-examination of the XRD pattern does not allow one to conclude that Nd metal is present. Indeed, the so-called (10.0) and (00.4) diffraction lines located normally at 20=28.12 ° and 30.25 ° respectively, are measured at 20=27.90 ° and 29.55 ° . The first one probably corresponds to the (222) or (11.0) diffraction line of C-Nd203 or Nd(OH)3, whereas the second one does not correspond to any known compotmd of Nd or Fe.

Other results reported by Brouder et al. (1986, 1988a) for (Fe/Nd)n films show that, from XAS measurements, the local environment of the Fe atoms is strongly modified between 77 and 293 K. So, at 77 K, the iron layer is strongly disordered, whereas at 298 K the pure spectrum of bcc Fe is recorded. The films were prepared by alternate evaporation deposited onto various substrates. As a function of the thickness it is observed that thick Fe layers induce a large magnetic moment in Nd. Moreover Ku is reported as clearly induced by the structure of the film. Therefore the magnetic properties are overall influenced by the mutual coupling of Nd and Fe: at low temperature Fe should induce ferromagnetic coupling in Nd. Such a result is, thereby, not in agreement with that reported by White (1990). On another part Pieeuch et al. (1988) and Baczewski et al. (1989, 1990) have compared (Nd/Fe)n and (Tm/Fe)n structures (see sect. 3.2.1.6.)

3.2.1.4. (Fe/Gd)n films. The magnetism and structure of Fe/Gd)n films have been first studied by Morishita et al. (1985). In the case of (3.30-4.6nm Fe/3.50-4.90nm Gd)50 multilayers a new magnetic layer having a "compensation temperature" has been found. This temperature decreases as the thickness ratio of Gd and Fe layers decreases. This was called a new "ferrimagnet". Later on Kamiguchi et al. (1989) and Fujimori et al. (1990) have also pointed out this compensation phenomenon of ferrimagnetism. They report magnetization and magnetoresistance variations as a function of the applied magnetic fields and temperature. From magnetoresistance measurements, they observe an anomalous field dependence which is discussed in terms of the spin-flop type magnetization of artificial ferromagnetism. No structural results are reported. This is not the case for films studied by Morishita et al. (1985) who report that the bce and hcp structures of Fe and Gd respectively, are well observed with the thicker layers, whereas for periodicity of about 1 nm the samples are anaorphous, and exhibit magnetization quite similar to amorphous Gd30FeT0 coevaporated films.

One must mention AES analyses reported by Umemura et al. (1985) in the case of (10nm Fe/10nm Gd)12 multilayers, which show that the atomic content of oxygen throughout the Gd layers is almost the same as that of Gd. It is concluded, as for (Fe/Sm). layers where the presence of Sm203 was detected, that the degree of oxidation clearly affects Ku.

Theoretical studies of the phase transitions, magnetization, susceptibility and compensation points have been carried out by Camley (1989), Camley and Tilley (1988), and LePage and Camley (1990). The results are discussed in terms of equilibrium

160 M. GASGNIER

structure of a magnetic superlattice formed from two ferromagnetic materials which couple antiferromagnetically at the interfaces. It is concluded that a variety of phases can exist in such a system.

3.2.1.5. (Fe/Tb)nfilms. As a preliminary remark one must draw attention to the fact that the indexing of XRD and EDP reported by different authors is somewhat erroneous. First, Sato and Habu (1987) indexed two X-ray diffraction lines, recorded at 19.15 ° and 26.20 °, as the (10.1) and (110) planes relative to the rare earth and iron, respectively. However these two lines, with interplanar spacings as 0.235 nm and 0.1745nm, do not correspond to the (10.1) plane of the hcp rare earth (d10.1 ~0.275nm) nor to the bcc iron (dll0 = 0.203 nm). Such lines should be linked to the formation of an intermetallic TbxFey alloy. On the other hand, one intense line has been forgotten: located at 16.90 °, it corresponds to the (200) plane of the rare-earth dihydride (d200 = 0.264 nm).

Second, Shin et al. (1987) for Tb/Fe95Co5 multilayers, claim that their XRD shows the (10.2) plane of the terbium. This peak is located at 15 °, with a corresponding interplanar spacing of 0.298nm, but the dl0.2 value of Tb metal is reported to be 0.210urn; The indexing is clearly wrong, and this X-ray line should correspond either to the (200) plane of TbO2 or to the (11.3) plane of Tb2Fe17.

Third, Cherifi et al. (1990) from EDP report that their films present three kinds of crystals. In fact they observe the classical hydrogenation of rare-earth thin films: the TEM image shows clearly the formation of large hydride crystals (with pole figures) which have grown throughout the metallic Tb matrix. Moreover, the parameter of the dihydride seems to fluctuate from one sample to one another, which is probably due to a small amount of iron diffusion into the TbH2 lattice. Finally, another pattern can be indexed as a fcc lattice with a parameter equal to 0.495 nm, and not as 0.525 nm which is the value for the dihydride. This parameter (0.495 urn) corresponds to the oxinitride TbNzO x (Gasgnier et al. 1976). Therefore the three types of crystals correspond to: Tb, TbH2 and TbNxOy.

Fourth, N. Sato (1986) reports that after annealing two broad peaks at 17.50 ° and 25.50 ° should correspond to the (00.1?) and (110) planes of Tb and Fe. The deduced interplanar spacings, 0.256nm and 0.179urn, should correspond to a TbxFey alloy, and to the (200) plane of the y-Fe (fcc) phase respectively. Moreover, for small-angle-X-ray diffraction two peaks are observed, whereas Shah and Sellmyer (1990) and Tanaka et al. (1987) observe only one peak. AES profiles reported by N. Sato (1986) indicate a large quantity of oxygen inside the Tb layers. In the same way Yamauchi et al. (1988) report that the (00.1.9) diffraction line of the Tb is clearly observed. Consequently the magnetic results reported by Shin et al. (1987) from ferromagnetic resonance measurements, Yamauchi et al. (1988), N. Sato (1986), N. Sato and Habu (1987) and N. Sato et al. (1987) must be regarded with great care. However the latter authors observe that for Fe/Gd, Tb or Dy a compensation point occurs for a R content close to 25%. Ku, He, Ms and the Curie temperature show clear changes at the compensation compositions. Although the crystallographic results of Yamauchi et al. (1988) are not dearly described, these authors observe a systematic change of the temperature dependence of magnetization. It also

THE INTRICATE WORLD OF RARE EARTH THIN FILMS t61

depends on the periodicity and the thickness ratio. Very thin films (below 1 nm Fe and Tb) are composed of only ferromagnetically coupled Fe-Tb regions. However, ferrimagnetic coupling Fe-Tb, ferromagnetic Fe and Tb, and/or magnetically compensated Tb regions are found in films with 1 nm Fe/1 nm Tb layers.

Shah and Sellmyer (1990) study the layer-thickness dependence of hysteresis loops and conclude that magnetization and Ku, which depend on the Fe layer thickness, can be interpreted in terms of both the compositionally modulated distribution of Tb and Fe atoms and their ferrimagnetic coupling. The authors report a modeling analysis which offers information about the micromagnetic structure. The behavior of the anisotropy and constituent magnetization near the compensation point are discussed. Tanaka et al. (1987) in the case of FeCo/Tb films (240 nm thick), deposited by two-source magnetron sputtering, report on the magnetic properties as a function of the [(FeCo)+ (Tb)] compositional modulation. The AES profile shows that oxygen is localized at the sample surface. It is observed that with increasing compositional modulation the Kerr rotation and Ms increase, whereas He, Ku and the Curie temperature decrease. Above a thickness of 2.9 nm, the magnetic anisotropy changes from perpendicular to in-plane. This indicates a decrease of the ferrimagnetic coupling and an increase of the ferromagnetic coupling between the same kind of atoms.

3.2.1.6. (Fe/Nd, Er, Tm)nfilms. Piecuch et al. (1988) and Baczewski et al. (1989, 1990) have investigated the in-plane and perpendicular anisotropy directions of (Tm/Fe)n and (Nd/Fe)n multilayers. The samples are prepared by alternate evaporation of the two metals under a vacuum of 10-6pa, onto a substrate held at 410K. M6ssbauer spectra (figs. 20, 21) show clearly that the two structures are quite different. Additional magnetization measurements (hysteresis loops) allow one to conclude that (Nd/Fe)n samples exhibit strong perpendicular anisotropy while (Ym/Fe)n (and also (Er/Fe)n) samples exhibit in-plane anisotropy. It is concluded that it is not possible to consider the anisotropy pair ordering with associated magnetic dipolar interactions as a major source of the anisotropy. This is explained in terms of modifications of the R crystal

t ; " - . . ) 13 AFe 38ANd

a VELOCITY (MM/S) b

t " , I o ~ " ° o

. . . • o * ° ~ ,

• . , °

1 3 ~ F e

-4 -~ o' ,' g VELOCITY (MM/S)

Fig. 20. M6ssbauer spectra of (a) Nd/Fe and (b) Tm/Fe multilayers at T = 4 . 2 K and H = 0 . The Fe layer is 1.3 nm thick.

162 M. GASGNIER

,=,,

31 AFe

38 A Nd

a

Tz 4.2K

0 6 12 VELOCITY ( M M / S ) b

. ° .

T= 4.2K

31AFe

i t I I I - 8 .4 0 4 8

VELOCITY(M M ] S )

Fig. 21. Mtssbauer spectra of (a) NdlFe and (b) Tm/Fe multilayers at T=4.2K and H=0. The Fe layer 3.1 nm thick. (By courtesy of Dr. G. Marchat, Laboratoire Physique du Solide, Universit~ Nancy I, Vandeeuvre- les-Nancy, France).

field, i.e., according to the sign of the second-order Stevens factor which seems to induce the anisotropy direction.

3.2.2. (Co/R)n films 3.2.2.1. (Co/(Pr, Nd))n films. Suzuki et al. (1987a,b) have investigated the variations of Ms and Ku as a function of the modulation length and temperature. The films are prepared by means of a dual e-beam system. The two magnetic properties increase as modulation and temperature both decrease. It is deduced that Ku stems from Nd atoms which are adjacent to Co atoms in the vicinity of the interface. A model of the magnetic structure is reported. It is shown that Ku does not exceed that of coevaporated Nd0.25Co0.75 films. At 293 K anisotropy is low and films show an in-plane magnetization. XRD and RHEED patterns reveal that Nd and Co atoms do not form a coherent interface and that the films are amorphous. At 293 K anisotropy is low and films exhibit an in-plane magnetization whereas at 77 K the films are perpendicularly magnetized. Miyazaki et al. (1989) also observe an enhancement of the magnetization at 77 K which is explained by the ferromagnetic coupling between Co and Pr or Nd at the interfaces. According to these authors, Ku originates from the anisotropic pair ordering at the adjusting interfaces. Takahashi et al. (1989) investigate the magnetic properties of (Co/Pr), films prepared by e-beam evaporation under oxygen. Ms, Ku, polar Kerr rotation and hysteresis loops are studied as functions of oxygen partial pressure and of temperature. It is observed that polar Kerr rotations are large.

3.2.2.2. (Co/Gd)n films. T. Nakamura et al. (1987) have carried out syntheses of amorphous (Co/Gd), sputtered films with anisotropy modulated superstructures. Webb et al. (1985) have investigated the structural and magnetic properties of such specimens. The modulated films were sputtered onto a thin Cr layer deposited previously itself onto oriented substrates. From XRD it is observed that the longer sequences exhibit both fcc and hcp Co structures, whereas smaller sequences are amorphous. Deposition


onto substrates kept at 653 K, leads to the formation of the fcc GdCo2 alloy. The probable explanation for the absence of GdCo3 (the stable phase at the average composition of the symmetric modulated films) is the kinetic preference for GdCo2 in these highly nonequilibrium samples. Such an explanation is quite probable (Gasgnier 1982). It is observed that films are strongly textured with the (220) plane parallel to the substrate, and that the d220 spacing decreases slowly as the period increases. The magnetic measurements carried out at 293 K do reveal that the magnitude of the Co moment opposite to that of Gd decreases as the bilayer thickness increases. Thus, as the magnetization, with a field parallel to the film surface, quickly saturates, it is concluded that a high degree of in-plane anisotropy exists. After deposition at 653 K it is observed that coercivity reaches a maximum value (400kAm -1) as the bilayer thickness increases from 4 to 8 nm. This is tentatively correlated to an increase of the grain size of the films and not to the temperature. The magnetization data are analyzed assuming the films consist of a mixture of GdCo2 and Co. It is found that as the periodic thickness increases as the compensation temperature decreases, and that the GdCo2 and Co moments exhibit an antiferromagnetic coupling. Webb et al. (1988b) defined the Co/GdCo2 system as a "macroscopic ferrimagnet". They have investigated the giant exchange anisotropy in Co/GdCo2 amorphous multilayers deposited at 293 K. The exchange anisotropy is produced by heating near 770 K and rapid cooling. One finds a temperature dependence of the exchange anisotropy with a compensation point at l l 0K, which can be controlled by changing the layering. It is also found that after annealing the Gd2Co17 permanent magnet forms at the interface. Webb et al. (1988a) have shown that Hc decreases near the compensation temperature (120K) instead of diverging. Toxen et al. (1988) have studied multilayers ( l -2 ~tm thick) Co/GdCox (x--2, 3, 5 and 8.5) in order to define the shifting of the hysteresis loops. It is observed that the loops are unidirectionally displaced for x = 3-5, and not for x = 5-8.5. XRD indicates that the samples are microcrystalline or amorphous. The former should be relative to the GdCo5 alloy which should be at the origin of the unidirectional anisotropy, and not Gd~Co17 as reported by Webb et al. (1988a, b).

The magnetization process of (Co/Gd)~ multilayers prepared by e-beam evaporation in a vacuum of 10 -5 Pa has been reported by Tsunashima et al. (1988). It is shown that around 150K a peculiar magnetization process occurs, which is attributed to a transition of Gd spins from aligned to twisted states in agreement with the surface spin reorientations described by Camley (1987). Okuno et al. (1986) have studied the electric resistivity and the magnetization of modulated (Gd + Co) films prepared by rf magnetron sputtering with double targets and a revolving substrate. As a function of exposure time (in seconds per revolution) compositionally modulated homogeneous, amorphous and crystalline films can be prepared. In the same way electric resistivity, Ms and Hc vary with the structure variation and exposure time.

The effect of oxygen on modulated (Co/Gd)n rf diode sputtered films, has been investigated by Choe et al. (1988). It is shown from AES that Gd, Co and O2 profiles vary widely according to the layer thicknesses, and the application or absence of substrate bias (65 V and 0 V). XRD showed the coexistence of the fcc and hcp Co phases, hcp

164 M. GASGNIER

Gd phase, and GdCo2 after annealing. As the period thickness increases the average magnetic moment per Co atom increases. It is deduced that the 0 V bias substrates lead to better coherent films, and that Gd atoms are magnetically deactivated by the formation of Gd203.

3.2.2.3. (Co/Tb)n films. From RBS spectra Honda et al. (1986) have shown that multilayered structures have a higher resistance to oxidation. The films (300nm thick) are prepared by rf sputtering and a negative bias voltage applied to the substrate is changed alternatively between 0 V and 100 or 200 V periodically. Anisotropy field, Ms and He exhibit a compensation point with a number of layers up to about 20 layers. With decreasing Ms, perpendicular He and Ku increase, which helps to stabilize the written bits (down to 2 ~tm in diameter). Honda et al. (1987) report the variation of the same magnetic parameters and Kerr rotation as a function of temperature, applied field and thickness. It is observed that films prepared by modulating bias voltage are modulated compositionally between 14.4 and 20.1 at.% Tb. The short periodic modulation film (0.4 nm thick) realizes the ideal perpendicular rectangular hysteresis loop with the highest Ku, and exhibits a high Kerr effect. N. Sato et al. (1987) report that Ms, He and Ku have maximum values for Tb thickness close to 0.4 nm (these values are somewhat smaller than those of (Fe/Tb)n films). Moreover Co substitution for Fe increases these values. This is also clearly observed in the Kerr rotation angle. Therefore, (FeCo/Tb)n multilayers with large Ms and He and low Curie temperature seem suitable for magneto- optical recording media.

One must point out the experiments of Marshall and Dobbertin (1986) who have studied the cross-section of (Co/Tb)n films (400 nm thick), deposited by magnetron sputtering, by means of a TEM. The Tb layers are amorphous and vary randomly in thickness, whereas Co layers are polycrystalline and relatively uniform in thickness. The interfaces appear to be fairly sharp but not smooth.

3.2.2.4. (Co/Dy)n films. Shan and Sellmyer (1988) have studied the magnetic and microstructural characteristics of these multilayers prepared by multiple-gun sputtering. An accurate indexing of the pattern leads to conclude that for thicker layers there is coexistence of the hop Co [(10.0) and (10.2) diffraction lines] and of the DyH2 [(111) diffraction line] phases; and that for thinner layers there is probably formation of a disordered alloy (the intense line measured at 20--36.25 ° does not correspond to any known compound relative to Co or Dy). One must point out that, from magnetic measurements, the interface is considered as the main source of the perpendicular anisotropy. It is found to be described according to the single-ion model (due to spin- orbit interactions) associated with the rare-earth ions (Shan et al. 1989, Sellmyer and Shah 1989).

N. Sato et al. (1987) report for (Co/Dy)n films results which are equivalent to those found for (Co/Tb)n multilayers. The main difference is that the magnetic property values are smaller for (Co/Dy)~ layers: for instance Ku is twice as small.

THE INTRICATE WORLD OF RARE EARTH THIN FILMS t65

3.2.3. (2gi/R)n films 3.2.3.1. (Ni/Ce)n layers. The solid state reaction in (Ni/Ce)n films has been studied extensively by Brouder et al. (1988a-d) and Guilmin et al. (1988). Amorphous samples are prepared by alternate evaporation and then investigated by XAS in a dispersive mode. Ni K and Ce Lnl edges are recorded as the temperature increases from 77 to 300 K. The average valence of Ce is deduced as a function of the diffusion parameter according to two different models. This parameter reaches a maximum value of about 3.25 in both cases. For the thicker Ni and Ce films, the formation of the CeNi2 alloy has been observed. The great similarity between the spectra leads to the conclusion that the local environment of Ni in the amorphous phase is reminiscent of that of Ni in CeNi2.

3.2.3.2. ~i/Dy)n layers. Shan and Sellmyer (1988) report that magnetizations, at 293 K, of these systems are much weaker than those of (Fe/Dy)n and (Co/Dy)n films. This is due to the weaker exchange coupling in Ni as compared to Fe and Co.

3.2.4. Other multilayer systems 3.2.4.1. YCo/(Nd, Gd, Er)Co/YCo sandwiches. Amorphous samples prepared by dc triode sputtering have been studied at 4.2 K, by Dieny et al. (1990). In the case of (Gd-Co) layer a transition towards ferromagnetic arrangement takes place at a certain critical field; it is associated with the formation of Bloch walls within the Co sublattices at the interfaces. In the ease of (Nd-Co) layer anisotropy, magnetization and coercivity are not the same in films of different natures. Under applied field, the magnetization reversal does not occur at the same field values for the different layers. Consequently, Bloch walls within the Co sublattices are again created and lie almost entirely inside the (Y-Co) films. However, walls appear only when the magnetization in the less coercive layer reverses. Both phenomena are involved in the case of (Er-Co) films. Such a study should permit to create samples with unique planar Bloch wall parallel to the film surface.

3.2.4.2. (TbFe/Ni-Fe-Mo) bilayer films. The exchange interaction between amorphous ferrimagnetic TbFe and crystalline soft magnetic material (Permalloy) Ni-Fe--Mo has been investigated by Hellman et al. (1987). It is shown that an unexpected unidirectional anisotropy occurs in such a system. It is observed that the direction of the easy axis in Tb- Fe is in fact tilted at a small angle with respect to the normal of the Ni-Fe-Mo moment which lies in the film plane. The tilt depends critically on the deposition parameters. Thus, the unidirectional anisotropy induced in the Permalloy by the TbFe film is unique in that it is large, stable to high in-plane fields, but reversible by application of a perpendicular field.

3.2.4.3. (PtMnSb/TbFe) bilayerfilms. A PtMnSb/TbFe bilayer, prepared by rf sputtering, allows one to improve the magnetic and magneto-optical properties of the PtMnSb film as reported by Koyama et al. (1987). Compared to a PtMnSb monolayer the Kerr rotation peak shifts to a shorter wavelength, and Hc is 6 times larger (~56kAm-1).

166 M. GASGNIER

3.2.4.4. (Fe/TbFe) bilayers. The magnetic exchange coupling phenomena have been studied for Fe/TbFe bilayer systems by Marinero et al. (1988). The Fe moment causes an uniaxial alignment in the plane of the substrate. Variations of Hc of the Fe layer and of the shape of the hysteresis loops are discussed in terms of coupling interactions between the ferromagnetic layer and the ferrimagnetic alloy.

3.2.4.5. (Zr-Fe/TbFe)n amorphous multilayers. Katayama et al. (1987) have studied the variation of saturation magnetization as a function of the composition modulation period. As the multilayers becomes thinner, Ms increases. This is explained by the fact that magnetization of Fe within the ZrFe film is induced by the TbFe film.

3.2.4.6. (ZnS/GdFe) multilayers. The magneto-optic recording performance of the system GdFe/ZnS/glass is improved by inserted a dielectric film (MgF2, SiO) between ZnS and glass as reported by Sagasaki et al. (1985a,b).

3.2.4.7. (TbFe/SiO)n multilayers. Inoue et al. (1985), for TbFe/SiO/TbFe sandwich films formed by evaporation, observed a considerable improvement in Kerr angle readout, and little enhancement of the Faraday angle. The magnetic Kerr rotations of these amorphous layers prepared by e-beam evaporation has been studied by R. Sato et al. (1988). It is shown that such modulated films enhance the Kerr rotation to 25 degrees for a total thickness of 650 nm. An important result is that the refractive index averaged over the multilayers forms an effective refractive index of the film for the light with wavelengths considerably large compared to the layer thicknesses. This parameter is thus effectively modulated.

3.2.4.8. Insulating~magneto-optic~insulating systems. 3.2.4.8.1. Si3N4. Coulman and Anthony (1986) have shown that Si3N4 has better characteristics than SiO or SiO2 to prevent interdiffusion between layers and oxidation of TbFeCo films. 3.2.4.8.2. Si02/GdTbFe. A. Suzuki et al. (1988) have investigated the interface of Si- rich SiO2/GdTbFe bilayers. From AES and XPS measurements they observe that the formation of FeSiz, as an interface layer, works as a blocking layer against O2 penetration. Moreover any excess Si plays an important role in the improvement of the magneto-optical properties. 3.2.4.8.3. Dieleetric/Nd-Dy-Fe-Co-Ti/Si~N4-AlN on plastic. Aoyama (1988) has observed that Hc and Kerr rotation are enhanced in the case of the following sequence: dielectric film/Nd-Dy-Fe-Co-Ti film/Si3N4-A1N film/plastic substrate. Such a system prevents the magnetic film from degassing the substrate.

3.2.4.9. Amorphous (TbxFel-x/Al203)n multilayers. Such a system has been studied by Krishnan et al. (1988). Samples are prepared by sequential rf sputtering. The A1203 thickness is kept constant at 4nm and the TbFe layer varies from 3 to 100nm. For thicknesses <4nm the magnetization of the TbxFel-x (x=20 and 22) layer increases


strongly, indicating some partial oxidation of Tb. For larger thicknesses, magnetization remains constant, but He and Ku increase. Variation of coercivity is controlled by various parameters such as the microstructure of the film. The fact that Ku reaches a high value, while He remains small, indicates that these two parameters are not simply related.

3.2.5. Formation of sandwiched layers: R(Dy, Tb) ions implanted in Fe and Ni films. Structure and magnetic properties

The effect of high-dose ion implantation on structure and magnetic properties of 3d- metal films has been investigated by Suezawa et al. (1983, 1985), Gond6 and Suezawa (1986) and Gond6 et al. (1983, 1984), and by Tsukahara and Kanayama (1983) and Tsukahara et al. (1983). It has been shown previously (Grant 1978, Poate 1978) that implantation of metal ions into crystalline metal cause the formation of an amorphous layer and alloying of the metals takes place at the same time. Such a phenomenon has been observed whatever the energy implantation (70 or 400 keV) and for high doses (between 1016 and 1017 ions/cm2). Gond6 et al. (1984), Gond6 and Suezawa (1986) and Suezawa et al. (1985) report, for Tb+/Fe films, that the magnetic moment of the Fe decreases as the Tb ion dose increases. Moreover an uniaxial magnetic anisotropy is induced in Fe films (20-70nm thick) at 293 K with an easy axis parallel to an applied static magnetic field. The magnetization behaviour is suggested to be close to a multilayer structure consisting of a Tb-Fe layer sandwiched by Fe layers. Gond6 and Suezawa (1987) have shown that magneto-optical rotations of Fe films are changed by the implantation of Tb + ions. For dosages up to 3×1015 ions/cm 2 Faraday and static polar Kerr rotations increase slowly, and then decrease rapidly for higher doses. Such an increase has not been observed in the case of Tb-Fe films prepared by conventional methods. In the case of Dy+/Ni films, Suezawa et al. (1983) and Gond6 et al. (1983) conclude to the formation of a paramagnetic Dy-Ni alloy layer formed at high Dy + doses. Concurrently the magnetic moment of the Ni film decreases. Tsukahara and Kanayama (1983) and Tsukahara et al. (1983) have implanted Dy + ions (at 400keV) into Fe films (50-150 nm thick). It is explained that Ms decreases monotonically with increasing Dy concentration. It takes about 8 at.% to make a Fe film completely amorphous. They also observed by Lorentz microscopy that implantation-induced changes in the domains and domain-wall structures due to the reduction and destruction of anisotropies, decreased the magnetization; and caused a possible variation of exchange constant and the distribution of the alloy concentration.

3.3. R-Fe, Co/hydrogen and other gaseous contaminants: changes in magnetic properties

In a previous chapter of this Handbook series (Gasgnier 1982) it has been demonstrated that magnetic characteristics of amorphous R-TM thin films might be dramatically changed when the samples are contaminated by absorbed (or adsorbed) gases. In this connection, one must mention some other interesting results. Schelleng et al. (1984)

168 M. GASGNIER

and Forester et al. (1984) report that the inclusion of hydrogen sharply reduces the compensation temperatures by about 200 K and the Curie temperatures by 50 K in the case of Gdl_xFex:Hy films (x= 0.0-0.9, y=0 , 1.25, 3.0; 1 ~tm thick). The exchange parameters JFe-Fe and JFe-rd show small relative decreases whereas Jrd-Gd undergoes a large change [from ferromagnetic (y = 0) to antiferromagnetic coupling (y = 3)], which is explained in terms of anionic behavior of the hydrogen. Vittoria et al. (1984) notice from ferromagnetic resonance field measurements that the Gd sublattice is more affected than the Fe sublattice by the presence of hydrogen. The magnetic moment of the former is reduced in comparison to the unhydrided material. Naoe et al. (1982) have studied the influence of H2 addition on Ku for GdCo amorphous films. They observe that this parameter increases when Co content is under 75at.% (Ms <4x 10-2T) and decreases when Co content is over 75 at.% (Ms > 4× 10 -2 T). Moreover, the compensation composition shifts to higher Gd content. Niihara et al. (1984) report similar results for TbCo films. They add that H2 additions lead to the formation of rectangular Kerr hysteresis loops. XRD (Forester et al. 1984) and EDP (Naoe et al. 1982) results indicate that the RH2 compound is formed during hydrogenation. In the case of Dyl_y(Or Hol_y)TbyFeHx (y = 0.85, 0.75; x = 0-3.3) compounds Annapoorni et al. (1989, 1990) report that Curie temperature, exchange field, magnetic moments decrease as the hydrogen ratio increases.

The influence of contaminant gases on the magnetic properties of R-TM films is very significant. One can mention, for example, that nitrogen decreases Ku as demonstrated by Hoshi et al. (1982) and Hashimoto et al. (1987). The latter noted that N atoms affect Tb atoms by decreasing the Tb sublattice magnetization in Tb-Fe-Co films, and consequently remarkably decrease the magnetostriction. Heitmann et al. (1987) notice, for GdTbFe films, that compensation temperature, Curie temperature and Ku decrease strongly with increasing impurity concentration in the films. However the influence of nitrogen is about a factor of 3 less than that of oxygen and water. They add that it is due to the deactivation of Tb atoms. In the same way, Frausto et al. (1986) have observed that carbon and oxygen impurities increase Ms and decrease He. However, oxygen contamination seems to be more complex as reported by Tsunashima et al. (1980), van Dover et al. (1986), and Frankenthal et al. (1986) for GdFe, GdCo, and TbF2 films. To prevent oxidation of R-TM films it is now well known that protective layers as SIO2, SiO or Si3N4 are used. However the problems due either to the diffusion of oxygen or to the formation of compounds at the interfaces remain complex. For instance, consider the formation of either R203 or FeSi2: if the first is formed the magnetic properties of the films are destroyed (Anthony et al. 1986), while the second works as a blocking layer against oxygen penetration (Suzuki et al. 1988).

The protection of amorphous R-TM films is very difficult to carry out. Forester et al. (1983) have taken out a patent which demonstrates that a thin palladium layer (2- 3 nm), overlaying a GdFe film, increases resistance to poisoning by atmospheric gases. However the sample rapidly absorbed hydrogen. In this case the films did not fracture or disintegrate and remained firmly adherent to the substrate.


3.4. RNi5 and RCos as hydrogen storage films

3.4.1. LaNis alloy LaNi5 alloy is a well-known hydrogen storage medium. It is a suitable material for energy storage, heat pumps, hydrogen purification (used as filters), H2/D2 separation and battery electrode. However the problem of H2 absorption-desorption is very sensitive in the case of crystalline alloys. Indeed, upon H2 absorption the LaNi5 lattice expands, and this expansion leads to the pulverization of the material into particles, which complicates technological applications. This has been reported by H. Uchida et al. (1984) who observe particle pulverization under the lower stresses induced by the repeated volume change of the alloy during the H2 absorption-desorption cycles. To prevent this scattering phenomenon H. Uchida et al. (1987) have mixed LaNi5 powder with silicone rubber and the mixture is formed into a sheet. Various procedures have been used to define the optimal properties of thin and thick films. The crystalline state is an important parameter: the amorphous or crystalline character plays a leading role in the absorption-desorption mechanism.

3.4.1.1. Hydrogen absorption - Crystalline states. The determination of the H2 content in thermally evaporated amorphous films (0.6-2 gm thick) has been reported by Sakaguchi et al. (1985c). They observe, first, that the H2 concentration increases as film thickness increases, and second, that the H2 content is higher at lower temperature (333 K). The maximum amounts of H2 reaches 1.8-2.0 H2 atoms for a formula weight of LaNis. The authors notice that the formation of a thin oxide layer at the surface of the films hardly affects the H2 absorption. Wulz and Fromm (1986b) for films deposited by successive evaporation of the two components, layer by layer, observe that the H2 absorption rate for a microcrystalline film is 0.5-1.5 orders of magnitude higher than that for a crystalline film. Preadsorption of oxygen reduces the reaction rate of the microcrystalline sample by 2 orders of magnitude. Moreover, the absence of H20 molecules at the surface could explain the formation of La203 as surface segregation. S.K. Singh et al. (1985) report that microcrystalline and amorphous films deposited by thermal evaporation have a higher absorption capacity than that of the bulk. In the case of amorphous and microcrystalline (about 80% crystallinity) sputtered films (0.53 and 0.57 ~tm thick respectively), Sakaguchi et at. (1988, 1989a, 1990) have shown that the thicker films are more suitable to absorb hydrogen. Moreover the concentration increases monotonously with increasing H2 pressure whatever the variation in temperature and film thickness. In crystalline films it is concluded that H2 atoms seem to occupy only sites strongly influenced by La, whereas in amorphous layers they occupy two types of sites: one influenced by La and the other comprised of more Ni atoms. The absence or the narrowing of a plateau, recorded from pressure-composition isotherms in the case of powders, could be due to impurity occlusions, or to H-H interactions affected by the film thickness, or by stresses induced at the film-substrate boundary as explain by Larsen et al. (1981) for thin films (150nrn thick), H. Uchida et al. (1989) and Kojima et al. (1989) for flash-evaporated layers, and Sakaguchi et al. (1988) for sputtered samples.

170 M. GASGNIER

In the course of hydrogen absorption-desorption cycles Adachi et al. (1985a) observe that amorphous films do not form powders even after 150 cycles. H. Uehida et al. (1989) report that after 80 cycles, the crystalline films become amorphous by generating dislocations. Their crystalline samples exhibit a large 1-12 storage capacity (H2/LaNi5 > 5) and were found markedly pulverized and peeled off from the glass substrate, whereas the amorphous specimens with a lower solubility (H2/LaNi5 < 0.5) show neither pulverization nor the peeling effect. By using aluminium and copper foil substrates, Sakaguchi et al. (1986a) show that amorphous flash-evaporated films do not disintegrate after 75 cyles. S.K. Singh et al. (1985) have observed by TEM that hydrogenation leads to enhancement of amorphosity.

For sputtered films Sakaguehi et al. (1988) report larger thermal conductivities than for bulk samples. The mechanical properties show that the film-substrate adhesion occurs in the following order for the substrate used: Ni foil > Ni > AI foil > Cu foil > Cu > A1 > glass. Such an order appears to be due to the difference of the thermal expansivity at the film-substrate interface.

3.4.1.2. Electric resistivity. The effect of H2 absorption on the electric resistivity of LaNi5 films has been studied by Adachi et al. (1981, 1982, 1985a,b) and Sakaguchi et al. (1985b,e). The films (0.3-1.8 ~tm thick) prepared by evaporation of the powder placed on a tungsten filament and deposited onto quartz plate, are amorphous. As a function of temperature, thickness, and H2 pressure, the variation of the resistivity with the time of H2 absorption-desorption cycles presents an initial increase and a sharp decrease during H2 absorption. Figures 22a--c show the variations of the electric resistance as a function of the time of application of 1-12 pressure. The resistivity decreases as the number of cycles is increased; increases as the temperature is raised to 363 K; and saturates at a H2 pressure of 1.2× 106 Pa. However, Adaehi et al. (1985a) noticed that the low 1-12 uptake for the

t

0

6.5

,~ 6.0

5.5i

30 60 30 60 a Time/rain b Time/min

uE 9£

~8.C

..%

6 3b 6b Time/rnin

Fig. 22. Variation of the resistivity versus time during activation (first and second cycles at 313 K, others at 363 K; hydrogen pressure 2.5×106 Pa): (a) thick LaNi 5 film (0.63 btm); (b) thin LaNi 5 film (0.20 p.m); (e) very thin LaNi 5 film (0.038 btm). (By courtesy of Prof. G.Y. Adachi, Dept. Applied Chemistry, Fac. Engineering, Osaka Univ., Osaka, Japan).

THE INTRICATE WORLD OF RARE EARTH THIN FILMS 17i

films in comparison with that for the bulk, is due to the amorphous character and to the presence of a surface oxide such as Ni-free La203 which is a passivation layer for H2 absorption. For thinner films (50-150 nm) Ramakrisna and Srivastava (1987) claim that the dependence of resistivity on hydrogenation time is originates solely from the surface characteristics of the films. The resistivity, for aged layers, drops rapidly after exposure to air. Such a phenomenon is explained to be due to the formation ofa La203-free Ni surface layer. S.K. Singh et al. (1985) observe a curious variation of the electric resistivity which decreases to nearly zero during the early exposure on hydrogenation and then increases and reaches a saturation value. Larsen et al. (1981) report measurements of resistance as a function of H2 pressure.

3.4.1.3. Hydrogen separation and permeation. Adachi et al. (1984) have investigated the property of flash-evaporated LaNi5 films for the separation of hydrogen. This material is less expensive than thin palladium films. The LaNi5 film (10 gm thick) is deposited onto a stainless steel disc which is inserted into a special apparatus, where Hz-Ar and H2-N2 gas mixtures are blown. It is observed that above 333 K hydrogen does not permeate the films. For Hz-C3Hs, Hz-CH4, Hz-N2 and Hz-Ar gas mixtures, Sakaguchi et al. (1986b) have studied hydrogen separation in the case of stainless steel discs/Ni or A1 films/LaNi5 flash-evaporated films. The results are discussed first in terms of microcracks formed during H2 absorption, second as a function of the film thickness, and third according to the nature of the intermediate metallic layer. In particular it is observed that A1 allows the highest value of H2 concentration. Sakaguchi and Adachi (1990) have studied the influence of CO on the hydrogenation of amorphous LaNi5 films and on hydrogen separation. The H2-CO gas separation is performed by using films deposited onto Ni- coated polyimide membranes. In the case of multilayer Ni (1.4 gm)/LaNi5 (0.1 gin) films the H2 permeability (penetration rate) is greater than that for Ni films up to 373 K. Moreover, LaNi5 films are found to have excellent resistance to harmful CO in comparison with the crystalline bulk material (H2 is concentrated to more than 98 tool% in the permeated gas).

Another interesting experiment has been reported for Hz-D2 gas mixtures by Sakaguehi et al. (1989b). The rf magnetron sputtered LaNi5 films are deposited onto teflon and polyimide membranes. Isotope separation is mainly influenced by the difference in solubility of H2 and Dz atoms in metals, the difference in diffusivity in metals, and the polymer's own isotope effects. LaNi5 films have a permeability coefficient about twice as large as that of Ni films, and less than one-thousandth that of Pd films. Previously, Adaehi et al. (1986, 1987), in the ease of amorphous WO3/Metal/LaNi5 sandwich-type films, have studied the hydrogen permeability for various metals. The amorphous WO3 films, which have electrochromic properties, become blue only under the area covered by the LaNi5 layer when H2 is introduced into the system. The authors conclude on the following order for hydrogen permeability:

LaNis, Pt, Pd > Fe > Ni, Co, Ti > Mn > Cu > Mg, Cr > A1 > Au, Ag, Zn.

172 M. GASGNIER

In the same way, Shirai et al. (1990) have studied the H2 penetration into amorphous V205 films. For a LaNis/VzOs/WO3 multilayer system, the diffusivity at the VzOs/WO3 interface seems to be much smaller than that at the Cu/WO3 interface.

3.4.2. Other RNis alloys Other studies report that MmNi4.sMn0.5 films (Mm--mischmetal, generally as a (La, Pr, Ce, Nd) mixture) have resistivities almost identical to that of LaNi5 films. However, the former are more easily oxidized (Adachi et al. 1982). S.K. Singh et al. (1985) prepared RNi5 films (R = Sm, Gd, Ho, Mm and Mm cerium free) by thermal vapor deposition; these are initially amorphous, and then crystallize on annealing. S.K. Singh et al. (1985) conclude that the amorphous state absorbs the hydrogen more easily.

3.4.3. RCos alloy (R = La, Sin) Sakaguchi et al. (1985a, 1987) have studied the effects of hydrogen absorption on the electric resistivity of LaCo5 films deposited as LaNi5 layers (Adachi et al. 1985a). The resistivity behavior of LaCo5 specimens during H2 absorption-desorption cycles resembles that for the LaNi5 films. However, LaCo5 films absorb less 1-12. But the amount of absorbed H2 increases with increasing film thickness. The pressure-composition isotherms indicate a monotonous increase with increasing pressure, while a plateau pressure is absent.

For SmCo5 films Sakaguehi et al. (1985a,b) report that, as a function of thickness, the resistivity varies differently depending on the 1-12 absorption-desorption cycles. Hydrogen molecules are absorbed on the surface and then dissociate into atoms. The dissolved H2 anions diffuse into the films and then react with Sin, giving a highly conductive hydride which lowers resistivity. It is asserted that the H2 concentration in SmCo5 is of an order of magnitude 5 times smaller than that of LaNi5 films (in the bulk the ratio is close to 3/7).

3.4.4. Remark R(Ni, Co)5 thin and thick films are available as materials for hydrogen storage. The different authors referred to throughout sect. 3.4 report the possibility of a lot of applications. However, to our knowledge, no patent has been taken out during the last decade. This should be explained from the fact that these materials do not present the perfect characteristics of stability during aging, annealing, H2 absorption-desorption cycling, etc. The formation of compounds such as RH2, R203, . . . seem to attest this explanation.

3.5. Polytypic structures

Verma and Krishna (1966) have reported the main properties of polytypic materials. Different notations have been used to describe the stacking sequence of successive packed layers in the hexagonal unit cell. This has been chosen as the basic lattice because it


includes at one and at the same time the cubic (C), rhombohedral (R) and hexagonal (H) structures. The different structures are characterized by the following law relative to the lattice parameters: a = constant, c = n x h (n = number of block layers, h = spacing between two layers).

3.5.1. Ferromagnetic samarium-nickel alloys Polytypic and intergrowth properties of SmxNiy alloys have been studied by S. Takeda et al. (1982, 1983), S. Takeda (1983), Horikoshi et al. (1985) and Komura (1989). This system appears somewhat complex. So, the following intermetallic compounds have been observed:

SmNi2:

SmNi3:

Sm2 NiT:

SmsNi19:

3C;

3R;

2H, 3R, 4H, 5T (trigonal) 9R and 12R"

2H, 3R, 4H, 5T, 6T, 7T, 9R, 12R, 15R and 18R. A model of stacking sequences is shown in fig. 23.

HREM studies show, first, that such structures can coexist inside thin crystals electrolytically polished, and second, that anomalous intergrowths can occur. For instance, in the first case small "blocks" of Sm2Ni7 can grow in the matrix of SmsNi19, and in the second case small "blocks" of Sm7Ni29 and SmNi4 can grow in the same matrix. Such intergrowths can be caused by a small amount of concentration fluctuation in one part of the specimen. Moreover, such crystals are characterized by various complicated defect structures: non-periodic stacking sequences and stacking faults of the block layers. The

oT • T .,I-T )°0~ °° X OSrn

X

~o0~o )oo0 ~ ~ A ~ X

oo X c oo y / )°°0 Y

c ')-I°-°~ B" V I )~°~ v

Oo A A X X

x x

_G I x x

a b c d e f

Fig. 23. Projections onto (1;20) plane along [010] direction of (a) SmTm2, (b) 3R polytype of SmzTm7, (c) 2H polytype of Sm2TmT, (d) 3R polytype of SmsTm19 , (e) 2H polytype of SmsTmj9 , and (f) SrnTm 5. (By courtesy of Prof. S. Takeda, College of General Education, Osaka Univ., Osaka, Japan).

174 M. GASGNIER

presence of intergrowth phases and of defects could affect the physical properties of these materials, but apparently the above-mentioned authors have not resolved this problem up to now. So, the problem of layer sequences, intergrowths, syntaxies, . . . , becomes very complex because a great number of compounds can be formed but also each of them can be characterized by a wide range of crystalline structures (ten at least, in the case of SmsNi19).

3.5.2. Samarium-cobalt alloys The approach of using crystallographic polytypic structures was been reported first by Cromer and Larson (1959) and later on by Parth6 and Moreau (1977) who have discussed the problem in terms of stacking-blocks of various rare earth alloys. C.W. Allen et al. (1974a,b, 1977); Melton and Perkins (1976), Melton and Nagel (1977) and Fidler and Skalicky (1978, 1981) have investigated by electron microscopy the polytypic stacking faults and defect structures in R2Co17 and SmCo5 materials. C.W. Allen et al. (1974a) have reported the first atomic arrangements for six structural modifications (2H, 1R, 4H, 5H, 6H1 and 61-12) of R2Coa7. They correlate such structures, by the way of R sites, to magnetic properties. For example they conclude that an intrinsic fault in the 1R structure could provide a source for domain-wall nucleation. The authors illustrate the various stacking sequences for different stacking faults in 2H and 1R R2Col7 alloys.

More detailed results have been given by Komura et al. (1981), S. Takeda (1983), and Sahashi et al. (1983). The studies were carried out on thinned materials by electron microscopy (TEM, EDP and HREM). This has allowed them to observe the classical structures as: SmCo3-3R, Sm2CoT-2H and 3R and SmsCo19-2H and 3R; and to find new long-period structures such as Sm2Co7-4H and 15R and SmsCo19-18R types. The lattice parameters for the 15R and 18R structures are respectively:

15R: Sm2Co7: a=0.50nm and c= 19.50nm, i.e., 15×l.3nm

18R: Sm5Co19: a=0.50nm and c=31.00nm, i.e., ~18× 1.72nm (1.30 and 1.72nm being, respectively, the values of the c parameters of the 2H basic structure for each alloy). HREM imaging permits one to observe stacking faults inside the stacking sequences. This also allows one to build these sequences, recognize the different polytypic structures, and determine the possible stacking sequences. Thus, the 18R polytype relative to the Sm5Co19 alloy can be depicted according to three different sequences. An interesting conclusion comes from the experiments by S. Takeda (1983). He notices that, for electrolytically polished specimens, the axial ratios co/ao obtained from EDP are about 6-8% greater than those obtained by the X-ray method. Such a discrepancy was not observed in the case of crushed specimens. The author concludes that possibly a chemical reaction of inclusions occurred in the course of polishing.

Other studies have dealt with the eutectic decomposition of these alloys. Linetski and Salo (1989) report, from X-ray investigations, that thick (20-200~tm) sputtered amorphous layers, as SmxCoy (18-34% Sm), can form a great number of alloys: Sm2C017, Sm2C024, Sm2C026, SmC05, SmC07, SmCo8, SmCo8.5, SmCo9, SmCo9.5, SmC012, SmC013 and other unidentified phases. The results are discussed on the basis of


the equilibrium diagram. It is concluded that the formation of a wide range of continuous metastable solid solutions on crystallization from the amorphous state is probably due to the similarity of the free energies and related crystal structures of the SmC05 and Sm2Co17 phases. Such observations seem to be a general phenomenon as reported by Gasgnier (1982) for other binary amorphous R-TM alloys. The amorphous system can be also taken as thermodynamically far from equilibrium and the amorphous ~ crystalline transition and the reerystallization which follow as the temperature increases, are often very complex. Moreover one cannot exclude the important role of impurities (overall oxygen) which can act as catalysts. Pan et al. (1989) have studied polished and ion-beam thinned SmCo5 platelets between 673 and 1023 K. They observed first, the formation of Sm2Co17 precipitates (as homogeneous centers formed at 693 K) and second, the eutectic decomposition below 1023 K (formation of Sm2Co 7 and Sm2Co17 phases). It is noticed that at 1023 K the coercivity degraded abruptly, but it can be restored after annealing at 1123-1273 K. Such a phenomenon has been attributed to the various microstructure changes as a function of the temperature.

Shen and Laughlin (1990) have prepared near stoichiometric (Sm0.75Pr0.25)sCo19 materials. TEM studies were carried out after ion-milling of the specimens. Thermo- magnetic analysis indicates that this alloy consists mainly of the 5:19 phase (>85%), 2:7 phase and 1:5 phase (<3%). The authors have observed the coexistence of the 5:19 (rhombohedral) and 2:7 (either rhombohedral or hexagonal)phases (faulted regions), the presence of stacking faults and strained zones. They observed that within high-strain zones the supersatured 5:19 phase transforms to less-strained 5:19R and 2:7H phases. The transformation seems to be heterogeneous. Figure 24 shows HREM images of these

Fig. 24. Polytype phases relative to a (Sm, Pr)sCo19 alloy: (a) lattice image of the 5:19R phase; (b) lattice image of the 2:7H phase. (By courtesy of Prof. E. Laughlin, Carnegie Mellon Univ., Pittsburg, PA, USA).

176 M. GASGNIER

Fig. 25. Electron diffraction patterns of the two (Sm, Pr)5Co19 phases: (a) [1010] zone axis for the 5:19R phase; (b) [2110] zone axis for the 5:19R phase; (c) [i010] zone axis for the 2:7H phase; (d) [2110] zone axis for the 2:7H phase. (By courtesy of Prof. E. Laughlin).

phases. The pat terns in figs. 2 5 a - d are representative of each structure. In the interface region they show a clear or ientat ion relat ionship be tween the two phases.


3.5.3. Rare earth trialuminides

The characteristics of rare arth trialuminides, as thin films, have been described previously (Gasgnier 1982). However, a structural problem has arisen since the conclusions of this review. Indeed, Schiffmacher (1983) has shown that EDP computer simulations do not fit the patterns obtained by photography. The discrepancies may possibly be due to deviations from either the exact stacking positions of the atomic planes as described in the bulk (Buschow and van Vucht 1965), or from the sites of the cationic atoms in each plane, or yet of the stacking order of layers themselves. This problem is illustrated by the presence on TEM photographs of the (00.l) diffraction spots with 1 = 1, 2 . . . . , 6 for instance in the case of the 6H polytype (stacking sequence = 6), in contrast to computer simulations where the spots with l = 1, 2 . . . . , 5 do not appear.

A.K. Singh and Srivastava (1979-1983, 1985) have obtained results similar to those of Schiffmacher (1983) and Gasgnier (1982). They showed that such polytypic structures migh be not only formed with pure Gd, Tb, Ho, Er and Y elements, but also with (Gd, Tb), (Gd, Ho) and (Gd, Er) intermetallics. However the conclusions of Singh and Srivastava do not appear to be clearly established. Indeed, they explain the formation of modulated phases in terms of the reduction of electron energies which is manifested in the type of contact between the Fermi surface and the Brillouin zone. But since the films are initially amorphous and crystallize instantaneously under a focused e-beam such a hypothesis seems irrelevant: first because the Fermi surface does not exist for an amorphous material, and second, because in their theory the authors claim that this Fermi surface is spherical, which is far from being true.

In another study Harris et al. (1984) have observed the formation of ERA13 by interaction of thin erbium films deposited onto aluminium (non-anodized and anodized) substrates. At low temperature (550 K) there is formation of Er2A1 and Er3A12, at 573 K the ERA13 alloy is formed. At 673 K XRD reveals that this alloy is the only intermetallic compound present and that it is stoichiometrically uniform. One must notice that in the case of an ErD2 thin film significant interdiffusion takes place with formation at 673 K of the ERA13 alloy. It is also observed that erbium does not alloy with A1203 between 673 K and 773 K. This oxide inhibits the reaction of Er with A1.

3.6. R-noble metal alloys

3.6.1. The R-Cu system

3.6.1.1. Amorphous R-Cu films (R = Y,, Tb, Dy). 3.6.1.1.1. CUxYl-x. Martin et al. (1985) and Frigerio et al. (1985) have studied the electronic and chemical structure of amorphous CUxYl-x films grown by triode sputtering. XPS and UPS valence band spectra are characteristics of the Y and C u d bands. The two bands overlap with significant electron transfer from Y to Cu atoms. The binding energy of the Cu core levels increases on alloying, in apparent contradiction with charge- transfer arguments. From the Auger LVV transition, it is asserted that the effective Coulomb interaction on Cu sites decreases by alloying with Y. Valence band, core-level

178 M. GASGNIER

spectra and optical properties give a realistic picture of the electronic structure of these alloys. 3.6.1.1.2. Dy-Cu and Tb-Cu. Coey et al. (1981) and von Molnar et al. (1980, 1982a,b) have studied the random anisotropy and spin freezing properties of Dy--Cu thick films (0.6-160 ~t thick). It is shown that such amorphous alloys, as highly anisotropic random magnets, do not develop a spontaneous moment at any temperature. These systems are not spin glasses. The spin-freezing transition at 18 K and the asperomagnetic model proposed by Coey et al. (1981) have been discussed by Pickart et al. (1984) and Moch et al. (1986) in terms of spin-like glass behavior for Dy-Cu and Tb-Cu alloys. 3.6.1.1.3. Cu addition to Tb-Fe-Co. The addition of Cu to TbFe, TbFeCo and TbCo alloy films improved the magneto-optical characteristics and overall He and Kerr rotation angle (K. Uchida et al. 1987, Nakajima and Sato 1986, Told 1986).

3.6.1.2. Crystalline R-Cu films (t? = Y, Ce, Dy, Ho, Er and Yb). 3.6.1.2.1. (Cu/Y)n. R.W. Johnson et al. (1989a,b) have shown that compositionally modulated (Cu/Y)n films form an amorphous CuxYl-x phase at 293 K. The amorphization reaction occurs both at the original Cu/Y interface and within the Y grain boundaries (fig. 26). The authors refer to the Y hcp --+ Y fcc transition in the case of the thinner

Fig. 26. High-resolution phase-contrast image showing grain-boundary amorphization reaction in Y/Cu thin films. The reaction results in a nonatomically smooth reaction front. The 0.3 nm interplanar distance corresponds to the (111) plane of YH 2 (see text). (By courtesy of Dr. C. Ahn, California Institute of Technology, Pasadena, CA, USA).

Y films, which is unlikely. However, XRD clearly shows that the interplanar spacing, which is close to 0.3 nm, is well correlated with the (111) reflection of the YH2 compound. Once again this misunderstanding is greatly prejudicial to the theoretical models given by the authors. 3.6.1.2.2. Ce/Cu interface. The Ce/Cu interface has been studied by means of XPS and UPS measurements by Braaten et al. (1989). The cerium metal is deposited onto thin Cu film (30nm thick). It is observed that, at 293 K, a thick interface is formed (>10nm)


which contains about 80 at.% Ce ions. These Ce ions are in their trivalent state. After exposure to oxygen Ce 4+ ions are formed and the copper film is not oxidized. 3.6.1.2.3. Cu-Dy, Cu-Ho, Cu-Er. The crystallization behavior in amorphous vacuum- deposited Cu-Dy, Cu-Ho and Cu-Er films has been investigated by Shikhmanter et al. (1982, 1983a) and Venkert et al. (1987). Either Dy(or Er)0.a0Cu0.60 films or (Cu/Ho)n (45 at.% Ho) multilayers have been studied. The nucleation and crystallization processes are determined by TEM and EDP. As expected from the R-Cu phase diagram (Franceschi 1982), the DyCu and ErCu alloys (CsCl-type structure) are formed at about 430K. Kinetics of crystallization and nucleation sites are discussed and analyzed with simple models. The presence of the R203 compound has been observed in all cases. For (Cu/Ho)n samples it is reported that the initially crystallized films (160 nm thick) become nearly amorphous after heating at 373 K, and become crystalline again at 533 K due to the formation of HoCu2 and Ho203. The mixing process and the depth profiling have been analyzed by XPS, UPS and AES measurements. It is observed that, first, the topmost layer formed is Ho203, which is induced by surface segregation of Ho, and second, the interfaces are not sharp due to interdiffusion between the two metals. 3.6.1.2.4. Yb/Cu. Y.S. Huang and Murgai (1989) report that Yb/Cu films annealed up to 873 K form the YbCu2 alloy. In the course of this reaction the ytterbium valence changes from 3 to 2.2. It is asserted that the YbCu2 alloy is characterized by a homogeneous mixed valence state. The results are discussed in terms of the number of f holes and 4ff contributions to the photoemission spectra.

3.6.1.3. R-Cu samples as precursors for synthesis catalysts. Nix and coworkers (Nix and Lambert 1987, Nix et al. 1988a, 1989a) and Jaffey et al. (1989) have shown that at 300- 1100K pure Nd and Sm overlayers on Cu (100) and Cu (11 l) substrates transform to Nd(Sm)Cu and Nd(Sm)Cu5 intermetallie phases. The interaction of Nd with Cu has been widely studied by AES, XPS, UPS and LEED. It is shown that at 300 K pure Nd films grow on the Cu substrate by a layer-by-layer mechanism. At higher temperatures (800 K) rearrangement occurs with the formation of alloy phases. Nix et al. (1988a) compared the results obtained for Cu (111) and Cu (100) substrates, and those reported by Jaffey et al. (1989) for the Sm/Cu (111) system. Such studies have been carried out in order to broadly investigate the properties of the Nd(or Ce)-Cu intermetallic catalyst precursors as reported by Nix and Lambert (1989a,b), Nix et al. (1987, 1988b, 1989b), Owen et al. (1987), Bryan et al. (1988), Hay et al. (1988) and Jennings et al. (1989). The oxidation of Nd (or Ce) overlayers; oxidation by dissociative chemisorption of CO; sorption, chemisorption and desorption of H2; treatments with CO2, CO/Hz, N2 and N20/H2; and, overall the activation and performance of methanol synthesis catalysts have been studied. The whole of these results, obtained by different experimental procedures, shows that the mechanism by which low-temperature methanol synthesis occurs on these catalysts is quite different from that which operates on commercial Cu/ZnO/A1203 catalysts (Nix et al. 1989b). Jennings et al. (1989) have shown that for R/Cu precursors, CQ causes strong irreversible deactiviation, whereas inclusion of Ti, or A1, or Zr enhances poison resistance.

180 M. GASGNIER

3.6.1.4. Ion-beam mixing. In order to prepare the new high-Te superconductors as thin films, a large number of methods have been used. One of them, ion-beam mixing, has been investigated by Borgensen and Lilienfeld (1989) and Mathevet et al. (1990). The former have irradiated their Cu/Y/Cu samples ~vith 600 keV Xe ions. The results are analyzed by RBS spectra. The formation of YCu2, YCu4, YCu5 and YCu7 alloys has been determined. It is concluded that, as a function of temperature, the mixing phenomenon varies strongly. At 100K it is dominated by thermal spike effects, whereas at 323 K the rapid growth of the hexagonal YCu7 phase becomes predominant. In another investigation, Mathevet et al. (1990) have irradiated La(OH)3/Cu bilayers with 3.65 MeV Au ions, at 300 K and 700 K. The results are analyzed by RBS spectra and XRD. It is concluded that a homogeneous depth distribution is not reached, and that ion irradiation simultaneously breaks down the La-O-H bonds and pushes in the Cu atoms. This induces the formation of unknown alloys and/or compounds. These results seem to indicate that the above methods of ion- beam mixing do not form a preferential route for fabricating the ternary RBa2Cu307 and La2_x SrxCuO4 ceramics.

3.6.2. The R-Au system 3.6.2.1. Amorphous GdAu and GdFeAufilms. The magnetic properties, Hall conductivity, Curie temperature and resistivity of GdxAUl-x films (x = 0.26-0.72) have been studied by Gambino et al. (1981). It is suggested that conduction-electron spin polarization determines the magnitude of the spontaneous Hall effect. Gambino and McGuire (I 984) have determined that the addition of a non-S-state heavy lanthanide (Tb, Ho, Er or Tin) to ferromagnetic Gd-Au does not increase the spontaneous Hall effect to a greater extent than would be caused by a similar increase in Gd. In contrast, the addition of Nd leads to a significant increase in this transport parameter, von Molnar et al. (1982b) have shown that Dy-Au amorphous alloys are highly anisotropic magnets. They develop a spontaneous moment at any temperature, and never reach infinite susceptibility. One must also point out the work of Hartmann and McGuire (1983) and Hansen and Hartmann (1986) relative to the magnetic and magneto-optics properties of GdFe-Au films. We also note the investigations of De Luca et al. (1981) relative to the bias-field dependence of domain drag propagation velocities in GdCoAu bubble films.

3.6.2.2. Crystalline films. Schwarz and Johnson (1983) have studied (La/Au)n multilayers at temperatures of 323-353K. The unannealed samples are characterized by the coexistence of the well-crystallized Au and ~-La (fcc) and/or (~-La or LaH2 phases (the interplanar spacings being equal). The most interesting result is the formation, after heating at 353 K for 4 h, of a single amorphous phase. This is essentially due to the fast diffusion behavior of Au in La, and the existence of a negative heat of mixing in the amorphous alloys. The latter provides the necessary chemical driving force for the reaction.

Raaen (1990) has investigated the Ce/Au system by means of XPS. Ce films of various thicknesses are deposited onto Au films (>20nm thick). XPS core-level intensities for


Au 4f and Ce 3d emissions indicate the formation of a mixed amorphous interface (5 nm thick) with an average volume content of Ce estimated at -35%. The Au 4f level shifts by 0.8 eV to higher binding energies which may be explained by changes in final-state screening caused by alloying of Ce and Au.

Shikhmanter et al. (1983b) have carried out TEM experiments in order to study the crystallization behavior of some R-Au (R = Gd, Tb, Dy and Er) vapor-deposited amorphous films (120nm thick). Crystallization takes places in the temperature range of 463-513K, and further heating by an additional 50K leads to the formation of the RAu alloys (CsC1 structure type). Further annealing at 533 K induces an allotropie transformation such as CsC1 type (cubic structure) ~ CrB type (orthorhombic structure). The former is metastable, while the latter is, as in the bulk, more stable at low temperatures. The presence of R203 crystallites can act as catalyst for the transformation. It is concluded that conditions amenable to heterogeneous nucleation will appear on the R-Au films at higher temperatures than in the R-Cu films (413-423 K) or R A g films (388-398 K).

L.I. Johansson et al. (1982a,b) have studied the chemically shifted surface core-level binding energies and surface segregation in Eu-Au and Yb-Au alloys. Photoemission spectra show that Au atoms deposited on the top of an Eu film dissolve into the film more readily at 293 K than for an Yb film. The authors studied mainly the intensity ratio [surf/Ibulk of Au, Eu and Yb 4f lines, and the chemical shifts upon alloying for different Au, Eu and Yb thicknesses and annealing temperatures. The most important feature is the persistence of the rare-earth surface 4f signal with increasing Au content.

3.7. R-Pd alloys (R=Ce, Eu, Er, Yb)

3.7.1. Valence change in R-Pd alloys 3.7.1.1. Ce-Pd amorphous crystalline samples. Comparison to other materials. The Ce valence-state disparity between crystalline and amorphous Ce-TM alloy films has been studied by Lu et al. (1985, 1986) and Croft et al. (1984, 1985). For CePd3 and CePdt.5 films (700 nm thick) Lm absorption spectra show that crystalline samples possess a lower valence state (3.17) than amorphous films (3.30). Moreover, Ag substitution for Pd in crystalline CePd3 acts to stabilize nearly pure Ce 3+ behavior. In the case of Cel-xMxPd3 materials (M=Y, La), the Ce valence decreases from 3.17 at x=0 to 3.09 at x=0.75 (M = La), and increases to 3.23 (M = La) and 3.29 (M = Y) for x = 0.40. (In the case of Th 4+ and U 4+ substitutions the valence decreases to 3.10 at x = 0.40.) The results are discussed in terms of lattice-parameter changes, electronegativity arguments and band filling. These valence changes have also been determined for other metals, such as Cu, Ni, Co, Fe, Mn, Mo, Ru, Rh and A1 (or AlSo).

Parks et al. (1983) have established a linear relation between the Lm-based valence estimates (from 3.00 to 3.21) and the bulk-property based valence estimates (from 3.00 to 4.00) in the Ce(Ag or Rh, Pd)3 systems. Then, Parks et al. (1984) in the case of fracturing clean RPd3 samples (R = La, Ce, Pr, Nd) have observed a 4f-derived resonant photoemission. The authors speculate that a mixed-valence state can occur in Ce systems

182 M. GASGNIER

only if the 4f holes are locally screened. The contraction of a valence electron may explain the anomalously large lattice contraction observed in these systems.

3.7.1.2. Eu and Yb-Pd amorphous specimens. For amorphous films of EuxPd~_x (0.16 ~<x ~< 0.35) and YbxPdl-x (0.29 ~<x ~< 0.66), Malterre et al. (1986) have shown that Lm edges demonstrate a concentration-induced valence change. The samples (1 ~tm thick) are prepared by co-evaporation. Two peaks indicating a mixed-valence state are recorded. As a function of the concentration it is shown that Eu valency decreases from 3.00 to 2.00 as x increases (in the same way as in crystalline EuPd5 and EuPd2 samples). The local Eu environments in amorphous samples look like those of the bulk. For Yb this valence decrease is observed between x = 0.29 (valence 2.90) and x = 0.66 (valence 2.12).

3.7.2. Rx-Pdy crystallographic properties The phase diagrams of the R-Pd alloys (R = Y, Sin, Gd, Dy, Ho and Er) have been first investigated by Loebich and Raub (1973a,b). They report the formation of 7 different alloys. However, Moreau and Parth6 (1973) and Palenzona and Iandelli (1974) have shown that the SmsPd2 and Sm4Pd5 compounds are of Sm4Pd3 and Sm3Pd4 stoichiometry. Such results have been also corroborated by Jordan and Loebich (1975) from XRD and magnetic measurements. They also deduce an effective valence of +3 for Sm.

In the range of low R content (below 20 at.%) extensive work has been done by Brooks et al. (1976), Hirst et al. (1976) and Hughes et al. (1980a,b). Physical and mechanical properties exhibit numerous anomalies. These seem to be correlated to the presence of long-range order in the Pd-R solid-solution alloys close to the solid solubility limit. In the case o fa Pd-12.5 at.% Ce electropolished disc, D.A. Smith et al. (1982) have shown by TEM the existence of the Pd7Ce superlattice. The crystallographic structure would be a stacking fec sequence such as A(4Pd)B(Pd3Ce)C(4Pd). The presence of this phase should explain the physical anomalies reported by the above-mentioned authors. In the same way, Kuwano et al. (1981) have observed equivalent EDP, and conclude that the PdTCe alloy is formed as a superstructure and that it is stable below 1170K. They also found another phase, PdsCe, an ordered stacking structure with a rhombohedral symmetry. (The crystallographic structure of the PdsR alloy has not been reported by Jordan and Loebich (1975).) Then, Kuwano et al. (1985) report that the PdsCe phase was in fact defined by a hexagonal symmetry with two polytypes of stacking structure, i.e., L-PdsCe and H-PdsCe types, stable at low and high temperature respectively.

The Pd-rich side (5-21 at.%) of the Pd-R systems (R=Y, Ce, Eu, Sm, Gd, Dy, Ho, Er) has been extensively investigated by Sakamoto et al. (1985, 1986, 1988, 1990a,b, 1991) and Takao et al. (1989, 1990). The phase diagrams, the electric resistance versus temperature, and the XRD and EDP results (fig. 27) are systematically reported for alloys prepared by arc-melting. The hydrogen solubility has been measured in ordered and disordered PdTCe alloys. The main results for the yttric lanthanides appear to have the following characteristics:


Fig. 27. Electron diffraction patterns of annealed Pd-x at.% R alloys. (a,b) Pd-12.5 at.% Sm: the zone axes are [001] and [010], respectively (PdsSm phase). (c) Pd-14.3 at.% Eu: the zone axis is [101] (coexistence of the Pd7Eu and Pd3Eu phases). (d) Pd-17.5 at.% Gd: the zone axis is [101] (coexistence of the PdvGd and Pd3Gd phases). (By courtesy of Profs. Y. Sakamoto and K. Takao, Nagasaki Univ., Nagasaki, Japan).

(1) Format ion o f an ordered structure of the LI2-type Pd3R phase and/or o f PdsR

(R = Sm) and the format ion o f Pd7R; (2) It is accompanied by a peri tectoid react ion as: c~-Pd +LI2- type Pd3R ~-~ Pd7R;

184 M. GASGNIER

(3) The transition temperature (order-disorder transition) decreases with decreasing R content, it corresponds to the solid solubility limit of R in the (t-Pd solid solution below the peritectoid reaction temperature,

(4) The magnitude of this transition temperature may be attributed to the metallic radius of the R metals and decreases from Eu to Er.

Figures 27a,c illustrate the PdsSm phase for the Pd-12.5 at.% Sm alloy. The pattern in fig. 27a, relative to the Pd-14.3 at.% Eu alloy, shows the coexistence of the Pd7Eu and LI2-type Pd3Eu phases. Lastly, EDP (fig. 27d) of the Pd-17.5 at.% Gd alloy, is commonly observed for all the PdTR alloys. It is characterized by two types of superlattice reflections.

One must point out that in the case of Pd-Ce alloys Sakamoto et al. (1990a) have greatly refined the results given by D. Rossi et al. (1975) and Kuwano et al. (1985). It is reported that two PdsCe phases, H-PdsCe and L-PdsCe (i.e., formed at high and low temperatures), with hexagonal (CusCa-type layers) and fcc (long- period antiphase superstructure) structures can be observed. The formation of the Pd7Ce phase is accompanied by a peritectoid reaction: (x-Pd+L-PdsCe--+~Pd7Ce for higher Ce content, whereas a phase transition a-Pd ~ (~-Pd + PdTCe occurs for lower Ce content. At 1074-t- 10 K the L-Pd5 Ce ~ H-Pd5 Ce transition occurs. This temperature is higher than those determined for heavy lanthanides.

3.8. Superconducting materials

The main results obtained in the field of thin superconducting films and crystals have recently been summarized by Gasgnier (1991). This review paper brought into perspective the numerous efforts which have been made, since 1960, to try to obtain better superconducting performance with various alloys and compounds. But, since the discovery of the new high-Te superconducting ceramics (RBaCuO, BiSrCaCuO, PbSrYCaCuO, YSrCuO, NdCeCuO, ... ) the importance of the other materials has diminished abruptly. It is not feasible in this chapter to deal with the properties of the thin films of these new materials, because this subject is nowadays much too extensive. (The reader should refer to specialized review papers and Handbooks).

However, one must draw atteotion to articles which report on some new (non- high-temperature) supercrnducting compounds. Cendlewska and Rojek (1987) and Bohdziewiez et al. (1989) have prepared, by cathode sputtering, thin LuRhl.2Sm 4 films. Their Tc is 3.72 K, i.e., somewhat lower than for the bulk (4.08 K). Structures on the resistivity curve near 4.70 K indicate, possibly, the existence of another superconducting phase with higher Tc. In the case of ErRhnB4 and Er0.sHo0.sRh4B4 ferromagnetic superconducting films, Mancini and Noee (1986, 1987) have studied the electromagnetic properties in the presence of an external homogeneous magnetic field and the reflection, transmission and absorption coefficients of an electromagnetic wave normally incident on the surface of the layer. It has been found that there exists a critical temperature, below which spontaneous magnetization occurs as a function of thickness. It is concluded that ErRh4B4 exhibits a sharp decrease of the reflection coefficient near


0.8K (first-order transition to a normal state with ferromagnetic ordering) which seems to be a manifestation of spin-fluctuation effects due to the ferromagnetism. For Er0.sHo0.sRh4B4 this coefficient shows a very small deviation, therefore superconductivity and magnetic order cannot coexist in this compound. These results confirm previous investigations relative to the surface impedance penetration depth (C.Y. Huang et al. 1985).

One must also point out that Xu and Shelton (1987) and Xu (1987) have synthetized Lu2Fe3Si5 alloys with a Tc of6.11 K (the addition of transition metals reduced Te). In the same way RsOs4Si15 (R = Y, Er, Tb) and Y4Os4Sil3 bulk compounds are superconductors with a Te of 10.8, 5.5, 3.2 and 9.8 K, respectively. Under hydrostatic pressure Tc degrades significantly (Kuboth et al. 1989). One can conclude that the synthesis of new materials is always possible in the near or remote future.

3.9. Miscellaneous R-M alloy films and thin crystals

3.9.1. Y, La-Pb multilayer samples The formation of the RPb3 alloy has been studied by Ronay et al. (1982). This investigation has been carried out by means of multilayer samples such as: Y, La(5-20 nm)/Y, La- Pb("phase-in" layer)/Pb(200 nm)/Al(100 nm). After aging, RBS experiments show that no compounds are formed between La and Pb, nor between Y and Pb. Moreover the grain size of lead is not reduced. The formation of holes and hillocks around the holes is clearly observed, and is related to the oxidation of the interface.

3.9.2. Transport properties in U-R films (R = Gd, Yb) The competing magnetic, localization and phonon effects on the transport properties of amorphous magnetron-sputtered U-R films (200 nm thick) have been described by Freitas et al. (1988). While UxYbl-x films are well nonmagnetic, it is clearly shown that UxTbl_x and UxGdl-x samples are, respectively, spin glasses and random-anisotropy dominated systems. For both these systems U addition leads to a linear decrease of the freezing temperatures. For x = 0.40 these temperatures are high enough to indicate positive average exchange. The signature of U moment is not found. The magnetoresistance is negative (as it is for UxDyl-x and UxNdl-x systems). Coexistence between spin disorder and weak localization is evidenced from magnetoresistance and resistivity measurements in UxGdl-x samples.

3.9.3. Quasicrystal Co-Er alloys An icosahedral dominant phase was reported by H. Li et al. (1988) to exist in rapidly quenched CosoEr2o alloys, made by melt spinning in He. The quasicrystals are strongly magnetic, with sperimagnetic characteristic similar to those observed in amorphous films of the same composition. The quasicrystal--+ crystal transition occurs at 660-900 K.

186 M. GASGNIER

4. Metalloid R-compounds

4.1. Rare-earth chalcogenide and bismuth systems

4.1.1. RAs films (R = Tb, Dy, Er, Yb and Lu) The growth of RAs single crystals as epitaxial films on GaAs is important for forming semiconductor/metal/semiconductor heterostructures. Numerous researches have been done in the field of the GaAs/RAs/GaAs structures (R=Er, Yb, Lu) and then, more recently, in the field of GaAs/ErPl_xAsx/GaAs, GaAs/Scl_xErxAs/GaAs and InP/ErPxSbl_x/InP structures. The aim of these experiments is to obtain a nearly perfect lattice match to GaAs. One of the main electrical characteristics of the RAs materials is that they exhibit a metallic behaviour with resistivities of 50-90 ~tf2 cm. Therefore the high melting point of RAs materials and their excellent electric conductivity make them promising candidates for stable contacts to GaAs, and for use as base metallization in metal-base transistors, resonant tunnelling/transistors or quantum-well systems.

4.1.1.1. ErAs, ErxSel_xAs and ErPxAsl-x specimens. These materials seem to exhibit the highest performances. To our knowledge the first experiments were carried out by Waldrop (1985) in order to realize rare-earth metal (Tb, Dy, Er) Schottky barrier contacts to GaAs. (The Schottky-barrier height is 0.85 eV). However, a direct contact cannot be made on this basis since the R-GaAs interface is thermodynamically unstable. At this interface GaAs dissociates and forms an interfacial RAs layer of more than 1 nm in thickness.

Since then, Palmstrorn et al. (1988-1990), S.J. Allen et al. (1989) and Zhu et al. (1990) have studied the ErAs and ErxSCl_xAs epitaxial layers buried in GaAs prepared by MBE. Palmstrom et al. (1988, 1989) have characterized the single-crystal film growth of (100) ErAs on (100) GaAs by RHEED, LEED and RBS. The structure GaAs (50 nm)/ErAs (1-1.5 nm)/GaAs gave minimum yields of ~7%, slightly higher than that obtained from a perfect single crystal. This is due to the presence of stacking faults in the overgrown GaAs layer and also to a slight misorientation of the ErAs film with respect to the substrate (attributed to a partial relaxation of the ErAs thin layer). The resistivity of such structures decreases from 70 ~tf~ cm at 293 K to 17 ~tff2 cm at 1.5 K. At low temperature, Hall measurements show that conduction is dominated by electrons with an effective n-type mobility. However, it has been noticed that the overgrowth of ultrathin GaAs films on ErAs is difficult due to the poor GaAs wetting of the RAs surface, which results in three-dimensional growth.

Remark: Nearly identical results have been obtained with LuAs films (Palmstrom et al. 1989). For a 6.5nm thin layer the resistivity decreases from 90~tf2cm at 293K to 47 ~tf2 cm at 1.5 K. It is noticed that the presence of Lu203 prevents the film growth.

Zhu et al. (1990) report epitaxial microstructures characterized by HREM and RBS. It is observed that ErAs can have an excellent epitaxy on (100) GaAs substrates. On the other hand the overgrown GaAs layer can present twins, threading dislocations (for thick ErAs layers), different epitaxial orientations (such as (111) GaAs on (100) ErAs)


and different phase boundary (such as {122} GaAs/(100) ErAs). It is also confirmed that this overgrown GaAs layer develops by an island growth mechanism. S.J. Allen et al. (1989) have studied the magnetotransport and spin-disorder scattering of these structures. They observe that ErAs epitaxial layers are a relatively low-density semimetal ordering magnetically at low temperatures (<5K). At low temperatures (-5 K) spin- disordered scattering produces a resistive anomaly at the antiferromagnetic-paramagnetic phase boundary.

Palmstrom et al. (1990) have prepared a new kind of material: a multilayer GaAs (50nm)/Sc0.32Er0.68As(20nm)/(100) GaAs that seems to be more attractive than the pure GaAs/ErAs/GaAs heterostructures. They report room-temperature resistivities of 50 ~tf2 cm and a lattice matching to GaAs estimated to be ~<0.1%. This low resistivity could be due to less strain and defects in the lattice-matched sample. RHEED oscillations during ScAs, ErAs and ScErAs growth indicate a monolayer-by-monolayer growth. Other kinds of materials have been prepared by MBE by Le Correet al. (1989a,b, 1990), Guivarc'h et al. (1989) and Caulet et al. (1990). Such materials as ErPxAsl-x (or Sbl-x) have been chosen because perfectly matched layers on GaAs and InP substrates can be obtained. Indeed, since the ErAs lattice parameter is larger than that of GaAs (+1.4%) and the ErP one is smaller (-1%), the ErPxASl_x alloy is used to match the lattice GaAs. Such a hypothesis has been verified by HREM which reveals an abrupt ErP0.6As0.4/GaAs interface with a very low density of dislocations. However, dislocations and microtwins are observed in the overgrown GaAs layer. The crystalline quality of this layer is better for (111) GaAs substrates than for (001) GaAs substrates. Compared to ErAs films, it seems that ErP0.6As0.4 layers do not degrade after several months in the atmosphere, whereas the former are oxidized after one month exposure. The resistivity of the latter (~85 ~tf2 cm) is intermediate between those of ErAs (60 gf2 cm) and ErP (150 ~t~cm). Moreover, a Schottky barrier fabricated from ErP0.6As0.4 films on n-type (001) GaAs exhibits a barrier height of 0.88 eV. Hall measurements show that such materials are low-density semimetals with predominantly electron conduction. One notes that Le Correet al. (1989b) have taken out a patent.

4.1.1.2. YbAsfilms. Richter et al. (1988) have investigated thin single-crystals YbAs films grown epitaxially on GaAs by MBE. XPS indicates the absence of oxide impurities and the presence of only trivalent Yb. The epitaxial film is composed entirely of YbAs which has a moderate imperfection of its crystalline quality and a lattice misfit o f~8x 10 -3 with respect to GaAs.

4.1.1.3. gb-As2S3films. Efendiev et al. (1988, 1989) have studied the formation of ternary compounds as YbAs4S7 and Yb3As4S 9 during thermal evaporation and interaction of amorphous As2S3 and polycrystalline ytterbium. They claim that after annealing at 573 K there is formation of C-Yb203 and of YbAs4S7 with an orthorhombic lattice.

188 M. GASGNIER

4.1.2. RSb films (R =Sm, Tm, Yb) Only a few RSb materials have been few studied. However as reported by Le Corre et al. (1989a,b) these materials are comparable to the RAs ones. As to pure thin films, Dzhabua et al. (1987), Dadiani et al. (1989) and Glurdzhidze et al. (1990) have reported the temperature dependences of the resistivity, Hall coefficient, Hall mobility and thermoeleetromotive force at 80-300 K. The layers are deposited by vacuum thermal evaporation from two independent sources. The values of the physical parameters agree with those obtained for a variable valence systems. In this way TmSb, SmSb2 and YbSb2 compounds were formed.

4.1.3. RBi films (R=Gd) Baba et al. (1989) have studied the formation of the GdxBiy compounds at various annealing temperatures. Sputtered thin films of Gd-Bi (4:3 in atomic ratio) show that after annealing under vacuum at 803 K the GdnBi3 phase is formed. At lower temperature this phase is not observed, whereas at higher temperature GdsBi3 and GdBi phases grow. Compared to the bulk, Gcl4Bi3 films have the same Curie temperature of 330K, but the residual resistance is several times larger.

4.2. Pb(Eu, Yb)(Te, Se, S) thin films

These materials are useful for IR lasers of 2.5-6 ~tm range, which are themselves useful for an optical source for a gas sensing system (molecules in a gas or adsorbed onto surfaces). Moreover, a 3 ~tm laser is feasible for long-distance optical communication using fluoride glass. These materials have the highest continuum wavelength operating temperature ever recorded with lead salt diode lasers.

4.2.1. Lead-europium films Partin (1983a,b, 1984, 1985, 1987, 1988) and Partin and Thrush (1984) have prepared Pbl_xEuxTe~-ySey (x = 0.015, y = 0.020) films by MBE. This alloy is either covered with a PbTe film (20 nm thick) to form a single-quantum-well laser, or deposited onto PbTe (100) or (111) substrates for diode lasers. It is assumed that there is a good lattice match to PbTe. It is shown that the laser emission energy as a function of composition increases as the relative Eu content increases. The photoluminence properties at 4.2 K, in PbTe/PbEuTeSe multiquantum wells have been reported by Goltros et al. (1985).

Another procedure to prepare Pbl_xEuxTe films has been used by Krost et al. (1985). This technique, called hot-wall epitaxy, allows one to obtain single-phase material. The layers are deposited onto BaF2 (111) or KC1 (100) substrates. Krost et al. (1985), however, have not obtained good crystalline films with Eu content over 5%. They report numerous optical and magneto-optical data for x=0.01 and 0.06. Ishida et al. (1986, 1987, 1988a,b) have succeeded in preparing Pbl_xEux(Te, S) films with high EuTe and EuS content (x ~< 0.26) and PbTe/Pbl_xEuxTe superlattices. Multilayers in the


form of PbTe wells (4-25 nm)/Po.95Eu0.05Te barrier layers (14nm)/PbEuTe buffers (4- 9 ~tm)/KC1 (100) substrates are available to obtain high-operating-temperature lasers in the 3-6 ~tm range. Experimental absorption edges agree well with the theoretical ones calculated assuming that the conduction band offset is equal to that of the valence band. In the case of PbTe/Pbl_xEuxTe (2-4 ~tm)/BaF2 (111) systems the energy band gaps, obtained from optical transmission spectra, vary nonlinearly beyond a EuTe ratio close to 0.075 and vary linearly with tempearature between 50 and 300 K. Single-phase films with Eg (energy gap) ~<0.83 eV and x ~< 0.26 are obtained. Electrical properties (carrier concentration and mobility) are measured at 77 K. High carrier concentration and low resistivity are obtained up to x = 0.06 (Eg = 0.55 eV) and high resistivities are measured for x > 0.07 and Eg > 0.60 eV In the case of PbS/Pbl-xEuxS/BaF2 (111) heterojunctions, the energy band gap can reach a maximum of 0.92 eV (x = 0.22) and Eg increases rapidly with EuS content up to x = 0.05. Suryanarayanan and Das (1990) have used co-evaporation to prepare thin samples deposited onto BaF2 (111) substrates with 0 <x < 0.55. It is observed that the band gap increases more or less linearly with increasing x up to x = 0.1. The data indicate that the Eu 2+ is stable for all values of x studied.

The above-mentioned authors have observed that both optical and electrical properties depend on crystallographic characteristics. In this way the choice of PbTe (111) buffers, with a lattice constant close to that of a PbEuTe film, leads to an important strain effect, whereas BaF2 substrates, with a lattice mismatch of 4%, induce very small strain effect. On another part, it clearly appears that there is a strong deviation from Vegard's law. Moreover, the dependence of the lattice constants of Pbl_xEuxTe films on EuTe content (0 <x < 0.55) shows a discrepancy between the results of Partin (1987, 1988), Ishida et al. (1988a), Krost et al. (1985) and Suryanarayanan and Das (1990). Such a deviation is also observed in the case of Pbl_xEuxS materials (Ishida et al. 1988b). This result has not been understood up to date; it could be explained if the affinity of Te to Pb is different from that to Eu.

TEM observations carried out by Salamanca-Young et al. (1988) reveal new crystallographic properties. As a function of Eu content (0.20 ~< x ~< 0.75) and of substrate (BaF2) temperature the following results have been obtained for films prepared by MBE. One must recall that Pbl-xEuxTe is defined by a NaCl-type structure (a0 = 0.646-0.652 nm as a function of Eu content). At low substrate temperatures (~573-673 K) and low Eu content (x = 0.20) no ordered compounds are formed. (The multiphase formation observed by Krost et al. (1985) at very low concentration was the result of the higher substrate temperature (723 K) and of the hot-wall epitaxy method.) For x = 0.35 it is asserted that an ordered compound or a superlattice appears of which the lattice constant given is equal either to 1.125 nm or to 1.083 nm according to text and table, respectively. However these values do not correspond to 3 x3 x3 unit cells of PbTe as built by the authors. But the corresponding EDP exhibits weak spots located at 1/3 and 2/3 between (000) and {422} spots. Such extra spots can also be indexed according to a hcp deriving from the fcc one (as for Au, Ag, RH2). In this way one can argue that a hcp surface superstructure with ah = 0.460 nm (or ao/v~) and Ch = 0.750 nm (Ch/ah = 1.633) might be formed. For x=0.51, another fcc superstructure is formed by a 2 x 2 x 2 unit cell (the

190 M. GASGNIER

cubic parameter being well equal to 1.30nm). In this case the EDP results correspond to this structure. For x=0.75 no disordered structures are observed. However, alloys with 0.40 ~< x ~< 0.51 exhibit a spinodal decomposition characterized by long-wavelength periodicities (1.44 up to 2.10 nm). Such a decomposition indicates that the solid solution for x ~ 0.50 is unstable at room temperature.

4.2.2. Lead-ytterbium films Pbl_xYbxTe films have been prepared by MBE onto BaF2 substrates by Partin (1983b, 1988). Ytterbium bonds strongly to the PbTe coverage film and it has a small diffusion coefficient. Ytterbium introduces a donor level into PbTe near the valence-band edge caused by the yb2+-+ Yb 3+ +e - transition. The lattice constant versus Yb content (0 ~< x ~< 0.30) does not obey Vegard's law. The optical and electrical properties of samples prepared by co-evaporation have been reported by Das and Suryanarayanan (1989a-c).

5. Conclusion

In an earlier chapter (Gasgnier 1982) concerning R alloys and compounds as thin films, three main wishes were emphasized. The first related to accurate characterization of the materials. This way is now broadly opened: microstructural properties and microchemical analyses are effective tools used by a great number of laboratories. The second one seems, for its part, more difficult to realize. Indeed, the fabrication of "ideal" and "reproducible" thin films always seems to be a critical problem. The presence of narrow and/or extended defects, of amorphous or unexpected compounds or alloys, of passivating layers, etc., is difficult to monitor. The last wish, and maybe the most important, was to draw attention to the exchange of information between physicists and chemists, as well as to the accurate knowledge of the complex properties of the rare earth elements. Unfortunately, as revealed by numerous articles, these problems remain often unknown to various researchers.

Lastly, in the present state, one can readily predict the future of R elements for industrial applications. Two of them seem to be a sure thing: supermagnets and superconductors. Another appears to be quite likely: multilayer devices such as (R/TM)n, (R/R~)n and heterostructures, in spite of the interfacial problems. However, as these new materials have been synthesized in the course of the last ten years, it is not impossible to think that new other alloys, or intermetallics, or compounds will arise in the near future. Rare earths are multifaceted elements and can be adapted accordingly to various unexpected routes.

References

Adachi, G., K. Niki and J. Shiokawa, 1981, J. Less- Common Met. 81, 345.

Adachi, G., K. Nieki, H. Nagai and J. Shiokawa, 1982, J. Less-Common Met. 88, 213.

Adachi, G., H. Nagai and J. Shiokawa, 1984, J. Less- Common Met. 97, L9.

Adachi, G., H. Sakaguchi, K. Niki, N. Nagai and J. Shiokawa, 1985a, L Less-Common Met. 108, 107.

THE INTRICATE WORLD OF RARE EARTH THIN FILMS i91

Adachi, G., H, Sakaguchi, K. Niki, H. Nagai and J. Shiokawa, 1985b, Bull. Chem. Soc. Jpn. 58, 885. In Japanese.

Adachi, G., H. Sakaguchi, T. Shimoghori and J. Shiokawa, 1986, J. Less-Common Met. 116, L13.

Adachi, G., H. Sakaguchi, T. Shimoghori and J. Shiokawa, 1987, J. Less-Common Met. 133, 271.

Adachi, G., H. Sakaguchi and K. Nagao, 1992, J. Alloys & Compounds 181, 469.

Affrossman, S., 1981, Surf. Sci. 111, 1. Aguilera-Granja, E, and J.L. Morfin-L6pez, 1990,

Solid State Commtm. 74, 155. Ahmed-Mokhtar, N., J.R P6trakian, R. Philip, R.

Fraisse and B. Lazarides, 1982, Thin Solid Films 88, 177.

Aidun, J.B., 1986, Shock Waves in Condensed Matter (Plenum Press, New York) p. 519.

Alameda, J.M., M.C. Contreras, J.E Fuertes, A. Li6nard and EH. Salas, 1990, J. Magn. & Magn. Mater. 83, 75.

Allen, C.W., D.L. Kuruzar and A.E. Miller, 1974a, IEEE Trans, Magn. MAG-10, 716.

Allen, C.W., A.E. Miller and D.L. Kuruzar, 1974b, in: Proc. 8th Int. Congr. on Electron Microscopy, Vol. 1 (Canberra, Australia) p. 638.

Allen, C.W., K.C. Liao and A.E. Miller, 1977, J. Less- Common Met. 52, 109.

Allen, J.W., L.I. Johansson, R.S. Bauer, I. Lindau and S.B.M. Hagstr6m, 1978, Phys, Rev. Lett. 41, 1499.

Allen, J.W., L.I. Johansson, I. Lindau and S.B.M. Hagstr6m, 1980, Phys. Rev. B 21, 1335.

Allen Jr, S.J., N. Tabatabaie, C.J. Palmstrom, G.W. Hull, T. Sands, E De Rosa, H.L. Gilchrist and K.C. Garrison, 1989, Phys. Rev. Lett. 62, 2309.

Allibert, C.H., 1989, J. Less-Common Met. 152, L1. Alvarado, S.E, M. Campagna and W. Gudat, 1980,

J. Electron. Spectrosc. Relat. Phenom. 18, 13. Andersen, J.N, J. Onsgaard, A. Nilsson, B. Eriksson,

E. Zdansky and N. Mhrtensson, 1987, Surf. Sci. 189/190, 399.

Andersen, J.N., I. Chorkendorff, J. Onsgaard, J. Ghijsen, R.L. Johnson and E Grey, 1988, Phys. Rev. B 37, 4809.

Angadi, M.A., and EV. Ashrit, 1981a, Phys. Status Solidi a 67, K119.

Angadi, M.A., and RV. Ashrit, 1981b, J. Phys. D 14, L125.

Angadi, M.A., and RV. Ashrit, 1981c, Vacuum 31, 161.

Angadi, M.A., and EV. Ashrit, 1983a, J. Mater. Sci. 18, 3177.

Angadi, M.A., and EV. Ashrit, 1983b, Phys. Status Solidi a 77, 685.

Annapoomi, S., G. Markandeylu and K.xZS. Rama Rao, 1989, J. Appl. Phys. 65, 4955.

Annapoomi, S., G. Markandeylu and K.V.S. Rama Rao, 1990, J. Appl. Phys. 68, 1394.

Antepenko, R.J., and D.M. Holtoway, 1980, Appl. Spectrosc. 34, 206.

Anthony, T.C., J. Brag, S. Naberhuis and H. Birecki, 1986, J. Appl. Phys. 59, 213.

Aoyama, A., 1988, Jpn. Kokai Tokkyo Koho JP 88 80 408. Patent in Japanese.

Apostolov, A.V., K.I. Grozdev, V.S. Shopov and I.V. Velichkov, 1981, L Phys. F 11, L269.

Apostolov, A.V., K.I. Grozdev and LV. Velichkov, 1983, Czech. J. Phys. B 33, 1154.

Arakawa, T., N. Suezawa, G. Adachi and J. Shiokawa, 1988, Appl. Surf. Sci. 33/34, 286.

Ashrit, EV., and M.A. Angadi, 1980a, J. Less-Common Met. 75° 147.

Ashrit, P.V., and M.A. Angadi, 1980b, J. Phys. D 14, L125.

Ashrit, EV., and M.A. Angadi, 1981, Phys. Status Solidi a 63, K77.

Ashrit, P.V., and M.A. Angadi, 1982, Vacuum 32, 101.

Ashrit, RV., and M.A. Angadi, 1983, Proc. Nuel. Phys. Solid State, Phys. Syrup. 23(C), 656.

Ashrit, EV., S.M. Shivaprasad and M.A. Angadi, 1980, Thin Solid Films 72, L5.

Ashrit, EV, EE. Girouard and V.V. Truong, 1984, J. Less-Common Met. 102, L15.

Aylesworth, K.D., Z.R. Zhao, D.J. Sellmyer and G.C. Hadjipanayis, 1988, J. Appl. Phys. 64, 5742.

Aylesworth, K.D., Z.R. Zhao, D.J. Sellmyer and G.C. Hadjipanayis, 1989, J. Magn. & Magn. Mater 82, 48.

Aylesworth, K.D., D.J. Sellmyer and G.C. Hadji- panayis, 1990, J. Appl. Phys. 67, 5725.

Aylesworth, K.D., D.J. Sellmyer and G.C. Hadji- panayis, 1991, J. Magn. & Magn. Mater. 98, 65.

Baba, K., H. Ishii, I. Yamaguchi, O. Nakamura and T. Takeda, 1989, Mater. Res. Soc. Syrup. Proc. 151, 289.

Baberschke, K., M. Farle and M. Zomack, 1987, Appl. Phys. A 44, 13.

Bachurin, V.I., V.E. Zhuravski, E.S. Kharlamockhin and V.E. Yurasova, 1981, Sov. Techn. Phys. Lett. 7, 311.

192 M. GASGNIER

Bacon, EM., D.E Cowgill, C.E. Hickox, R.J. Walco, S.R. Subia Jr and A.A. Riedel, 1984, Rev. Sci. Instrum. 55, 42.

Baczewski, L.T., M. Piecuch, J. Durand, G. Marehal and R Delcroix, 1989, Phys. Rev. B 40, 11237.

Baczewski, L.T., M. Piecuch, J. Durand, G. Marchal and P. Delcroix, 1990, J. Magn. & Magn. Mater. 83, 68.

Badia, E, C. Ferrater, A. Lousa, B. Martinez, A. Labarta and J. Tejada, 1990, J. Appl. Phys. 67, 5652.

Bauer, E., and J. Kolaczkiewicz, 1985, Phys. Status Solidi b 131, 699.

Beaudry, B.J., and K.A. Gschneidner Jr, 1978, Preparation and basic properties of the rare earth metals, in: Handbook on the Physics and Chemistry of Rare Earths, Vol. 1, eds K.A. Gschneidner Jr and L. Eyring (North-Holland, Amsterdam) ch. 2.

Beavis, L.C., 1980, Metal Tritides Helium Emission, microfilm DAND79-0645 (Sandia National Labo- ratory, Albuquerque, NM).

Beavis, L.C., and W.J. Kass, 1977, J. Vac. Sci. & Technol. 14, 509.

Blancard, C., J.M. Esteva, R.C. Karnatak, LR Connerade, U. Kuentgens and J. Hormes, 1989, J. Phys. B 22, L575.

Blancard, C., J.M. Esteva, R.C. Karnatak, J.E Connerade, U. Kuentgens and J. Hormes, 1990a, in: 2nd Eur. Conf. Progr. X-Ray Synchrotron Radiat. Res., Nuovo Cimento, Spec. Vol., p. 113.

Blancard, C., J.M. Esteva, R.C. Karnatak, B.K. Sarpal, J.E Connerade, U. Kuentgens and J. Hormes, 1990b, 2nd. Eur. Conf. Progr. X-Ray Synchrotron Radiat. Res., Publ.: Nuovo Cimento, Spec. Vol., p. 117.

Boeva, O.A., K.N. Zhavoronkova, M. Smutek and S. Cern~,, 1986, J. Less-Common Met. 118, 1.

Bohdziewicz, A., B. Cendlewska, M. Kazimierzki, J. Szymazek and J.J. Wnuk, 1989, Phys. Status Solidi a 114, K49.

Borgensen, P., and D.A. Lilienfeld, 1989, J. Appl. Phys. 66, 3298.

Bosca, G., J. David, L. Allay, J.M. Darmon and Y. Victor, 1981, Rev. Phys. Appl. 16, 387. In French.

Boulesteix, C., 1982, Defects and phase transformations in rare earth sesquioxides, in: Handbook on the Physics and Chemistry of Rare Earths, Vol. 5, eds K.A. Gschneidner Jr and L. Eyring (North-Holland, Amsterdam) oh. 44.

Boulesteix, C., 1984, Phys. Status Solidi a 86, 11. Braaten, N.A., J.K. Grepstad and S. Raaen, 1989, Phys.

Rev. B 40, 7969.

Bracconi, P., and R. Laesser, 1987, Appl. Surf. Sci. 28, 204.

Bracconi, P., and R. Laesser, 1988, Z. Phys. Chem. N.E 163, 615.

Braceoni, P., E. P6rschke, K.H. Klatt and R. Laesser, 1987, J. Vac. Sci. & Technol. A 5, 235.

Bracconi, P., E. P6rschke and R. Laesser, 1988, Appl. Surf. Sci. 32, 392.

Brat, N.S., and Y.M. Gupta, 1986, in: Shock waves in Condensed Matter (Plenum Press, New York) p. 513.

Bras, J., M. Fagot and J. Dejanque, 1988a, J. Microsc. Spectrosc. Electron. 13, 439.

Bras, J., J. Dejauque and M. Fagot, 1988b, Solid State Commun. 68, 117.

Bras, J., J. Dejauque, M. Fagot and K. Biyadi, 1990, J. Magn. & Magn. Mater. 83, 203.

Br6chignae, C., Ph. Cahuzac, E Carlier, M. de Frutos, A. Massov and J.-Ph. Roux, 1991, Z. Phys. D 19, 195.

Brooks, J.W., M.H. Loretto and I.R. Harris, 1976, Met. Sci. 10, 897.

Brouder, C., M. Piecuch, G. Marchal, P. Delcroix and A. Bruson, 1986, Proc. Eur. Mat. Res., Ed. Phys. (Paris) p. 85.

Brouder, C., G. Krill, E. Dartyge, A. Fontaine, G. Tourillon, P. Guilmin and G. Marchal, 1988a, Mat. Sci. & Eng. 97, 109.

Brouder, C., G. Krill, P. Guilmin, G. Marchal, E. Dartyge, A. Fontaine and G. Tourillon, 1988b, Phys. Rev. B 37, 2433.

Brouder, C., G. Krill and M. Piecuch, 1988c, J. Less- Common Met. 140, 67.

Brouder, C., G. Krill, W. Felsch, P. Guilmin, G. Marchal, E. Dartyge, A. Fontaine and G. Tourillon, 1988d, J. Less-Common Met. 145, 123.

Brousseau-Lahaye, B., C. Colliex, J. Frandon, M. Gasgnier and P. Trebbia, 1975, Phys. Status Solidi a 69, 257.

Bryan, S.I., J.R. Jennings, S.J. Kipling, G. Owen, R.M. Lambert and R.M. Nix, 1988, Appl. Catal. 40, 173.

Burmistrova, O.P., M.A. Mittsev and A.M. Mukhuchev, 1983, Sov. Phys. Solid State 25, 25.

Burzo, E., and H.R. Kirchmayr, 1989, Physical properties of R2Fe14B-based alloys, in: Handbook on the Physics and Chemistry of Rare Earths, Vol. 12, eds K.A. Gschneidner Jr and L. Eyring (North- Holland, Amsterdam) oh. 82.

Buschow, K.H.J., 1984, Amorphous alloys, in: Handbook on the Physics and Chemistry of Rare


Earths, Vol. 7, eds K.A. Gschneidner Jr and L. Eyring (North-Holland, Amsterdam) oh. 52.

Buschow, K.H.J., and J.H.N. van Vucht, 1965, Philips Res. Rep. 22, 233.

Buschow, K.H.J., EC.E Bouten and A.B. Miedema, 1982, Rep. Progr. Phys. 45, 937.

Buxbanm, R.E., 1982, Univ. Microfilms Int., Order No. DA 8209248, 161pp.

Cadieu, EL, 1988, J. Vac. Sci. & Technol. A 6, 1668. Cadieu, EJ., H. Hedge and K. Chen, 1989, IEEE Trans.

Magn. MAG-25, 3788. Cadieu, EJ., H. Hedge and K. Chen, 1990, J. Appl.

Phys. 67, 4969. Camley, R.E., 1987, Plays. Rev. B 35, 3608. Camley, R.E., 1989, Phys. Rev. B 39, 12316. Camley, R.E., and D.R. Tilley, 1988, Phys. Rev. B 37,

3413. Carbone, C., and E. Kisker, 1987, Phys. Rev. B 36,

1280. Carbone, C., R. Rochow, L. Braicovich, R. Jungblut,

T. Kachel, D. Tillman and E. Kisker, 1990, Phys. Rev. B 41, 3866.

Caulet, J., A. Le Corre, B. Guesnais, G. Ropars and A. Guivarc'h, 1990, J, Cryst. Growth 102, 309.

Cendlewska, B., and A, Rojek, 1987, Jpn. J. Appl. Phys. Part I, Suppl. 26-3 (Part 2), 1295.

Cem), S., and Z. Pientka, 1987, Surf. Sci. 191,449. Cem~r, S., and M. Smutek, 1990, J. Catal. 123,275. Cerri, A., D. Mauri and M. Landolt, 1983, Phys. Rev.

B 27, 6526. Chapman, J.W,, G.R. Morrison, D. Fort and D.W.

Jones, 1981, J. Magn. & Magn. Mater. 22, 412. Chee, K.T., EE. Girouard and V.V. Truong, 1979, Appl.

Opt. 18, 1702. Chen, D.Y., Y.M. Gupta and M.H. Miles, 1984, J. Appl.

Phys. 55, 5984. Cheng, S.E, V.L. Sinha, Y. Xu, J.M. Elbicki, E.B.

Boltich, W.E. Williams, S.G, Sankar and D.E. Laughlin, 1988, J. Magn. & Magn. Mater. 75, 330.

Cheng, S.E, B.G. Demczyk, D.E. Laughlin and W.E. Wallace, 1990, J. Magn. & Magn. Mater. 84, 162.

Cherifi, K., P. Donovan, C. Dufour, Ph. Mangin and G. Marchal, 1990, Phys. Status Solidi a 122, 311.

Chizhov, EE., A.N. Kostygov and VI. Petinov, 1982, Solid State Commun. 42, 323.

Choe, G., M.E Becker and R.M. Walser, 1988, J. Appl. Phys. 64, 6104.

Chorkendorff, I., J. Onsgaard, H. Aksela and S. Aksela, 1983, Phys. Rev. B 27, 945.

Chorkendorff, I., J. Kofoed and J. Onsgaard, 1985a, Surf. Sci. 152/153, 749.

Chorkendorff, I., J. Onsgaard, J. Schmidt-May and R. Nyholm, 1985b, Surf. Sci. 160, 587.

Ciszewski, A., and A.J. Melmed, 1984a, J. Cryst. Growth 69, 253.

Ciszewski, A., and A.J. Melmed, 1984b, Surf. Sci. 145, L471.

Ciszewski, A., and A.J. Melmed, 1984c, J. Phys. (Paris) Colloq. 45(Suppl. 12), C9-39.

Cochet-Muchy, D., and S. Pa'idassi, 1988, J. Plays. (Paris) Colloq. 49(Suppl. 12), C8-661.

Coene, W., E Hakkens, T.H. Jacobs, D.B. de Mooij and K.H.J. Buschow, 1990, J. Less-Common Met. 157, 255.

Coey, J.M.D., 1991, Permanent magnets, in: Handbook on the Physics and Chemistry of Rare Earths, Vol. 16, eds K.A. Gschneidner Jr and L. Eyring (North- Holland, Amsterdam) ch. 112.

Coey, J.M.D., T.R. McGuire and B. Tissier, 1981, Phys. Rev. B 24, 1261.

Colliex, C., M. Gasgnier and E Trebbia, 1976, J. Phys. (Paris) 37, 397.

Colliex, C., T. Manoubi, M. Gasgnier and L.M. Brown, 1985, Vol. II, Scanning Electron Microscopy, SEM Inc., Ed. A.M.E O'Hare (Chicago, IL, USA) p. 489.

Connerade, J.P., and R.C. Kamatak, 1990, Comm. At. Mol. Phys. 24, 1.

Comer, W.D., and EM. Saad, 1977, Physica 86/87, 1331.

Comer, W.D., EM. Saad, D.W. Jones and R.G. Jordan, 1978, Inst. Phys. Conf. Ser. 37, chp. 8, 222.

Comer, W.D., H. Bareham, R.L. Smith, EM. Saad, B.K. Tauner, S. Farraut, D.W. Jones, B.J. Beaudry and K.A. Gschneidner Jr, 1980, J. Magn. & Magn. Mater. 15118, 1488.

Coulman, D., and T. Anthony, 1986, Mater. Res. Soc. Symp. Proc. 54 (Thin Films-Interfaces Phenom.) p. 547.

Cowgill, D.E, 1977, Nucl. Instmm. Methods 145, 507.

Cowgill, D.E, 1979, IEEE Trans. Nucl. Sci. NS-26, 1697.

Cowgill, D.E, 1981, IEEE Trans. Nucl. Sci. NS-28, 1851.

Croft, M., R. Neifield, C.U. Segre, S. Raaen and R.D. Parks, 1984, Phys. Rev. B 30, 4164.

Croft, M., E Lu, M.E. Melczer, A. Zolandz, G. Hall and E.G. Spencer, 1985, J. Magn. & Magn. Mater. 47/48, 115.

Cromer, D.T., and A.C. Larson, 1959, Acta Crystal- logr. 12, 855.

194 M. GASGNIER

Cukier, M., B. Gauth6 and C. Wehenkel, 1980, L Phys. (Paris) 41,603.

Curzon, A.E., 1982, L Phys. D 15, L69. Curzon, A.E., 1984, J. Less-Common Met. 98, 149. Curzon, A.E., and H.G. Chlebeck, 1972, J. Less-

Common Met. 27, 411. Curzon, A.E., and H.G. Chlebeck, 1973, J. Phys. F 3,

1. Curzon, A.E., and M. Gasgnier, 1985, L Electrochem.

Soc. 132, 1255. Curzon, A.E., and O. Singh, 1979, Thin Solid Films

57, 157. Curzon, A.E., and O. Singh, 1981a, Thin Solid Films

76, 185. Curzon, A.E., and O. Singh, 1981b, J. Less-Common

Met. 78, 261. Dadiani, T.O., E.V. Dokadze, Z.U. Dzhabua, T.S.

Lochoshvili, L.N. Glurdzhidze and V.V. Sanadze, 1989, Soobeshch. Akad. Nauk. Gruz. SSR 134, 365.

Das, S.K., and R. Suryanarayanan, 1989a, J. Appl. Phys. 66, 4843.

Das, S.K., and R. Suryanarayanan, 1989b, Thin Solid Films 175, 221.

Das, S.K., and R. Suryanarayanan, 1989c, C.R. Acad. Sci. (Paris) 308(II), 481.

De Luca, LC., R.J. Gambino, A.E Malozemoff and L. Berger, 1981, J. Appl. Phys. 52, 6188.

Demczyk, G.B., and S.E Cheng, 1990, J. Magn. & Magn. Mater. 88, 376.

den Boer, M.L., C.L. Chang, S. Horn and V. Murgai, 1988, Phys. Rev. B 37, 6605.

Dexpert-Ghys, J., C. Loier, Ch. Henry La Blanchetais and E Caro, 1975, J. Less-Common Met. 41, 105.

Dieny, B., D. Givord, J.M.B. Ndjaka and J.M. Alameda, 1990, L Appl. Phys. 67, 5677.

Domke, M., C. Laubsehat, M. Prietsch, T. Mandel, G. Kaindl and W.D. Schneider, 1986, Phys. Rev. Lett. 56, 1287.

Dowben, EA., D. LaGraffe and M. Onellion, 1989, J. Phys.: Condens. Matter 1, 6571.

Dudfis, J., 1991, private communication (Fak. Electroteeh. Informatcky, Ko~ice, Slovakia).

Dudfis, L, and A. Fehrr, 1984, in: Proc. 17th Conf. Low Temperature Physics (LT17), Vol. 1 (ALl4), eds U. Eckern, A. Schmid, W. Weber and H. Wtihl (North-Holland, Amsterdam) p. 159.

Dudfis, J., and A. Fehrr, 1987, Jpn. L Appl. Phys. 26 (Suppl. 26-3) 823.

Dudfis, J., A. Fehrr and V. Kavecansk~,, 1985, Phys. Lett. 109A, 113.

Dudfis, J., A. Feh~r and M. Konc, 1986, Acta Phys. Slov. 36, 301.

Dudfis, J., A, Fehrr and S. Jfinos, 1987a, J. Less- Common Met. 134, L9.

Dudfis, J., A. Feh~r and S. J~nos, 1987b, Acta Phys. Polon. A 72, 263.

Dudks, L, A. Feh~r and S. Jfinos, 1987c, Acta Phys. Hung. 62, 77.

Dudfis, J., A. Fehrr and J. Daniel-Szab6, 1987d, Acta Phys. Sol. 37, 50.

Dud~s, J., D. Knezo, A. Feh~r and H. Ratajczak, 1990, Physica B 165/166, 217.

Dzhabua, Z.U., T.O. Dadiani, L.N. Glurdzhidze, E.V. Dokadze and V.V. Sanadze, 1987, Soobshch. Akad. Nauk. Gruz. SSR 127, 605:

Efendiev, E.G., A.I. Manedov, T.M. Ilyasov and R.G. Rustamov, 1988, Inorg. Mater. 23, 183.

Efendiev, E.G., T.M. Ilyasov, A.I. Manedov and EG. Rustamov, 1989, Inorg. Mater. 24, 1080.

Egelhoff Jr, W.E, and G.G. Tibbetts, 1980, Phys. Rev. Lett. 44, 482.

Egelhoff Jr, W.E, G.G. Tibbetts, M.H. Hecht and I. Lindau, 1981, Phys. Rev. Left. 46, 1071.

Eick, H.A., C. Baenziger and L. Eyring, 1956, J. Am. Chem. Soc. 78, 5147.

Eley, D.D., and D. Needham, 1984, Proc. Roy. Soc. London, A 393, 257.

Ellinger, EH., and W.H. Zachariasen, 1953, L Am. Chem. Soc. 75, 5650.

Eschenfelder, A.H., 1980a, in: Ferromagnetic Materi- als, ed. E.E Wohlfarth (North-Holland, Amsterdam) ch. 6, p. 345.

Eschenfelder, A.H., 1980b, Springer Series in Solid State Sciences 14 (Springer Verlag, Berlin, New York) oh. 6-4, p. 210.

Esteva, J.M., R.C. Karnatak, LC. Fuggle and G.A. Sawatzky, 1983a, Phys. Rev. Lett. 50, 910.

Esteva, J.M., R.C. Karnatak and J.E Connerade, 1983b, J. Electron Spectrosc. Related Phenom. 31, 1.

Eyfing, L., 1979, The binary rare earth oxides, in: Handbook on the Physics and Chemistry of Rare Earths, Vol. 3, eds K.A. Gschneidner Jr and L. Eyring (North-Holland, Amsterdam) oh. 27.

F/ildt, A., and H.E Myers, 1983, Solid State Commun. 48, 253.

F~ildt, A., and H.E Myers, 1984a, Phys. Rev. Lett. 52, 1315.

F~ildt, it., and H.E Myers, 1984b, Phys. Rev. B 30, 5481.

Ffildt, A., and H.E Myers, 1985, J. Magn. & Magn. Mater. 47/48, 225.


Fgldt, A., and H.E Myers, 1986, Phys. Rev. B 34, 6675.

F~ildt, /k., D.K. Kristensson and H.E Myers, 1988, Phys. Rev. B 37, 2682.

Fang, R.Y., D.S. Dai, X.L. Rao, Z.X. Liu, J. Lan and H. Wan, 1988, Wuli Xuebao 37, 1065. In Chinese.

Farle, M., and K. Baberschke, 1987, Phys. Rev. Lett. 58, 511.

Fade, M., M. Zomack and K. Baberschke, 1985, Surf. Sci. 160, 205.

Farle, M., A. Berghaus and K. Baberschke, 1989, Phys. Rev. B 39, 4838.

Felmlee, T.L., and L. Eyring, 1968, Inorg. Chem. 7, 660.

Ferrater, C., B. Martinez, E Badia, R. Ribas, A. Lousa and J. Tejada, 1990, J. Magn. & Magn. Mater. 83, 69.

Fidler, J., 1987, IEEE Trans. Magn. MAG-23, 2106. Fidler, J., and P. Skalicky, 1978, Phys. Status Solidi a

50, 73. Fidler, J., and P. Skalicky, 1981, Philos. Mag. A 44,

427. Fidler, J., and Y. Tawara, 1988, IEEE Trans. Magn.

MAG-24, 1951. Fidler, J., K.G. Knoch, H. Kronmgller and G.

Schneider, 1989, J. Mater. Res. 4, 806. Fidler, J., C. Groiss and M. Tokunaga, 1990, IEEE

Trans. Magn. MAG-26, 1948. Forester, D.W, P. Lubitz and C. Vittoria, 1983, US

Patent 386 465. Forester, D.W., E Lubitz, J.H. Schelleng and C.

Vittoria, 1984, J. Non-Cryst. Solids 61162, 685. Franceschi, E., 1982, J. Less-Common Met. 87, 249. Franciosi, A., A. Raisanen, A. Wall, S. Chang, E

Philip, N. Trouiller and D.J. Peterman, 1988, Appl. Phys. Lett. 52, 1490.

Frandon, J., B. Brousseau and E Pradal, 1980, Phys. Status Solidi b 98, 379.

Frankenthal, R.P., R.B. van Dover and D.J. Siconolfi, 1986, J. Vac. Sci. & Technol. A 4, 1631.

Frausto, RR., W.B. Johnson and C.E. Wickersham, 1986, Proc. SPIE, Inst. Soc. Opt. Eng. 695 (Opt. Mass Data Storage 2) p. 56.

Freitas, P.R, T.S. Plaskett, J.M. Moreira and VS. Amaral, 1988, J. Appl. Phys. 64, 5453.

Frigerio, J.M., M. Martin, J. Rivory and Tran Mirth Duc, 1985, in: Rapidly Quenched Metals, Vol. 1, ed. H. Warlimont (North-Holland, Amsterdam) p. 1003.

Fujimori, H., Y. Kamiguchi and Y. Hayakawa, 1990, J. Appl. Phys. 67, 5716.

Gambino, R.J., and T.R. McGuire, 1984, IEEE Trans. Magn. MAG-20, 1341.

Gambino, R.J., T.R. McGuire and K. Fukamichi, 1981, J. Appl. Phys. 52, 2190.

Gasgnier, M., 1980, Phys. Status Solidi a 57, 11. Gasgnier, M., 1982, Rare earth alloys and compounds

as thin films, in: Handbook on the Physics and Chemistry of Rare Earths, Vol. 5, eds K.A. Gschneidner Jr and L. Eyring (North-Holland, Amsterdam) ch. 41.

Gasgnier, M., 1989, Phys. Status Solidi a 114, 11. Gasgnier, M,, 1990, Mater. Lett. 9, 161. Gasgnier, M,, 1991, J. Mater. Sci. 26, 1989.

Gasgnier, M., and L.M. Brown, 1983, unpublished data (Univ. Paris-Sud, France).

Gasgnier, M., Ch. Henry La Blanchetais and P Caro, 1976, Thin Solid Films 31, 283.

Gasgnier, M., L. N6vot, P Baillif and J. Bardolle, 1983, Phys. Status Solidi a 79, 531.

Gasgnier, M., G. Schiffmacher, L. Albert, E Cam, H. Dexpert, J.M. Esteva, C. Blancard and R.C. Karnatak, 1989, J. Less-Common Met. 156, 59.

Gerken, E, J. Barth, K.L.I. Kobayashi and C. Kunz, 1980, Solid State Commun. 35, 179.

Gerken, E, J. Barth and C. Kunz, 1981, Phys. Rev. Lett. 47, 993.

Gerken, E, J. Barth, R. Kammerer, L.I. Johansson and A.S. Flodstr6m, 1982, Surf. Sci. 17, 468.

Gerken, E, A.S. Flodstr6m, J. Barth, L.I. Johansson and C. Kunz, 1985, Physica Scripta 32, 43.

Gimzewski, J.K., D.J. Fabian, L.M. Watson and S.A. Hrossman, 1977, J. Phys. E 7, L305.

Gimzewski, J.K., S. Affrossman, M.T. Gibson, L.M. Watson and D.J. Fabian, 1979, Surf. Sci. 80, 298.

Glurdzhidze, L.N., M.Yu. Stamateli, T.S. Lochoshvili, E.V. Dokadze, ZM. Dzhabua and T.O. Dadiani, 1990, Soobshch. Akad. Nauk Gruz SSR 138, 533.

Goltros, W, J. Nakahara, A.V. Nurmiko and D.L. Partin, 1985, Appl Phys. Lett. 46, 1173.

Gonchar, EM., V.K. Medveded, T.R Smereka, Ya.B. Lozovyi and G.V. Babkin, 1987, Soy. Phys. Sol. State 29, 1629.

Gonchar, VV., O.K. Kanash and A.G. Fedorus, 1985, Phys. Chem. Mech. Surf. 2, 1621.

GondS, Y., and Y. Suezawa, 1986, J. Magn. & Magn. Mater. 54/57, 283.

Gond6, Y., and Y. Suezawa, 1987, IEEE Trans. Magn. MAG-23, 3317.

Gond6, Y., Y. Suezawa, T. Nakao and K. Kakuno, 1983, J. Magn. & Magn. Mater. 31/34, 329.

196 M. GASGNIER

Gondr, Y., Y. Suezawa and R. Tsuchiya, 1984, IEEE Trans. Magn. MAG-20, 1314.

Gorodetskii, D.A., and A.V. Martynyuk, 1989, Phys. Chem. Mechn. Surf. 5, 503.

Gorodetskii, D.A., and S.A. Shevlyakov, 1980, Sov. Phys. Crystallogr. 25, 377.

Grady, D.E., and M.J. Ginsberg, 1977, J. Appl. Phys. 48, 2179.

Grant, WA., 1978, J. Vac. Sci. & Technol. 15, 1644. Grieb, B., K.G. Knoch, E.-Th. Henig and G. Petzow,

1989, J. Magn. & Magn. Mater. 80, 75. Grrssinger, R., X.C. Kou, R. Krewenka, H.R.

Kirchmayr and M. Tokunaga, 1990, IEEE Trans. Magn. MAG-26, 1954.

Grfitter, E, E. Meyer, H. Heinzelmarm, L. Rosenthaler, H.-R. Hidber and H.-J. Giintherodt, 1988, J. Vac. Sci. & Technol. A 6, 279.

Grfitter, P., Th. Jung, H. Heinzelmann, A. Wadas, E. Meyer, H.-R. Hidber and H.-J. Gtintherodt, 1990a, J. Appl. Phys. 67, 1437.

Grfitter, E, A. Wadas, E. Meyer, H. Heinzelmann, H.- R. Hidber and H.-J. Gfintherodt, 1990b, J. Vac. Sci. & Technol. A 8, 406.

Gschneidner Jr, K.A., 1971, J. Less-Common Met. 25, 405.

Gsehneidner Jr, K.A., 1980, in: Science and Technol- ogy of Rare Earth Materials, eds E.C. Subbarao and W.E. Wallace (Academic Press, New York) p. 25.

Gschneidner Jr, K.A., 1985, J. Less-Common Met. 110, 1.

Gschneidner Jr, K.A., 1992, J. Alloys & Compounds 180, 1.

Gschneidner Jr, K.A., and A.H. Daane, 1988, Physical Metallurgy, in: Handbook on the Physics and Chemistry of Rare Earths, Vol. 11, eds K.A. Gschneidner Jr and L. Eyring (North-Holland, Amsterdam) ch. 78.

Gschneidner Jr, K.A., B.J. Beaudry and J. Capellen, 1990, Metals Handbook, 10th Ed., Vol. 2, (ASM International, Metals Park, OH) p. 720.

Gu, B.X., H. Homburg, S. Methfessel and H.R. Zhai, 1990, Phys. Status Solidi a 120, 159.

Guilmin, E, C. Brouder, G. Krill, W Felseh, G. Marchal, E. Dartyge, A. Fontaine and G. Tourillon, 1988, J. Phys. (Paris) Colloq. 48(Suppl. 12), C8- 1757.

Guivarc'h, A., J. Caulet and A. Le Corre, 1989, Electron. Lett. 25, 1051.

Gupta, S.C., and Y.M. Gupta, 1985, J. Appl. Phys. 57, 2464.

Gupta, Y.M., 1983a, J. Appl. Phys. 54, 6094.

Gupta, Y.M., 1983b, J. Appl. Phys. 54, 6256. Hansen, P., and M. Hartmann, 1986, J. Appl. Phys.

59, 859. Harada, T., M. Ikeda, S. Yamashita and K. Hara, 1988,

Jpn. Kokai Tokkyo Koho JP 8865611. Patent in Japanese.

Harris, J.M., E.P. Boespflug, D.M. Holloway and J.L. Provo, 1984, Sandia National Lab. Rpt. SAN83- 1054, UC-25.

Hartmann, M., and T.R. McGuire, 1983, Phys. Rev. Lett. 51, 1194.

Hashimoto, S., Y. Ochiai, M. Kaneko, K. Watanabe and K. Aso, 1987, IEEE Trans. Magn. MAG-23, 2278.

Hauser, J.J., 1985, Solid State Commtm. 55, 163. Haussler, P., and E Battman, 1980, Z. Phys. B 38,

43. Hay, C.M., J.R. Jennings, R.M. Lambert, R.M. Nix,

G. Owen and T. Rayment, 1988, Appl. Catal. 37, 291.

Hecht, M.H., A.J. Viescas, I. Lindau, J.W. Allen and L.I. Johansson, 1984, J. Electron. Spectrosc. Relat. Phenom. 34, 343.

Heinzelmann, H., E Griitter, E. Meyer, L. Rosenthaler, H.-R. Hidber and H.-J. Giintherodt, 1987, Surf. Sci. 189/190, 29.

Heitmann, H., A.M.J. Spruijt, E Willich and H. Wilting, 1987, J. Appl. Phys. 61, 3343.

Hellman, E, R.B. van Dover and E.M. Gyorgy, 1987, Appl. Phys. Lett. 50, 296.

Hirst, J.R., M.L.H. Wise, D. Fort, J.EG. Farr and I.R. Harris, 1976, J. Less-Common Met. 49, 193.

Hole, J., S. Besenicar and D. Kolar, 1990, J. Mater. Sci. 25, 215.

Holloway, D.M., R.J. Antepenko and WE. Swartz Jr, 1978, Appl. Spectrosc. 32, 106.

Homburg, H., Th. Sinnemarm, S. Methfessel, M. Rosenberg and B.X. Gu, 1990, J. Magn. & Magn. Mater. 83, 231.

Homma, H., K.Y. Yang and I.K. Schuller, 1987a, Phys. Rev. B 36, 9435.

Homma, H., K.Y. Yang and I.K. Schuller, 1987b, Interfaces, Superlattices, Thin Films, eds J.D. Dow and I.K. Schuller (Mater. Sci. Soc. Pittsburg R.A.) p. 557.

Honda, S., M. Ohkoshi and T. Kusuda, 1986, IEEE Trans. Magn. MAG-22, 1221.

Honda, S., N. Nawate, M. Yashiyama and T. Kusuda, 1987, IEEE Trans. Mag. MAG-23, 2952.

Horikoshi, H., S. Takeda and Y. Komura, 1985, Jpn. J. Appl. Phys. 24, L210.

THE INTRICATE WORLD OF RARE EARTH THIN FILMS !97

Hoshi, Y., M. Naoe and S. Yamanaka, 1982, J. Appl. Phys. 53, 2344.

Hosoda, N., I. Nishiguchi, Y. Ohtani, H. Uchida and T. Takahashi, 1988, Kidoriu 12, 36. In Japanese.

Hosoito, N., K. Yoden and T. Shijo, 1988a, Hyperfine Interact. 41,583.

Hosoito, N., K. Yoden, K. Mibu and T. Shinjo, 1988b, J. Phys. (Paris) Colloq. 48(Suppl. 12), C8-1777.

Hosoito, N., K. Yoden, K. Mibu, T. Shinjo and Y. Endoh, 1989, L Phys. Soc. Jpn. 58, 1775.

Huang, C.Y., C.E. Olsen, G. Kozlowski, H. Mat- sumoto, H. Umezawa, E Mancini, M.B. Maple, M.C. Hamaker, M.S. Torikachvili, J.P. Whitehead and EE. Wang, 1985, J. Appl. Phys. 57, 3104.

Huang, G.X., Q.Z. Lu, L.H. Wu, S.Y. Shi, W.M. Gao, S.E Yu, H.C. Hua, G.A. Wang and C.H. Zheng, 1990, Phys. Scripta 41,372.

Huang, Y.S., and V. Murgai, 1989, Solid State Commun. 69, 873.

Hubberstey, P., RE Adams and R.J. Pulham, 1976, Radial Effects Triitittm Technol. Fusion React., Proc. Int. Conf. 1975, eds J.S. Watson and EW. Wiffen (NTIS, Springfield, Va, USA), Ill-270.

Hughes, D.T., J. Evans and I.R. Harris, 1980a, J. Less- Common Met. 74, 255.

Hughes, D.T., L Evans and I.R. Harris, 1980b, J. Less- Common Met. 76, 119.

Hussain, A.A.A., 1980, J. Less-Common Met. 72, 71. Hussain, A.A.A., 1981, Thin Solid Films 77, 331. Hussain, A.A.A., and T.S. A1-Bassam, 1979, Thin

Solid Films 59, 77. Idczak, E., and K. Zukowska, 1981, Thin Solid Films

75, 139. Inoue, A., M. Ikematsu, T. Miyama and T. Fujii, 1985,

IEEE Transl. J. Magn. Jpn. TJMJ-1-3, 363. Ishida, A., S. Matsuura, H. Fujiyasu, H. Ebe and K.

Shimohara, 1986, Superlattiees & Microstructttres 2, 575.

Ishida, A., S. Matsuura, H. Mizuno and H. Fujiyasu, 1987, Appl. Phys. Lett. 51, 478.

Ishida, A , S. Matsuura, H. Mizuno, Y. Sase and H. Fujiyasu, 1988a, J. AppI. Phys. 63, 4572.

Ishida, A., N. Nakahara, T. Okamura, Y. Sase and H. Fujiyasu, 1988b, Appl. Phys. Lett. 53, 274.

Iwamura, E., K. Nagahama, T. Suzuki and T. Umeda, 1990, J. Jpn. Inst. Met. 54, 111. In Japanese.

Jaffey, D.M., A. Gellman and R.M. Lambert, 1989, Surf. Sci. 214, 407.

Jfinos, S., A. Feh6r and J. Dudfis, 1987, Czch. J. Phys. B 37, 5.

Jaswal, S.S., M.A. Langell, Y.G. Ren, M.A. Engelhardt and D.J. Sellmyer, 1988, J. Appl. Phys. 64, 5577.

Jaswal, S.S., WB. Yelon, G.C. Hadjipanayis, Y.Z. Wang and D.J. Sellmyer, i991, Phys. Rev. Lett. 67, 644.

Jennings, J.R., R.M. Lambert, R.M. Nix, G. Owen and D.G. Parker, 1989, Appl. Catal. 50, 157.

Johansson, B., 1979, Phys. Rev. B 19, 6615. J'ohansson, LJ., J.W. Allen, T. Gustafsson, I. Lindau

and S.B.M. Hagstr6m, 1978, Solid State Commun. 28, 53.

Johansson, L.I., J.W. Allen and I. Lindau, 1981, Phys. Lett. 86 A, 442.

Johansson, L.I., A. Flodstr6m, S.E. H6mstr6m, B. Johansson, J. Barth and E Gerken, 1982a, Solid State Commun. 41,427.

Johansson, L.I., A. Flodstr6m, S.E. H6mstr6m, B. Johansson, J. Barth and E Gerken, 1982b0 Surf. Sci. 117, 475.

Johnson, D.A., 1969, J. Chem. Soc. A 1525 and 2578. Johnson, D.A., 1977, Adv. Inorg. Chem. Radioelem.

20, 1. Johnson, R.W., C.C. Ahn and E.R. Rather, 1989a,

Appl. Phys. Lett. 54, 795. Johnson, R.W., C.C. Ahn and E.R. RaUler, 1989b,

Phys. Rev. B 40, 8139. Jordan, R.G., and O. Loebich Jr, 1975, J. Less-

Common Met. 39, 55. Kaindl, G., B. Reihl, D.E. Eastman, R.A. Pollack,

N. M~rtensson, B. Barbara, T. Penncey and T.S. Plaskett, 1982, Solid State Commun. 41, 157.

Kaindl, G., W.D. Schneider, C. Laubschat, B. Reihl and N. MS.rtensson, 1983, Surf. Sci. 126, 105.

Kajiura, M., T. Morishita, Y. Togami and K. Tsushima, 1987, IEEE Transl. J. Magn. Jpn. TJMJ-2-2, 171.

Kamiguchi, Y., Y. Hayakawa and N. Fujimori, 1989, Appl. Phys. Lett. 55, 1918.

Kammerer, R., J. Barth, E Gerken, A. Flodstr6m and L.I. Johansson, 1982, Solid State Commun. 41, 435.

Kamprath, N., L. Wickramasekara, H. Hedge, N.C. Liu, J.K.D. Jayanetti and EJ. Cadieu, 1988a, J. Appl. Phys. 63, 3696.

Kamprath, N., N.C. Liu, H. Hedge and EJ. Cadieu, 1988b, J. Appl. Phys. 64, 5720.

Kamprath, N., X.R. Qian, H. Hedge and EJ. Cadieu, 1990, J. Appl. Phys. 67, 4948.

Kandasamy, K., and N.A. Surplice, 1981, Phys. Transition Metals, Inst. Phys. Conf. Ser. 55, p. 587.

Kandasamy, K., and N.A. Surplice, 1982, J. Phys. C 14, L61.

198 M. GASGNIER

Kandasamy, K., and N.A. Surplice, 1985, J. Phys. D 18, 1377.

Kanski, J., and P.O. Nilsson, 1979, Phys. Rev. Lett. 43, 1185.

Kanski, J., and G. Wendin, 1981, Phys. Rev. B 24, 4977.

Kass, W.J., 1977, J. Vac. Sci. & Technol. 14, 518. Katayama, T., H. Awano and Y. Nishihara, 1987, IEEE

Transl. J. Magn. Jpn. TJMJ-2-2, 188. Kawahata, T., N. Ninomiya, Y. Ohtani, H. Uchida and

T. Takahashi, 1990, Kidoriu 16, 104. in Japanese. Knoch, K.G., J. Fidler, E. Bischoff and E.-Th. Henig,

1989a, Mater. Lett. 8, 301. Knoch, K.G., G. Schneider, J. Fidler, E.-Th. Henig and

H. Kronmfiller, 1989b, IEEE Trans. Magn. MAG- 25, 3426.

Knoch, K.G., B. Grieb, E.-Th. Henig, K. Kronmiiller and G. Petzow, 1990a, IEEE Trans. Magn. MAG- 26, 1951.

Knoch, K.G., E.-Th. Henig and J. Fidler, 1990b, J. Magn. & Magn. Mater. 83, 209.

Koestler, C., R. Ramesh, C.J. Ether, G. Thomas and J. Wecker, 1989, Acta Metall. 37, 1945.

Kojima, T., A. Denda and H. Uchida, 1989, Kidorui 14, 96. In Japanese.

Kolaczldewicz, J., and E. Bauer, 1986, Surf. Sci. 175, 487.

Komura, Y., 1989, Phase transitions 16/17, 495. Komura, Y., S. Takeda and Y. Kitano, 1981, Sci. Rep.

RITU A 29(Suppl. 1), 13. In English. Kosak, M.M., R.S. Pan6i~in and Z.V. Stasfik, 1987,

Ukr. Fiz. Zh. 32, 751. In Russian. Kostygov, A.N., V.E Degtyareva, Yu.G. Morozov, P.E.

Chizhov and V.I. Petinov, 1977, Sov. Phys. Solid State 19, 1553.

Koyama, M., R. Ohyama, T. Kovanagi, Y. Watanabe and K. Matsubara, 1987, Nippon Oyo. Giki Gakkaishi 11, 173. In Japanese.

Kozlovskii, L.V., 1989, Latv. PSR. Zinat. Akad Vestes. Fiz. Teh. Zinat. Ser. 6, 65. In Russian.

Kozlovskii, L.V., E.M. Reikhrudel and G.V. Smirnit- skaya, 1981, Sov. Phys. Techn. Phys. 26, 991.

Krishnan, R., M. Porte, M. Tessier, J.P. Vitton and Y. Le Corre, 1988, J. Less-Common Met. 145, 613.

Krizek, J., and K.N.R. Taylor, 1975, J. Phys. F 5, 774. Krost, A., B. Harbecke, R. Fraymonville, H. Schlegel,

E.J. Fantner, K.E. Ambroth and G. Bauer, 1985, J. Phys. C 18, 2119.

Kuboth, M., H.E Braun, L. Schellenberg and J. Muller, 1989, Physica C 162/164, 407.

Kumar, R., M.H. Mintz and J.W. Rabalais, 1984a, Surf. Sci. 147, 15.

Kumar, R., M.H. Mintz and J.W. Rabalais, 1984b, Surf. Sci. 147, 37.

Kunze, U., and W. Kowalsky, 1988, Appl. Phys. Lett. 53, 367.

Kuwano, N., T. Shiwaku, Y. Tomokiyo and T. Eguchi, 1981, Jpn. J. Appl. Phys. 20, 1603.

Kuwano, N., S. Higo, K. Yamamoto, K. Oki and T. Eguchi, 1985, Jpn. J. Appl. Phys. 24, L663.

Kuzmenko, V.M., and V.I. Melnikov, 1982, Sov. Phys. JETP 55, 474.

Kuzmenko, V.M., and VI. Melnikov, 1988, Sov. J. Low Temp. Phys. 14, 533.

Kuzmenko, V.M., B.G. Lazarev, V.I. Melnikov and A.I. Sudovtsov, 1972, Ukr. Fiz. Zh. 17, 1923. In Russian.

Kuzmenko, V.M., B.G. Lazarev, V.I. Melnikov and A.I. Sudovtsov, 1976, Ukr. Fiz. Zh. 21,883. In Russian.

Kuzmenko, V,M., V.I. Melnikov and A.I. Sudovtsov, 1980, Phys. Met. Metallogr. 54(2), 165.

Kuzmenko, V.M., V.I. Melnikov and VA. Rakhubovskii, 1984a, Sov. Phys. JETP 59, 612.

Kuzmenko, V.M., A.N. Vladychkin, V.I. Melnikov and A.I. Sudovtsov, 1984b, Sov. Phys. JETP 59, 102.

Kuzmenko, V.M., B.G. Lazarev and V.I. Melnikov, 1986a, Soy. J. Low Temp. Phys. 12, 431.

Kuzmenko, V.M., A.N. Vladychkin and A.I. Su- dovtsov, 1986b, Sov. J. Low Temp. Phys. 12, 714.

Kwo, J., M. Hong and S. Nakahara, 1986, Appl. Phys. Lett. 49, 319.

LaGraffe, D., EA. Dowben and M. Onellion, 1985, Surf. Sci. 160, 587.

LaGraffe, D., EA. Dowben and M. Onellion, 1988, Phys. Rev. B 38, 10357.

LaGraffe, D., P.A. Dowben and M. Onellion, 1989a, Phys. Rev. B 40, 970.

LaGraffe, D., P.A. Dowben and M. Onellion, 1989b, Phys. Rev. B 40, 3348.

LaGraffe, D., P.A. Dowben and M. Onellion, 1989c, in: Growth Characterization and Properties of Ultrathin Magnetic Films and Multilayers, Mater. Res. Soc. Symp. Proe. 151, 71.

LaGraffe, D., PA. Dowben and M. Onellion, 1990a, Phys. Lett. A 147, 240.

LaGraffe, D., P.A. Dowben and M. Onellion, 1990b, J. Vac. Sci. & Technol. A 8, 2738.

Landolt, M., R. Allenspach and M. Taborelli, 1986, Surf. Sci. 178, 311.

Lang, J.K., Y. Baer and P.A. Cox, 1981, J. Phys. F 11, 121.


Larsen, J.W., M.L. Fuller and B.R. Livesay, 1981, Alternative Energy Sources 2(8), 3533.

Le Corre, A., J. Caulet and A. Guivarc'h, 1989a, Appl. Phys. Lett. 55, 2298.

Le Corre, A., J. Caulet and A. Guivarc'h, 1989b, French Patent No. 89 04899.

Le Corre, A., B. Guesnais, A. Guivarc'h, D. Lecrosnier, J. Caulet, M. Minier and G. Ropars, 1990, J. Cryst. Growth 105, 234.

LePage, J.G., and R.E. Camley, 1990, Phys. Rev. Lett. 65, 1152.

Li, D., C.W. Hutchings, P.A. Dowben, C. Hwang, R.T. Wu, M. Onellion, B. Andrews and J.L. Erskine, 1991, J. Magn. & Magn. Mater. 99, 85.

Li, H., S. Jiang, M. Qiu, Y. Guo and R.C. O'Handley, 1988, Jinshu Xuebao 24, A131. In Chinese.

Li, L., ELi, D. Yang, L Tian and Z. Lin, 1990, Wuli Xuebao 39, 788. In Chinese.

Li, Z., H. Hahn and R.W. Siegel, 1988, Mat. Lett. 6, 342.

Lii, Z.Y., H. Okuno, T. Numata and Y. Sakurai, 1983, Nippon Oyo Jiki Gakkaishi 7, 47.

Linetski, Ya.L., and I.R Salo, 1989, Phys. Met. Metall. 68(0 , 115.

Linetsld, Ya.L., R.M. Raigorodskii, E.L. Khatsernova and V.Yu. Tsvetkov, 1990, Izv. Vyssh. Uchebn. Zaved. Chem. Mater. 7, 64.

Liu, N.C., N. Kamprath, L. Wickramasekara and EJ. Cadieu, 1988, J. Appl. Phys. 63, 3589.

Loboda, V.B., and I.E. Protsenko, 1981a, Cryst. Res. Technol. 16, 357.

Loboda, V.B., and I.E. Protsenko, 1981b, Cryst. Res. Technol. 16, 489.

Loboda, V.B., I.E. Protsenko and A.V. Yaremenko, 1980, Kristall und Teknik 15, 43.

Loboda, V.B., I.E. Protsenko and V.G. Sharnonja, 1982, Ukr. Fiz. Zh. 27, 1343. In Russian.

Loebich Jr, O., and E. Raub, 1973a, J. Less-Common Met. 30, 47.

Loebich Jr, O., and E. Raub, 1973b, J. Less-Common Met. 31, 111.

Lowe, W.R, E.M. Gyorgy, D.B. McWhan, L.H. Greene, W.L. Feldman and J.M. Rowell, 1985, J, Appl. Phys. 58, 1615.

Lozovyi, Ya.B., V.K. Medveded, T.P. Smereka and G.V. Babkin, 1982, Sov. Phys. Solid State 24, 1213.

Lozovyi, Ya.B., V.K. Medveded, T.P. Smereka, G.V. Babldn and B.M. Palyukh, 1984, Soy. Phys. Solid State 26, 738.

Lu, E, M. Croft, A. Leiberich and G. Hall, I985, in: New frontiers in Rare Earth Science and

Applications, eds Xu Guangxian and Xiao Jimei (Science Press, Beijing) p. 374.

Lu, E, M. Croft and E.G. Spencer, 1986, Phys. Rev. B 33, 5950.

Ltibcke, M., B. Sonntag, W. Niemaml and E Rabe, 1986, Phys. Rev. B 34, 5184.

Ma, E., B.X. Liu, X. Chen and H.D. Li, 1987, Thin Solid Films 147, 49.

Mahmoud, S., and Z.S. el Mandouh, 1987, J. Mater. Sci. 22, 651.

Maienschein, J.L., 1978, Nuct. Technol. 38, 387. Maier-Komor, P., 1989, Nucl. Instr. Meth. Phys. Rev.

A 282, 133. Malinowski, M.E., 1981, J. Vac. Sci. & Technol. 19,

120. Malterre, D., A. Siari, J. Durand, G. Krilt and

G. Marchal, 1986, J. Phys. (Paris) Colloq. 47(Suppl. 12), C8-991.

Mancini, E, and C. Noce, 1986, Nuovo Cimento D 7, 1.

Mancini, E, and C. Noce, 1987, Physica 145 B, 342. Manoubi, T., C. Colliex and P. Rez, 1990, J. Electron.

Spectrosc. Relat. Phenom. 50, 1. Marinero, E.E., G.S. Sprokel and H. Notarys, 1988,

Mater. Res. Soc. Symp. Proc. (Multilayers) 245, 1033.

Marshall, A.N., and D.C. Dobbertin, 1986, Ultrami- croscopy 19, 69.

Martin, M., Tran Minh Duc, J. Rivory and J.M. Frigerio, 1985, Solid State Commun. 55, 683.

Martinez, B., M.A. Moreu and J. Tejada, 1988a, J. Phys. (Paris) Colloq. 49(Suppl. 12), C8-1807.

Martinez, B., M.A. Moreu, A. Ruiz, A. Labarta, X. Obradors, E Briones and J. Tejada, 1988b, IEEE Trans. Magn. MAG-24, 1694.

Mason, M.G., S.T. Lee, G. Apai, R.E Davis, D.A. Shirley, A. Franciosi and J.H. Weaver, I981, Phys. Rev. Lett. 47, 730.

Materlik, G., J.E. Miiller and J.W. Wilkins, 1983a, Phys. Rev. Lett. 50, 267.

Materlik, G., B. Sonntag and M. Taush, 1983b, Phys. Rev. Lett. 51, 1300.

Mathevet, J.R, A. Traverse, J. Chaumont and S. Megtert, 1990, J. Mater. Res. 5, 1970.

Matthew, J.A.D., G. Strasser and EP. Netzer, 1983, Phys. Rev. B 27, 5839.

Mauri, D., and M. LandoR, 1981, Phys. Rev. Lett. 47, 1322.

McGuiness, RJ., I.E. Harris, E. Rozendaal, J. Onnerod and M. Ward, 1986, J. Mater. Sci. 21, 4107.

200 M. GASGNIER

McGuiness, P.J., E. Devlin, I.R. Harris, E. Rozendaal and J. Ormerod, 1989a, J. Mater. Sci. 24, 2541.

McGuiness, P.J., I.R. Harris, U.D. Scholz and H. Nagel, 1989b, Z. Phys. Chem. N.E 163/165, 587.

McGuiness, P.J., X.J. Zhang, X.J. Yin and I.R. Harris, 1990a, J. Less-Common Met. 158, 359.

McGuiness, P.L, X.J. Zhang, H. Forsyth and I.R. Harris, 1990b, J. Less-Common Met. 162, 379.

McMinn, R., A. Aknetey and P.E. Donovan, 1990, in: Proc. Int. Phys. Electron. Microsc. Analysis Group. Roy. Microsc. Soc. Conf. (Institute of Physics, Bristol, UK) Vol. 1, p. 183.

Mehrhoff, T.K., 1980, GEPP-TIS-482 (Microfilm), 24pp.

Melmed, A.J., V. Maurice, O. Franck and J.H. Block, 1984, J. Phys. (Paris) Colloq. 49(Suppl. 12), C9- 47.

Melmed, A.J., V. Maurice, O. Franck and J.H. Block, 1987, J. Cryst. Growth 84, 123.

Melton, K.N., and H. Nagel, 1977, J. Appl. Phys. 48, 2608.

Melton, K.N., and R.S. Perkins, 1976, J. Appl. Phys. 47, 2671.

Mibu, K., N. Hosoito and T. Shinjo, 1989, J. Phys. Soc. Jpn. 58, 2916.

Mibu, K., N. Hosoito and T. Shinjo, 1990, Hyperfine Interact. 54, 831.

Miller, R.E, M. Syms and L.S. Julien, 1979, J. Phys. D.: Appl. Phys. 12, 1985.

Miller, S.A., 1988, Shock Waves in Condensed Matter (North-Holland, Amsterdam) p. 605.

Mitchell, D.J., and R.C. Patrick, 1981, J. Vac. Sci. & Technol. 19, 236.

Mitchell, D.J., and J.L. Provo, 1985, L Appl. Phys. 57, 1855.

Mittsev, M.A., and A.M. Mukhuchev, 1982, Soy. Phys. Solid State 24, 1284.

Mittsev, M.A., and A.M. Mthkhuchev, 1983, Sov. Techn. Phys. Lett. 9, 154.

Miyahara, T., H. Ishii, T. Hanyu, H. Ohkuma and S. Yamaguchi, 1982, J. Phys. Soc. Jpn. 51, 1834.

Miyamoto, K., and A. Tazaki, 1985, Jpn. Kokai Tokkyo Koho JP 85 602 526. Patent in Japanese.

Miyazaki, T., M. Tukahashi, T. Shimamori and T. Wakiyama, 1989, in: Proc. MRS Intern. Meet. Adv. Mater. Multilayers, Vol. 10 (Materials Research Society, Pittsburgh, PA) p. 379.

Moth, Th., B. Lippold and A. Handstein, 1986, Phys. Status Solidi a 98, K161.

Moreau, J.M., and E. Parthr, 1973, J. Less-Common Met. 32, 91.

Morishita, T., Y. Togami and K. Tsushima, 1985, J. Phys. Soc. Jpn. 54, 37.

Morishita, T., Y. Togami and K. Tsushima, 1986, J. Magn. & Magn. Mater. 54/57, 789.

Morishita, T., Y. Togami and K. Tsushima, 1987, IEEE Transl. J. Magn. Jpn. TJMJ-2-2, 169.

Morozov, Yu.G., A.N. Kostygov, VJ. Petinov and EE. Chizhov, 1975, Phys. Status Solidi a 32, K119.

Morozov, Yu.G., A.N. Kostygov, A.E. Petrov, P.E. Chizhov and V.I. Petinov, 1976, Sov. Phys. Solid State 18, 804.

Moser, H.R., B. Delley, W.D. Schneider and Y. Baer, 1984, Phys. Rev. B 29, 2947.

Mfiller, J., and N.A. Surplice, 1977, J. Phys. D 10, 213.

Murgai, V., Y.S. Huang, M.L. den Boer and S. Horn, 1988, Solid State Commun. 66, 329.

Nakajima, K., and T. Sato, 1986, Jpn. Kokai Tokkyo Koho JP 86 117 749. Patent in Japanese.

Nakamura, O., K. Baba, H. Ishii and T. Takeda, 1988, J. Appl. Phys. 64, 3614.

Nakamura, T., S. Kagami, H. Mariko and H. Yamamoto, 1987, IEEE Transl. J. Magn. Jpn. TJMJ-2-2, 175.

Naoe, M., Y. Hoshi, T. Ishiwatari and S. Yamanaka, 1982, J. Appl. Phys. 53, 7807.

Netzer, EP., and E. Bertel, 1982, Adsorption and catalysis on rare earth surfaces, in: Handbook on the Physics and Chemistry of Rare Earths, Vol. 5, eds K.A. Gschneidner Jr and L. Eyring (North-Holland, Amsterdam) ch. 43.

Netzer, EP., and J.A.D. Matthew, 1987, Inelastic electron scattering measurements, in: Handbook on the Physics and Chemistry of Rare Earths, Vol. 10, eds K.A. Gschneidner Jr and L. Eyring (North- Holland, Amsterdam) ch. 72.

Niemann, W., W. Malzfeldt, P. Rabe and M. Liibcke, 1986, J. Phys. (Paris) Colloq. 47(Suppl. 12), C8- 931.

Niemann, W., W. Malzfeldt, P. Rabe, R. Haensel and M. Lfibcke, 1987, Phys. Rev. B 35, 1099.

Niihara, T., S. Takayama, K. Kaneko and Y. Sugita, 1984, Appl. Phys. Lett. 45, 872.

Nilsson, A., B. Eriksson, N, M~rtensson, J.N. Andersen and J. Onsgaard, 1987, Phys. Rev. B 36, 9308.

Nilsson, A., B. Eriksson, N. M~trtensson, J.N. Andersen and J. Onsgaard, 1988, Phys. Rev. B 38, 10357.

Nix, R.M., and R.M. Lambert, 1987, Surf. Sci. 186, 163.


Nix, R.M., and R.M. Lambert, 1989a, J. Phys. Chem. 93, 4189.

Nix, R.M., and R.M. Lambert, 1989b, Surf. Sci. 220, L657.

Nix, R.M., T. Rayment, R.M. Lambert, J.R. Jennings and G. Owen, 1987, J. Catal. 106, 216.

Nix, R.M., R.W. Judd and R.M. Lambert, 1988a, Surf. Sci. 203, 307.

Nix, R.M., R.W. Judd and R.M. Lambert, 1988b, Surf. Sci. 205, 59.

Nix, R.M., R.W Judd and R.M. Lambert, 1989a, Surf. Sci. 215, L316.

Nix, R.M., R.W. Judd, R.M. Lambert, J.R. Jennings and G. Owen, 1989b, J. Catal. 118, 175.

Numata, T., H. Kiriyama and S. Inokuchi, 1988, J. Appl. Phys. 64, 5501.

Nyholm, R., I. Chorkendorff and J. Schmidt-May, 1984, Surf. Sci. 143, 177.

Oesterreicher, H., H. Bittner and K. Shuler, 1979, J. Solid State Chem. 29, 191.

Okuno, H., Y. Sakaki and Y. Sakurai, 1986, J. Phys. D 19, 873.

Onsgaard, J., and I. Chorkendorff, 1986, Phys. Rev. B 33, 3503.

Onsgaard, J., and O. Ellegaard, 1984, Nucl. Instr. Meth. Phys. Res. B 2, 666.

Onsgaard, J., and A. Ignatiev, 1982, Surf. Sci. 115, 270.

Onsgaard, J., S. Tougaard and P. Morgen, 1979, Appl. Surf. Sei. 3, 113.

Onsgaard, J., S. Tougaard, E Morgan and F. Ryborg, 1980, J. Electron Spectmsc. Relat. Phenom. 18, 29.

Onsgaard, J., I. Chorkendorff and O. Sorensen, 1983, Physica Scfipta T 4, 169.

Onsgaard, J., I. Chorkendorff, O. Ellegaard and O. Sorensen, 1984, Surf. Sci. 138, 148.

Owen, G., C.M. Hawkes, D. Lloyd, J.R. Jennings, R.M. Lambert and R.M. Nix, 1987, Appl. Catal. 33, 405.

Palenzona, A., and A. Iandelli, 1974, J. Less-Common Met. 34, 121.

Palmstrom, C.J., N. Tabatabaie and S.J. Allen Jr, 1988, Appl. Phys. Lett. 53, 2608.

Palmstrom, C.J., K.C. Garrisson, S. Mounier, T. Sands, C.L. Schwartz, N. Tabatabaie, S.J. Allen Jr, H.L. Gilchrist and EE Miceli, 1989, J. Vac. Sci. & Technol. B 7, 747.

Palmstrom, C.J., S. Mounier, T.G. Finstad and RE Miceli, 1990, Appl. Phys. Lett. 56, 382.

Pan, S.M., Z.B. Zhao, H. Jin, E Tian and R.Z. Ma, 1989, J. Magn. & Magn. Mater. 78, 371.

Parker, S.EH., R.J. Grundy and J. Fidler, 1987a, J. Magn. & Magn. Mater. 66, 74.

Parker, S.EH., RJ. Pollard, D.G. Lord and R.J. Grundy, 1987b, IEEE Trans. Magn. MAG-23, 2103.

Parks, R.D., S. Raaen, M.L. den Boer, V. Murgai and T. Mihalisin, 1983, Phys. Rev. B 28, 3556.

Parks, R.D., S. Raaen, M.L. den Boer, Y.S. Chang and G.E Williams, 1984, Phys. Rev. Lett. 52, 2176.

Parmigiani, E, 1982, Phys, Lett. A 92, 419. Parth~, E., and J.M. Moreau, 1977, J, Less-Common

Met. 53, 1. Partin, D.L, 1983a, Appl. Phys. Lett. 43, 996. Partin, D.L, 1983b, J. Vac. Sci. & Technol. B 1, 174. Partin, D.L., 1984, J. Electron. Mater. 14, 493. Partin, D.L., 1985, Supeflattices & Microstructures 1,

131. Partin, D.L., 1987, Mater. Res. Soc. Syrup. Proc. 90,

47. Partin, D.L, 1988, IEEE Trans. Quantum Electron.

QE-24, 1716. Partin, D.L., and C.M. Thrush, 1984, Appl. Phys. Lett.

45, 193. Pickart, S.J., H.A. Halpern, R.J. Gambino and T.R.

McGuire, 1984, J. Appl. Phys. 55, 1763. Piecuch, M., L.T. Baczewski, J. Durand, G. Marchal,

E Deleroix and H. Nabli, 1988, J. Phys. (Paris) Colloq. 49(Suppl. 12), C8-1755.

Poate, J.M., 1978, J. Vac. Sci. & Technol. 15, 1636. Protsenko, I.E., 1988, Soy. Phys. J. 6, 460. Provo, J.L., 1979, J. Vac. Sci. & Teehnol. 16, 230. Quemerais, A., B. Loisel, G. Jezequel, J. Thomas and

J.C. Lemonnier, 1981, J. Phys. F 11, 293. Raaen, S., 1990, Solid State Commun. 73, 389. Rahman Khan, M.S., 1977, J. Bangladesh Acad. Sci.

1,1. Rahrnan Khan, M.S., 1978, Indian J. Phys. 52 A, 561. Rahman Khan, M.S., 1981, Indian J. Phys. 55 A, 23. Rahman Khan, M.S., 1984, Thin Solid Films 113,

207. Rahman Khan, M.S., 1987a, J. Mater. Sci. Lett. 6,

160. Rahman Khan, M.S., 1987b, Bull. Mater. Sci. 9, 181. Rahman Khan, M.S., and R.E Miller, 1979, J. Phys.

D 12, 271. Raisanen, A., A. Wall, S. Chang, R Philip, N. Trouiller,

A. Franciosi and D.J. Peterman, 1988, J. Vac. Sci. & Technol. A 6, 2741.

Rajora, O.S., and A.E. Curzon, 1984, J. Mater. Sci. Lett. 3, 627.

Ramakrisna, K., and O.N. Srivastava, 1987, J. Mater. Sci. Lett. 6, 15.

202 M. GASGNIER

Ramesh, R., J.K. Chen and G. Thomas, 1987, J. Appl. Phys. 61, 2993.

Ratajczak, H., and I. Grsciafiska, 1990, Acta Phys. Polonica A 77, 723.

Ratajczak, H., T. Lucifiski, A. Kowalczyk, I. Grsciafiska and P. SovLk, 1989, J. Magn. & Magn. Mater. 81,341.

Ratajczak, H., I. Grsciafiska and A. Kowalczyk, 1990a, Acta Phys. Slov. 40, 223.

Ratajczak, H., I. G6sciafiska and T. Lucifiski, 1990b, Phys. Status Solidi a 118, 189.

Ran, C., 1982, J. Magn. & Magn. Mater. 30, 141. Ran, C., 1983, J. Magn. & Magn. Mater. 31/34, 874. Ran, C., and S. Eichner, 1981a, Phys. Rev. Lett. 47,

939. Rau, C., and S. Eichner, 1981b, Springer Ser. Chem.

Phys. (Springer N.Y.) Vol. 17, p. 138. Ran, C., and S. Eichner, 1986, Phys. Rev. B 34, 6347. Ran, C., and C. Jin, 1988, J. Phys. (Paris) Colloq.

49(Suppl. 12), C8-1627. Ran, C., K. Waters and N. Chen, 1990, J. Elect.

Spectrosc. Relat. Phenom. 51,291. Rayane, D., D. Mrlinon, P. Cabuad, B. Hoareau, H.

Tribollet and B. Broyer, 1989, Phys. Rev. A 39, 6056.

Reichl, R., and K.H. Gaukler, 1986, Appl. Surf. Sci. 26, 196.

Reichl, R., and K.H. Gaukler, 1988, Appl. Surf. Sci. 91, 460.

Reihl, R., and EJ. Himpsel, 1982, Solid State Commun. 44, 1131.

Reshentnikova, L.V., and M.Kh. Yuldasheva, 1979, Bull. Acad. Sci. USSR, Set. Phys. 43, 74.

Richter, H.J., R.S. Smith, N. Herses, M. Seehman- Eggebert and E Wennekers, 1988, Appl. Phys. Lett. 53, 99.

Rodewald, W, and W. Femengel, 1988, IEEE Trans. Magn. MAG-24, 1638.

Rodewald, W., and P. Schrey, 1990, J. Magn. & Magn. Mater. 83, 206.

Ronay, M., C.E Aliotta and C.M. Serano, 1982, J. Appl. Phys. 53, 4919.

Rosengren, A., and B. Johansson, 1982, Phys. Rev. B 26, 3068.

Rossi, D., R. Ferro and R. Marazza, 1975, J. Less- Common Met. 40, 345.

Rossi, G., 1987, Physica Seripta 35, 590. Rossi, G., and A. Barski, 1985, Phys. Rev. B 32,

5492. Rossi, G., and A. Barsll, 1986, Solid State Commun.

57, 277.

Rossi, G., J.J. Yeh, I. Lindau and J. Nogami, 1984, Phys. Rev. B 29, 5389.

Rossi, G., J.J. Yeh, I. Lindau and J. Nogami, 1985, Surf. Sci. 152/153, 743.

Sagasaki, M., T. Kobayashi, S. Tsunashima and S. Uchiyama, 1985a, IEEE Transl. J. Magn. Jpn. TJMJ-1-3, 369.

Sagasaki, M., T. Kobayashi, S, Tsunashima and S. Uchiyama, 1985b, Nippon Oyo Gill Gakkaishi 9, 105. In Japanese.

Sahashi, M., T. Mizoguchi and K. Inomata, 1983, J. Magn. & Magn. Mater. 31/34, 225.

Sakaguchi, H., and G. Adachi, 1990, J. Less-Common Met. 162, 231.

Sakaguehi, H., H. Nagai, G. Adachi and L Schokawa, 1985a, J. Mater. Sci. Lett. 4, 347.

Sakaguchi, H., N. Taniguehi, G. Adachi and J. Shiokawa, 1985b, in: New Frontiers in Rare Earth Science and Applications, Proc. Int. Conf. on Rare Earths Developments and Applications, eds Xu Guangxian and Xiao Jimei (Science Press, Beijing) Vol. 2, p. 1076.

Sakaguehi, H., N. Taniguchi, H. Nagai, K. Niki, G. Adachi and J. Shiokawa, 1985c, J. Plays. Chem. 89, 5550.

Sakaguchi, H., G. Adachi and J. Shiokawa, 1986a, J. Less-Common Met. 118, L1.

Sakaguchi, H., H. Nagai, G. Adachi and J. Shiokawa, 1986b, J. Less-Common Met. 126, 83.

Sakaguchi, H., Y. Yagi, N. Taniguchi, G. Adaehi and J. Shiokawa, 1987, J. Less-Common Met. 135, 137.

Sakaguchi, H., N. Taniguchi, H. Seri, J. Shiokawa and G. Adachi, 1988, J. Appl. Phys. 64, 888.

Sakaguchi, H., H. Seri and G. Adachi, 1989a, Kidorui 14, 92. In Japanese.

Sakaguchi, H., Y. Yagi, J. Shiokawa and G. Adachi, 1989b, J. Less-Common Met. 149, 185.

Sakaguchi, H., H. Seri and G. Adachi, 1990, J. Phys. Chem. 94, 5313.

Sakamoto, Y., T.B. Flanagan and T. Kuji, 1985, Z. Phys. Chem. N.E 143, 61.

Sakamoto, Y., M. Yoshida and T.B. Flanagan, 1986, J. Mater. Res. 1, 781.

Sakamoto, Y., K. Takao, M. ¥oshida and T.B. Flanagan, 1988, J. Less-Common Met. 143, 207.

Sakamoto, Y., K. Takao and M. Ohmall, 1990a, J. Less-Common Met. 162, 343.

Sakamoto, Y., EL. Chert, M. Furukawa and K. Minc, 1990b, J. Less-Common Met. 159, 191.

Sakamoto, Y., K. Takao and Y. Nagaoka, 1991, J. Mater. Sci. Lett. 10, 341.


Salamanca-Young, L., D.L. Partin and J. Heremans, 1988, J. Appl. Phys. 63, 1504.

Salas, EH., and M. Mirabal-Garcia, 1989, J. Appl. Phys. 66, 5523.

Salas, EH., and M. Mirabal-Garcia, 1990a, Phys. Rev. B 41, 10859.

Satas, EH., and M. Mirabal-Garcia, 1990b, J. Magn. & Magn. Mater. 83, 109.

Sarpal, B.K., C. Blancard, J.R Connerade, J.M. Esteva, J. Hormes, R.C. Karnatak and U. Kuentgens, 1991, J. Phys. B 24, 1593.

Sato, N., 1986, J. Appl. Phys. 59, 2514. Sato, N., and K. Habu, 1987, J. Appl. Phys. 61, 4287. Sato, N., K. Habu and T. Onaya, 1987, IEEE Trans.

Magn. MAG-23, 2614. Sato, R., N. Saito and T. Morishita, 1988, IEEE Trans.

Magn. MAG-24, 2458. Savrin, V.D., A.V. Elyutin, N.E Mikhailova and Z.V.

Eremenko, 1988, Russ. J. Inorg. Chem. 33, 1250. Schelleng, J.H., D.W. Forester, E Lubitz and C.

Vittoria, 1984, J. Appl. Phys. 55, 1805. Schiffmacher, G., 1983, Progr. Cryst. Growth Charact.

17(I/4), 379. Schneider, G., 1988, Ph .D. Thesis, Universit~it

Stuttgart (Germany). Schneider, W.D., C. Laubschat and B. Reihl, 1983,

Phys. Rev. B 27, 6538. Schwarz, R.B., and W.L. Johnson, 1983, Phys. Rev.

Lett. 51,415. Sellmyer, D.J., 1991, plenary lecture, 19th Rare Earth

Conf. Res., Lexington, KN, USA. Sellmyer, D.J., and Z.S. Shah, 1987, J. Appl. Phys. 61,

4323. Sellmyer, D.J., and Z.S. Shan, 1989, in: Proc. MRS

Intern. Meet. Adv. Mater. (Multilayers), Vol. 10 (Materials Research Society, Pittsburgh, PA) p. 379.

Shan, Z.S., and D.J. Setlmyer, 1988, J. Appl. Phys. 64, 5745.

Shah, Z.S., and D.J. Sellmyer, 1990, J. Appl. Phys. 67, 5713.

Shan, Z.S., S. Naris, K.D. Aylesworth and D.J. Sellmyer, 1988, J. Appl. Phys. 63, 3218.

Shah, Z.S., D.J. Sellmyer, S.S. Jaswal, Y.J. Wang and J.X. Shen, 1989, Phys. Rev. Lett. 63, 449.

Shen, Y., and D.E. Laughlin, 1990, J. Appl. Phys. 67, 7510.

Shikhmanter, L., M. Talianker and M.R Dariel, 1982, Thin Solid Films 90, 51.

Shikhmanter, L., M. Tlianker and M.E Dariel, 1983a, J. Phys. & Chem. Solids 44, 745.

Shikhmanter, L., M. Talianker and M.E Dariel, 1983b, J. Less-Commnn Met. 92, 247.

Shin, S.C., M.L. Cofield and R.H.D. Nuttall, 1987, J. Appl. Phys. 61, 4326.

Shinjo, T., K. Mibu, S. Ogawa and N. Hosoito, 1989a, MRS Symp. Proc. (Growth Charact. Prop. Ultrathin Magn. Films-Multilayers) 151, p. 87.

Shinjo, T., K. Yoden, N. Hosoito, J.R Sanchez and J.M. Friedt, 1989b, J. Phys. Soc. Jpn. 58, 4255.

Shirai, H., H. Sakaguchi and G. Adachi, 1990, J. Less- Common Met. 159, L17.

Sigrist, M., G. Chassaing, J.C. Francois, E Antoman- geli, N. Zema and M. Piacentini, 1987, Phys. Rev. B 35, 3760.

Singh, A.K., and O.N. Srivastava, 1979, Jpn. J. Appl. Phys. 18, 1603.

Sing/a, A.K., and O.N. Srivastava, 1980, Z. Metallkd. 71, 57.

Singh, A.K., and O.N. Srivastava, 1981, Thin Solid Films 81,367.

Singh, A.K., and O.N. Srivastava, 1982, J. Less- Common Met. 88, 97.

Singh, A.K., and O.N. Srivastava, 1983, Z. Metallkd. 74, 440.

Singh, A.K., and O.N. Srivastava, 1985, Z. Metallkd. 76, 760.

Singh, O., and A.E. Curzon, 1982, Solid State Commun. 44, 1121.

Singh, S.K., A.K. Singh and O.N. Srivastava, 1985, Int. J. Hydrogen Energy 10, 523.

Singleton, J.H., and L.N. Yannopoulos, 1975, J. Vac. Sci. & Technol. 12, 414.

Smith, D.A., I.E Jones and I.R. Harris, 1982, J. Mater. Sci. Lett. 1, 463.

Smith, H.K., A.G. Moldovan, R.S. Craig, W.E. Wallace and S.G. Sankar, I980, J. Solid State Chem. 32, 239.

Smith, R.L., W.D. Corner and B.K. Tanner, 1980a, J. Phys. E 13, 620.

Smith, R.L., W.D. Corner and B.K. Tanner, 1980b, J. Magn. & Magn. Mater. 20, 265.

Smutek, M., and S. Cern), 1985, Thermodyn. Acta 91, 31.

Stadelmaier, H.H., EJ. Cadieu and N.C. Liu, 1987, Mater. Lett. 6, 80.

Stenborg, A., and E. Bauer, 1987a, Surf. Sci. 185, 394.

Stenborg, A., and E. Bauer, 1987b, Phys. Rev. B 36, 5840.

Stenborg, A., and E. Bauer, 1988, Solid State Commun. 66, 561.

204 M. GASGNIER

Stenborg, A., J.N. Andersen, O. Bj6rneholm, A. Nilsson and N. Mfirtensson, 1990, J. Electron. Spectrosc. Relat. Phenom. 52, 47.

Strasser, G., 1988, Vak-Technik 37, 213. In German. Strzeszewski, J., A. Nazareth, G.C. Hadjipanayis, K.D.

Aylesworth, Z.R. Zhao and D.J. Sellmyer, 1988, Mat. Sci. & Eng. 99, 153.

Strzeszewski, J., T. Tsoukatos and G.C. Hadjipanayis, 1990, J. Appl. Phys. 67, 4966.

Suezawa, Y., Y. Gond6, T. Nakao and K. Kakuno, 1983, J. Magn. & Magn. Mater. 35, 323.

Suezawa, Y., R. Tsuchiya and Y. Gond6, 1985, Jpn. J. Appl. Phys. 24, L140.

Surplice, N.A., and W. Brearley, 1978, Surf. Sci. 72, 84.

Surplice, N.A., and K. Kandasamy, 1982, J. Phys. D 15, 1117.

Suryanarayanan, R., and S.K. Das, 1990, J. Appl. Phys. 67, 1612.

Suzuki, A., R. Matsuda, K. Taki, Y. Watanabe and S. Mizutani, 1988, Jpn. J. Appl. Phys. 27, 25.

Suzuki, Y., H. Masuda, T. Shibata and N. Koshizuka, 1987a, IEEE Transl. J. Magn. Jpn. TJMJ-2-2, 173.

Suzuki, Y., H. Masuda, T. Shibata and N. Koshizuka, 1987b, IEEE Trans. Magn. MAG-23, 3704.

Taborelli, M., R. Allenspach, G. Boffa and M. Landolt, 1986a, Phys. Rev. Lett. 56, 2869.

Taborelli, M., R. Allenspach and M. Landolt, 1986b, Phys. Rev. B 34, 6112.

Takahashi, M., T. Takeda, H. Watanabe and T. Wakiyama, 1989, Nippon Oyo Jiki Gakkaishi 13, 323. In Japanese.

Takao, K., Y. Sakamoto, M. Yoshida and T.B. Flanagan, 1989, J. Less-Common Met. 152, 115.

Takao, K., K.L. Zhao and Y. Sakamoto, 1990, J. Mater. Sci. 12, 1255.

Takeda, K., H. Ishii and O. Nakamura, 1989, Jpn. Kokai Tokkyo Koho JP 89122105. Patent.

Takeda, S., 1983, J. Sci. Hiroshima Univ. A 46, 149. In English.

Takeda, S., K. Kitano and Y. Komura, 1982, J. Less- Common Met. 84, 317.

Takeda, S., H. Horikoshi and Y. Komura, 1983, J. Micros. 129, 347.

Tanaka, M., H. Yuzurihara and T. Tokita, 1987, IEEE Trans. Magn. MAG-23, 2955.

Tang, W., S. Zhou, R. Wang and C.D. Graham Jr, 1988, J. Appl. Phys. 64, 5516.

Thole, B.T., G. van der Laan, J.C. Fuggle, G.A. Sawatsky, R.C. Karnatak and J.M. Esteva, 1985, Phys. Rev. B 32, 5107.

Tibbetts, G.G., and W.E Egelhoff Jr, 1980, L Vac. Sci. & Technol. 17, 458.

Tiwald, T.E., J.A. Woollam and D.J. Sellmyer, 1988a, J. Appl. Phys. 63, 3215.

Tiwald, T.E., J.A. Woollam, Z.S. Shan and D.J. Sellmyer, 1988b, Mater. Res. Soc. Symp. Proc. 103 (Multilayers) 239.

Tkach, VI., V.E Bashev, A.B. Lysenko and I.S. Miroshnichenko, 1980, Phys. Met. Metall. 48(1), 183.

Toki, K., 1986, Jpn. Kokai Tokkyo Koho JP 86104 445. Patent in Japanese.

Tougaard, S., and A. Ignatiev, 1981, Surf. Interface Anal. 3, 3.

Toxen, A.M., T.H. Geballe and R.M. White, 1988, J. Appl. Phys. 64, 5431.

Tsukahara, S., and T. Kanayama, 1983, J. Magn. & Magn. Mater. 31/34, 927.

Tsukahara, S., T. Kanayama and H. Tanoue, 1983, J. Magn. & Magn. Mater. 35, 319.

Tsunashima, S., T. Shinoda, H. Miyatake and S. Uchiyama, 1980, J. Appl. Phys. 51, 5901.

Tsunashima, S., T. Ichikawa, M. Nawate and S. Uchiyama, 1988, J. Phys. (Paris) Colloq. 49(Suppl. 12), C8-1803.

Uchida, H., H. Uchida and Y.C. Huang, 1984, J. Less- common Met. 101,459.

Uchida, H., T. Ebisawa, K. Terao, N. Hosoda and Y.C. Huang, 1987, J. Less-Common Met. 131, 365.

Uchida, H., T. Ebisawa, A. Denda, T. Itoh and S. Tsuzuki, 1989, Z. Phys. Chem. N.E 164S, 1313.

Uchida, K., M. Murakami and H. Kawabata, 1987, Jpn. Kokai Tokkyo Koho JP 87 287 453. Patent in Japanese.

Umemura, S., H. Tajika, E. Kita and A. Tasaki, 1985, IEEE Trans. Mag. MAG-21, 1985.

Urbaniak-Kucharczyk, A., 1986, Phys. Status Solidi b 134, 751.

Urbaniak-Kucharczyk, A., 1988, Phys. Status Solidi b 149, 543.

van Dover, R.B., E.M. Gyorgy, R.P. Frankenthal, M. Hong and D.J. Siconolfi, 1986, J. Appl. Phys. 59, 1291.

Varkanova, R.G., 1982, Russ. J. Phys. Chem. 56, 420. Varkanova, R.G., and L.V. Morozova, 1981, Russ. J.

Phys. Chem. 55, 1777. Varkanova, R.G., and L.V. Morozova, 1984, Russ. J.

Phys. Chem. 58, 1760. Varkanova, R.G., and A.S. Nazarov, 1977, Russ. J.

Phys. Chem. 51, 397.


Varkanova, R.G., L.V. Morozova and Kh.Kh. Khanudova, 1982, Russ. J. Phys. Chem. 56, 933.

Venkert, A., N. Shamir, M. Talianker, U. Atzmony and M.E Dariel, 1987, J. Vac. Sci. & Technol. A 5, 1730.

Verma, A.R., and P. Krishna, 1966, Polymorphism and Polytypism in Crystals, J. Wiley and Sons, New- York.

Vittoria, C., J.H. Schelleng, P. Lubitz and D.W. Forester, 1984, J. Appl. Phys. 55, 2450.

von Molnar, S., C.N. Guy, R.J. Gambino and T.R. McGuire, 1980, J. Magn. & Magn. Mater. 15/18, I391.

yon Molnar, S., B. Barbara, T.R. McGuire and R.J. Gambino, 1982a, J. Appl. Phys. 53, 2350.

von Molnar, S., T.R. McGuire, R.J. Gambino and B. Barbara, 1982b, J. Appl. Phys. 53, 7666.

Waldrop, J.R., 1985, Appl. Phys. Lett. 46, 864. Wall, A., A. Raisanen, S. Chang, P. Philip, N. Trouiller,

A. Franciosi and D.J. Peterman, 1987, J. Vac. Sci. & Teehnol. A 5, 3193.

Wall, A., A. Raisanen, S. Chang, P. Philip, N. Trouiller, A. Franciosi and DJ. Peterman, 1988, J. Vac. Sci. & Teehnol. A 6, 1575.

Weaver, J.H., and D.W. Lynch, 1973, Phys. Rev. B 7, 4737.

Weaver, J.H., and C.G. Olson, 1977a, Phys. Rev. B 16, 731.

Weaver, J.H., and C.G. Olson, 1977b, Phys. Rev. B 15, 590.

Webb, D.J., R.G. Walmsley, K. Parvin, RH. Dickinson, T.H. Geballe and R.M. White, 1985, Phys. Rev. B 32, 4667.

Webb, DJ., A.N. Marshall, Z. Sun, T.H. Geballe and R.M. White, 1988a, IEEE Trans. Magn. MAG-24, 588.

Webb, D.J., A.N. Marshall, A.M. Toxen, T.H. Geballe and R.M. White, 1988b, IEEE Trans. Magn. MAG- 24, 2013.

Weller, D., and S.E Alvarado, 1985, Z. Phys. B 58, 261.

Weller, D., and S.E Alvarado, 1986, J. Appl. Phys. 59, 2908.

WeUer, D., and S.R Alvarado, 1988, Phys. Rev. B 37, 9911.

Weller, D., and D.D. Sarma, 1986, Surf. Sci. 171, L425.

Weller, D., S.E Alvarado and M. Campagna, 1985a, Physica 130B, 72.

Weller, D., S.E Alvarado, M. Campagna, W. Gudat

and D.D. Sarma, 1985b, J. Less-Common Met. 111, 277.

Weller, D., S.E Alvarado, W. Gudat, K. Schr6der and M. Campagna, 1985c, Phys. Rev. Lett. 54, 1555.

Wertheim, G.K., and G. Crecelius, 1978, Phys. Rev. Lett. 40, 813.

White, R.L., 1990, J. Phys. Soc. Jpn. 59, 3018. Wieliezka, D.M., and C.G. Olson, 1990, J. Vac. Sci.

& Technol. A 8, 891. Wu, R., and A.J. Freeman, 1991, J. Magn & Magn.

Mater. 99, 81. Wulz, H.G., and E. Fromm, 1986a, J. Less-Common

Met. 118, 293. Wulz, H.G., and E. Fromm, 1986b, J. Less-Common

Met. 118, 315. Xu, Y., 1987, Rep. IS-T-1280, Order No. DE87013602,

102 pp. Xu, Y., and R.N. Shelton, 1987, Jpn. J. Appl. Phys. I

26(Suppl. 26-3), 1269. Yamaguchi, S., 1982a, J. Electrochem. Soc. 129,

1145. Yamaguchi, S., 1982b, Soy. Phys. Crystallogr. 27,

480. Yamaguchi, S., 1982c, Exp. Technik Physics 30, 251.

In German. Yamaguchi, S., 1982d, J. Phys. D 15, 347. Yamamoto, H., S. Hirosawa, S. Fujimura, K. Tokuhara,

H. Nagata and M. Sagawa, 1987, IEEE Trans. Mag. MAG-23, 2100.

Yamashita, S., M. Mokeda and K. Hara, 1988, Jpn. Kokai Tokkyo Koho JP 88 84 005. Patent in Japanese.

Yamauchi, K., K. Habu and N. Sato, 1988, J. Appl. Phys. 64, 5748.

Yang, K.A., H. Homma and I.K. Sehuller, 1988, J. Appl. Phys. 63, 4066.

Yeh, J.J., J. Nogami, G. Rossi and I. Lindau, 1984, J. Vac. Sci. & Technol. A 2, 969.

Yoden, K., N. Hosoito, K. Kawaguchi, K. Mibu and T. Shinjo, 1988, J. Appl. Phys. 27, 1680.

Zajac, S., 1977, Physica B 86-88, 51. Zhao, Z.B., S.K. Xia, R.Z. Ma and S.M. Pan, 1989a,

J. Less-Common Met. 155, 75. Zhao, Z.B., S.K. Xia, R.Z. Ma, J. Ping, M. Baihe and

S.M. Pan, 1989b, Solid State Commun. 69, 1011. Zhao, Z.B., S.K. Xia, C.R. Wang and R.Z. Ma, 1989c,

J. Phys.: Condens. Matter 1, 7513. Zhao, Z.B., R.Z. Ma and M. Baihe, 1989d, Scripta

Metall. 23, 743. Zhavoronkova, K.N., and O.A. Boeva, 1989, React.

Kinet. Catal. Lett. 40, 291.

206 M. GASGNIER

Zhavoronkova, K.N., and A.V. Peshkov, 1978, Dep. VINITI publ. No. 480-78 (23pp).

Zhavoronkova, K.N., and A.V. Peshkov, 1979, React.

Kinet. Catal. Lett. 12, 259. Zhu, J.G., C.B. Carter, C.J. Palmstr~m and S. Mounier,

1990, Appl. Phys. Lett. 56, 1323.

Handbook on the Physics and Chemistry of Rare Earths VoL 20 edited by K.A. Gschneidner, Jr. and L. Eyring © 1995 Elsevier Science B.V. All rights reserved

Chapter 137

HYDROGEN IN RARE-EARTI-I METALS, INCLUDING RIt2+x PItASES*

E V A J D A

Laboratoire des Solides Irradiés, CNRS, Ecole Polytechnique, 91128 PaIaiseau, France

C o ~ e ~ s

Symbols and abbreviations 1. Introduction 2. Hydride preparation and phase diagrams

2.1. Specimen preparation 2.1.1. Metallic or a-phase 2.1.2. Dihydride or [3-phase 2.1.3. Trihydride or y-phase

2.2. Phase diagrams 3. Structural properties

3.1. a-Phase solid solntions 3.2. [3-Phase dihydrides

3.2.1. The hydrides of Eu and Yb 3.2.2. ,/-Phase trihydrides

4. Kinetics and thermodynamics

207 4.1. a-Phase solid solutions 232 208 4.2. [3-Phase dihydrides 236 210 5. Electronic properties 243 211 5.1. Solid solutions 244 211 5.2. (Mainly) t-phase hydrides 248 212 5.2.1. Metal-serniconduetor transitions 251 214 5.2.2. Discussion of specific hydrides 255 214 5.2.3. Spectroscopic studies 265 216 6. Magnetic properties 266 216 6.1. «*-Phase solid solutions 267 221 6.2. (Mainly) [3-phase systems 271 231 6.2.1. Speeific RH2+ x hydrides 273 231 7. Summary and outlook 286 232 References 287

S y m b o l s a n d a b b r e v i a t i o n s

A~ac acoustic eleetron-phonon coupling ep parameter C~» Cl3

A,~,op t optic electron-phonon coupling parameter

a lattice parameter CAM

Aa/Ax static lattice expansion (due to H) CF

Aa~AT dynamic (thermal) lattice expansion E a

AF antiferromagnetic (ism) E d

c commensurate Ef

e lattice parameter E m

c concentration E b

c « , ~ concentrations in the « and [3-phase AE

Cm~x limiting concentration EPR

specific heat

elastic constants for transverse wave propagation in a hexagonal crystal

c-axis modulated

crystal electric field

activation energy

activation energy for diffusion

activation energy for formation

activation energy for migration

binding energy

electronic energy gap

electron paramagnetic resonance

* This review is dedicated to the memory of J.N. Daou, a pioneer of the rare-earth hydrides.

207

208 P. VAJDA

FM

Herllc HerA_c HF Hs ic

INS

LRO

M-I

M-S

3N, 4N

ne NMR

O PAC

QENS

SRO

T

Tan

Tc T~

TH Tr

TM

Tm

Tm

TM_s(T)

ferromagnetic (ism)

critical field parallel to the c-axis

critieal field perpendicular to the c-axis

enthalpy of formation

heat of solution

incommensurate

inelastic neutron scattering

long-range order

metal-insulator transition

metal-semieonductor transition

99.9%, 99.99% purity

conduetion electron density

nuclear magnetic resonance

octahedral site perturbed angular correlation quasielastic neutron scattering

short-range order

tetrahedral site

anomaly temperature Curie temperature

critical temperat~re

helieoidal temperature

intermediate temperature

temperature of resistivity maximum

temperamre of resistivity minimum

melting temperature

temperature of metal-insulator transition in the heating run

TM-s(D

TN Tp

X

XPS

Y

YeJ Fi

A

6

B+

P, Pr,~~ GS

Dm,mag

Ap °

Apù T

rm 690

O~ Op Z

temperature of metal-insulator transition in the cooling run

Néel temperature

peak temperature (for recovery)

deviation from stoichiometry

X-ray photoelectron spectroscopy reaction order

electronic specific-heat coefficient

electronic angular momentum stares in a crystal electric field

energy gap in the magnon spectrum stoichiometric deficit

positive muon effective paramagnetie moment resistivity, residual

magnetic resistivity term, in the ground stare

additional resistivity due to hydrogen

additional resistivity due to quenching relaxation time

magnetic propagation vector

Debye temperature

Einstein temperature paramagnetic Curie temperature

magnetic susceptibility

1. Introduction

The rare earths absorb hydrogen readily and form solid solutions and/or hydrides exothermally at temperatures of several hundred °C. Their phase diagrams consist, in general, of three basic parts: (a) the metallic solid solution, or c-phase, with the H atoms inserted in the tetrahedral interstices of the host-metal lattice; (b) the equally metallic dihydride B-phase, where the two H atoms occupy ideally the two available tetrahedral sites; this phase crystallizes in the fcc fluorite system; (c) the insulating trihydride, or y- phase, which possesses an hcp unit cell with both tetrahedral sites and the one octahedral site filled up. A schematic view is given in fig. 1. Exeeptions are the divalent lanthanides Eu and Yb, whose dihydrides are already insulators and exhibit an orthorhombic structure, and Sc whose very small unit cell does not normally accept more than two H atoms.

An interesting feature of the phase diagram in fig. I is the relatively large existence region of the pure « and, in partieular, of the [3-phase (whieh extends up to the trihydride

HYDROGEN IN RARE-EARTH METALS, INCLUDING RH2+ x PHASES 209

I - -

\

(X i f x

0 1 2 3 at.H / at.R

Fig. 1. Sehematic phase diagram for R-H systems, et, solid solution; et*, ordered H-sublattice in some R-H sotid solutions; B, dihydride; ¥, trihydride.

for the light lanthanides La, Ce and possibly Pr). This means that the excess H atoms in solution will, from a certain concentration on, interact with each other and form hydrogen sublattices, which are stable at low temperature and might, in some cases, deform the host lattice. This hydrogen ordering is observed as an anomaly in several physical properties and has been characterized by neutron scattering. Thus, it was shown that, in the hcp c- phase of several rare earths including Sc, Y and the heavy trivalent lanthanides from Ho to Lu, the hydrogen atoms, at temperatures below N200 K, form zig-zag ehains of H-H pairs along the c-axis. In the super-stoichiometric dihydrides RHz+x, on the other hand, the octahedral (x) hydrogens can sometimes order in a Ni3Mo-type structure such that, for a stoichiometric composition with x = 0.25, one observes one filled (420) plane followed by three empty ones.

Another exciting feature is the possibility of observing a continuous decrease in the earrier density when absorbing hydrogen, which gives rise to a metal-insulator (M-I) transition somewhere in the interval between 2 and 3 atoms H per atom R. Moreover, temperature dependent M-I transitions have been observed in the B-phase between 250 and 300K both in sub-stoichiometric LaH3-x and CeH3_x as weil as in superstoichiometric YH2+x and in RH2+x (R = Gd, Ho, Er) with x ,~ 0.1-0.3, which are driven by the order-disorder transformation in the H sublattice mentioned above.

A further physical property which is strongly influenced by the hydrogen eoneentratiõn in solution, x, is the magnetism both of the R-metals and of their dihydrides. Thus, not only the number of the x-atoms direetly aets upon the RKKY interaction responsible for the magnetism but, also, their eventual ordering into an H sublattiee leads to modifications of the crystal-field symmetry with the appearance of new magnetic phases. It is also interesting, though in the end not too surprising, that the cerium hydride CeH2+x is a magnetically ordering (except for x = 0.05, which is paramagnetie) heavy-fermion system with a Kondo lattice, like many other Ce-based eompounds due to their hybridized 4f-eleetrons.

In view of what was said above, one can already see the importanee of a reliable eharaeterization of the H eoneentration in the specimens. In partieular, the distinetion between the two tetrahedral H atoms and the octahedral (x) excess H atoms in the [3-

210 R VAJDA

RH2+x systems, is essential for any comparison between results from various laboratories. We shall, therefore, always try to separate the true concentration in the dihydride (somewhere from 1.85 to 2.0 atoms H per atom R) from the x-concentration in a particular compositiòn, thus specifying e.g. RH1.9»+010 instead of just summing up RHz05. A special subsection will be devoted to specimen preparation and characterization to emphasize the importance of the subject.

The field is at present in full development and the last decade has seen the production of a large amount of new and reliable data mainly in the non-stoichiometric «- and B-phase systems. This is due to the availability of purer rare earths (there is orten a qualitative property change when going from 3N to 4N material), to more reliable specimen characterization, and to the application of modern measuring techniques, e.g. low-temperature specific-heat and resistivity, NMR, internal friction, neutron- and other spectroscopies. We feel, therefore, that a critical review of these data in the present volume of this Handbook fills a certain gap after the "Hydride-chapter" (26) by Libowitz and Maeland (1979) in volume 3 (devoted, by the way, to Non-metallic compounds). More recent reviews in the field were those by Arons (1982) (new version Arons 1991) mostly on magnetic properties; Wiesinger and Hilscher (1991) also on magnetism and mainly on H in intermetallic compounds; and a general review by Vajda and Daou (1995) in a Metal-Hydrogen-Systems compendium. A survey of surface and activation properties of hydrogen on rare earths has been given by Schlapbach (1992). The outline of the present chapter is as follows: Sect. 2: Phase diagrams, including a subsection on specimen preparation. Sect. 3: Structural properties, both of the alloy and of possible H sublattices. Sect. 4: Kinetics and thermodynamics, comprising various thermally activated pro-

cesses. Sect. 5: Electronic properties, including results from electric resistivity, specific heat,

NMR, EPS etc., but leaving magnetism for the next section. Sect. 6: Magnetic properties, including the Kondo effect. Sect. 7: Summary and outlook.

2. Hydride preparation and phase diagrams

The establishment of reliable T-c phase diagrams in the R-H systems is intimately connected with an unambiguous specimen characterization and, hence, with a strict control of the preparation conditions. The lack of such a control in the past has frequently led to contradictory experimental results, in particular where non-stoichiometric compositions are concemed. It is, therefore, necessary to include in this section a relatively broad subsection on specimen preparation in order to optimize the sample quality, to determine the hydrogen concentration in the particular phase and, last but not least, to compare the data of different experiments.


2.1. Specimen preparation

Hydrogen is absorbed exothermally by rare earths and the specimens can be readily prepared by direct action of the gas at a temperature of several hundred °C. Nevertheless, for a successful preparation of weil characterized samples without mechanical and/or chemical defects, several conditions should be satisfied:

(1) A specimen should consist of a single, undivided piece (foil or bulk) to assure a uniform H concentration in all parts; when divided samples are needed, as for powder-diffraction or susceptibility experiments, it is preferable to hydrogenate a bulk specimen and crush it afterwards.

(2) The original metal specimen should be of high purity and good metallurgical quality: stress-free, without textures and microcraeks; high-temperature annealing (at half the melting point) and degassing is usually required.

(3) The preparation chamber should permit the maintenance of the specimen at rather high temperatures (above 500°C) in a good vacuum (4 10-7 Torr) before hydrogenation, because of the strong affinity of the rare earths towards oxygen and nitrogen. Quartz tubes with ttmgsten crucibles for the specimen a rea good choice. A hydrogen filter (e.g. PdAg tubes) might be necessary for purification.

(4) One should possess good instrumentation for precise pressure measurements, to warrant a reliable volumetric concentration determination. Capacitance manome- ters are the ideal pressure sensor-transducers for absolute readings to 10 -3 between 0 and 10bars.

In the following, we shall describe the preparation conditions for the three principal phases, a, ~ and y, distinct by their solubility limits and the critical temperatures for phase transitions or for hydrogen-configuration changes.

2.1.1. Metallic or a-phase The ~t-phase is a solid solution where the hydrogen atoms are distributed statistically in the tetrahedral (T) interstices of the metal lattice and behave as impurities. For the heavy lanthanides from Ho to Lu, as welt as for Sc and Y, there exist two varieties in the metallic phase, c~ and ct*, the latter being metastable at low temperatures and representing,

B* in fact, an ordered configuration of the H sublattice; its limiting concentration, Cmax, is independent of T (see sect. 3 for more details). For La through Dy, no «*-phase is observed (though there might be some traces in Dy), and the c~-phase does not form below a temperature T« of several hundred °C. The hydrogen solubility in the existence range of the c-phase increases with the atomic number of the lanthanide and seems to be related with the lanthanide contraction: it is, e.g. at 500°C, ten times larger in Lu than in La (Sc and Y behave in this context like heavy lanthanides); it increases linearly with the melting temperature of the rare earth.

In table 1, the various critical temperatures and concentrations in the c-phase of the rare earths are collected. We note that, in view of the high mobility of hydrogen in the ct- phase compared to the «*- or ~-phases, temperatures of T >~ 500°C are most appropriate for charging. Finally, it is important to know that the characteristics listed in table 1 are

212 P. V A J D A

Table 1

Cr i t i ca l t e m p e r a t u r e s and eoncen t r a t ions in the c - p h a s e a

R Vat T m (°C) T«~~ b (°C) T . . . . (°C) T . . . . (oc) c ~ x (a t .H /R) C~oo*c

( c m 3 / m o l ) ( a t .H /R)

Sc 15.039 1541 - n .m. c n .m. 0.35 n .m.

Y 19.893 1522 - n .m. 4 0 0 0 .20 />0.32

L a 22 .602 918 350 - - - 0 .04

C e 2 0 . 6 9 6 798 380 - - - 0 .06

P r 20 .803 931 380 - - - 0 .06

N d 20 .583 1021 280 - - - 0 .08

S m 2 0 . 0 0 0 1074 200 - - - 0 .15

G d 19.903 1313 180 - - - 0 .24

T b 19.310 1356 140 - - - 0 .26

D y 19.004 1412 (80) ? ? <0.01 0.28

H o 18.752 1474 - 90 n .m. 0.03 0 .30

E r 18.449 1529 - 120 340 0 .06 0 .32

T m 18.124 1545 - 140 380 0.11 0 .34

L u 17.779 1663 - 160 4 2 0 0 .20 0 .36

a F r o m D a o u and V ia l l a rd (1972) .

b T«~~ is t he (ct ~ [3) t r ans i t ion t e m p e r a t u r e

ex t r apo l a t ed to c a -- 0.

c n .m. , no t m c a s u r e d .

hardly modified by the impurity contents of the metal when going from 4N to 3N material, in contrast to the B-phase described below.

2.1.2. Dihydride or il-phase The dihydride phase crystallizes in general in the fcc fluorite-type structure, with an ideal composition of RH» The frequently noted stoichiometric deficit, RH2_6, is caused by impurities and structural defects of various kinds such as surfaces and grain boundaries. Thus, 6 is smaller for bulk specimens than for powder and for specimens made of originally 4N material than for those from 3N; it can reach values of up to 0.2, leading to "pure" dihydrides with a formula RH1.8.

The « -4 ~ transformation from hcp to fee is accompanied by a shift of atomic planes and can cause severe damage unless certain precautions are taken. Thus, an anneal of several hours at T = 500-800°C (depending on the rare earth) is a good procedure before the introduction of H to form the dihydride. In fact, at these temperatures the hydrogen will readily diffuse through the whole specimen, without the inhomogeneous formation of H-rich ~-RH2+x regions near the surface and H-deficient two-phase regions comprising «- and ~-areas in the bulk causing pressure gradients and possible destruction of the sample. The ~--~ ~ transformation will occur smoothly and will be total for the whole specimen. Single-crystal work on hydrides was limited until now to the system CeH2+x because of the favourably low melting point of Ce-metal (Libowitz 1972, Abeln

HYDROGEN IN RARE-EARTH METALS, INCLUDING RH2« PHASES 213

1987), which permits hydrogenation in the liquid phase and the crystal growth from the charged melt. Otherwise, the loss o f monocrystallinity during the a--* 13 transition is difficult to avoid, and the only relatively successful test known to us was made on TbD2 where a Tb-crystal was deuterated very slowly at T ~ 0 . 8 Tm (Daou and Vajda, unpublished). But even with the above precautions, the resulting specimens are brittle and all mechanical manipulafions such as cutting or fixing of leads should be done on the metal before hydrogenation. In partieular, eleetric contacts are normally made from platinum wire spot-welded on the metal ends before hydrogen is introduced into the sample. An additional problem that occurs sometimes is the low chemical stability o f the hydrides in air (especially for the light lanthanides), as they can form hydroxides and decompose; they should always be stored in vaeuum or, at least, in dry air.

The other important problem in the preparation o f p-phase specimens is their eharacterization. As already mentioned above, the particular properties induced by the octahedrally dissolved excess H atoms in a superstoichiometric system [3-RH2÷x, require a precise determination o f their concentration and, therefore, o f the true concentration for the saturated dihydride, 13-RH2_6, i.e. o f the value o f 6. To achieve this, one can use the fact that the equilibrium pressure at the isothermal plateau o f the dihydride RH2_6 is very low (10 -6 Torr at 500-600°C) while, above its upper limit, it begins to increase rapidly (orte needs e.g. -1 Torr to absorb x = 0.01 H/R in excess o f the upper limit at the hydrogenation temperature o f ~400°C). This means that, at the same temperature, the

Table 2 Lower boundaries of the pure [3-phase RH2_6; solubility lirnit x~x of their solid solutions ~-RH2_6+x; and

transition temperatures T l (13 ~ ~/) and T u (~, --~ 13); for Y, Tb and Lu

R 2 - 6 Ref. X~max (at.H/R) Ref. T~ (°C) Ref. rù (°c) Ref.

Y 3N 1.80 1 0.2, 0.33 7, 8 300 8 400 8 1.90 2 300 8 400 8

Y 4N 1.97-1.99 3 0.10 3 300 8 400 8 Tb 3N 1.92-1.94 4 0.35 4 250 8 350 8

285 7 362 7 Tb 4N 1.96-2.00 5 0.25 5 250 8 350 8

285 7 362 7 Lu 3N 1.82 1 0.25 8 320 8 410 8

1.85 7 0.38 7 326 7 416 7 Lu 4N 1.97-1.99 6 0.03 6 320 8 410 8

326 7 416 7

References (1) Daou et al. (1984a) (2) Juckum (1980) (3) Vajda and Daou (1991), Daou and Vajda (1992) (4) Vajda et al. (1985)

(5) Vajda et al. (1987a) (6) Daou et al. (1988b) (7) Mintz et al. (1976) (8) Daou and Vajda, unpublished.

214 R VAJDA

stability of the H atoms at the T sites will be much higher than that of the x-atoms at the O sites, giving an easy means to separate the two H species by simply pumping oft the less stable x-atoms at e.g. 500-600°C in a vacuum of < 10 -6 Torr. After that, one is certain to have a saturated "pure" dihydride leit; and the super-stoiehiometric RI-I2+x compound ean then be formed by just selecting the right P-T value, for example 10- 100 Torr at a temperature which is high enough to absorb the hydrogen but which should not be too low in order avoid the formation of the y-phase (cf. table 2). In table 2, we are also giving examples of the maximum solubility X~max of the octahedral hydrogens in the ~-phase before transformation into the y-phase; one notes the strong purity dependence ofx~max attaining a factor 10 in the ease of Lu.

2.1.3. Trihydride or y-phase Most R-H systems exhibit a seeond phase transformation [3--+ y in the interval RH2- RH3. The y-phase possesses an hcp structure, but with a bigger unit cell than the metal because of symmetry loss due to an off-center displacement of the H atoms occupying the T and O sites (see seet. 3). Those exhibiting only one (a ~ [3) transformation are the two divalent lanthanides Eu and Yb, Se (too small to incorporate a third H atom under normal pressure conditions) as well as the systems La-H, Ce-H and Pr-H, with a big enough unit cell to permit a complete occupation of the O sites in the [3-phase. The latter, however, exhibit second-order transformations with slight cubie-to-tetragonal deformations of the host lattice.

Thus, the problems encountered during the first transformation « ~ [3 are aggravated in the ~ ~ 7 one: the brittleness increases due to growing H coneentration and also because of the generally lower absorption temperatures (ef. table 2). The extreme chemical instability requires that a sample be maintained under hydrogen atmosphere, with no air contact, whatsoever. It is advised to perform the desired measurements in situ.

2.2. Phase diagrams

In fig. 1, we presented a schematic phase diagram showing the three principal phases of the general R-H system. The actual phase diagrams had been determined in the past for some of the light rare earths (La, Ce, Nd) and described among others by Libowitz and Maeland (1979) in the earlier review on this subject in this Handbook series. In the meantime, the known phase diagrams, such as La-H and Ce-H, have been given additional attention and new ones, Pr-H, Y-H and Lu-H, have been, at least in part, established. Among the more remarkable new phenomena is the confirmed existence of a high-temperature peritectic in the light R-H systems (Bischof et al. 1985) permitting the hope of growing single crystals of these hydrides [in addition to those already fabricated in the Ce-H system by Libowitz (1972)]. Most interesting, however, is the observation of hydrogen sublattice ordering at low temperatures (mostly below 300K) in both a- and B-phase systems. This seems to be a general phenomenon, which is sometimes accompanied by a distortion of the host lattice. This will be treated in more detail in

¢..) o

kù

~3

E E--,

1530 1478oC:: (o-.p) 1330-

I t 3 0

930

730

5 3 0

3 3 0

HYDROGEN IN RARE-EARTH METALS, 1NCLUDING RH2+ x PHASES 215

Weight Percent Hydrogen 0z 04 0« 08 1 15 z 3 «

0 0 0 0

0 0 0 0 o 0

0 0 /0 , ,>0o

o e~aa Oe & • "%,

(œY) x l t~ o *,x

xla eß

/ &

.a ,IP'*

13o ............................................... ,,y2 .............. , ~ ' •

-70 ~ , t ! ! !

ù~ - 2 7 0 . . . . . . . . . , . . . . . . . . . . . . . . . . 0 I 0 20

\ \

t u t

Il

r . . . . . . . . . ~ . . . . . . . . . ~ . . . . . . . . . f . . . . . . . . . i . . . . . . . . .

30 40 50 60 70 80

Atomic Percen t Hydrogen

Fig. 2. Phase diagram in the Y-H system assessed from thermodynamic and structural data. Note the abscissa scale with x = H/(Y + H) in at.% and the designations (x', 6 and ê for the et*, [3 and ¥ used in this review. The various symbols refer to different investigations, details are found in Khatamian and Manchester (1988).

sect. 3, where we shall also present partial phase diagrams as proposed from various physical measurements.

In figs. 2 and 3, we are exhibiting the phase diagrams for the systems Y-H and La-H, respectively, which resulted from a critical assessment by Khatamian and Manchester (1988, 1990) of the available data. Note in particular the tetragonally distorted low- temperature phase in the La-H system near the trihydride discovered by Klavins et al. (1984) and the ordered «*-phase in a-YHx. The latter has been seen in several c~-RHx systems (cf. also the Lu-H system in fig. 4) and has been determined by neutron scattering (Blaschko et al. 1985) to be due to H-H pairs ordered in chains along the c-axis. Figure 5 gives the Pr-H phase diagram, which resembles the La-H diagram at high temperature.

For all other systems, reliable data are still lacking, in particular in the region of the y-phase existence (i.e. in the heavy R-H systems from Nd-H on), though there is some progress noted in the RH2+x systems at low temperatures (cf. sect. 3).

216 E VAJDA

1200

1100

1000

81111

700

..~ 600

400 310

3OO

L

~7 ~7

Weight Percent Hydrogen 0.5

0 0

283'C

0

1.5 2 25

200

100

0

- t 0 0

0 I0 20 30 40 50 60 70 BO La Atom/e Percent Hydrogen

Fig. 3. Phase diagram in the La-H system assessed from thermodynamic and structural data. Note the abseissa seale with x=H/(La+ H) in at.% and the designation 6 for the 13 used in this review. The various symbols refer to different investigations, details are found in Khatamian and Manchester (1990).

3. Structural properties

3.1. a-Phase solid solutions

The site occupation by hydrogen in solid solution in the rare earth metals has been determined in the early eighties, after some controversy, through unambiguous ion- channeling experiments on single crystals of c-LuDx (Danielou et al. 1981) as well as by neutron diffraction on c-YDx (Khatamian et al. 1981), on c-TmDx (Daou et al. 1983), and on a-ScDx (Saw et al. 1983). It has been established that the hydrogen atoms were localized on the T sites of the hcp lattice over the entire measured temperature range between 4 K and 300 K. Later quasi-elastic neutron-scattering experiments (e.g. Anderson et al. 1989) and NMR studies (Barnes et al. 1989) at high temperatures extended the validity of the T-site occupation to the whole domain of c-phase existence where a site can still be specified (several hundred °C).

In table 3, we present the lattice parameters in the hcp a-phase for various hydrogen (or deuterium) concentrations and at various temperatures, together with their expansivities,

HYDROGEN IN RARE-EARTH METALS, 1NCLUDING RH2+ ~ PHASES 217

0

1000

8 0 0

600

6" o 1-

40O

200

F /

-200 ~- i I i 0 0 . 2 0 . 6

1 2 i I

Lu- H

I I r I 1 1.2 1.6

at.H/Lu

l i:t 2 2.2

Fig. 4. Phase diagram in the Lu-H system constructed from resistivity and thermodynamic data. Open circles, Daou (1965) and unpubl, data; solid cireles, Beaudry and Spedding (1975); open squares, Subramanian and Smith (1982); solid squares, Jones et al. (1964); crosses, Daou et al. (1988b).

o• I I i 1 ! I i

1100 Pr(i ) p -

1 0 0 0

q

(s) + PrH x(s )

900 // -Pr (s,bcc) j _ _ __.

8001 "w~~-~---~d-pr ' ~ Y

700 ( s , f c c ) /

600 / Pr(s) + PrHx(s)

I I I I I I I 10 20 30 40 50 60 70

Atomic Percent Hydrogen

Fig. 5. Phase diagram in the Pr-H system constructed from thermodynamic data. Note the abscissa scale with x = H/(Pr+ H) in at.%. The various symbols refer to different investigations, details are found in Bischof et al. (1985).

both static (caused by H insertion) and dynamic (thermal), determined in most cases by X- ray crystallography. We note that the c/a-ratio of the high-temperature c-phase decreases

218 R VAJDA

Table 3 Crystallographic parameters of the tl.c.p, a-phase, RH(D)x

x (H/R ratio)

T(K) Aa

a (Ä) c (A) a~x (10-4/at%)

Ac Aa Ac

cAx a A T c & T (10-4/at%) (10-6/K) (10~/K)

Ref.

Sc 0.33D 300 3.338 5.299 2.68

0.15 80 3.318 5.2775 3.47

0.15 300 3.3215 5.286 2.71

0.30 80 3.3295 5.2845 2.91

0.30 300 3.3340 5.2945 2.63

Y 0.19 300 3.6636 5.7900 2.22

0.176D 300 3.662 5.778 2.15

0.12 300 3.6542 5.7654 1.37

0.12 775 3.670 5.8175 2.28

0.22 300 3.6637 5.7940 1.93

0.22 775 3.678 5.838 2.23

Gd 0.2 775 c/a = 1.5890

Tb 0.2 775 3.6515 5.7735 5.52

0.2 1000 3.6573 5.7947 5.33

0.2D 800 3.6511 5.7752 5.36

0.2D 1000 3.6568 5.7945 5.23

Dy 0.2 675 3.6269 5.7255 4.15

0.2 950 3.6334 5.7550 4.11

0.2D 700 3.6304 5.7318 4.57

0.2D 950 3.6372 5.7580 4.64

Ho 0.2 645 3.6087 5.6985 3.38

0.2 900 3.6178 5.7220 3.94

0.2D 635 3.6103 5.7021 3.58

0.2D 875 3.6197 5.7237 4.19

Er 0.035 300 3.5636 5.5960 3.43

0.27 775 3.6035 5.700 3.63

Tm 0.08 300 3.5462 5.5795 3.20

0.09D 300 3.5466 5.5868 2.73

0.11 300 3.5478 5.5890 2.90

0.175 775 3.572 5.656 3.53

Lu 0.205 300 3.5267 5.6071 2.98

0.20 300 3.5250 5.6082 2.76

0.20 775 3.5412 5.6385 2.73

0.19D 300 3.5222 5.6040 2.68

0.19D 775 3.5400 5.6386 2.78

1.77 1

2.85 5.0 2.0 2

1.96 5.0 8.5 2

1.87 3.6 6.7 2

1.52 6.6 7.75 2

5.33 3

4.57 4

4.59 5.3 20.2 5

3.81 11.9 22.9 5

4.76 2.9 16.4 5

3.68 12.2 14.9 5

6

3.57 7.1 16.3 6,7

3.22 7.1 16.3 6,7

3.57 7.8 16.7 6,7

3.21 7.8 16.7 6,7

3.21 6.5 18.7 6,7

2.97 6.5 18.7 6,7

3.49 7.5 18.3 6,7

3.23 7.5 18.3 6,7

3.47 9.9 16.2 6,7

3.16 9.9 16.2 6,7

3.78 10.8 15.8 6,7

3.31 10.8 15.8 6,7

5.47 3

3.87 13.8 16.7 8

5.95 3

4.36 9

5.09 6.2 25.0 9

4.06 8.7 14.8 9

5.05 3

5.18 9.2 13.2 10

2.78 10.9 10.9 10

5.18 9.9 14.9 10

2.88 12.3 12.2 10

continued on next page

HYDROGEN IN RARE-EARTH METALS, INCLUDING RH2+ « PHASES

Table 3, notes

219

References (1) Saw et al. (1983) (2) Daou and Vajda, unpublished. (3) Beaudry and Spedding (1975) (4) Khatarnian et al. (1981)

(5) Juckum(1980) (6) Daou et al. (1981a) (7) Chiheb (1980)

(8) Bormet (1975) (9) Boanet and Daou (1979) (10) Daou and Bonnet (1974)

with increasing x for Gd, Tb, Dy and Ho, while it increases slightly for Er, Tm and Lu (Daou et al. 1981a), reflecting the evolution of the anisotropy and of the anharmonicity of the interatomic potential upon H insertion. Another interesting point is the exceptional behaviour of the static expansivity in the low-temperature a*-ScH(D)x: it is larger in the basal plane than along the c-axis leading to a decreasing c/a-ratio with increasing x, in contrast to all other «*-phase systems, probably a consequence of the unusually large elastie anisotropy ratio C *= C12/C13 in Sc (cf. Vajda et al. 1990b, 1991e).

As already mentioned several times before, the hydrogen atoms in certain «- RHx systems have a tendency to organize themselves in short-range-ordered (SRO) or long-range order (LRO) structures when cooled below temperatures corresponding to their mobility limit. The earliest manifestation of such low-temperature ordering was the appearanee of a resistivity anomaly near 170K in ct*-LuHx (Daou et al. 1976), which had been ascribed to a condensation into H-H pairs after interpreting the results of low-temperature electron irradiation experiments (Daou et al. 1977) and internal- friction measurements (Vajda et al. 1983a). The same anomaly was detected in all a*-RH(D)x systems, with R = Sc, Y, Ho, Er, Tm and Lu (for a review see Daou and Vajda 1988). Strong anisotropy manifestations in the magnetic system ~t*-ErH(D)x gave a further early indication as to a c-axis alignment of these H-H pairs (Daou et al. 1980a). The ordered configuration was finally identified through diffuse-neutron scattering experiments on single crystals of «*-LuDx (Blaschko et al. 1985, 1989a) as second- neighbor D-D pairs on T sites along the c-axis surrounding a Lu-atom (fig. 6). Several of these pairs then condense into zig-zagging quasi-linear chains parallel to the c-axis and shift along the b~axis in the basal plane, while the chains, on the other hand, interact repulsively to form a three-dimensional superstructure in the metal lattice (fig. 7). The above configuration was afferwards confirmed on the systems «*-ScDx (Blaschko et al. 1989c) and ct*-YDx (Fairclough et al. 1993). The number of pairs in a chain (i.e. the chain length) differs from one system to another and seems to correlate with the elastic anisotropy of the metal; the chain density varies as a function of H concentration.

In table 4 we have collected various characteristics of the ordered structures in the a*-phase, such as the anomaly temperatures (Tan) in electric resistivity or the binding energies as determined from a kinetic analysis of the resistivity data in the vicinity of the anomaly via an Arrhenius plot (cf. Daou et al. 1988a). An immediately visible result (fig. 8) is the correlation between Tan and the c/a-ratio, indicating a lower ordering temperature (i.e. a higher mobility of H) for a c/a-ratio closer to the ideal (8/3) 1/2 = 1.63 (i.e. in systems with less distortion). Note also the isotope effect, with a 4-5 K higher Tan

220 P. VAJDA

Fig. 6. HCP unit cell of LuD x in the «*-phase showing two adjacent D-D pairs (dashed lines) shifted along the b-axis. To, T l and T 2 are first and second neighbour tetrahedral sites along the c-axis (Vajda et al. 1986).

0

D

o

° l 3~

C

a ¢ 3 q a/¢~ _ L

0 o o 1:3

0 0 o

~ :o o~ o

°! 0 0

~o o o o Q

0 o o

~ °° o

0

O

° I o

D o

O

O

O I1

o

O

Fig. 7. Various two-chain arrangements made of D-D pairs on adjacent c-axes along the b-direction in a*-LttI) x. Open circles, metal atoms; open squares, empty T-sites; solid squares, occupied T-sites (Blaschko et al. 1989a).

Table 4 Characteristics of the ordered H-configurations in ct*-RH(D, T)x

R c/a T~ù (K) E b (meV) Xmax Rel. H D H D

S c

Y

Ho

Er

Tm

Lu

Lu a (lla)

L u a (llc) Lu ~ (T for D) '

1.592 152.5(5)

1.571 168.0(5)

1.570 174(1)

1.569 173(2)

1.571 169(1)

1.583 166(1)

160.5(5)

173.0(5)

179(1)

177(2)

174.5(10)

172(1)

174.0(5)

174.0(5)

180(1)

50(2)

61(2)

64(2)

63(2)

57(2) 0.35(2) 1

70(2) 0.20(1) 2

- 0.03 3

72(2) 0.065 4

- 0.11(1) 5

73(3) 0.20(1) 6

65(3) 7

74(3) 7

8

a Single crystal.

References (1) Daun et al. (1986b) (2) Vajda et al. (1987c) (3) Daou et al. (1987)

(4) Daou et al. (1981d) (5) Daou et al. (1981e) (6) Daou et al. (1986e)

(7) Vajda et al. (1986) (8) Jung and Lässer (1988)

HYDR.OGEN IN RARE-EARTH METALS, INCLUDING RH2÷ x PHASES 221

1 9 0 ~ , ,

1 8 0

v "~"~ 1 7 0

I.--

1 6 0

1 5 0

D

1 .57 1 .58 1 .59

c/a

Fig. 8. The anomaly temperature as a function of c/a- ratio of the metal R in c¢-RH(D)x systems (Daou and Vajda 1988).

in the case of deuterium and another 5-6 K for tritium (in the case of ct*-LuTx, Jung and Lässer 1988), again stressing the H mobility as an essential parameter for ordering; the same is true for the binding energy Eb.

3.2. il-Phase dihydrides

As already discussed in sect. 2, it has been a problem for some time to separate the excess hydrogen atoms, x on O sites, from the "pure" dihydride H atoms on T sites in the non-stoichiometric dihydrides RH2+x. Thus, the assumption was that, for therrnodynamic reasons, the O sites began to be occupied before a complete filling of the T sites: that, for example, RHzl0 contained 1.95 H atoms on T sites and 0.15 H atoms on O sites. As has been shown above, the substoichiometry of the "pure" dihydride depended more on the metallurgical state of the specimen than on thermodynamics. It is, in faet, possible to obtain practically ideal T-site occupation in the dihydride, to +0.01 H/R, when using high-quality samples and working at high temperatures. In the following tables, we shall, therefore, either specify the "pure" dihydride concentration (when possible) or at least separate the x-coneentration, avoiding the sum composition, e.g. giving RH1.97+0 ' 13 instead of RH2.10.

In table 5 the lattice parameters, a, of the cubic [3-RH2+x phases are presented as a funetion of x at several temperatures. The static and therrnal lattice expansions have been added when available. We note the well-known general contraetion (negative Aa/Ax- values) of the dihydride lattice with increasing x, which is an expression of the strong ionic character ofi ts interaction with the excess H atoms on O sites; an example is given in fig. 9 for the oase of YH2+x, where the break in the a(x)-curve at x = 0.10 H/Y indicates the limit of the pure [3-phase.

Another phenomenon which can be observed through the lattice parameter is the low- temperature ordering within the x-sublattice. It can either lead to a tetragonal distortion of the originally cubie unit cell given as a and e in table 5, such as in the cases of LaH2+x (fig. 10, for x = 0.80, Klavins et al. 1984), CeH2+x (fig. 11, for x = 0.16, Boroch and Kaldis 1989) and SmH2+x (for x=0.3, Greis et al. 1981, Zogal and UHéritier 1991) or just give rise to anomalies in the thermal behavior of the lattice parameter a such as e.g. in the case of GdH2+x for x ~> 0.2 (fig. 12, Chiheb et al. 1993). Such ordering was first established in

222 P. VAJDA

Table 5 Crystallographic parameters of the [3-phase, RH(D)2+x

x (H(D)/R ratio) Aa/Ax

T (K) a (Ä) 104a (at.% H, D) -l

Aa/AT a

(104/K) Ref.

Sc 0 298 4.784

Y 0 298 5.2095

873 5.248

0D 298 5.1996

873 5.242

0 298 5.2082 -0.50

0.05 298 5.2070 -0.50

0.10 298 5.2056 -0.50

0 90 5.2032 -0.45

0.05 90 5.2019 -0.45

0.10 90 5.2002 - 1.15

La 0 298 5.6698

773 5.7005

0 298 5.6656 -1.3

0.27 298 5.6498 -1.3

0.53 298 5.6270 -1.3

0.60 298 5.6239

30 a 5.604 (a) 5.619 (c)

0.80 298 5.6218

30 a 5.598 (a) 5.654 (e)

0.92 298 5.6186 -0.5

0.28D 298 5.6295 -1.8

0.41D 298 5.6164 -1.8

0.70D 298 5.6176

30 a 5.600 (a) 5.616 (c)

0.78D 298 5.6111

30 a 5.587 (a) 5.649 (c)

0.91D 298 5.6100

1.00D 298 5.6064

Ce 0 298 5.581

0.16 298 5.650 -1.8

200 a 5.5500 (a) 5.5727 (c)

0.24 b 340 5.5612

200 a 5.5455 (a) 5.5715 (c)

1

2.3 2

18 2

2.2 2

20 2

5.0 3

5.5 3

6.2 3

4.2 3

2.6 3

2.0 3

6.0 4

16.5 4

5

5

5

5

5

5

5

6

5.0 7

7



Table 5, continued

R x (H(D)/R ratio) T(K) a (Ä) Aa/Ax 104a

(at.% H, D) -~

Aa~AT a

( 10-6/K) ReL

Ce (cont'd)

er

Nd

Sm

0.63 b

0.90

0.18D

0.29D

0.9D

0.96D

0

0.25

0.47

0D

0.29D

0.48D

0

0.27

0.47

0D

0.09D

0.29D

0

0.15

0.26

0.45

0D

0.20D

0.40D

0.33

0.33D

285

300

295

4.2 a

370

4.2 ~

295

295

298

298

298

298

298

298

298

773

298

298

298

298

298

298

295

85

295

85

295

85

295

85

295

295

295

295 a

295"

5.5375

5.5364

5.565

5.547 (a) 11.13 (e)

5.564

5.544 (a) 11.125 (c)

5.546

5.536

5.518

5.498

5.483

5.505

5.484

5.472

5.4689

5.5005

5.465

5.444

5.430

5.455

5.447

5.431

5.3773

5.3738

5.3693

5.3648

5.3637

5.3556

5.3521

5.3430

5.365

5.3518

5.3400

3.7780 (a) 5.3647 (e)

3.7716 (a) 5.3503 (c)

-1.35

-1.35

-1.35

-1.25

-1.25

-1.25

-1.4

-1.4

-1.4

-1.5

-1.5

-1.5

-1.0

-1.1

-1.0

-1.35

-1.2

-1.2

-1.2

10

13.5

8.1

19.5

4.3

2.1

5.6

3.4

4.5

3.2

9

9

10

10

10

10

10

I0

4

4

10

10

10

10

10

10

11

11

11

11

11

11

11

11

12

12

12

12

12


224

Table 5, continued

R x(H(D)/Rraf io)

E VAJDA

2" (~) a (Ä) Aa/Ax 104a

(at.% H, D) -~

Sm (cont~) 0.3 295 5.365

98 a 5.344 (a) 5.362 (c)

Gd 0 298 5.3022

773 5.3305

295 5.3025

95 5.2978

0.10 295 5.2990

95 5.2935

0.19 295 5.2960 -0.65

95 5.2905 -0.7

0.25 295 5.2926

95 5.2845

Tb 0 295 5.2485

90 5.2430

0.09 295 5.2433

90 5.2375

0.24 295 5.2380 -0.7

90 5.2308 -0.85

Dy 0 298 5.2060

773 5.2365

295 5.2056

90 5.1996

0.10 295 5.2020

90 5.1950

0.19 295 5.2000

90 5.1931

0.27 295 5.1988 -0.5

90 5A911 -0.7

Ho 0 295 5.165

Er 0 298 5.1290

773 5.158

Tm 0 298 5.0925

773 5.122

Yb 0.55 295 5.192

0,27 500 5.253

0,44 517 5.192

0.70 295 5.178 -1.8

Aa/AT a

(lO-~/K) Rel.

13

13

8.3 4

16 4

4.4 14

4.4 14

5.0 14

5.0 14

5.3 14

5.3 14

14 14

3.8 14

7.6 14

3.4 14

7.15 14

7.15 14

8.0 14

3.8 14

8.0 4

17 4

5.6 14

5.6 14

6.6 14

6.6 14

7.7 14

5.8 14

14 14

4.9 14

15

7.8 4

15.5 4

7.8 4

23.5 4

16

16

17

1


HYDROGEN IN RARE-EARTH METALS, INCLUDING RH2+ x PHASES

Table 5, continued

225

Aa/Ax R x (H(D)/R ratio) T (K) a (Ä) 104a

(at.% H, D) -I

Aa/AT a

( 10-6/K)

Rel.

Yb (cont'd) 0.5 295 5.192

0.6 295 5.180

0 <x < 0.5 473-573 5.253

0.5D 295 5.182

0.6D 295 5.168

0 <x < 0.5D 473-573 5.236

Lu 0 298 5.0338

773 5.062

0D 298 5.022

773 5.054

6.5

14.5

7.6

18

18

18

18

18

18

18

4

4

4

4

a cubic --~ tetragonal transformation below ~200-350 K.

References (1) Bashldn et al. (1978) (2) Juekum (1980) (3) Daou and Vajda (1992) (4) Bonnet and Daou (1977) (5) Klavins et al. (1984) (6) Kaldis et al. (1987)

b Corrected data.

(7) Boroeh and Kaldis (1989) (8) Boroch and Kaldis (1987) (9) Schefer et al. (1984) (10) Müller et al. (1979) (11) Daou et al. (1989b) (12) Greis et al. (t981)

(13) Zogal and UHéritier (1991) (14) Chiheb et al. (1993) (15) Pebler and Wallaee (1962) (16) Drulis et al. (1988a) (17) Iwasieczko et al. (1992) (18) Knappe and Müller (1986)

5.203

5.202

5.201

5.200

YH 2+x

"X~ ,~~~ a 295K

I J 0.1 0.2

x ( a t . H / Y )

v

m

- 5.208

- 5.207

- 5.206

5.205

Fig. 9. Lattice parameter of YH2+ x as a function of x at room tempera~re and at 90 K (Daou and Vajda 1992).

t h e s y s t e m CeD2+x ( a n d l a t e r c o n f i r m e d fo r R D 2 + x w i t h R = L a a n d Pr ) w h e r e s u p e r l a t t i c e

r e f l e c t i o n s h a v e b e e n f o u n d b y n e u t r o n s c a t t e r i n g ( T i t c o m b et al. 1972, K n o r r e t al. 1978

a n d F e d o t o v et al. 1982) , i n d i c a t i n g d i f f e r e n t o r d e r e d s t r u c t u r e s as a f u n c t i o n o f x .

226 E VAJDA

5.67

5.65 Z

o3 Z o 5,65 W

I--

~5.61 -

5.59 o

I I I I l

La H2.8o

Q T , , ~ . . ~ r . ~ x x x x I

I I I I I I 50 I00 150 200 250 500

TEMPERATURE (K)

Cell p a r a m e t e r s vs. t e m p e r a t u r e

C E H 2 . 1 6

Fig. 10. Temperature dependence of the lattice parameters for LaHz80, showing the cubic---* tetragonal transformation below 248 K (Klavins et al. 1984).

CUB. , a --~ 5 . 5 7 5 0

1 TETR., a

TETR., c -~

5 . 5 7 0 0

- 5 . 5 6 5 0

-15.6600

5 . 5 5 5 0

5 . 5 5 0 0

I I I I I I I I I I I I I I J

110 130 150 170 190 2 1 0 2 3 0 2 5 0 2 7 0 2 9 0 3 1 0 330 3 5 0 3 7 0 T e m p e r a t u r e K

Fig. 11. Temperamre dependence of the lattice parameters for CeHz~ 6, showing the cubic--*tetragonal transformation below 290 K (Boroch and Kaldis 1989).


a(Ä)

5.300

5.295

5.290

5.285

Gd H 2.x

X=0

I I I_ 20 100 200 T(K) 300

j ' > < - > <

Fig. 13. Ni3Mo-type structure (DO2z) of the octahedral H- sublattice in TbD2+ x as determined by neutron diffraction by André et al. (1992). Solid circles (small), Tb atoms; dashed solid circles, H atoms on T sites; solid circles (large), H atoms on O sites.

Fig. 12. Temperature dependence of the lattice parameters for GdH2+x, for 0~<x~<0.25. The anomaly near 180K for x = 0.22 and the strong non-linearity near room temperature are indications for x-superlattice ordering (Chiheb et al. 1993).

In heavy ~-RH2+ x systems, the first manifestations of a possible structural transformation (SRO and LRO) in the H sublattice were signalled as resistivity anomalies in [3-TbH(D)2+x in the range 150-250K (Vajda et al. 1985, 1987a). These manifestations were purity dependent, in the sense that hydrides from originally 3N-metal exhibited an LRO H sublattice starting with higher x-concentrations than for those from 4N- material, indicating hydrogen trapping by impurities. Detailed neutron scattering studies on this system (André et al. 1992) have shown that the octahedral D-atoms were ordering for 0.1 ~< x ~< 0.25 in a DO22 structure (Ni3Mo-type) such that every occupied (420)- plane was followed by three empty ones (fig. 13) corresponding to a stoichiometric composition of TbD2.25. Similar ordering manifestations were observed in most other ~-RI-I2+x systems, and in table 6 we have listed the anomaly temperatures for typical selected concentrations as determined from resistivity, specific heat or differential thermal analysis (DTA) measurements. Figures 14-16 illustrate the situation by presenting partial phase diagrams in the (T, x)-ranges of the ordered H-configurations. We note maxima close to partieular compositions, e.g. CeHz5 or GdHz25, possibly corresponding to stoichiometric compound formation and, in several cases, the presence of more than one anomaly. The one at lower temperature is possibly due to a SRO-mardfestation. Furthermore, one remarks that the ordering temperatures are roughly the same throughout the R-series, which means that the H mobility for the same concentration x is independent of R and the lanthanide contraction is only manifest as a diminishing solubility limit in the ~-phase, Xömax. A theoretical treatment of the phenomenon was undertaken by Ratishvili and Vajda (1993) and Ratishvili et al. (1993, 1994) using the mean-field approximation of the static-concentration-waves theory, who were able to reproduce parts of the phase diagram in the TbH2÷x and in the CeH2+x systems.

228 l a. VAJDA

Table 6 Anomaly temperatures due to H-ordering in ~5-RH(D)z+x-systems

Y

La

Ce

Pr

Nd

x (H/R ratio) T~ (K) Rel.

0.05 150 1

0.085 150 1 200

0.10 200 1

0.6 197 2

0.7 239 3

0.75 241 4

0.76D 251 5

0.8 248 2

0.91D 251 5

1 241 6 270

1D 211 6 230.5 233.5 274

0.I 215 7

0.2 250 7

0.25 300 7

0.34 340 7

0.6 275 7

0.65 240 7

0.7D a 250 8

0.75D a 317 8

0.86D a 292 8

0.81 240 9

0.08 170 10

0.23 >300 I0

0.53 >300 10

0.61 >300 10

0.65 253 3,10

0.76 250 10

0.06 185 11

0,1 200 11

0.19 265 11

0.32 >300 11

0.44 >300 11

0.56 165 11 295

R x (H/R ratio) Tan (K) Ref.

Nd 0.64 210 11

0.65 245 11 280

0.70 240 3

Sm 0.075 t80 12

0.16 180 12

0.26 240 12

Gd 0.08 155 13,14

0.14 155 13,14

0.17 185 13,14

0.16D 210 13,14

0.215 285 13,14

0.25 255 13,14

0.25D 260 13,14

0.305 200 13,14

Tb-3N 0.045 150 15

0.10D 150 15

0.15 150 15

0.215 170 15

Tb-4N 0.07 190 16

0.15 215 16

0.20 250 16

0.25 >300 16

Dy 0.055 155 17

0.10 150 17

0.13 175 17

0.18 170 17

0.22 260 17

0.27 210 17

Ho 0.065 150 18

0.11 160 18 230

0.14 240 18

Er 0.045 150 19

0.05D 150 19 175

0.088 180 19

0.09D 230 19

0.091 225 19


HYDROGEN 1N RARE-EARTH METALS, INCLUDING RH2+ x PHASES

Table 6, notes

229

a Corrected data.

References (1) Daou and Vajda (1992) (2) Klavins et al. (1984) (3) Bieganski and Drulis (1977) (4) Chowdhury et al. (1989) (5) Ito et al. (1982) (6) Ito et al. (1983) (7) Burger et al. (1991)

(8) Abeln (1987) (9) Libowitz (1972) (10) Burger et al. (1988) (I1) Daou et al. (1992) (12) Vajda et aI. (1989b) (13) Vajda et al. (1991a) (14) Vajda and Daou (1993)

(15) Daou et al. (1986a) (16) Vajda et al. (1987a) (17) Vajda and Daou (1992a) (18) Daou and Vajda (1994) (19) Vajda and Daou (1994)

300

280

2 6 0

~_ 2 4 0

220

200

/ f

I

/

/ cu b!

/o

I I I \ o

cub. l * Iv

/ ffI

I I ~ o

1 t I

1 8 0 I I I I

0.5 0.6 0.7 0.8 0.9 1.0 X (D. H/La)

Fig. 14. Partia! phase diagram of LaH(D)2+x , for 0.5 <~x ~< 1, constructed from specific-heat and X- ray diffraction data. Solid line, deuterium; dash- dotted line, hydrogen; dash double-dotted line, phase boundary between the compositions LaD2.50 and LAD2.75; dotted line, phase boundary between LaDz75 and LaD3 (Kai et al. 1989).

400

300

200 p,,

100

Ce H 2,x

~I ,o,ra0o°ù,

-I

I (a)! 0 0.5 x( at.H / Ce)

0.2 b I I

T(K

201

1 0 0 i I r 0 O .2

0.4 0.6 0.8 x ' I ~ I

I J

(b) I p I i

0.4 0.6 0.8 x(at.H/at.Nd)

Fig. 15. (a) Partial phase diagram of CeH(D)2+x , for 0 ~<x ~< 0.96, constructed from resistivity (solid circles) (Burger et al. 1991), differential thermal analysis (solid squares), and neutron data (erosses) (Abeln 1987). (b) Partial phase diagram of NdH2+x, for 0 ~< x ~< 0.65, constructed from resistivity data (Daou et al. 1992).

230 P. VAJDA

3 0 0 0

A 25O

2 0 0

150

0.1 0.2 0 .3 x ' ' ' ( a )

I I I

0.1 0.2 0 .3 x(at .H(D) /at .Gd)

p..

300

200

100

I I

I3 /oI--~-

IJ 5 10 15 20 25

(b)

x (at%)

300

1-

2OO

DyH 2+x

B 'SROi I I

' ' ( c )

100 r 0 0.1 0.2 0.3

x(at .H/at .Dy)

Fig. 16. (a) Partial phase diagram of GdH2+ x (open circles) and GdD2+ x (solid circles) for 0 ~<x ~< 0.3, constructed from resistivity data (Vajda et al. 1991a). (b) Partial phase diagram of TbD2+ x constructed from neutron scattering data (André et al. 1992), indicating the ordered DO22 structure in the low-T [3-phase for x>0 .1 . (c) partial phase diagram in DyH2+~, for 0 ~<x ~< 0.3, constructed from resistivity data (Vajda and Daou 1993).


Table 7 Lattice parameters of the orthorhombic dihydrides of Eu and Yb at 295 K (from Haschke and Clark 1975)

R a (Ä) b (Ä) c (A)

Eu 6.254 3.806 7.212 Yb 5.889 3.576 6.789

3.2.1. The hydrides of Eu and Yb The pure dihydrides of the divalent metals Eu and Yb are orthorhombic and their lattice parameters are given in table 7. In the case of Yb, however, the metal ion in the higher hydrides undergoes a valency change (cf. sect. 5) permitting the reappearance of the fcc B-phase (see table 5).

Table 8 Lattice parameters of the h.c.p, trihydrides ~/-RHz+ x at 295 K

R x (H/R ratio) a (Ä) aù = ax/~ c (Ä) Refl

Sc 0.65 a 3.380 5.854 6.135 1 Y 1.00 3.672 6.360 6.657 2 Nd 0.82 3.849 6.667 6.893 3 Sm 0.82 3.7870 6.559 6.7926 4

0.84D 3.7726 6.534 6.7632 4 Gd 0.91 3.73 6.46 6.71 5

1 3.76 6.51 6.705 6 Tb >0.9 3.700 6.409 6.658 7 Dy >0.9 3.671 6.359 6.615 7 Ho >0.9 3.642 6.308 6.560 7 Er >0.9 3.621 6.272 6.526 7 Tm >0.9 3.599 6.234 6.489 7 Lu >0.9 3.558 6.163 6.443 7

a Under a pressure of

References (1) Bashkin et al. (1978) (2) Forker et al. (1994) (3) Bashkin et al. (1977)

10 kbar.

(4) Greis et al. (1981) (5) Sturdy and Mulford (t956)

(6) Zogal (1987) (7) Pebler and Wallace (1962)

3.2.2. y-Phase trihydrides Since the original experiments of Pebler and Wallace (1962) very little ädditionat work on the structural properties of the hexagonal trihydrides has been performed. Mansmann and Wallace (1964) have established that the deuterium atoms in HoD3 occupied three different non-equivalent sites, attributing its structure to the space group P 3cl (D4d). This led to a reassessment of its lattice parameters as well as ofthose for the other R-trihydrides by introducing a larger basal-plane constant, an = a ß . As to newly discovered systems, there are the trihydrides of Sc produced under high pressure (Bashkin et al. 1978) and those ofNd (Bashkin et al. 1977), which we added to the older values listed in table 8.

232 R VAJDA

4. Kinetics and thermodynamics

In this section, we shall present the available data conceming the dynamical properties of hydrogen in its various ordered and disordered configurations, both in the (x- and in the B-phase. This applies to different activation energies (or enthalpies) and to more specific vibrational properties such as hydrogen local modes, Debye temperatures OD of the metal-host lattice, and Einstein temperatures OE of the H sublattice. The data are taken from nuclear magnetic resonance (NMR) experiments, inelastic relaxation (internal friction and Gorsky effect), inelastic and quasi-elastic neutron scattering (INS and QENS, respectively), H-"defect" recovery after quenching or electron irradiation, and, generally from thermal dependeneies of various physical properties (e.g. resistivity, lattice parameters, specific heat) measured at elevated temperatures.

4.1. a-Phase soßd solutions

In table 9 we give the activation energies for diffusion Ed, and the corresponding relaxation times r0, considering ~ = r0 exp(Ed/kBT), mainly for the three systems which have a low-temperature solid solution «*-phase with R = Sc, Y, and Lu. All techniques consistently yield Ed-values in the range 0.5-0.6 eV for the four measured systems. The relaxation times exhibit relatively large fluctuations, but show a tendency, at least in the case of ct-ScHx, of increasing r0 with increasing concentration x. The latter seems reasonable considering the correlation between the attempt jump frequency to an adjacent site, f 0 = rö 1, and the probability x, that such a site is occupied, f0 e( (1 -x ) .

The H(D)-concentration dependence of the internal-friction amplitude Q-l, in the ct*-RH(D)x systems with R=Sc, Y, and Lu (Vajda et al. 1990b, 1991c, 1983a) is very close to linear; this raised some questions as to the origin of the observed peaks, since a H-H pair interaction could be expected to yield a square x-dependence. The problem was solved by Cordero (1993) who calculated the relaxation strength of tetrahedral H - H pairs, taking into account blocking effects and the formation of complexes; he found a roughly linear x-dependence for concentrations c > 0.01.

Low-temperature results of experiments with positive muons (Gygax et al. 1993) have given an activation energy of 0.054 eV in SCH0.0», which is an order of magnitude lower than the Ed'S of table 9, but seems to correspond nicely to the pair-binding energies Eb, obtained from resistivity studies (=0.05 eV, cf. table 4 in sect. 3) and f-rom neutron scattering (=0.06 eV, Berk et al. 1991), as weil as to the energy for fast localized motion observed below room temperature in NMR (=0.052eV, Lichty et al. 1989). The same mechanism could be responsible for the very low-T peak (< 1.4 K) in the elastic energy loss in YH0.1, attributed to tunneling between T sites (Cannelli et al. 1991, Leisure et al. 1993a).

Quenching across the ordering temperature in the «*-phase (cf. sect. 3) or energetic electron irradiation at low temperature creates disorder in the ordered configurations, i.e. hydrogen "defects" which, upon heating, migrate and recombine in a recovery stage centered at a peak temperature Tp. Applying a chemical rate equation to the recovery

HYDROGEN IN RARE-EARTH METALS, INCLUDING RH2+ ~ PHASES

Table 9 Diffusion energies and relaxation times of H in ct-RH(D)~

233

R x E« (eV) r o (10-14s) Rel.

Se 0.057 0.54(1) 0.7 1

0.11 0.54 1.2 1

0.27 0.505 3.3 1

0.1 0.61 » (3) 0.07 2

0.2 0.57(3) 0.7 2

0.2D 0.58(3) 1.0 2

0.3 0.54(3) 3.6 2

Y 0.20 0.51 (2) 9.1 3

0.20 0.57(3) 0,3 4

0.10 0.57(3) 9 5

0.14 0.62(3) 0,6 5

0.20 0.56(5) 10 5

0.20D 0.55(3) 50 5 Gd 0.05~0.09 0.52(2) 6.1 6

Lu 0.20 0.56(5) 10 7

0.20D 0.64(3) 0.37 7

0.15 0.52(2) 20 8

0.05 0.57»(2) 9

0.05D 0.63(2) 9

References (1) Han et al. (1987) (2) Vajda et al. (1990b) (3) Lichty et al. (1987)

(4) Anderson et al. (1989) (5) Vajda et al. (1991e) (6) Herbst and Kronmüller (1981)

(7) Vajda et al. (1983a) (8) Torgeson et al. (1989) (9) Völkl et al. (1987)

Table 10 "Defect" migration energies, Ere, at a peak temperature, Tp, after a quench or electron irradiation, in «-RH(D)x

Em (er) T o ~ ) Ref. H D H D

Sc 0.27(2) 0.30(1) 152 160.5 1

Y 0.20(2) 0.27(2) 163 169 2

Er 0.26(3) 0.28(3) 172 177 3

Lu 0.26(2) 0.27(2) 164 170 4

Refer«nces (1) Daou et al. (1986a) (2) Vajda et al. (1987c)

(3) from Daou et al. (1981d) (4) Daou et al. (1986c)

p r o c e s s ( a f t e r d e t e r m i n a t i o n o f i t s r e a c t i o n o rder , 7 ~ 1), o n e c a n d e t e r m i n e t h e m i g r a t i o n

e n e r g y E m o f t h e r e c o v e r i n g d e f e c t s p e c i e s , g i v e n i n t a b l e 10. O n e n o t e s t h a t E m ,,~Ea/2,

234 P. VAJDA

Table 11 Enthalpies of solution in the heavy lanthanides for ~t-RH(D)2-systems

R H s (eV) Rel. H D

Gd Tb

Dy

Ho

Er Tm

Lu

0.19

0.15(1)

0.16(1)

0.14(1)

0.05-0.08

0.037(5) 0.025(5)

0.15(1) 0.15(1)

0.125(1)

Beaudry and Spedding (1975) Daou et al. (1981a)

Daou et al. (1981a)

Daou et al. (1981a)

Beaudry and Spedding (1975)

Beaudry and Spedding (1975) Beaudry and Spedding (1975)

Table 12 Hydrogen local mode energies in ct-RH(D)x

B(meV) [Ic .Le

Ref.

Sc

Y

Ce f.c.c.

Tm

Lu

0.19D

0.33D

0.05 0.16

0.25 0.34

0.10-0.18

0.03-0.06

0.18D

0.04

0.06 0.06D

0.19D

0.19

77

78 101

103

103

103.5, 106

99, 102.5

96

73, 77

96(1)

I00 (97, 101)

75

68, 76 102, 105

107

148

147.5

147.5

134

96

134

103

100 143.7

References (1) Blaschko et al. (1989b) (2) Udovic et al. (1990) (3) Udovic et al. (1992)

(4) Anderson et al. (1986, 1988) (5) Wegener et al. (1980) (6) Bennington et al. (1991)

(7) Pleschiutschnig et al. (1991) (8) Blaschko et al. (1988) (9) Udovic et al. (1993)

indicat ing that Em refers to the same diffusion process as Ed, the latter conta ining in

addi t ion E r ~ E m , an energy for ( thermal) "defec t " formation, a parameter which has

a l ready been disposed o f in the queneh or i rradiat ion proeess. The Tp-values cor respond

to the anomaly tempera tures Tan f rom table 4, emphas iz ing that the same order -d i sorder

process in the H sublattice is at the origin o f both manifestat ions.


O r,D

.o

Z

I I I I i I

c~-YH x (80K) ~ x=0.18

~/~ .~~~o 't~ "+'~~ ~,~o.o~

B ~-~ ' ~ x = O . O 3

I I I I L I 90 100 110

Energy Loss (meV)

Fig. 17. Inelastic energy loss spectra of ct-YH x for various x, obtained at 80 K by neutron scattering. Note the mode splitting for higher x, indicative of H - H pair interaction (Udovic et al. 1993).

Z

120

I I I i I I

c-axis e o o o e ° °

o •

O

, * c~-ScHo.a4 • ** (8K)

• *%, + +

• * + • + ,~'

• * * + + , * , + a-LuHo19

ù, : . ~ '. +++++;2:; +

m • • a-YHo,la

= = , = m = (8K)

næU næn

i 90

1

mode

I I I I I 100 110 120

Energy Loss (meV)

Fig. 18. Inelastic energy loss spectra along the c-axis at low temperature for c-ScH0.34, «-LuH0.~9 and «-YHats , indicating progressive mode splitting with increasing lattice constant of the system (Udovic et al. 1993).

The heat of solution, Hs, of hydrogen in the heavy lanthanides has been determined for the system RH(D)0.2 from equilibrium measurements in the a ~ ~ reaction and is given in table 11. The strongly decreasing tendency of Hs with increasing Z of the rare earth correlates with the decreasing atomic volume and with the inereasing melting temperature of R.

INS and QENS inelastic loss spectra have been measured to determine the local mode energies of H and/or D in a few c~-phase systems (table 12). They generally exhibit a soft vibration parallel to the c-axis and a 25-30% harder mode perpendicular to it. High- resolution spectra of the e-axis modes reveal a temperature- and concentration-dependent splitting (fig. 17) representing the dynamical coupling of the H-H pairs in the SRO chain structure of the «*-phase systems (cf. figs. 6, 7). A comparison of the three systems measured shows a sharpening of these bands in the order of increasing atomic volume (Se ~ Lu ~ Y), implying an increasing extent of the chain ordering (fig. 18).

The Debye temperatures OD in these solid solutions increase, as expeeted, with increasing H coneentration, such as roughly linearly in the ease of c~-LuH(D)x: OD(a-LuHx) = (157 + 75x) K in the interval 0 ~< x ~< 0.133, as determined from energy-

236 E VAJDA

280 ' ~ f , i

260 ~ LuD°'m» / '~

~ 2 4 0 200

,~~° ~____~~ I _ _ _ i . ~ ,~° I-- / / / / ~ /

w

uJ 200 ,~ 160

18 0 140

!6C 0 50 I00 150 200 250 300

TEM PERATURE (K}

Fig. 19. Debye temperature of Lu (dotted line) and of LuD«Is3 (solid line) as a function of temperature. Note the shifted ordinate scales (Vajda et al. 1986).

dispersive X-ray diffraction on a single crystal (Metzger et al. 1985) and from heat- capacity measurements (Vajda et al. 1986, fig. 19). A ~gD determination of a-LuHx with 0 ~< x ~< 0.18 from low-T specific-heat measurements (Thome et al. 1978) yielded a sharp maximum at 203.8 K for x = 0.015, attributed by the authors to H tunneling (ef. also sect. 5 for the electronic specific-heat eoefficient ~'eh and the above diseussion of T-T tunneling observed in inelastie relaxation measurements). Ultrasound spectroscopy measurements by Leisure et al. (1993b) yielded a general increase of all elastic constants upon addition of H into scandium" Ob(SeD0.18) was determined to 371 K as eompared to Ob(Sc)= 355 K, at room temperature. Finally, in the case of a-ErH(D)x, Cp measurements have given the same OD = 192-t-5 K for all x in the interval 0 ~<x ~< 0.03 (Schmitzer et al. 1987).

4.2. il-Phase dihydrides

In table 13, we present for four RH(D)2+x systems the diffusion energies and relaxation times of hydrogen atoms thermally excited out of the oceupied T sites in the pure dihydrides or of those occupying oetahedral sites in superstoiehiometric compounds. In LaH2+x, which remains the only system where extensive E« determinations as a function of the excess-hydrogen eoneentration x have been made (Schreiber and Cotts 1963), one notes a remarkable deerease of Ea with inereasing x, implying a lowering of the potential barrier for O-O and O-T jumps. The reason for this is not quite clear but might be related to the increasing ionicity, i.e. inereasing Coulomb repulsion between the x-atoms. We have also included the results of a ~t+-diffusion experiment, for completeness.

The "defect" migration eharacteristies following a queneh across the temperature region where possible H sublattiee ordering oeeurs are given in table 14. The wealth of data collected during the recent years in resistivity studies by the group at Orsay has permitted the establishment of two general phenomena. First, Em seems to follow


Table 13 Diffusion energies and relaxafion times in [3-RH(D)2+x

237

R 2 + x E a (eV) r o (s) Ref.

Sc 1.98 0.35(3) 8 × 10 -~° 1 Y 1.98 0.435(5) 2x 10 -12 2

1.98 0.34(9) 3 1.92-2.09 0.39 4

La 2.00 0.415(4 ) 3 × 10 -11 5 2.15 0.49(5) 3.5 × 10 -14 5 2.36 0.40(4) 2× 10 -13 5 2.27 0.35 1.3×10 -12 2 2.47 0.30(4) 7 × 10 -12 5 2.61 0.22(3) 4.5 X 10 -12 5 2.75 0.185(5) a 3 × 10 -1°" 6 2.85 0.14(2) 4.3 × 10 -12 5

3D 0.20 1.5× 10 -~2 7 Lu 2.03 0.33(3)~).38(4) 10 TM to 5× 10 -~° 1

a W_diffusion

References (1) Zogal et al. (1984) (2) Phua et al. (1983) (3) Bamfather et al. (1989)

(4) Sttdar et al. (1993) (5) Schreiber and Cotts (1963)

(6) Chowdhury et al. (1989) (7) Borsa et al. (1982)

the same x-dependence as Ed (cf. table 13 for LaH2+x), confirming the same potential- barrier mechanism for the two processes. Second, there exists, above a certain x-value (whieh depends on the rare earth under study), more than one "defeet"-recovery process, centered at different temperatures Tp and governed by different Ere. Figure 20 gives as an

15

Ë: 10 :=L

2" <~

t ,

5 ~~~, ~ |

~ 1 / I I I t I I | I I I 1 0 0 150 2 0 0 1 4 0 1 8 0 2 2 0

T(K)

o,~ 0 .3

o.2 "»

? 0.1

Fig. 20. Annealing of the quenched-in resistivity Apq, with its derivative on the right hand side, of GdH(D)2+x with x=0.25, showing an isotope effect on the peak temperamre near 160K and a second recovery process near 200K (Vajda et al. 1991a).

238

"Defect" migration energies, Ere, at a

P. VAJDA

Table 14 peak temperature, Tp, after a quench, in [3-RH(D)~+x

R x E m (eV) Tp (K) Rel.

Y 0.095 0.35(2) 172.5 1 0.1 0.31(2) 180 1

Ce 0.10 0.245 183 2 0.20 0.17 177 2 0.25 0.14 180 2

Pr 0.08 0.19 175 3 0.23 0.175 151 3 0.53 0.13 130 3 0.61 a 131 3

Nd 0.10 0.11 182 4 0.19 a 0.10 176.5 4 0.24 0.12» 167 4 0.32 0.14 156.5 4 0.60" 0.24 140 4 0.64 a 0.24 148.5 4

Sm 0.075 0.17(1) 170 5 0.16 0.13(1) 153 5

Gd 0.08 0.125(2 ) 144.5 6 0.12 0.13(2) 146 6 0.16D 0.12(2) 174 6 0.17 0.15(2) 172 6 0.25 a 0.09(1) 156 6

R x E m (eV) Tp (K) Rel.

Gd (ct'd) 0.25D" 0.095(1 ) 161 6 Tb 3N 0.10D 0.28(2) 150 7

0.15 0.24(2) 146 7 Tb 4N 0.15 0.15(2) 176 8

0.20 0.¤4(2) 173 8 Dy 0.055 0.16(2) 148 9

0.10 0.16(2) 146 9 0.13 0.145(1 ) 167 9 0.18 a 0.20 165 9 0.22 a 0.14 155 9

Ho 0.065 0.15 146.5 10 0.11 a 0.27 183 10 0.14 0.25 183 10

Er 0.048 0.18 141 11 0.045D 0.16 148.5 11 0.054 a 0.18 141 11

0.31 177 11 0.05D a 0.17 148 11

0.30 177.5 11 0.09 0.29 177 11 0.09D 0.28 178 11

a Complex recovery,

References (1) Danu and Vajda (1992) (2) Burger et al. (1991) (3) Burger et al. (1988) (4) Daou et al. (1992)

(5) Vajda et al. (1989b) (6) Vajda et al. (1991a) (7) Daou et al. (1986a) (8) Vajda et al. (1987a)

(9) Vajda and Daou (1992a) (10) Daou and Vajda (1994) (11) Vajda and Daou (1994)

170

150

130

0.1 I I

0.2 0.3 x(at.H(D)/at.Gd)

0 . 2

O . 1

w

Fig. 21. Activation energies E a, of the recovery process for the quenched-in resistivity in GdH2+ x (open symbols) and GdD2+ ~ (solid symbols) and the peak temperatures Tp, where this process takes place (Vajda et al. 1991a).

HYDROGEN IN RARE-EARTH METALS, INCLUDING RH2+ ~ PHASES 239

example the annealing curves of quenched GdH(D)I.%+0.2», exhibiting two recovery stages at Tpl = 156K (161 K for the deuterated specimen) and at Tp2 --- 195 K, respectively. This behaviour is most probably due to the recombination of defects created in different ordered configurations, of SRO-type for the former and of LRO-type for the latter. Figure 21 shows the x-dependence of the temperature for the principal recovery stage Tpl , and of its Em for all measured GdH(D)2+x specimens, indicating the appearance of a new process near x = 0.15, which corresponds nicely to the suggested phase diagram shown in fig. 16a. The same phenomenon is also clearly visible in the systems HoH2+x and ErH2+x (table 14), with simple recovery for low and for high x-values occurring at a low and at a high Tp, respectively, but with complex recovery containing both processes at intermediate x.

Table 15 presents the enthalpies for dihydride formation Hf; th•se for solution of hydrogen Hs in the ~-phase, obtained from phase-equilibria smdies; and the defect- formation energies Ef, as determined from the thermal expansion coefficients. Breaks in the x-dependencies of Hs are manifestations of structural transformations or of metal- insulator transitions or both (figs. 22, 23).

-I O0 e~ -1-

õ E

«

.E ZE "~ -50 ÷i

e4 -200 -1-

ö E

- 1 5 0 e., 13

._c -1 O0 u~

"w

0 . 3

, i J , i i

iii • III Olll 0 0 0 0 0 • • • • 6 •

O0 OoO O o a b s o r p t i o n

o • d e s o r p t i o n o"

1 J I I I I

1 I I I I I

ooO ° • @

o a b s o r p t i o n

• d e s o r p t i o n l I a L

0 . 5

a t o m r a t i o

O•e 00 ~o

o oO • e~ . o o

o

H / P r

1.0

Fig. 22. Variation of the solution enthalpy and entropy of H in the PrH2+ x system, for 0.55 ~< x ~< 0.97 (Ohki et al. 1989).

- I O0 ' I ' , , ,

o o q o o o o o õ •

r- " - o a b s o r p t i o n o o "I- 0 000000 "~ -50 • d e s o r p t i o n o ÷i o

t [ I I i |

e4 -200 , I , , ,

Œ o a b s o r p t i o n

ö • d e s o r p t i o n o • c o ° o ° •

- 1 5 0 • e •

-~ ~ o o °°° .~~ • ~ O0 0000 0

-I O0 o U3

0 . 3 0 . 5 .0

a t o m r a t i o H / N d

Fig. 23. Variation of the solution enthalpy and entropy of H in the NdH2. x system, for 0.32 ~<x~< 0.95. The break near x = 0.65 indicates a phase transformation (cf. fig. 15b) (Ohki et al. 1989).

In table 16 the Debye temperatures OD and the Grüneisen temperatures On are given, as characteristics of the acoustic dihydride lattice vibrations. On is generally obtained from specific-heat measurements, while On results from the fit of a Grüneisen law to low-T resistivity measurements (e.g. Daou et al. 1984a). The simultaneously obtained electron-phonon coupling constants will be given in the next section (sect. 5, table 19). An empirical formula connecting the Debye temperatures of a hydride and its metal

240 R VAJDA

Table 15 Enthalpies for dihydride formation, Hf; for H-solution in I]-RH2÷:systems, H~; for the transformation

RH 2 ~ RH3, Htr; and activation energies for defect formation in the dihydride, E r

R 2 + x -H« (eV) - H s (eV) Htr (eV) Ef (eV) Rel.

Sc 2 1.04 1

Y 2 1.18 1

La 2 1.08 1

2.2-2.6 0.51-0.39 0.41 0.25 2,3

Ce 2 1.00(1) 4

2.2-2.5 0.435-0.39 0.48 0.35 2,5

2.4-2.9 0.37-0.26 6

Pr 2 1.11 7

2.4-2.6 0.42-0.36 0.39 0.30 2,5

2.55-2.75 0.42 a 0.38 7

Nd 2 1.08 0.44 3,7

2.4-2.6 0.385-0.32 0.36 2,7

2.3-2.65 0.38 b 0.35 7,8

Sm 2 1.05 1

2.3-2.45 0.405-0.34 0.40; 0.42 2,6,8

Eu 2 0.96 9

Gd 2 1.02 0.49 1,3

>2.3 0.48 8

Tb 2 1.11 1

>2.25 0.50 8

Dy 2 1.06(1) 0.53 4,3

>2.25 0.48 8

Ho 2 1.17 1

>2.15 0.40 8

Er 2 1.06(1) 0.60 4,3

>2.10 0.43 s 8

Tm 2 1.00 s 0.66 4,3

>2.05 0.56 s 8

Yb 2 0.94 1

Lu 2 0.96(I) 0.75 4,3

2.05 0.54 8

a See fig. 22. b See fig. 23.

References (1) Libowitz and Maeland (1979) (2) Messer and Park (1972) (3) Bonnet and Daou (1977)

(4) Boeva et al. (1986) (5) Viallard and Daou (1972) (6) Ohki et al. (1984)

(7) Ohki et al. (1989) (8) Mintz et al. (1976) (9) Toguchi et al. (1982)

HYDROGEN IN RARE-EARTH METALS, INCLUDING RH2+x PHASES 241

Table 16 Debye, O D, and Grüneisen, Oü, temperatures of RH(D)z+x hydrides

R 2 + x O D (K) O G (K) Rel.

Se 1.88 465 1

1.99 759 2

2 710 3

Y 1.81 340 1

1.93 537 2

2 525 3

La 1.9-3.0 319-382 4

(1.91-3.0)D 341-379 4

Pr 2.65 356 a 5

Eu 1.85 b 170 6

Tb 1.93 240 7

Ho 1.86 240 7

Er 1.81 381 2

Yb 1.80 ~ 239" 6

1.90 b 243 a 6

2.37 350 ~ 8

2.41 352 a 8

Lu 1.82 240 1

2 361 9

a corrected data.

Referenees (1) Daou et al. (1984a) (2) Beattie 1972) (3) from Kai et al. (1989) (4) Kai et al. (1989) (5) Drulis and Bieganski 1979)

b orthorhombic.

(6) Drulis and Stalinski (1989) (7) Lucasson et al. (1985) (8) Drulls et al. (1988b) (9) Thome et al. (1978)

host, OD(MH) and OD(M), with the formation enthalpy HF, has been proposed by Jacob et al. (1981):

OD(MH) ]2 [ OD(M) J = 3.7HF (eV/atom) 0"87.

Finally, neutron-scattering expeilments on several RH(D)2+x-systems revealed loealized vibrational modes ascribed to H vibrations on O and on T sites, which are summarized in table 17. A third (higher-energy) peak is sometimes observed in superstoichiometric samples and attributed to the lowered symmetry of a tetrahedral site (T*) in the neighborhood of an x-atom. The role of SRO and LRO in the Ho-sublattice upon the evolution of the local modes (both their concentration- and temperature dependence) in a seiles of RH(D)2+x hydrides (R = Y, La, Ce, Tb, Dy) was demonstrated recently by

242 P. VAJDA

Table 17 Hydrogen local mode energies in [5-RH(D)2+x

2 + x E v (meV) O T T*

OE 0~) Ref.

Sc

Y

La

Ce

Pr

Nd

Eu

Gd

Tb

Dy

Ho

Er

1.88

1.85D

2

2D

1.81

1.80D

1.94

2.18

2.28

2.99

2.98

2.98D

1.98

2.01D

2.12D

2.72D

2.96

2.97D

1.94

1.98

1.7D

2.3D

2D

2.5D

2.06

1.85

2D

1.89

1.85D

1.93

1.93D

1.83

1.93D

1.86

1.86D

1.98

1.88

1.76D

127

90

103

73(2) 109(3)

72 100 127

65 120

61(2) 127(4)

43(2) 93(3)

75 106

54 75.5

75 83; 95

-45

63(2)

47(2)

78(2)

52

55

52

67; 82

77; 103

60; 72

128(4)

92(3)

108

120(3)

76

76

75

69

123(3)

129 a

91"

126

86

96

80-85

1570 1

1110 1

2

2

1475 1

1043 1

3

4

5

5

4

4

6

6

7

6

4

4

3

4

3

3

8

8

4

12

12

1392 9

984 9

1415 10

1000 10

1438 9

1017 9

1460 I0

1032 10

3

1485 9

1050 9



Table 17, continued

243

R 2 +x E,, (meV) 0 T T*

oB (K) Ref.

Tm 1.96

1,90D

Yb 2

1,98

Lu 1.82

1.82D

89

89; 115

130

131; 138

1508

1066

1531

1083

9

9

11

12

1

1

Average of three infrared lines.

References (1) Daou et al. (1984a) (2) Rush et al. (1966) (3) Hunt and Ross 1976) (4) Parshin et al. (1978)

(5) Kamitakaharaand Crawford(1982) (6) Vorderwisch et al. (1980) (7) Glinkaetal. (1977) (8) Knorr et al. (1978)

(9) Burger et at. (1984) (10) Lucassonetal. (1985) (11) Maeland (1970) (12) Drulis (1993)

Udovic et al. (1995). We have added the Einstein temperatures OE, characteristic for the optical vibrations in the pure dihydride lattice, corresponding to hcoT = kBOE, which has been determined (Daou et al. 1984a) from an analysis of the high-T resistivities of RH2 and RD2 in the harmonic approximation, i.e. under the assumption of OE(H) = BOE(D). They increase with decreasing lattice parameter, i.e. with decreasing M-H distance, resulting in higher optieal mode energies for the heavier lanthanides and for Sc.

5. Electronic properties

The controversy concerning the electronic state of hydrogen in rare earths between the protonic and the aniõnic model has been settled in favour of an elaborate form of the latter, namely the "hydridic" model proposed by Switendick (1970-1972) in the early 1970s and developed later by Gupta (Gupta 1978, Gupta and Burger 1980), Kulikov (1985) and others. In this model, confirmed by numerous experiments, especially during the past two decades, hydrogen forms within the metal bonding and antibonding R-H and H-H (for RHy with y >~ 2) bonds located below the d-band of the host. A direct consequence is the decrease of the carrier density upon hydrogenation, and a modification of the Fermi surface, where the Fermi level Er is pushed downwards. This results, for example, in an apparent diminution of the Fermi-surface anisotropy as observed in resistivity studies on single crystals of c~-LuDx (Vajda et al. 1986) and in changes of its nesting features in the case of non-stoichiometrie [~-phase hydrides as suggested from magnetic manifestations in ~-GdH2+x (Vajda et al. 1991a). This will be treated in detail in the next section. The decrease of the conduction-electron density is responsible for a general decrease of all related processes such as s-d scattering, electron-phonon coupling and, in particular, the magnetic interactions mediated through the Ruderman-Kittel-Kasuya-Yosida (RKKY) electron polarization.

244 P. VAJDA

The eleetrie resistivity p, which is the principal subject ofthis seetion, evolves in several stages. First, p inereases when dissolving H in the a-phase, «-RHx, where the hydrogen atoms aet as impurity scattering eenters for the eonduetion eleetrons; it deereases in the dihydride, ~-RH2, reaehing lower values than in the pure metal, mainly due to reduced eleetron-phonon eoupling; then the resistivity increases again upon adding of excess (x) H atoms in solution on octahedral sites, [3-RH2+x; fmally, the hydrides end up as insulators, going through a metal-semieonduetor (M-S) transition somewhere between RH2 and RH3 (in the B-phase for La to Pr, in the y-phase for all heavier lanthanides and Y):

R ~ a-RHx + [3-RH2(_o) --~ ~-RH2+x --- RH3(_~).

In the following we shall present detailed diseussions of the various specifie c- and B-phase systems, treating - in addition to the resistivity data - heat-eapaeity measurements and, when available, results from optieal and photoeleetron speetroscopy. Specific phenomenä such as superconductivity and the Kondo effects will be treated, while a speeial subseetion shall be devoted to the field of the M-S transitions where reeently a new impetus has been given.

5•1• Solid solutions

The effeet of dissolving hydrogen atoms as scattering centers for the conduction electrons can be measured either in the metastable low-T a*-phase or in the high-T solid-solution a-phase. Thus, the specifie resistivity of an added H atom is measured near 0 K as a residual-resistivity increase Aprrées in the former ease, and at some higher temperature in the latter. The condensation of hydrogen in the ordered H-H ehain eonfiguration of the a*-phase at 150-180K (cf. seet. 3) does not seem to influenee Ap~ s signifieantly (it is praetically the same at 4.2 K and at room temperature, cf. figs. 24, 25, 28), though a slight decrease of the eleetronie charge density was observed in NMR-measurements in a-ScHx and a-YHx upon H ordering (Liehty et al. 1989). In table 18 we present the values for Ap~ s in the six existing a*-phase systems, both at zero eoneentrations (i.e. determined from the initial slope of the experimental p(x)-eurves) and at maximum eoneentrations, the latter being usually smaller due to a saturation effect. The few investigations of a possible isotope effeet on Ap~ s were not eonclusive in the case ofa*-YH(D)x (Vajda et al. 1987e) but showed a deerease with inereasing isotope mass in the ease of a*-LuH(D, T)x, possibly implying a deereasing vibration amplitude of the interstitial hydrogen isotope (Daou et al. 1986e, Jung and Lässer 1988)•

In figs. 24-28 we show several isothermals, p(x), of different RH(D)x-systems, which are useful for the determination of the solubility llmlt Xma x (ef. table 1), sinee the lower resistivity of the ~-phase (see next subseetion) leads to a decrease ofAp~ s when exeeeding the a-phase limit into the two-phase (a+ [3)-region; we also list these Xma x « values in table 18.

The eleetronic speeific-heat coeffieient Yel is extraeted from an extrapolation to zero of the low-temperature linear part in the ep/T=f(T) plot. It usually inereases with

245

a Determined from the initial slope of the ,o(x)-dependence. b Determined at the maximum concentration in the c-phase.

R Xma x ~pH~(0) a (~tff2 crrdat.%H) Ap,o~(Xm=)H b (p~ff2 cm/at.%H) Rel.

Sc 0.30 2.3 1 0.35 3.6 2.6 2

Y 0.19 3 0.20 4.2 3.4; 3.1; 3.2(D) 4,5

Ho 0.03 3.8 2.4 6 Er 0.03 3.6 3.3 3,7

0.06 3.51Ic 3.111c; 3.0Hb 8 Tm 0.11 4.2 3.25 3,9

9.011c; 3.911b 6.0llc; 3.911b 10 Lu 0.205 3.75 3.15 3,11,12

3.3; 3.1(D) 3.05; 2.95(D) 13,14 2.30") 15

0.1839 2.15(D)11c; 3.75(D)llb 16

References (1) Jensen and Zalesky (1980) (2) Daou et al. (1986b) (3) Beaudry and Spedding 1975) (4) Vajda et al. (1987c) (5) Juckum (1980) (6) Daou et al. (1987)

15(:

(7) Daou et al. (1981d) (8) Vajda et al. (1987b) (9) Daou et al. (1981c) (10) Vajda et al. (1989c) (11) Daou and Bonnet (1974)

(12) Daou et al. (1976) (13) Daou et al. (1986c) (14) Daou et al. (1981e) (15) Jung and Lässer (1988) (16) Vajda et al. (1986)

0

4 2 K

lOO

E 0 c

¢Z

50


Table 18 Residual resistivity increase per at.%H, Ap~s,n for a-RH(D, T)~

o I I 1 I I _ 0 0.1 0 .2 0 .3 0 .4 0 .5

x=at ,H(D) /at .Sc

Fig. 24. Resistivity isothermals for ScH x (open symbols) and ScD x (solid symbols) at 4.2 K and 0°C as a function of H(D)-concentration x, indicating maximum solubility for Xm~=0.35(2)atM(D)/Sc (Daou et al. 1986b).

246 E VAJDA

+ 1 2 0

8 0

50 ~ 1oo

ù ~ ~ ~o ~ 4 40 '~ «

6O

'0 Q I I I I I 0 0 . 0 5 0 . 1 0 0 . 1 5 0 . 2 0 0 . 2 5

x . a t . H ( D ) / a t . Y

Fig. 25. Resistivity isothermals for YH x (open symbols) and YD x (solid symbols) at 4.2 K and 0°C as a function of x, indicating maximum solubility at Xmax = 0.20(1)at.H(D)/Y (Vajda et al. 1987c).

1 5

1 4 0 .~, ~ ~ ~ - ~ ù ~ ~ " ' '~ -~"

I / ~ - ~ * ~ + ~

1 2 0 / I 1 I I I 0 . 0 1 . 0 2 . 0 3 . 0 4 . 0 5

x / a t . H ( D ) / a t . H o

1 0 E o c - t

t¢ ¢1

15 .=

lO c~

5

0 o o:os ö s e "

x ( a t . H / a t . E r)

Fig. 27. Residual resistivity of ErH~ crystals ]Ic as a function of x, indicating maximum solubility for Xmx = 0.065(5) at.H/Er (Vajda et al. 1987b).

Fig. 26. Néel temperature TN, and residual resistivity of HoH~ (open symbols) and HoD x (solid symbols) as a function of x, indicating maximum solubility at Xm~x = 0.03 at.H(D)/Ho (Daou et al. 1987).

increasing x, sometimes passing through a maximum, such as in the case of ct*-LuHx, where it rises sharply from 7el=8.35mJ/gatK 2 at x = 0 to 11.34 for x=0.015 and then decreases continuously to 6.96 at the c-phase limit (fig. 29); Thome et al. (1978) and Stierman and Gschneidner (1984) attribute the sharp peak to hydrogen tunneling.


P42K et PSOK P296K~ 9C mu. Qcm in u.Qcm J120

8C ~ t 1]0

7( f J ~ " ~ "296K 4100

~o ~ ~ ~ -~.~~ ~o

30 60

20 50

10 1,0

I I I I I 0.1 0.2 ot.H/otLu

Fig. 28. Resistivity isothermals tor LuH x at 4.2 K, 90 K and 296 K as a fimction of x, indicatJng maximum so]ubi]ity for x=a * = 0.20(])at.H/Lu (Daou et a]. ] 976).

g-

i

e i

è

12 ~ r

il

I0

9

8

7 \

\

\

4

3

2

I

0 ~ 0 10 20 30 40

\ \

\ \

T~ 0 2

Qt%H

\ \

\ \

\ %

1 I t 50 60 70

ATOMIC PERCENT HYDROGEN

I.[xiO -6 «

Q9

80

Fig. 29. Variation of the electronic specific-heat coefficient in the Lu-- H system as a function of the H- concentration. The inset shows the variation of the room temperature magnetic susceptibility. Note the abscissa scale, with cn=H/(Lu+H) (Thome et al. 1978).

248 E VAJDA

The determination of Yel in magnetically ordering systems is more delicate because of the superposition of a magnetic term in Cp, which has to be subtracted. The only two existing experiments on tx-ErHx and ct-TmHx gave, for the former: )'el = 10.4- 13.0mJ/gatK 2 for 0 ~<x ~< 0.03 at.H/Er (Schmitzer et al. 1987), and for the latter (which is uncertain): )'el = 10.5-17.5 mJ/g atK 2 in the interval 0 ~<x ~< 0.03 at.H/Tm (Daou et al. 1988e).

5.2. (Mainly) t~-phase hydrides

The mobility (and sometimes also the number) of the charge carriers in the dihydrides depends strongly on the possible presence of ordered and/or disordered electronic and/or atomic configurations. The electronic configurations concern the magnetically ordering dihydrides and will be treated in detail in sect. 6. The atomic configurations occur in the superstoichiometric RH2+x systems where the octahedral excess hydrogen atoms x exhibit a tendency to order in SRO or LRO structures for concentrations exceeding a certain R-dependent value Xcrit, somewhere in the range 0.05 ~<Xent ~< 0.15 (for a discussion see sect. 3). The ordering transitions occur at various temperatures between 150 and 350 K, depending on the system and on the concentration x, and exert an increasing influence on the conduction-electron scattering as measured through the electric resistivity. Therefore, in table 19 the electric resistivities have been listed for judieiously selected concentrations in all measured RH2+x systems, at three different temperatures: pres, obtained, where feasible, by extrapolation to zero K, in order to eliminate as much as possible the influence of spin-disorder scattering; Pls0n, showing the role of the phonon contribution to scattering; P295 K, adding the part due to structural disorder of the hydrogen superlattice (where existing), which has already broken down in most cases at room temperature. Systems with concentrations close to the B-phase limit somefimes undergo temperature-dependent M-S transitions, which are marked by an asterisk in table 19, and shall be discussed in more detail in a special subsection below.

In table 20 the electronic specific-heat coefficients )'el of the measured RH2+x systems are presented. The high values in the cases of R = Ce and Yb are indicative of heavy- fermion behaviour in these valence-fluctuating compounds (see below). Otherwise, the hydrides have rauch lower yel-values eompared to the et-phase systems (el. sect. 5.1), which is mainly a consequenee of the strongly decreased density of stares at the Fermi surface N(Ev). In the same table the acoustic and optic electron-phonon coupling parameters, A).ae and A).opt, are given, obtained from an analysis of resistivity data (see sect. 4). The coupling to the optical (hydrogen) phonons is found to be much weaker than that to the acoustic (host-metal) phonons, due to much smaller partial densities of states in the former~case. In addition, the authors (Daou et al. 1984a) observed a strong reduction of the acoustic coupling parameter when going from the metal to the dihydride, A~ac(R)»A~ac(RH2), confirming the relation between N(EF) and )'el

mentioned above.


Table 19 Residual resistivities, p~~, and the resistivities at 150K and at 295K, for ~-RH2+x systems

R 2 + x p~~ (gQcm) PlSOK (I xf~cm) P295K (~t~cm) Rel,

Sc 1.88 0.49 3.0 7.7 1

1.85D 0.42 2.9 8.5 1

Y 1.97 0.38 4.7 12.2 2,3

1.97D 0.21 4.9 12.8 2,3

1.97 + 0.04 11.9 17.7 26.5 2,3

1.98 + 0.085 22.3 28.4 37.5 2,3

1.97+0.10 a 143.7 141 1551, 175T 2,3

La 2.00 1.37 8.7 19.0 4

2.00D 0.50 8.4 19.5 4

2.70 a 190 700 5

2.80 a 350 3000 5

2.90 a 2500 9 x 104 5

2.93 5x 107 5× 105 5

Ce 2.00 0.8 19.2 26.4 6

2.02 5.5 21.5 29.2 6

2.02D 8.0 23.3 31.5 6

2.10 27.8 44.0 59.2 6

2.25 16.0 46.5 122.5 6

2.40 120 365 735 6

2.65 980 2500 5850 6

2.70 a 1100 5000 5

2.78 a 800 1000 5

2.81 l x l07 8×104 7

2.85 ~109 3× 10 » 7

Pr 1.97 -4.0 17.6 29.0 8,9

1.98+0.08 30.7 41.5 59 8,9

1.97 + 0.23 17.4 46.2 145 8,9

1.98 + 0.53 22 87 400 8,9

1.96+0.61 83.8 210 620 8,9

1.97 + 0.76 112 460 860 8,9

Nd 2.00 0.18 12,8 23.1 10

2.00D 0.32 12.5 22.9 10

2.06 29.65 43,0 59.5 10

2.19 23.4 47.3 115.5 10

2.32 30.0 60.4 147 10

2.44 39.3 70 160 10

2.56 47.8 121 420 10

2.63 465 900 2300 10

2.65 a 1900 3400 6600 10

continued on hext page

250 E VAJDA

Table 19, cont inued

R 2 + x Pres (~tQem) PlSOK (~tff2cm) P295K (~tff2cm) Rel.

Sm 1.98 8.8 29.5 39.0 11

2.00+0.03 16.7 42.8 55.7 11

1.98 + 0.075 25.0 45 58.5 11

2.00+0.16 61.6 76 96.5 11

1.96+ 0.26 86.7 117 177 11

Gd 1.99 0.20 35.5 44.05 12,13

1.85D 0.4 35.6 45.0 12,13

1.97+0.04 14.65 43.5 52.3 13

1.98+0.14 72 70.0 81.4 13

1.98+0.25 51.3 88.4 138.2 13

1.97+0.305 a 139 415 498 14

Tb 1.96 0.5 24.9 33.3 14,15,16

1.91D 0.8 25.3 34.1 14,15,16

1.97 + 0.07 29.3 32.3 39.0 14,15,16

1.96+0.15 46.5 48.5 67.5 14,15,16

1.97+0.20 50.2 57.4 92.1 14,15,16

2.00+0.245 23.8 85 155 14,15,16

Dy 1.99 0.45 16.6 24.5 17

1.93D 0.5 16.7 25.4 12

1.97 + 0.02 5.45 20.8 29.65 18

1.98+0.10 38.8 48.8 59.8 18

1.98 + 0.18 52.75 62.6 77.2 18

1.99 + 0.22 43.4 63.7 117. 18

1.99 + 0.27 47.4 61.3 93 18

Ho 2.00 0.4 11.5 19.5 17

1.86D 2.1 13.3 23.4 19

1.99 + 0.02 23.5 28 40.0 20

1.98 + 0.08 57 60.5 74 20

1.98+0.12 a 190 171 1991, 204T 20

1.99+0.14 a 455 355 3701, 380]" 20

Er 1.95 <0.5 7.9 15.0 17

1.76D < 1.5 9.4 17.6 12

1.96 + 0.03 12 20.5 28.8 21

1.985 + 0.07 29.5 36 47 21

(1.98 + 0.09)D a 167 165 1971, 223]" 21

1.985 +0.091 a 360 295 3201, 340T 21

Tm 1.96 0.19 9.15 17.2 12

1.90D 0.19 9.25 18.2 12

Yb 1.90 1013 7

2.33 5x 10 s 102 5 22

2.62 >109 5×103 1 22

eontinued on next page


Table 19, continued

25t

R 2 + x Pres (p~~'2cm) P,50K (~t~'2cm) P~951~ (gff~cm) Rel.

Lu 1.98 0.10 4.6 11.0 23

1.93D 0.12 4.7 12.0 23

(1 .99+ 0.03)D 3.45 18.8 41.7 23

(1.99 + 0.06)D 50 280 612 23

1 .98+0.15 112 649 t335 23

1.97 + 0.20 502 2165 3640 23

a M - S transition present.

References (1) Daou et al. (1984a) (2) Daou and Vajda (1992) (3) Vajda and Daou (1991) (4) Vajda et al. (1991b) (5) Shinar et al. (1988, 1989) (6) Burger et al. (1991) (7) Libowitz (1972) (8) Burger et al. (1988)

(9) Daou et at. (1989a) (10) Daou et al. (1992) (11) Vajda et al. (1989b) (12) Burger et al. (1984) (13) Vajda et al. (1991a) (14) Vajda and Daou (1993) (15) Daou et al. (1986a) (16) Vajda et al. (1987a)

(17) Daou et al. (1988b) (18) Vajda and Daou (1992a) (19) Lucasson et al. (1985) (20) Daou and Vajda (1994) (21) Vajda and Daou (1994) (22) Srnirnov et al. (1992) (23) Daou et al. (1988c)

5.2.1. Metal-semiconductor transitions

The first unambiguous observation of a temperature-dependent M-S transition was made on CeH2+x crystals for 0.7<~x~<0.8 by Libowitz and eoworkers (Libowitz and Pack 1969, Libowitz 1972). This transition was inverse to the classical behavior in that the specimens were metallic at low temperature (below a TM-S ~ 250K) and turned semiconducting above it. The authors related this electronic transition to a structural cubic--+ tetragonal transformation in the Ce lattice upon cooling. The experiments were recently repeated using a contact-free high-frequency technique (Shinar et al. 1988, 1989) eonfirming Libowitz' data on CeH2÷x and yielding new results on the system LaH2+x (fig. 30). The authors interpreted their data in the framework of a variable-range-hopping model (Shinar et al. 1990), reformulating the original proposal by Libowitz (1972) in particular. At low temperature, the conductivity is governed by a delocalized band at the Fermi energy associated with the superlattice which is formed by interacting vacancies on octahedral sites Vo. At higher temperature (and at lower Vo-concentrations, i.e. at higher x), this band breaks down leading to loealized states and loss of metallic conduction. The resulting effective energy gap varies between 36 and 280 meV in the range 0.80 ~< x ~< 0.90. LaH2.93 is already a pure semiconductor over the entire measured temperature range, with an intrinsic gap of 480meV, in the same way as CeH2.81 and CEH2.85 (Libowitz 1972).

Recently, M-S transitions with strong hysteresis effects have been observed by the group at Orsay in the heavy rare-earth dihydrides GdH2+x, HoH2+x, ErH2+x and in YH2+x, with a surprisingly low superstoiehiometry, of the order of x ~ 0.1-0.3 (Vajda and Daou 1991, 1994, Daou and Vajda 1994, see e.g. fig. 31). Again, it is clear that the M- S transitions are driven by the collapse of a superlattice but, this time, the structural

252 P. VAJDA

Table 20 Electronic specific-heat coefficient, V,j, and acoustic and optic electron-phonon coupling parameters, A~,a~ and

A~,opt, for RH(D)2÷x compounds

References (1) Daou et al. (1984a) (5) Sehlapbach et al. (1986) (9) Lueasson et al. (1985) (2) From Kai et al. (1989) (6) Drulis and Bieganski (1979) (I0) Drulis et al. (1988b) (3) Kai et al. (1989) (7) Drulis and Stalinski (1989) (11) Thome et al. (1978) (4) Abeln (1987) (8) Burger et al. (1984)

o r d e r i n g c o n c e r n s t h e direct o c t a h e d r a l H o l a t t i ce o f t h e x - a t o m s a n d not t h e i r V o -

v a c a n c i e s , s u c h as in t h e s u b s t o i c h i o m e t r i c t r i h y d r i d e s , d e s c r i b e d a b o v e . T h e f a c t t h a t

HYDROGEN 1N RARE-EARTH METALS, INCLUDING RH2+ ~ PHASES 253

Fig. 30. Normalized resistivity pn(T)=- ,o(T)/p(295K) of various LaH x speci- merls as a function of reciprocal temperature, showing the metal-semiconductor transition (Shinar et al. 1990).

Fig. 31. Temperature dependence of the electric resistivity of three YH2+ ~ specimens, in the relaxed (R) and in the quenched (Q) state, with x = 0.085, 0.095 and 0.10. Lower inset: enlarged view of the low-temperature minimum in the case of x = 0.085. Upper inset: a fit of the low-temperature part of the resistivity for x = 0.10 by an expression of the type p(T) =po(T/To) 1/2 exp(T/To) -v4, indicating a Mott mechanism as origin for the S-M transition (Vajda and Daou 1992b).

the transitions occur in these dihydrides at x-values close to the 13/(~ + y) phase boundary, is an indication that two factors are simultaneously required in order for the transitions to take place: (1) the existence of an order-disorder transformation in the x-sublattice and (2) a significant decrease of the carrier concentration, due e.g. to the presence of nuclei of insulating y-phase microdomains. This transition is manifest by a diverging resistivity (fig. 32, Daou and Vajda 1992). Furthermore, the higher the sample resistivity, the lower the TM-S (i.e. the weaker the Ho-superlattice); or, in other words, specimens with lower cartier density exhibit lower band stability. This rule seems to be valid for all investigated

254 R VAJDA

150 E o

Q.

100

0 0.05 I

0.1

œ ,

5.203

5.202

5.201

I 5,200

i p

5.208

~ l ~ j El 295K 5.207

- ' - ' - " - " ~ ' - P 5,206 =

5.205

a,S \ I I

0.1 x (~tt.H / y ) 0,2

50- P i ~

~ ~~"POK 0 I I 0 0.05 0.1

x(at.%H/at.%Y) Fig. 32. Resistivity isothermals at 0 K and at 295 K as a function ofx in the YH2+ x system. Note the diverging resistivity when approaching x=0.1. The inset gives the lattice parameter as a function ofx for T=90K and 295 K; the break at x = 0. I 0 indicates the ~-phase limit (Vajda and Daou 1992b).

systems, including LaH2+x and CeH2+x, covering three orders of magnitude in resistivity (Vajda 1995).

Finally, and most interestingly, these compounds exhibit an additional S-M transition (upon heating) at low temperatures, fig. 31 (Vajda and Daou 1992b), which has not been observed in the light RU2+ x systems. The p-minimum at TS-M occurs at 30- 120K in the various hydrides; its depth and position increase with increasing sample resistivity, with TS-M and TM-S approaching each other. This S-M transition might therefore be related to weak localization of the carriers due to scattering on atomic disorder of the excess H atoms. A fit of the experimental points to an expression of the type p(T)c((T/To) 1/2 exp(T/To) -1/4, where the prefactor eould be due to multiphonon scattering, is not unreasonable (note the inset concerning YH21 in fig. 31). The temperatures TS-M, TM-Sl and TM-sT (taken in cooling and heating runs, respectively) as weil as the eorresponding resistivities PM-S~ and PM-sT are collected in table 21 for

HYDROGEN IN RARE-EARTH METALS, INCLUDING RH2÷ x PHASES 255

Tabie 21 Temperatures for the various metal-semiconductor transifions, Ts_ M and TM_S, and the resistivities PM-S at

TM_S, for RH(D)2+x systems

R 2 +x Ts_ M (K) TM-S I (K) TM_ s ~ (K) PM-S I PM-S T Ref. (~t~ cm) (~f2 cm)

Y 1.97+0.095 37 n.o. a 283(1) n.o. 84 1,2

1.97+0.10 79 235(1) 256(1) 170 185 1,2

(1.96 + 0.095)D n.m. b n.o. 315(2) n.o. 60 3

(1.98 +0.10)D n.m. 248(1) 275(1) 120 138 3

La 2.70 n.m. n.m. 260(10) n.m. 850 4,5

2.80 n.m. n.m. 230(10) n.m. 5000 4,5

2.84 n.m. n.m. 220(5) n.m. 3 × 104 4,5

2.90 n.m. n.m. 260(3) n.m. 6 x 105 4,5

Ce 2.70 n.m. n.m. 260(10) n.m. 5500 4

2.78 n.m. n.m. 230(10) n.m. 2400 4

2.715 n.m. 245(5) n.m. 1×104 n.m. 6

2.74 n.m. 200(10) n.m. 1.7 x 104 n.m. 6

2.77 n.m. 220(5) n.m. 2.3 × 104 n.m. 6

Nd 2.00 + 0.65 n.o. 290(3) .n.o. 6500 n.o. 7

Gd 1.97+0.305 105 260(1) 265(1) 484 501 8

Ho 1.99+0.106 40.5 264(1) 273(1) 106 108 9

1.99+0.11 55 264(1) 285(1) 126 129 9

1.98+0.12 100 255.»(1) 260.5(1 ) 210 212 9

1.99+0.14 132.5 252(1) 255(1) 425 428 9

Er 1.985+0.088 32 242(1) 260(1) 160 170 10

1.985+0.091 120 237(1) 245(1) 383 395 10

(1.98 + 0.08)D 20.5 262(2) 290(1) 61.5 92.5 10

(1.955 + 0.09)D 79 244(1) 260(1) 223 239 10

(1.97+ 0.09)D 39 246(1) 257(1) 264 275 10

a n.o., not observed.

References (1) Vajda and Daou (1991) (2) Daou and Vajda (1992) (3) Vajda and Daou, unpubl. (4) Shinar et al. (1988)

b n .m, not measured.

(5) Shinar et al. (1990) (6) Libowitz (1972) (7) Daou et al. (1992)

(8) Vajda and Daou (1993) (9) Daou and Vajda (1994) (10) Vajda and Daou (1994)

all of the measured systems. (Also, note the remarks concerning surface M-S transitiõns at the end of sect. 5.2.3 and in the diseussion of CeH2+x in seet. 5.2.2.)

5.2.2. Discussion of specific hydrides The formation of the hydrogen superlattice in several LaD2+x compounds was clearly seen in the form of specific-heat peaks at 250-270 K (fig. 33) and also as breaks in the x-

256 R VAJDA

30

E 20 o

i

?

0 1 0

i I i I I

x = 2 . 5 5

2 .78 - -

1 O 0

X = 2 . 6 5

2 , 7 5 /" 2.80

<5-~ 2.90

200 300 T (K)

Fig. 33. Heat capacities of four LaD x specimens as a function of T, indicating a transition near 250K (Kai et al. 1989).

dependence of the electronic specific-heat coefficient ~/el, at concentrations corresponding to particular ordered configurations: x = 0.25, 0.5, and 0.75, by Kai et al. (1989). The small but definitely non-zero value for Yel in LaH(D)3.0 (see table 20) indicates the presenee of some charge carriers and is interpreted by the authors as due to a semi-metallic band overlapping the top of the valence band and the bottom of the conduetion band. In an EPR experiment detecting an Er3+-ion in LaH2+x, Drulis and Hoffmann (1985) have determined mainly a cubic Er environment in the case o fx ~ 0, but only Er sites of axial and orthorhombic symmetry for x > 0. The observation of superconductivity (for the first time in a rare-earth hydride) was reported in LaHzl0, with a Te =0 .17K (from Kai et al. 1989); this small value is due to a small electron-phonon coupling term and is consistent with the electronic structure calculations of Gupta and Burger (1980), who predicted a superconducting transition, if any, at a T e ~ 0 K. On the other hand, measurements in the two-phase system LaH2_x, in the range 0 ~< x ~< 2 between La and LaH2, have indicated percolating superconductivity of the La-metal, with a Tc = 6 K (corresponding to that of the fcc [5-La, stable above 300°C), up to concentrations of LaH1.75 and traces even in LaH2 (Vajda et al. 1991b).

With its broad R-phase range (extending up to x = I) and its hybridizing f-eleetron, CeH2+x is a fascinating system. It was here that Libowitz and Pack (1969) grew the first hydride single crystals, in which the first M-S transitions were observed in resistivity experiments (Libowitz and Pack 1969, Libowitz 1972) for 0.7 ~<x ~<0.8, see sect. 5.2.1 above. Shinar and coworkers, who later repeated Libowitz' experiments, give a nice illustration of the very x-sensitive behavior of CeH2+x specimens in fig. 34, where two samples exhibit a M-S transition near 250 K while the third one is a pure semiconductor with a gap of A E = 2 1 0 m e V below 240K and 100meV above. Zamir

HYDROGEN 1N RARE-EARTH METALS, INCLUDING RH2+ x PHASES 257

10.0

ä. 1.o

O.li

T(K)

5 0 0 5 0 0 2 0 0 160 i i i xX ~

x x

x x

× x

x x

x CeH z.81 ××

• CeHz.8 2 x x

o GeH 2 .78 x x

% % o O

i I L I

IO00/T(1/T)

Fig. 34. Normalized resistivity ph(T) =_ p(T)/ p(295 K) as a hmction of reciprocal temperature for three CeH2+ x specimens, showing M-S transltlons and pure semiconductor behaviour. The actual H content of the CeH2.81 sample was probably somewhat higher than indicated (Shinar et al. 1989).

et al. (1984) observed concentration-dependent M-S transitions in NMR-experiments for x > 0.65 attributed to a Mott mechanism. Schlapbach et al. (1986) reported peaks near the Fermi surface in photo-eleetron spectra below 70K for x=0.7, the latter interpreted as due to low-temperature removal of H atoms from the surface to the bulk and consequently pushing back of d-states towards EF to form a metallic band: a typical surface phenomenon. The complicated magnetic phase diagram due to the interplay between antiferromagnetic (AF) and ferromagnetic (FM) interactions will be treated in sect. 6, but here we have to mention the observation of an incoherent Kondo effect for 0 ~<x ~< 0.34 transforming into a coherent lattice below T ~ 20K (fig. 35, Vajda et al. 1990a, Burger et al. 1991). It is encouraging that the low-temperature behavior (for T ~< 2.5K, cf. inset in fig. 35) follows a T2-1aw, which is expected according to the heavy-fermion model, as postulated from the high value for the specific-heat 7eI (see table 20). At the same time, the quenehed CeH210 specimen (see inset in fig. 35) exhibits a flatter T2-dependence than the slowly cooled one, indicating an additional spin-wave contribution in the magnetically ordered lattice. In general, the order~lisorder situation of the octahedral (x) H atoms exerts a strong influence upon the electric resistivity, as seen from the x-dependence of the residual resistivity (fig. 36): two plateau-like regions for 0.1 ~< x ~< 0.3 and for x > 0.5 indicate the oecurrence of structural ordering of the x-atoms below a temperature Ts given in the inset (cf. also sect. 3). The effeet of a quench from room temperature across the ordering interval on p is seen in fig. 37 for three CeH2+x specimens, showing its low efficiency for the two x-richer samples where the ordering fange extends up to 300K and above; the recovery of the introduced Apq takes place at the low-temperature end of the ordering interval emphasizing the beginning mobility of the x-atoms (cf. seet. 4).

258 P . V A J D A

4 0

o 3 5 C

ùE 4- Q.'- 3 0

2 5

2 0 1

I I i I ~ l l ~ l I I i I ~ l l J [ J I

o

i I i I l l l t l ] ~ i I J ~ l ~ l i I

2 5 10 2 0 5 0 1 0 0 3 0 0 T(K)

Fig. 35. Resistivity of CeHz05 and CeHz10, after subtraction of the phonon contribution, as a function of log T in the relaxed (R, open symbols) and in the quenched (Q, solid symbols) stare. The inset shows the p=pr+AT 2 dependence at low temperature. The break near 200K is due to CF-splitting (Vajda et al. 1990a).

1 0 ¸

1 0 '

A E o c=

1 2

L ~ I ~ ~ . . . . , I

! ! / /

4 0 G

~°°~ \ ~ 2 0 C

10(~

I 2.5

t I t I i I

2 . 2 2 . 4 H / C e 2 . 6

Fig. 36. Residual resistivity of CeH2+ x and the structural ordering temperatures (inset) as a fimetion ofx (Burger et al. 1991).

Praseodymium forms, like La and Ce, B-phase hydrides up to x = 1, and this permits one to observe the approach towards a potential M - S transition. The resistivities o f three x-rich PrH2+x specimens (Burger et al. 1988) shown in fig. 38 indicate a strongly hysteretic structural transformation at 200 ~< T ~< 250 K for x = 0.76 which is probably a precursor for a M - S transition. The p-isothermals seen in fig. 39 show an ordering plateau for 0.1 ~< x ~< 0.5 at T ~< 200 K and probably another one for x > 0.6.

The resistivity isothermals of NdH2÷x exhibited in fig. 40 show an ordering plateau between x ~ 0 . 1 and 0.5 (just as PrH2+x) and a strong increase, up to 6000~tf2 cm, for x = 0.65 (close to the ~/(~ + y) phase boundary) as the concentration approaches the M - S transition (Daou et al. 1992).

In SmH2+x, where the phase boundary is at X~ax ~0 .45 (Daou et al. 1989b), the resistivity curves (fig. 41) show that SRO already begins below x = 0.1, and that a clear LRO-stage exists for x = 0 . 2 6 (Vajda et al. 1989b).

The heat capacity of the semiconducting orthorhombic europium hydride was measured by Drulis and Stalinski (1989) for EuHl.•5 and by Drulis (1993) for EuD2, who observed a k-type anomaly for the magnetic transition at Tc = 15.8K for the former and at Tc = 16.3 K for the latter (see sect. 6). The T-dependence of Cp above ~ 5 0 K exhibits a marked isotope effect which was analysed by Drulis (1993) on the basis o f hydrogen optical modes as determined from infrared absorption spectra.


B i 120 110

,oo / j _ T , ~ o

60- } 50-

~4o ~~o! ___~~_~_~~~ 20 90 4 0 ~ ~ 80 30 70 2O ~ ~ y . ~o 50 40 - o _ : i ~ ~ ~ ~ ~

a o ~ 20

10 I t I I I I 0 50 100 150 200 250 300 T(K) Fig. 37. Thermal variation of the resistivity for three CeH2+x specimens in the relaxed (open symbols) and quenehed (solid symbols) stare; Apq is the quenched-in resistivity inerease reeovering near 170 K (Burger et al. 1991).

The resistivity isothermals at zero K, Pres, and at room temperature/0295 K, of GdH2+x (fig. 42) are an indication of the LRO starting in the x-sublattice near x = 0.15 at low temperatures (Pres-maximum) and the continuous dissolution ofx-hydrogen atoms withõut ordering at 295 K (Vajda et al. 1991a). Fig. 43 shows the effect of quenching upon the x-sublattice and the magnetic transitions (see sect. 6) for x=0.16D and 0.21 as well as the M-S transition at 260 K for x = 0.305, at the [3-phase limit (Vajda and Daou 1993).

Figure 44 indicates, as in GdH2+x, the presence of LRO in the x-sublattice of TbH2+x for x ~> 0.15, an increasing ordering amplitude Apa~, and ordering temperature Ta~, with increasing x, while a small SRO-anomaly is visible for x=0.07 near 180K (Vajda and Daou 1993, Vajda et al. 1993). No M-S transition was observed in the sample with x =0.245 up to room temperature despite the proximity of the [3-phase boundary and

260 E VAJDA

o C

o .

9 0 0

8 0 0

7 0 0

6 0 0

5 0 0

4 0 0

3 0 0

I I I I

8 0 1 -

2 0

0 0 , 2 0 0 • 4 0 0 " 6 0 0 • 8 0

x ( a t . H / a t . P r )

I

,o+

+

o

o+ +•

+o

+ o

+,

B x = O ' 7 6

g + o

o ~ o OoO . °

• , o • o + .

• . . + ° + . • ~ o O

• o . o

• • - o ° -

I °

o o . o

~" x = 0 " 6 1 ; ~

oO

,o

o

o ° , , • . . % o-

2 0 0 ° . ' " "" " . "" o ° o,~,

o o o o o"

o oO° ,¢¢ ° o ° ,a'

oO ° ° .o "° "°

IO0"Z o ~° ° ° .°"

ù:il/o~2 .... ::o.:...o.o.O.o x=o.~~

I I J I [ 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0

T(K) Fig. 38, Thermal variation of the resistivity for three PrHz+ x specimens in the relaxed (open symbols) and quenched (solid symbols) stare; Apq is the quenched-in p inerease measured at 80 K and plotted as a function of x in the inset. Note the hysteresis between 200 and 250 K for x = 0.76 (Burger et al. 1988).

the large Apan; a transition is expected above ~320K. The evolution of the magnetic ordering will be treated in sect. 6.

The situation is similar in DyH2+x as for the other heavy lanthanide dihydrides (fig. 45). LRO occurs above x ~ 0.1, with the maximum effect apparently being attained before x=0.27 (Vajda and Daou 1992a). The latter alloy must already contain some y-phase precipitates, since its resistivity and the ordering amplitude are smaller than those for x=0.22 (el. also sect. 3). Ferreira et al. (1987) performed the first perturbed angular


8 0 0 ~ Pr H 2,x

7 0 0

600

OOK

500 E .i

«

4 0 0

3 0 0

200

100~- / ~ M / / / * ~ 4 . 2 K

O r I I I I O . 2 0 . 4 0 . 6 0 . 8 0

x ( a t . H / a t . t a t

Fig. 39. Resistivity isothermals of PrH2+ , at various temperatures as a function of x (Burger et al. t 988).

correlation (PAC) measurements on a rare-earth hydride with DyH1.83 and DyH2.95, in the pure [~- and y-phase, respectively. Along with the other data obtained, the authors estimated that the electronic contribution to the electric field gradient in the hcp y-phase is about three times that of the lattice contribution.

HoH2÷x (together with ErH2+x) is another superstoiehiometrie dihydride system exhibiting clear M-S transitions as observed in YH2+x (cf. fig. 32). They were measured for coneentrations 0.106 ~<x ~< 0.14, yielding effective gaps of a width AE ~ 25-45 meV, immediately after the appearance of LRO in the x-sublattice (Daou and Vajda 1994). This is seen in fig. 46, where the recovery of quench-induced disorder occurs in two

262 P. VAJDA

. ^4 0.1 0.2 0.3 0.4 0.5 0.6 ] u I J ] I I J

6

4

2

10 3

B, ~2 c~

295 K

2OO K

10«

5 }'18 fi]r x = ° I I I I I

0 0.1 0.2 0.3 0.4 0~5 0.6 Ö.7 x ( a t . H / at. N d )

Fig. 40. Resistivity isothermals of NdH2+x at various temperatures as a function of x (Daou et al. 1992).

180

110

90

6C

40

20

Sm H2+ x 160

= m ~ 140

120 / wo

. Y ~ ~ S - . , .o ~ .o

x~O 2O

o I k~ 510 110 150 200 2 ; 0 T/K 300

Fig. 41. Thermal variation of the resistivity for various SmH2÷ ~ specimens in the relaxed (R) and quenched (Q) state (Vajda et al. 1989b).

1OO E

o. 50

0 0 I 0.1 0.2 0.3

x(at.H(D)/at.Gd)

Fig. 42. Resistivity isothermals at 0 K and at 295 K of GdH(D)2÷x. The maximum of Pr near x=0.15 indieates low-temperature ordering (Vajda et al. 1991a).

~1_ ~ x--o.~o~ ~

300' ~ 110 IO0

!00 ~ " ~ ~ 6 D t 90 ~ ùo 100 Gd H 2.x 70

54K 60 f l ~ r I

400

30O

200

100 I

0L I r 0 100 200 300 T(K)

Fig. 43. Resistivity of GdH(D)z÷x, for x=0.16D, 0.21 and 0.305 in the relaxed (R) and in the quenched (Q) stare. Note the magnetlc transitions below ~100 K, the structural transformations around 200 K for all three alloys and the M-S transition near 260K for x=0.305 (Vajda and Daou 1993).


140

120

100

80

"-K

60

4 0

2 0

, /, TbH 2,x t

/ / x - - 0 . 2 4 5

_ . e ' Z : P ' W - x=O.15

_ ~ ~ "~x=O.07

0 100 200 300 T(K)

Fig. 44. Resistivity of TbHz+x for various x-values. Note the magnetic transitions below -40 K and the structural anomalies around 200 K. The inset shows the presence of an anomaly already for x = 0.07 due to SRO (Vajda and Daou 1993).

i I I

100 - Dy H 2.x

80 - ,~ ~ . ~ x--0.27 120

"K

4 0 -

J x=0,22

~ ~ 1 ~~°°

1 I I 5 0 0 100 200 T(K) 300

Fig. 45. Resistivity of DyHz÷ x for various x-values in the relaxed (R) and quenched (Q) state. Note the magnetic transitions below ~15 K (cf. fig. 64) and the stmctural anomalies around 200 K (Vajda and Daou 1993).

stages: the first corresponding to that seen for x = 0.08 (SRO), and the second being preponderant above x---0.1 (LRO). A similar situation has been described earlier in sect. 4 in the annealing of GdH2+x with x = 0.25 (fig. 20). Interesting enough, the strongly decreasing p in the semiconducting region above TM-S (~250 K) becomes smaller above T ~ 300 K than the lowest values in the metallic region at TS-M (~130 K). This is also seen in fig. 47, where the two isothermals p(0 K) and p(Tmax) cross each other near x = 0.13.

A similar situation is observed in ErH2+x (fig. 48), showing the transition from the purely metallic behaviour at low x to the M-S and S-M transitions at higher x, as soon as LRO becomes important (Vajda and Daou 1994). The effective gaps on the high- temperature side vary in the range 40 ~< AE ~< 60meV, while the low-temperature part shows localization behaviour down to the magnetically ordering domain (cf. sect. 6) where the separation between the two phenomena becomes difficult. The isothermal p(x) at room temperature (fig. 49) resembles that of YH2+x (fig. 32). The diverging part near x = 0.09 indicates the proximity of the ~/(~ + y) phase boundary.

The dihydride of Yb (like that of Eu) is non-metallic, since the Yb (and the Eu) ion is found in its divalent form. For higher hydrides, YbH2+x with x ~ 0.4, fluctuating valencies seem to prevail leading to heavy-fermion behaviour and high ye~-values (Drulis et al.

264

[ I I

Hort 2+x 500 ~ ,

o Ê " ~ x=0.14 500

400 400

1 3 2 . 5 K ~[

100 ~ ~ 2~4K

~ - x=0.08 60

2C ~::~2T3K 50

10 2 _ , ~ ~ * - ~ - * X " x=0 0' I I I

100 200 300 T(K)

Fig. 46. Resistivity of Hort2÷ x for various x-values in the relaxed (R) and quenched (Q) stare. Note the magnetic transitions below ~10K (cf. fig. 66), the structural anomalies around 200K (hysteresis!) and the M-S and S-M transitions for high x-values (Daou and Vajda 1994).

P. VAJDA

500

400i

A E 300 o

<3.

20O

100

o: 0

I I I

Hort 2+x

p (295K) or "T "

P ( M - S ) ~ (0K) I I

0.05 0.1 0.15 x(at.H/Ho)

Fig. 47. Resistivity isothermals at 0 K and at 295 K (of at TM-S in the case of M-S transitions) for Hort2+ x. Note the diverging p for x>0 .13 (Daou and Vajda 1994).

1988b and table 20). The latest work by Smirnov et al. (1992), who have measured the thermal conduetivity te, the eleetric resistivity as well as the thermoelectric power of YbH2+x in the range 0 ~< x ~< 0.7, indicates that the transition from the orthorhombic to the cubic phase (el. seet. 3.2.1) for x > 0.25 is accompanied by a valence change from 2 to 2.6. The authors attribute the thermal behaviour of t¢ and o f p in these compounds to an inhomogeneous mixed-valence system, aeting as a defeet-rich glass-like solid with carrier hopping between ions of different valencies, rather than to heavy fermions. The large ]tel would then be caused by the so-called non-magnetic atomic disorder (as analyzed by Gschneidner et al. 1990) due to the x-hydrogens, which gives rise to random exchange interactions between the Yb-ions and to spin-glass behavior.

For LuH2+x with 4N-pure starting material, the composition limit of the metallic ~- phase is rather low (cf. also seet. 2). This results in a percolating conduetivity due to the presence of the insulating y-phase as soon as x exceeds a few at.%, and at the same time blocking the ordering of the x-atoms (Daou et al. 1988b). An analysis of the resistivity data has given a large percolation faetor showing a tendency for the insulating phase to coat the metallic one along the grain boundaries. A small localization mimimum is seen for the samples with the highest p (but much lower in amplitude than in corresponding YH2+x, ErH2+x or HoH2+x samples, see above) and no M-S transition at high temperature,

HYDROGEN 1N RARE-EARTH METALS, INCLUDING RH2+ ~ PHASES

100 200 300 K

k = = ./,~-- 2,~SK --400 Q

100 ~ Q ~ " ~ ~ ~ ErH,.• =~ n2+x 30

~ x=0.03 20

X=0

10

0 0 100 200 300 T(K

265

300

E o C ,~~ 200

100

ErH (D) 2+x

°HT~ J D a

I I 0 0.05 0.1 X

i ~ Y

Fig. 49. Resistivity isothermals at 295 K for ErH(D)2+x, taken with increasing and decreasing temperature,

Fig. 48. Resistivity of ErH2+« for various x-values showing diverging p for x > 0.09 (Vajda and Daou in the relaxed (R) and quenched (Q) state. Note the 1994). magnetic transitions at low temperature (el. fig. 67), the structural anomalies around 200K (hysteresis!) and the M-S and S-M transitions for high x-values (Vajda and Daou 1994).

whatsoever, even in samples with a p ~ 3500 ~tf2 cm, stressing the necessary existence of LRO in the x-sublattice as one of the conditions for its occurrence.

5.2.3. Spectroscopic studies Experimental investigation of the electronic structure of dihydrides of Sc, Y and Lu using optical spectroscopy (Weaver et al. 1979) has shown several specific features dominated by intraband absorption at low energies (~< 1.5 eV) and by interband absorption above. The structures have been related to specific bands; it was shown partieularly that d- band absorption was broadened by increasing disorder due to the occupation of O sites. Similarly, XPS-studies of the Y - H system (Fujimori and Schlapbach 1984) have revealed a large chemical shift of the core levels going from Y to YH2, which indicates a charge transfer from Y to H; the valence-band spectra of YI-I2 and YH3 showed strong H-induced bands near 6 eV suggesting a mixing of Y 5sp states into the H ls band. A comparison of Compton profiles taken for metallic Lu and for LuH2 (Lässer et al. 1979) yields good agreement with Switendick's model, accommodating the two extra electrons in antibonding ls hydrogen wavefunctions. Finally, a surface S-M transition was observed in several hydrides of light and heavy rare earths at low temperatures using photoelectron spectroscopy as shown in fig. 50 (Schlapbaeh et al. 1987); cf. also the discussion for CeH2+x above.

t )-

I,- z

266 P. V A J D A

r~ I

I I I

I I

I I / , I L

! I I /

I I

i / i I ~~

,/ i I \

, / \ i I

/ I

/ / ^ \ /I I

« I !

/

I I

3 0 0 K 25 K

I ~ r

' S \.

ù / ù !/',,

/ / I I / /

,/ / ' i

! !

! _ /

' \ I f _CoH2,

CeH2.2

"\ " ' 1 G...dH~.o

I I I 8 6 4 2 O:E F 2 O:E F

-.,w- BINDtNG ENERGY (eV)

Fig. 50. Photoelectron spectra of the valence bands of several RH2+ x compounds taken at 25 K and at 3 0 0 K , showing a st trface S - M transition at low

temperature (Schlapbach et al. 1987).

6. Magnetic properties

The incompletely filled 4f-shell confers a magnetic moment to the lanthanide ions and it is the Ruderman-Kittel-Kasuya-Yosida (RKKY) meehanism via polarization of the conduetion electrons which is responsible for the oceurrence of long-range ordered magnetic structures in the lanthanide metals. Details can be found in numerous reviews, among others in vol. 1, ehs. 3, 6 and 7 (1978) ofthis Handbook series and a reeent one by Jensen and Mackintosh (1991). The addition of hydrogen, both in solution or resulting in hydride formation, leads to a decrease of the conduction electron density ne (of. sect. 5)

HYDROGEN IN RARE-EARTH METALS, 1NCLUDING RH2+ x PHASES 267

and to a general diminution of the magnetic manifestations dependent on ne through the RKKY-interaction. In fact, the observed decrease of the magnetic susceptibility and of the magnetic ordering temperatures upon hydrogenation was one of the early arguments in favour of an "anionic" versus a "protonic" mechanism for hydride formation. The eventual ordering of hydrogen at low temperatures (cf. sect. 3), which presents new symmetry situations such as the quasi-linear H-H chains along the c-axis in a*-phase systems or the tetragonal sublattices of the excess H atoms on octahedral sites in superstoichiometric dihydrides, can change the magnetism dramatically, leading sometimes to its complete suppression and sometimes to new magnetic transitions (e.g. Vajda and Daou 1984, 1993, Vajda et al. 1989a). The reason for this is a variation of the magnetic anisotropy and the magnetoelastic interactions, as weil as a modification of the crystal field (CF) or, more fundamentally, that of the Fermi surface.

Again, as for the electrical properties (sect. 5), the knowledge of the exact concentration of the excess H atoms x, dissolved in the dihydrides RH2+x is essential for a correct interpretation of the experimental data and for their comparison. We shall, therefore, stress this point in the following by separating, when possible, the pure dihydride (cf. sect. 2) from that of the excess atoms x. Below we have listed the relevant data on the magnetic manifestations in R-H systems resulting from investigations of the electric resistivity, specific heat, susceptibility, neutron diffraction, Mössbauer effect etc., concentrating on the most recent experiments, performed mainly since the eighties; for earlier compilations, the review by Arons (1982) may be usefully consulted. As before, we shall separate the discussion into two subsections on ct- and [3-phases and discuss the specific systems individually within each subsection.

6.1. ct*-Phase solid solutions

Among the magnetieally ordering lanthanide metals, only Ho, Er and Tm form a solid solution (in the metastable a*-phase, cf. sect. 3) at temperatures low enough for the occurrence ofmagnetic transitions. Hence, a particular effort toward the understanding of the influence of hydrogen upon their magnetic properties has been made in the last 10- 15 years, mairdy by the group at Orsay. The various magnetic structures are qualitatively the same for the pure metals on the one hand and for their solid solutions on the other. We shall present, in the following, the quantitative evolution of their different characteristic transition temperatures Tc, TN, etc., as weil as their paramagnetic Curie temperatures Op, and the corresponding effective magnetic moments/~ePff, when available.

Holmium possesses two magnetic transitions: below TN = 133 K the magnetic structure is a basal-plane helix, which transforms into a cone along the c-axis at Tc = 20 K. The only studies of the magnetism in a*-HoHx were done by resistivity measurements of polycrystals (Daou et al. 1987). These authors observed a regular decrease of TN with increasing x by ATN/AX - 2 K/at.%H(D) up to Xamax = 0.03 at.H(D)/Ho (fig. 26 in sect. 5). The constancy of TN for higher x-values is another indication for Xamax to be the solubility limit and the beginning of the two-phase (ct + [3)-region.

268 E VAJDA

56

54

52

~'=: 5 0

48

4 6

24 A

22

2O

18 0

0 . 0 5 0 . 1 0 a t .H /a t .Er I I

B (a) . /

/

I I 0 . 0 5 0 . 1 o

86

84

82

8 0 ~.z

78

76

0 . 1 5

x(at .H/at .Er)

Fig. 51. Variation of the main transition temperatures Tc, TH and T N in relaxed (open symbols) and quenehed (solid symbols) ErHx crystals I[c, as a function of x. The break indicates a-phase samration and the beginning precipitation of the 13-phase (Vajda et al. 1987b).

Erbium exhibits a complex magnetic behaviour, with at least four observable characteristic temperatures: below TN=85K, the moments order in a sinusoidal c-axis modulated (CAM) strue~are; at TH = 54 K, there appears a component perpendicular to the c-axis resulting in a helieoidal struemre; this intermediate phase exhibits a sequence of lock-in transitions of commensurate phases (spin-slip struetures) with wave vectors

4 5 6 1 rm = 2, 3 , T3, T~, ~ , ~ and ~ as observed by X-ray scattering (Gibbs et al. 1986), the latter loeking into a ferromagnetic cone along the c-axis at Tc = 19 K. Finally, Jensen and Cowley (1992) found that these higher harmonics were distorted by two-ion couplings of trigonal symmetry. Some of the intermediate spin-slip structures have also been observed

1 configuration at in resistivity and suseeptibility experiments, in particular the rm =~ Tel =27 K, and the infiuenee of hydrogen upon them has been studied. Thus, the two FM transitions at Tc and Tel shift to higher temperatures by ~0.5 K/at.%H upon the absorption of hydrogen, the two AF-transitions at TN and at TH to lower ones by ~1.5 K/at%H (Daou et al. 1981d, 1984b, Vajda et al. 1983b, 1987b, Ito et al. 1984, Burger et al. 1986b, Schmitzer et al. 1987), see also fig. 51. An additional increase of Tc and Tel (by ~2 K in the case of x = 0.06) oceurred in quenehed solid solutions, which was particularly striking in c-axis crystals (Vajda et al. 1987b). This shows the influence of structural order (H-H pairs oriented along the c-axis) on the magnetic one (c-axis cone) and stressing the magnetoelastie origin of the latter). The same effect, though smaller, is observed for TN and TH (eounteraeting the negative effect due to earrier removal) and is caused by the ehange in magnetie anisotropy. The energy gap A in the magnon speetrum, determined from an exponential fit of the magnetic contributions to resistivity Pm oc exp(-A/kBT), (Vajda et al. 1987b) and to speeific heat, cm c¢ T3exp(-A/kBT), (Sehmitzer et al. 1987) deereased by ~0.5-1 K/at.%H from a value A/kB = 11-14 K in pure Er. Magnetisation measurements on a*-ErHx single crystals (Burger et al. 1986b) exhibited strong anisotropy effects on the critical field for the FM transition Her. Thus,

HYDROGEN IN RARE-EARTH METALS, INCLUDING RH2+ ~ PHASES 269

TmHx H / / c

3¢

O E

~= 20 0

%

10

O~ ~ I I I 0 10 20 30 40 50

Hlnt(kOe) Fig. 52. Field dependence of the magnetisation of ct-TmI-I x crysta[s [Ic at 4.3 K, showing the strong decrease of the cfitical field for the ferri- to ferromagnetic transition with x (Daou et at. 1990).

Hcrlle decreased upon hydrogenation while Herz« inereased with increasing x; the latter was, in addition, anisotropic within the basal plane, Herllb > Hcrlla, for x > 0. Hcr generally decreased with increasing x in the case of polycrystals, while the paramagnetic Op dropped simultaneously from 40 to 31.5 K, and/tePfr remained roughly constant, 9.5 ~tB (Vajda et al. 1983b).

Thulium orders in an AF CAM structure below TN = 57.5 K and mrns "ferrimagnefic" (three spins up and four spins down) below a Tc=39.5 K. Contrary to Er, the addition of H diminishes both transition temperatures: TN and Tc decrease by ~1K/at.%H (Daou et al. 1980b, 1981b, 1983, 1988e, Ito et al. 1984, Vajda et al. 1989c), while magnetisation measurements parallel to the c-axis of monocrystalline specimens gave a 2K/at.%H decrease in Tc (Daou et al. 1990), stressing the anisotropy of the magnetic structure. This indicates that the process at Tc is governed by an electronic rather than a magnetoelastic mechanism, the variation of the electronic structure probably overwhelming the magnetoelastic interaction. At the same time, the critical field for the ferri-to-ferromagnetic transition parallel to c, Her[ic, decreases strongly upon hydrogenation (fig. 52). Furthermore, the anisotropy between c-axis and basal plane favours the basal-plane magnetisation and, possibly, even the appearance of basal-plane AF ordering (Daou et al. 1990). 6) 0 decreases from 19.1 K to 12.2 K and #Pfr from 7.61 ptB to 6.80~tB when going from pure Tm to «-TmH0.x0 (Daou et al. 1981b). Bennington et al. (1991) have noted, in inelastic neutron-seattering experiments, changes in the CF induced by hydrogen ordering, in particular a dispersionless peak near 15 meV, as welt as a coupling of magnetic excitations to H-vibration stares (cf. table 12 in sect. 4). A surprising phenomenon was observed in resistivity experiments on single erystals of ct-TmHx (Vajda et al. 1989c). While the introduetion of hydrogen essentially resulted in

270 E VAJDA

1 0 0

(~ TmH x / / b

~o ~ o . , " ~ . • "

~° . . . "o»t~..~ ~ ° ° ° o o ° ° ~ !. . . ;.f.~.

• i . . . . . . . . ~ - o • - 4 2 . 6

4 0 ." " ." • " / . " • - 3 1 . 0 "~

3 0 ' "" " ." " "" " " ~ " " " " ~ ~ " • " t ~~ . . . - " • - 30.6 • • o .

~o iii;.. il" ,~ ~ ~ ~ , ..... ....... ,oo _t. .,.,. ,.....,. • .o. , ' . ~ 10.4

10 1.5~ .~...«..... ». o...- ... • 1 . 3 J ~ I ; I " i I I I

0 . . . . " / I 2 4 6 I 8 l O K 0 50 100 150 2 0 0

T(K)

7 0 1 TmHx / /C ( b )

P 0.10

0 x=O I I I I 0 5 0 1 0 0 1 5 0 T (K) 2 0 0

Ê 70 O

6 0 O.

50

::k O.

Fig. 53. (a) Thermal dependence of the resistivity of ct-TmH x crystals [I b; the arrows indicate T N and the structural anomaly near 170K. The inset shows the low-temperature part demonstrating the growing contribution of the magnetic excitations with x. (b) Same as (a) for a-TmH x crystals ]1 c; the low-temperature part demonstrates the suppression of the ferrimagnetic ordering manifestation with x (Vajda et al. 1989c).

an increase o f the residual resistivity in the b-axis crystals (fig. 53a), the picture changed qualitatively for the c-axis crystals (fig. 53b). The low-temperature decrease in p due to ferrimagnetic ordering is strongly suppressed and vanishes completely for x > 0.05. The latter is attributed to a modification (by ~30% for x=0 .1 ! ) of the magnetic superzone gap produced by the periodic structures along the c-axis, due to the increase of Pres.


The temperature dependence of the magnetic resistivity term in the basal plane Pm,b(T), is best fitted through a combination Pm,b(T) e( ATn+ BT 2 exp(-A/kBT), where the first term predominates at low temperatures (T « A/kB) and possibly signifies the presence of an AF excitation, while the second term is due to magnon excitation in anisotropic ferromagnets. Both the power n and the spin-wave excitation gap A decrease in the hydrogenated crystals, i.e. from n ~ 5 to 2.5 and from A/kB ~ 38 K to 6 K, for x gõing from 0 to 0.1.

There also exist susceptibility measurements on two non-magnetic «*-phase solid solutions. In (x*-ScHx, Volkenshtein et al. (1983) fotmd X decreasing by nearly a factor of 2 between pure Sc and x = 0.36, illustrating the decrease of the density of electrons responsible for the measured paramagnetism. In ct*-LuHx, Stierman and Gschneidner (1984) observed, for the same reasons, a regular decrease of x for 0.01 ~<x ~< 0.06; at low temperatures, the behaviour is explained by superposition of spin fluctuations and hydrogen tunneling (cf. fig. 29 in sect. 5).

6.2. (Mainly) O-phase systems

A systematic study of the paramagnetic spin-disorder resistivity, pm(T), has been carried out on the heavy RH2 compounds (R = Gd through Tm) by Burger et al. (1986a) and Daou

Table 22 Spin-disorder resistivities, po , measured at T=Tr~, and ground-state magnetic

hydrides RH 2 moments, #Gs, for pure

R p°~(T~) (~t~2 cm) #as (/~B) Ref.

Ce 14 0.91 1,2,3

Pr ~4 1.54 2,4

Nd 4.3 1.06; 1.09 5,6,7

Sm 12 8

Eu s.c. a 7.1 9

Gd 28 6.5 10,11

Tb 15.3 7.4 12,13

Dy 4.25 6.4 13,14

Ho 5.8 3 4 13,15

Er 1.5 2.75 15,16

Tm 0 0 17

a S.C., semiconductor.

References (1) Vajda et al. (1990a) (2) Abeln (1987); Arons et al. (1987b) (3) Burger et al. (1991) (4) Daou et al. (1989a) (5) Senoussi et al. (1987) (6) Daou et al. (1992)

(7) Carlin et al. (1982) (8) Vajda et al. (1989b) (9) Bischof et al. (1983) (10) Vajda et al. (1991a) (11) Arons and Schweizer (1982) (12) Vajda et al. (1987a)

(13) Shaked et al. (1984) (14) Vajda and Daou (1992a) (15) Daou et al. (1988b) (16) Arons (1982) (17) Burger et al. (1986a)

272 P. VAJDA

Table 23a Characteristic magnetic temperatures in light RHz+x-systems

R 2 + x TC,N~ a (IC) Tral (IC) Tm~ (IC) Ref.

Ce 2.00 (2.4); 4.2; 6.9 14.5 42.5 1,2

2,00+0.02 (2.4); 4.2; 6.9 16 42 1,2

2.00+0.05 n.o. ~> 1.3 b 17.5 42 1,2

2.00+0.10 4.1; 6.8 21 33 1,2

2.00+ 0.25 3.1; 6.2 16 26 1,2

2.00+0.40 3.3; 4.3 1,2

2.00 + 0.60 3.3 1,2

1.95D (1.7); 5; 6.2 3,4

(1.95 + 0.05)D n.o./> 0.35 3,4

(1.95 + 0.44)D 4.0 3,4

(1.95 + 0.67)D 3.1 3,4

(1.95 + 0.82)D n.o. ~> 1.8 3,4

(1.95 + 0.96)D 4.1 3,4

Pr 1.97 3.35 28 5,6

1.96 + 0.03 2.0 6.0 16.5 5,6

1.96 + 0.08 (~5) 5,6

1.95+0.15 2.5 5.5 12.5 5,6

1.97+0.23 n.o. ~> 1.5 5,6

1.98+0.53 n.o. ~> 1.5 5,6

1.97+0.76 n.o. ~> 1.5 5,6

1.95D 3.3 3,7

2.25D n.o./> 2 3,7

Nd 2.00 6.6 8,9

1.99 + 0.06 6.0 8,9

2.00 + 0.32 5.3 8,9

2.00 + 0.44 2.65 8,9

2.00+0.56 2.9; 4.5 8,9

2.00+0.60 (1.75); 2.95 4.5 9.5 8,9

2.00+0.65 (2.15); 2.25 4.3 12.2 8,9

2.7 3.5 (5.5) 8,10

Sm 1.99 9.6 5,11 2.00+ 0.03 9.6 10.2 13.5 5,11

1.98+0.16 8.0 10.8 12.6 5,11

1.96+0.26 n.o. >/1.5 5,11

Eu 1.85 15.8 12,13 2 18.3 12,13

2D 16.3 14


HYDROGEN 1N RARE-EARTH METALS, 1NCLUDING RH2+ ~ PHASES

Table 23a, notes

273

a TNj stands for several TN (TN1, TN2, etc.). b n.o. >/ . . . . not observed above . . . .

References (1) Vajda et al. (1990a) (2) Burger et al. (1991) (3) Abeln (1987); Arons et al. (1987b) (4) Schefer et al. (1984) (5) Vajda et al. (1989a)

(6) Daou et al. (198%) (7) Arons et al. (1987a, c) (8) Senoussi et al. (1987) (9) Daou et al. (1992) (10) Drulis and Stalinski (1982)

(11) Vajda et al. (1989b) (12) Drulis and Stalinski (1989) (13) Bischof et al. (1983) (14) Drulis (1993)

et al. (1988a). It was noted that the overall variation ofpm followed the de Germes factor but that their absolute values were much smaller than those for the corresponding pure R-metals. This implies not only modifieations of the electronic band structure but also a significant reduction of the exchange interaction between conduction and f-electron spins. Deviations of the ground-state resistivities GS Pm, at the ordering temperature T = TN, from the theoretical free-ion values are shown to originate from orten large crystal-field (CF) effects. The values of Pm and of the ground-state magnetic moments #es are given in table 22. A theoretical basis for the CF-analysis in the RH2+x-systems has been given in the work of Lea et al. (1962) who had calculated the splitting of the (2J+ 1) degeneracy of the ionic ground state in a cubic environment. The interaction of these CF-exeitations with magnetism ean be observed principally by inelastic neutron scattering and also in the elassical measurements of specific heat, resistivity or susceptibility. (A detailed discussion is given by Arons 1991.)

Table 23a assembles the various characteristic temperatures for magnetie transitions as observed by different experimental techniques. We have separated the light RH2+x-systems (table 23a) from the heavy ones (table 23b), since the situation in the latter is often more complicated. Furthermore, this allows us to present a typical selection of coherent data covering a representative x-interval using the most recent and reliable results. Tc,N are the Curie and the Néel-temperatures (sometimes several TNi) for transition towards the FM and the AF stares, respectively; TM1 and Tml are the positions of the low-temperature maxima and minima in resistivity, corresponding to incommensurate ordering transifions and/or short-range ordered spin fluctuations (or Kondo effects for CeH2+x or YbH2+x); TM2 and Tm2 are the respective positions for a second possible higher-temperature magnetic transformation. The various TM,m are sometimes seen as additional kinks or shoulders in susceptibility and specific-heat measurements.

6.2.1. Specißc RH2+x hydrides The magnetic phase diagram of the CeH2+x-system is rather eomplex and has been established mainly from neutron diffraction (Schefer et al. 1984, Abeln 1987), susceptibility (Abeln 1987, Arons et al. 1987b) and resistivity measurements (Vajda et al. 1990a, Burger et al. 1991). There are two AF transitions in the pure dihydride CED1.95 (Abeln 1987) or CeH2.00 (Vajda et al. 1990a, Burger et al. 1991): TN1 =6.2K or 6.9K, TN2=5K or 4.2 K, possibly followed by another magnetic configuration at even lower temperatures, 1.7K or 2.4K. Neutron-seattering experiments on single crystals (Arons et al. 1987b)

274 P. VAJDA

Table 23b Characteristic magnetic temperatures in heavy RH2+x-systems

R 2 + x Tc,Nia (K) TM1 (K) Tml (K) TM2 (K) Tm2 (K) Rel.

Gd 1.94 18.3 1

1.97 + 0.04 17.75 23.7 53.7 1

1.98+0.14 11.5 60.3 1

1.96+0.17 14.5 36.6 54.3 74 1

1.97 + 0.21 (16) 57 80 1

1.97 + 0.305 65 105 1

3 1.8 2

Tb 1.96 18; 21 3

1.97 + 0.07 12.5 30.5 3

1.96+0.15 9.5 32.5 38.5 52 3

1.97+0.20 12 25 38 52.5 3

2.00D 16; 19 4

(2.00 + 0.18)D 32.5 42 4

2.00 + 0.245 36 42 4

Dy 1.99 3.7; 5.0 5

1.97+0.02 3.7; 5.0 5.5 5

1.98+0.10 ~<1.3 12 5

1.97+0.13 1.8 (10) (10.5) 16 5

1.99+0.22 10.7 20.5 5

1.99+0.27 2.55 8.6 10.7 18.7 5

2.00 3.4; 5.5 6

2.00 + 0.047 5.4 6

2.00 + 0.095 8.2 6

2.00+0.175 11.2 6

2.00 + 0,23 15.3 6

2.98 3.2 7

Ho 1.98 3.5; 4.7 6.3 24 8

1.99 + 0.02 3.75; 4.65 (2.65) 23 8

1.98 + 0.03 ~3.5 (1.45) 23 8

1.98 + 0.064 5.3 23 8

1.99+0.106 6.3 8

1.98+0.12 6.3 (~15) 25 8

1.99 + 0.14 6.3 (~13) 32 8

2.00 3.5; 5.2 6.9 6

2.00+0.035 3.0; 4.2 5.9 6

2.00 + 0.07 6.3 6

2.00+0.133 6.7 6

2.00+0.16 7.2 6

2D 4.0 ~9 9


HYDROGEN 1N RARE-EARTH METALS, INCLUDING RH2+x PHASES

Table 23b, continued

275

R 2 + x T«,N: (K) TM1 (K) Trùl (K) TMz (K) Tm2 (K) Ref.

Er 1.98 2.30 7.2 14.0 I0

(1.94+ 0.01)D 1.98 2.15 14.0 10

1.96+0.03 1.85 8.6 10

1.98 + 0.055 1.53 (2.1) 14.0 10

1.98+0.07 1.75 (2.1) 18.5 10

(1.97 + 0.09)D (2.15) (~5) 10

1.98 + 0.091 (2.2) ( - 5 ) 30 10

1.98 2.30 11

1.96 + 0.025 2.20 11

1.98 + 0.048 2.17 2.43 11

1.98+0.088 2.32 2.54 11

2D 2.15 9

Tm 1.96 n.o. >~ 1.5 b 12

Yb 1.80 n.o./>4 13

2.25 3.9 13

2.37 3.9 13

2.41 4 13

a T~ i stands for several T N (Tm, Tr~» etc.), b n.o. >/ . . . . not observed above . . . .

References (1) Vajda et al. (1991a) (6) Boukraa et al. (1993a) (10) Vajda and Daou (1994) (2) Carlin et al. (1980) (7) Carlin and Krause (1981a) (11) Boukraa et al. (1993b) (3) Vajda et al. (1987a) (8) Daou and Vajda (1994) (12) Burger et al. (1986a) (4) Vajda et al. (1993) (9) Shaked et al. (1984) (13) Drulis et ak (1988b) (5) Vajda and Daou (1992a)

permitted the analysis of the AF structure below Tm as MnO-type, with AF-coupted FM-planes modulated along [1101; the propagation vector is rm = 11111] + ½[110], cf. fig. 54a. The introduetion of excess H atoms x on O sites first induces the disappearance of the AF order (for x = 0.05), and then the appearance of FM order (for 0.05 ~< x < 0.6), followed by another AF order up to the highest concentrations measured (x = 0.96). The latter AF strucmre is close to that observed for x = 0, simplified by the lack of the [110] modulation (fig. 54b) caused by the absence of the RKKY-mediating conduction electrons. All magnetic transformatiõns are strongly influenced by the ordering state of the x-atoms (cf. sect. 3). Thus, a quench from room temperature into liquid nitrogen, conserving the random distribution of the octahedral H atoms, drastically modifies the magnetic manifestations, sometimes even leading to their disappearance, cf. e.g. fig. 55 for x = 0.1 and 0.2 (Burger et al. 199 t). The same is true for the Kondo transition observed in these systems (Vajda et al. 1990a): the coherent-incoherent transformation temperature shifts from 17.5 to 22K after a quench, while the two magnetic transitions at TNI and

276 P. VAJDA

«0 ~.-'-~5~--I 4--/Y

Fig. 54. (a) Magnetic structure of CeDI.95. The AF-coupled (111) planes show a modulation along [li0]. (b) Magnetic structure of CeDz91 . The modulation shown in (a) is suppressed (Abeln 1987).

/

ss ~ j ~ i,f----" ~0.2

50 ~ 4 5

o ~ ~ ' ',-o., 4 I , ° " ~ ~ - ~ n 4 0

° « J i ~ 35 35

3O

25 I I I I J

5 10 30 50 70 T(K)

Fig. 55. Thermal variation of the resistivity of CeHzl and CeH2. 2 in the relaxed (open symbols) and quenched (solid symbols) state. The arrows indicate the Kondo minima and maxima between 15 and 35 K, together with the magnetic anomalies at lower temperatures. Note the suppression of magnetism in the quenched specimens (Burger et al. 1991).

TN2 vanish (cf. fig. 35 in sect. 5.21 and the related discussion). Figure 56 summarizes the data in the form of a magnetic phase diagram.

HYDROGEN IN RARE-EARTH METALS, INCLUDING RHz+ x PHASES 277

0.2 0.4 0.6 0.8 1

g " 4

2

I I I I I I _1 I I 0 Ö 0.2 0.4 0.6 0.8

x(at.H/at.Ce)

Fig. 56. Magnetic phase diagram for CeH2+x, constructed from resistivity (Burger et al. 1991), susceptibility (Abeln 1987) and neutron scattering data (Schefer et al. 1984).

The pure Pr dihydride PrH1.97 possesses a TN = 3.35 K (Abeln 1987, Vajda et al. 1989a) and exhibits - like CeH2 - a resistivity minimum (Daou et al. 1989b) which is not related to an incommensurate magnetic structure. In the case of CeH2.00, it has been connected to a Kondo effect (Vajda et al. 1990a), while in PrH1.97 it is due to a CF effect. It was shown (Burger et al. 1990) that the experimental situation can be well reproduced assuming a magnetic ground stare, F5 in this case, and a non-magnetic first excited stare, F1, so that the contribution of spin-disorder scattering to p decreases first in a certain interval with increasing temperature, before increasing again due to the taking over by the phonon scattering. The progressive disappearance of the p-minimum and of the magnetic ordering for x > 0 (cf. fig. 57 and table 23a) can thus be explained by a splitting of the degenerate F5-triplet through the non-cubic CF symmetry. Investigations of CF-levels in PrH(D)2+x were performed by inelastic neutron scattering (Knorr et al. 1978, Arons et al. 1987c), specific heat (Drulis 1985) and by proton NMR (Belhoul et al. 1991); the latter results nieely confirm the above interpretation of the p-data through an orthorhombic CF distortion giving a singlet ground state. The magnetic structure of PrD2 was determined by neutron diffraction (Arons and Cable 1985, Abeln 1987) and is similar to that of CeD2 (fig. 54a), except for a different propagation vector: rm = 11111]- ½[112].

NdH2, apart from the orthorhombic semiconducting EuH2 (see below), is the only pure (x = 0) R-dihydride ordering ferromagnetically (Te ,-~ 6.5 K), see Carlin et al. (1982), Bohrt and Arons (1982), Senoussi et al. (1987). Upon introduction of x-hydrogen atoms, the FM is gradually suppressed, evolving for x )0 .5 towards complex AF structures (Daou et al. 1992) and behaving for still higher x (>0.65-0.7) like a spin glass (Senoussi et al. 1987). This effect is due to an interplay between RKKY-exchange interactions and the random uniaxial anisotropy energy, which appears for x > 0, and is sensitive to the concentration and the ordering state of the exeess hydrogens x. Thus, similar to CeH2+x (see above, fig. 55) a quench aeross the 200K region can completely suppress the magnetic ordering and turn the sample spin-glass like (e.g. fig. 58 for x=0.65).

278 P. VAJDA

0 10 20 30 K 40 [ [ I

5 5 T2 E B Pr H2. x

T1 5 4 , ' ~1oo~ ....

/

0.15

t 32

5 4 T3

2 8 oo! . . . . . . .

~F ~1 °oo o 2 4 K ~ ~ ~ ~ _ 1 0 . 5

6 5 1 - - I [ T I - 0 1 0 2 0 3 0 T / K 4 0

Fig. 57. Thermal variation of the resistivity of several PrH2+ x speeimens, showing the characteristic temperatures for magnetic transitions (Vajda et al. 1989a).

This effect becomes more pronounced when coming close to the M-S transition (and the y-phase region) near x=0.7 (of. sect. 5.2.2), a clear indication for a modification of the electronic band structure. A similar flattening of the initially k-type peaks for the magnetic transitions was seen in specific-heat measurements (Drulis and Stalinski 1982) when approaching x ,~ 0.7. A tentative magnetic phase diagram in fig. 59 (Daou et al. 1992) summarizes the experimental situation, possibly involving a two-phase region around x ~ 0.6 (cf. sect. 3, fig. 15).

The pure dihydride SmH2 has an AF structure of the MnO type, with a propagation vector rm=½[l l l ] (Arons and Schweizer 1982); it orders at TN=9.6K. For x > 0 , TN decreases progressively (down to 8K for x=0.16) and disappears completely for x > 0.25. Again, like the lighter RH2+x-systems (see above), structural disorder in the x-sublattice exerts a strong influence upon the magnetism. A striking example is given in fig. 60 where the (now possibly incommensurate) magnetism seems to have reappeared in the quenched x = 0.26 specimen. These phenomena are probably related to perturbations of the CF, which may lead to a splitting of the F8 ground-level quartet. Indications for this were noted, for x > 0, in the anomalous temperature variations of the resistivity (Vajda et al. 1989b) and the complex behaviour of the specific heat (Opyrchal and Bieganski 1978). In the latter experiment, their SmHz00 speeimen contained a non-negligible amount

HYDROGEN IN RARE-EARTH METALS, INCLUDING RH2+ « PHASES

--4.0

«

2.1

5 10 15 T(K)

2.0

279

1.9

B X = 0.65 R

~L 1 . 9 4 2 . 2 5 K

1.90 I ~ , I

1.5 2 ~, 2.5 K !

I 12"17K I

3.9

I ! I I I

T(K PM NdH2+ x

4 \ t +

2 -- FM I I I ?"~ S o

o o.2 0.4 0.6 0.8 x (at.H / at.Nd)

Fig. 59. Tentative magnetic phase diagram in the Ndl-I2+ x system, from resistivity (solid circles, Daou et al. 1992) and magnetisation data (crosses, Senoussi et al. 1987).

Fig. 58. Thermal variation of the resistivity of relaxed (R, solid circles) and quenehed (Q, solid triangles) NdHz6 5 in the magnetic region (Daou et al. 1992).

ofx-hydrogen atoms, which is reflected in a rather low TN --- 6.75 K and a bump near 10 K, whieh was not mentioned by the authors, and possibly corresponding to the TM1 of the p-measurements (cf. table 23a).

The orthorhombic EuH2 is (like YbH2) an insulator, since the divalent europium has lost both its valence electrons upon hydriding. The Eu 2+ ion has seven unpaired spins and is strongly magnetic, resulting in a FM transition at Tc = 16-18K (Mustachi 1974, Bischof et al. 1983, Drulis and Stalinski 1989, Drulis 1993).

The magnetic structure of pure GdH2 (like that of SmH2) is AF of MnO type, with a propagation vector ~m = ½[111] (Arons and Schweizer 1982). Additional x-hydrogens on O sites lead to incomrnensuracy, the structure becomes helicoidal, with an axis along [111]. Simultaneously, the TN, which was 18.3 K for x = 0, decreases regularly to TN = 11.5 K for x=0.14, the situation becoming more complicated for higher x (Vajda et al. 1991a). Thus, a second maximum at TM2 appears in the p-curves for x=0.16 (cf. fig. 43 in sect. 5.2.2) which grows in amplitude at the expense of the first maximum at TM1 until the complete vanishing of the latter for x near the phase boundary at x~max ~ 0.30. The extreme sensitivity to x-sublattice ordering is shown in the quench experiments. The maximum at TM2, which is evidently related to the ordered H structure, has disappeared to the benefit of a strong emergence of the maximum at TM1, which is obviously conneeted to the disordered (random) x-hydrogen atoms. Gd being a pure S ground state ion (L = 0), one does not expect any significant interaction with the CF; therefore, the strong variations of the magnetic manifestations have to be attributed to profound modifications of the Fermi surface and its nesting conditions. Figure 61 presents, as a summary, the tentative magnetic phase diagram of GdH2+x in the relaxed and in the quenched stare of the x-

280 P. VAJDA

0 1 0 2 0 T / K 3 0

1 0 5 f 11 Sm H2+x I. ."

104 5' : .. •

1;:I~-: :ii~io:~~'~~ii:: ° o °°~ 5•oooo

~°~°°°°°

6 9 . ~ . . "

~,~-/-~ ~oooo°°~- + , F r x~o, ° ....

37" j

3 6 . 5

3 6

2~ 20.

201 0

1 • °* o*

oO ° o

~° o o °°°

« . . . . ~ x = O o:R

I I 10 20 T/K 30

9 5

9 0

4.5

3 5

34 .5

Fig. 60. Thermal variation of the resistivity of several SmH2+ x specimens in the relaxed (open symbols) and quenched (solid symbols) stare. Note the reappearance of magnetism after a quench for x=0.26 (Vajda et al. 1989a,b).

p-

80

60

40

20

/ - / /

• ~ ~ f T : ~

+/4/ / / iC 2

• .~ Tml IC "~+ i"' icl

- /

AF hel • o/ ] I I

0 0.1 0.2 0.3 x(at,H(D)/at.Gd)

Fig. 61. Tentative magnetic phase diagram of GdH2+x (open symbols) and GdD2+ x (solid symbols) in the relaxed (solid lines) and in the quenched (dotted lines) stare obtained from resistivity studies (Vajda et al. 1991a). icl,» incommensurate or magnetically SRO phases; hel, helieoidal phase• For the various critical temperatures, see text and table 23b.

HYDROGEN IN RARE-EARTH METALS, INCLUDING RHz+ x PHASES 281

(a) / / k= [1/4 , 1/4 ,3/4]Æ [113]

/

(b) ;/

/ ,/ k'= [1/8. 1/8,3/4 ]//[116] ,

/ / /

/

Fig. 62. Magnetic structures of TbDz00; (a) commensurate phase observed for T < 16 K; (b) incommensurate phase in the interval 14.8 ~< T ~< 19 K. The projections of their magnetic moments upon the directions of the corresponding propagation vectors k are shown to the left of the structures (Vajda et al. 1993).

hydrogens in the interval 0 ~ x ~< 0.30 (Vajda et al. 1991a). The hexagonal y-phase GdH3 orders AF at TN = 1.8 K (Carlin et al. 1980).

The structure of pure TbH(D)2 below TN = 16 to 18 K as determined by neutron diffraetion (Arons et al. 1982, Shaked et al. 1984) is commensurate AF, modulated with a propagation vector r~n= ¼[113]; the spin axis is oriented parallel to [001]. Between TN (and even overlapping it by AT ,~ 2 K) and an intermediate transition temperature, TI = 19-21 K, one observes a sinusoidal incommensurate magnetic structure, with a propagation vector rim c ~ [0.12, 0.14, 0.76], close to the [116] direction (Vajda et al. 1993).The two configurations are shown in fig. 62. The superstoichiometrie compounds studied neutrono-graphically by Vajda et al. (1993) for the cases x = 0.18 (and 0.245), also exhibit two magnetie phases. One exists below Ty = 32.5 (and 36 K), and is eommensurate and modulated with a propagation vector r~ = ¼ [114], i.e. it is different from that in pure TbD2. The other exists between TN and T1 = 42 K (and 43 K), and is incommensurate with a ~ime ~ [0.24, 0.18, 1] and slightly varying with temperature. The overlap interval with the commensurate phase increases, with a roughly constant relative width AT~T2 ~ O. 1. The intricate interplay between structural ordering of the x-atoms (determined as DO22 for TbD2+x by neutron scattering by André et al. 1992, cf. sect. 3.2) and the magnetie ordering, which increases the ordered intervals and modifies the configurations, has also been observed through quenching effects in resistivity studies (Vajda et al. 1987a). This behavior is similar to that discussed above for GdH2+x (cf. fig. 43). It is encouraging that the configurations (both the commensurate and the incommensurate ones) are different for the hydrides with x = 0 and with x > 0, especially in view of the presenee of different H ordering in the two cases. In the same context, we also mention the existence of two types of Tb-atoms with regard to their surroundings in an ordered DO22 stmeture (fig. 13): 25% of them have two oceupied O sites as nearest neighbours and 75% only one, giving

282 P. VAJDA

l f i TbH(D) 2+x

40 * ~-

2O

0 0.1 0.2 x(at,H(D)/at,Tb)

Fig. 63. Magnetic phase diagram of TbH(D)z÷x exhibiting the existence region for the two commensurate phases (a) and (b) and the ineommensurate phase (c) (note the overlap regions!). Crosses, neutron data; open circles, resistivity data; open squares, susceptibility data, solid diamonds, specific heat data (Vajda et al. 1993).

a clear indication as to the different CF symmetries as a possible origin for the various magnetic phases. An analysis of the CF splitting in TbH2+x up to x ,~ 0.15 was made using specific-heat measurements by Drulis et al. (1984), who established F2 as the ground state singlet for small x and a contribution of a doublet (or triplet) for larger x, due to the axial symmetry of some Tb 3+ ions. The magnetic phase diagram in fig. 63 is made up from relevant neutron-diffraction, resistivity, susceptibility and heat capacity data and shows, in particular, the overlap region between the commensurate and incommensurate phases.

The magnetic structure of DyH2 is similar to that of TbH2. It is AF commensurate c _ 1 below TN = 3.7 K, with a propagation vector Zm-~ [113] (Shaked et al. 1984). A second

transition due to the appearance of an as yet undetermined intermediate structure (but probably similar to that oceurring in TbD2), is seen at TI=5.0K (Shaked et al. 1984, Bieganski et al. 1975, Vajda and Daou 1992a). The addition ofx-hydrogens suppresses the manifestations of the commensurate AF order: TN is no longer visible for 0.05 < x < 0.15 in the resistivity (Vajda and Daou 1992a), suseeptibility (Carlin and Krause 1981a) and Mössbauer measurements (Friedt et al. 1979). The presence of some structure in susceptibility curves (broad, flat peaks) could be evidence for short-range AF order (Boukraa et al. 1993a). For still higher x-values, x>0.15, however, new transitions appear, with a striking p-peak eentered at 10.7K (a precursor hump is observed at 10.5K for x=0.13) and a minimum at 19-20K (Vajda and Daou 1992a). The extreme sensitivity to x-hydrogen ordering is shown in fig. 64, clearly assigning the 10.7K peak as representative for the ordered H-configuration. A tentative magnetic phase diagram constructed from resistivity and susceptibility data (Vajda and Daou 1992a, Boukraa et al. 1993a) is shown in fig. 65. The break near x=0.1 is related to the phase boundary between SRO and LRO x-hydrogen ordering in the structural phase diagram (fig. 16 in sect. 3.2). Finally, the y-phase trihydride DyHz98 orders AF at 3.2 K (Carlin and Krause 1981a). Recent diffraction studies on DyD2 using cold neutrons (to compensate for the high thermal-neutron absorption of Dy) undertaken by Vajda et al. (1995) permitted to specify the low-temperature structure below TN as incommensurate, with a propagation vector r~ ~ [0.28, 0.28, 0.745], close to but not exactly 11113]. Surprisingly enough, this

HYDROGEN 1N RARE-EARTH METALS, INCLUDING RH~+~ PHASES 283

5 0

;o 45 c :::L

v CL

x = 0.27 [ -~'~~~~'/'~- ]72.6

2.5K 47.5 ~- " ~,ß72.5

47"4 ~ ~ 1 ~ ~ ~ ~ 72'4 j

1 ~ 3 4 K I

41{ 9K 72.8,

50 -- 10.7K ~N 72.61 ~1 I I ] 70 2 3 4 5K

45 J ~ 65

20.5K

B,,~.. DY H2+x x = 0"22 .~60

~o.71- ~,'-. ~ /

~~-~~ 2k ~: x°01~ 2 5.1

01 • ~" 11 3 51 7 "°L'° I | 0 10 20 T(K) 30

I I

2~

10

ic

AF-sao [

I A F - e

A F - c \, I I I

0.1 0.2 x(at.H/at.Dy)

0.3

Fig. 65. Tentative magnetic phase diagram of DyHz+ x indicating AF-commensurate and incommensurate and SRO phases, constructed from resistivity (solid eircles) and susceptibility (erosses) data (Vajda and Daou 1993).

Fig. 64. Resistivity of DyH2+x specimens in the magnetic region. Note the striking changes introduced by a quench (Q, solid inverted triangles) when compared to the slowly cooled samples (R, solid circles) (Vajda and Daou 1993).

incommensurate AF structure seems to coexist with a FM component, the latter vanishing at Tc = 5,8 I~, close .to the above mentioned TI.

The magnetic structure of HoD2 was determined by neutron diffraction to be of the same type as TbD2 (cf. fig. 62), except for the spin axis oriented close to [110] (Shaked

c _ 1 et al. 1984). It is AF, with a propagation vector r m - ~[113] below T~ ~ 5 K, and exhibits an undetermined intermediate structure between TN and Tl ~ 6.5-8 K. T1 is nicely seen as a maximum in the resistivity (fig. 66) and in the susceptibility (Boukraa et al. 1993a), while TN is just a break in the resistivity drop below Tb Only TN has been observed in specific-heat measurements (Bieganski and Stalinski 1976). An additional break in p is noted at 3.5K. The resistivity minimum near 23 K could be due to magnetic fluctuations but also, possibly, to CF effects, i.e. to excitations from a magnetic ground state (Fs) to a non-magnetic first excited state (F3), similar to PrH2 (Daou et al. 1989b, Burger et al. 1990). The situation in the superstoichiometric dihydrides evolves rapidly (fig. 66). Thus, the addition of only 0.02 at.H/Ho on octahedral sites leads to a nearly complete

0 suppression OfPmag , the resistivity drop due to ordering below TI, TN. For x ~> 0.05, only

284

t r ~ ~ ~ J J , ~ 57

B',~ /\~.~\,/x=o.o~ , ~ õô

Ê 2 3 25

"~ 7 x=o.o2 4,65 J~'\

~ , 2 \ \ ~ T 4 / x = O

~ ~.~~ 2 i 1 I I ~ i I I

0 1 2 3 4 6 7 8 T(K)

P. VAJDA

Fig. 66. Resistivity of various Hort2+ « specimens in the magnetic region showing the evolution of the critieal temperatures as a function ofx (Daou and Vajda 1994).

TI is l e r as a manifestation of magnetism in the form of a slope maximum near 6 K in p and as a flat maximum in X (Boukraa et al. 1993a). On the other hand, a second structure develops as a hump above T ~ 25 K for concentrations x > 0.12 (el. also fig. 46 in sect. 5) which could be due to the appearance of a new magnetic phase caused by the LRO in the x-sublattice, similar to GdH2+x and TbH2+x.

The magnetic structure of ErH2, the heaviest of the magnetically ordering dihydrides, is a complex AF below TN = 2.15-2.30 K (Bieganski and Stalinski 1976), with a mixture of both eommensurate and incommensurate components down to 1.5 K (Shaked et al. 1984). The incommensurate structure lines in the neutron diffraction pattern are at the same positions as those of the intermediate structures in TbD2, DyD2 and HoD2, showing their close relationship to each other. It should, in fact, be interesting to investigate ErH2 down to even lower temperatures in view of an eventual observation, by analogy, of the pure commensurate structure, since the measured "mixed" spectra might be representative only for the overlap region between the two phases such as noted in TbD2 (Vajda et al. 1993). This close relationship is also evident in the behaviour of the superstoichiometrie ErH2+x-system, in that it is similar to other heavy RH2+x compounds: a decrease of TN for small x and the appearance of a new magnetic structure at higher temperatures for x high enough to form a H sublattice (figs. 67 and 48). The tentative phase diagram for the characteristic temperatures in the magnetically ordering range (fig. 68) was constructed from the available resistivity (Vajda and Daou 1994) and susceptibility data (Boukraa et al. 1993b, Carlin and Krause 1981b). Again, as for DyH2+x, neutron- scattering measurements are required to determine the precise SRO and LRO magnetic configurations.


29.5 +

29

1.5

0.6

x = 0.088 " ~

~ ~ _ ~ \ x = o o 7

I I I I

121

119

117

2.5

12.0

0 1 2 3 4 T(K)

Fig. 67. Resistivity of various ErH2+ x speeimens in the magnetie region showing the evolution of the transition temperature with increasing x (Vajda and Daou 1994).

0.02 0.06 0,1 r I L I I . . . .

L Er H2+ x 3 ! g ~ pM

~-2~

1 I 1 _l f 0 0.04 0.08

x(at.H/at.Er)

Fig. 68. Tentative magnetic phase diagram of ErH2+ « indicating the different coexisting eommensurate and incommensurate phases as well as the SRO domains, constructed from resistivity (solid triangles, solid inverted triängles, Vajda and Daou 1994) and suseeptibility data (solid cireles, solid squares, Boukraa et al. 1993b; crosses, Carlin and Krause 1981b).

No magnetic transitions have been observed in TmH2 down to 1.5 K. An analysis of the spin-disorder resistivity, Pm, shows that the ground stare (F2) is non-magnetic but separated from the first excited magnetic state (F~ 2)) by AE ~ 170K - a Van Vleck paramagnet (Burger et al. 1986a, Shaltiel et al. 1991a). The only low-temperature investigation undertaken up to now in the TmI-I2+x system coneerned Tm-169 Mössbauer studies on samples with ill-defined eompositions by Waibel et al. (1980) who interpreted the spectra as evidence for the presence of two non-magnetic phases. Further thorough experiments should, however, be interesting in view of the great sensitivity of such a Van Vleck compound to minor changes in the surroundings of the Tm-ions. For example, it was shown in EPR-linewidth measurements of substitutional Gd and Er impurities (0.01 at.%) in TmH2 that the latter reduced the first CF-level separation AE by nearly a factor of two (Shaltiel et al. 1991b). Even greater effeets should be expected from interstitial type defects such as the oetahedral x-hydrogens.

The orthorhombic YbH2 is non-magnetic because of the divalency of the yb2+-ion, which becomes an analog of Lu 3+. In the fee superstoiehiometric dihydrides with x > 0.25, the presence of yb3+-ions, yielding a mixed-valence system, seems to lead to Kondo- lattiee behaviour, with a eoherent-incoherent transition near 4 K (Drulis et al. 1988b, but: cf. also the note in sect. 5.2.2).

286 R VAJDA

7. Summary and outlook

This review of experimental data concerning hydrogen in rare earths, both in the form of solid solutions and of hydrides, shows - as a first general result - the great influence of the initial metal purity upon the characterization of the fmal specimen and its physical and physico-chemical properties. A thorough control of the preparation conditions is a further (related) requirement for obtaining unambiguous and reproducible results.

Among the general regularities along the R-series, one can note the evolution of eertain dimension-dependent properties, for example a decreasing solubility in the B-phase (i.e. a narrowing of the pure R-phase region). On the other hand and for the same reasons, the solubility in the low-temperature «*-phase increases, as the eventual preeipitation of the B-phase is retarded in lattices with smaller unit cells. Similarly, for the J-dependent magnetic properties, such as the transition temperatures TN and the spin- disorder resistivities Pmag, the B-RH2 hydrides follow the de Gennes factor, just as in the pure metals.

As to the more prominent properties, one has to mention the hydrogen sublattice ordering occurring below room temperature both in the «*-phase solid solutions and in the [3-phase RHz+x systems. In the former case one observes zig-zagging chains along the c-axis made of H-H pairs on tetrahedral sites of the hcp lattice, and in the latter, the excess hydrogen atoms x on octahedral sites of the fluorite type fee lattice form a tetragonal DO22 configuration, at least in the heavy RH2+x compounds. This ordering has a striking influence on the magnetie manifestations, via modification of the Fermi surfaee and/or the crystal-field symmetry.

Also related to the above x-sublattice ordering are the recently observed metal- semiconductor transitions near room temperature in the heavy superstoichiometric dihydrides GdH2+x, HoH2+x, ErH2+x and in YH2+x for x dose to the R-phase boundary

(0.1< ~ Xmax < 0.3). Another M-S transition oecurring in these systems at lower temperatures (20-12010 seems to be due to carrier localization caused by atomic disorder. Analogous effects were noted in the light substoichiometric trihydrides (also in the B-phase) LaHz+x and CeH2+x in the range 0,7 < x < 0.9.

As to future developments, one expects a more intense neutron-scattering work both for the determination of structural phase diagrams (mainly concerning the H sublattice) and of magnetic phase diagrams, in particular the complex ineommensurate configurations in the heavy RHz+x compotmds. Inelastic neutron-scattering studies are required for the investigation of phonon-dispersion relations and of H local modes. Also, further work is needed for the determination of the precise electronic mechanism responsible for the M-S transitions. And, finally, little is known of the low-T properties of the y-phase trihydrides because of their inherent chemical instability.

Last but not least, a major effort should be devoted to the growth of monoerystalline hydride specimens other than CeH2+x, a prerequisite for the study of short-range-ordered configurations.


References

Abeln, A., 1987, Report no. Jül.-2152 (Jülich). Anderson, I.S., J.J. Rush, T.J. Udovic and J.M. Rowe,

1986, Phys. Rev. Lett. 57, 2822. Anderson, I.S., N.E Berk, J.J. Rush and T.J. Udovic,

1988, Phys. Rev. B 37, 4358. Anderson, I.S., D.K. Ross and J.E. Bonnet, 1989, Z.

Phys. Chem. NF 164, 923. André, G., O. Blaschko, W. Schwarz, J.N. Daou and

E Vajda, 1992, Phys. Rev. B 46, 8644. Arons, R.R., 1982, Rare earth hydrides, in: Landolt-

Bömstein New Seiles, Vol. 12c, ed. K.H. Hellwege, eh. 6.3.

Arons, R.R., 1991, Rare earth hydrides, in: Landolt- Bömstein New Series, Vol. 19dl, ed. H.EJ. Wijn, ch. 2.3.

Arons, R.R., and J.W. Cable, 1985, Solid State Commun. 55, 835.

Arons, R.R., and J. Schweizer, 1982, J. Appl. Phys. 53, 2645.

Arons, R.R., W. Schaefer and J. Schweizer, 1982, J. Appl. Phys. 53, 2631.

Arons, R.R., A. Abeln-Heidel and H. Mutka, 1987a, ILL Exptl. Report (Grenoble) p. 81.

Arons, R.R., A. Abeln-Heidel and C. Ritter, 1987b, ILL Exptl. Report (Grenoble) p. 186.

Arons, R.R., J.W. Cable and R.M. Nicldow, 1987c, J. Appl. Phys. 61, 3423.

Barnes, R.G., D.R. Torgeson, T.J.M. Bastow, G.W. West, E.EW. Seymour and M.E. Smith, 1989, Z. Phys. Chem. NF 164, 867.

Barnfather, K.J., E.EW. Seymour, G.A. Styles, A.J. Dianoux, R.G. Barnes and D.R. Torgeson, 1989, Z. Phys. Chem. NF 164, 935.

Bashkin, I.O., E.G. Ponyatovskii and M.E. Kost, 1977, Phys. Status Solidi b 83, 517.

Bashkin, I.O., E.G. Ponyatovskii and M.E. Kost, 1978, Phys. Status Solidi b 87, 369.

Beattie, A.G., 1972, J. Appl. Phys. 43, 3219. Beaudry, B.J., and EH. Spedding, 1975, Metall. Trans.

B 6, 419. Belhoul, M., R.L Schoenberger, D.R. Torgeson and

R.G. Barnes, 1991, J. Less-Common Met. 172-174, 366.

Bermington, S.M., R. Osborn, D.K. Ross and M.J. Benham, 1991, J. Less-Common Met. 172-174, 440.

Berk, N.E, J.J. Rush, T.J. Udovic and I.S. Anderson, 1991, J. Less-Cornmon Mer. 172, 496.

Bieganski, Z., and M. Drulis, 1977, Phys. Status Solidi (a) 44, 91.

Bieganski, Z., and B. Stalinski, 1976, J. Less-Common Mer. 49, 421.

Bieganski, Z., J. Opyrehal and M. Drulis, 1975, Phys. Status Solidi (a) 28, 217.

Bischof, R., E. Kaldis and E Waehter, 1983, J. Magn. & Magn. Mater. 31-34, 255.

Bischof, R., M. Tellefsen and E. Kaldis, 1985, J. Less- Common Mer. 110, 99.

Blaschko, O., G. Krexner, J.N. Daou and E Vajda, 1985, Phys. Rev. Lett. 55, 2876.

Blaschko, O., G. Krexner, L. Pintsohovius, E Vajda and J.N. Daou, 1988, Phys. Rev. B 38, 9612.

Blasehko, O., G. Krexner, J. Plesehiutschnig, G. Ernst, J.N. Daou and P. Vajda, 1989a, Phys. Rer. B 39, 5605.

Blaschko, O., J. Pleschiutsehnig, L. Pintschovius, LP. Burger, J.N. Daou and P. Vajda, 1989b, Phys. Rer. B 40, 907.

Blaschko, O., J. Pleschiutschnig, E Vajda, LE Burger and J.N. Daou, 1989c, Phys. Rev. B 40, 5344.

Boeva, O.A., K.N. Zhavoronkova, M. Smutek and S. Cern~, 1986, J. Less-Common Mer. 118, 1.

Bohrt, H.G., and R.R. Arons, 1982, J. Appl. Phys. 53, 2072.

Bonnet, J.E., 1975, Thesis (University of Paris). Bonnet, J.E., and J.N. Daou, 1977, J. Appl. Phys. 48,

964. Bonnet, J.E., and J.N. Daou, 1979, J. Phys. & Chem.

Solids 40, 421. Boroch, E., and E. Kaldis, 1987, Inorg. Chim. Acta

140, 89. Boroeh, E., and E. Kaldis, 1989, Z. Phys. Chem. NF

163, 117. Borsa, E, R.G. Barnes, B.J. Beaudry and D.R.

Torgeson, 1982, Phys. Rev. B 26, 1471. Boukraa, A., E Vajda and J.N. Daou, 1993a, in: Proc.

lnt. Conf. on Metal-Hydrogen Systems, Uppsala, Sweden, 1992, Z. Phys. Chem. NF 179, 413.

Boukraa, A., P. Vajda and J.N. Daou, 1993b, J. Magn. & Magn. Mater. 123, L5.

Burger, J.R, J.N. Daou, P. Vajda and A. Lucasson, 1984, J. Less-Common Met. 103, 381.

Burger, J.R, J.N. Daou, A. Lucasson and R Vajda, 1986a, Phys. Rev. B 34, 4782.

Burger, J.P., P. Vajda, J.N. Daou and G. Chouteau, 1986b, J. Phys. F 16, 1275.

288 R VAJDA

Burger, J.P., J.N. Daou and P. Vajda, 1988, Philos. Mag. B 58, 349.

Burger, J.P., J.N. Daou and R Vajda, 1990, Z. Phys. B 80, 233.

Burger, J.R, P. Vajda and J.N. Daou, 1991, J. Phys. & Chem. Solids 52, 779.

Cannelli, G., R. Cantelli, E Cordero, E Trequattrini, I.S. Anderson and J.J. Rush, 1991, Phys. Rev. Lett. 67, 2682.

Carlin, R.L., and L.J. Krause, 1981% Chem. Phys. Lett. 82, 323.

Carlin, R.L., and L.J. Krause, 1981b, Phys. Rer. B 23, 6149.

Carlin, R.L., R.D. Chirico, K.O. Joung, G.K. Shenoy and D.G. Westlake, 1980, Phys. Lett. A 75, 413.

Carlin, R.L., L.J. Krause, A. Lambreeht and H. Claus, 1982, J. Appl. Phys. 53, 2634.

Chiheb, M., 1980, Thesis (University of Paris-Sud). Chiheb, M., LN. Daou and E Vajda, 1993, in: Proe.

Int. Conf. on Metal-Hydrogen Systems, Uppsala, Sweden, 1992, Z. Phys. Chem. NF 179, 255.

Chowdhury, M.R., G.A. Styles, E.EW. Seymour, S.EL Cox, C.A. Scott and G.H. Eaton, 1989, J. Phys.: Condens. Marter 1, 4659.

Cordero, E, 1993, Phys. Rev. B 47, 7674. Danielou, R., J.N. Daou, E. Ligeon and P. Vajda, 1981,

Phys. Status Solidi a 67, 453. Daou, J.N., 1965, C.R. Aead. Sei. Paris, Ser. C 261,

1675. Daou, J.N., and J.E. Bonner, 1974, J. Phys. & Chem.

Solids 35, 59. Daou, J.N., and P, Vajda, 19??, unpublished. Daou, J.N., and R Vajda, 1988, Arm. Chim. (Paris) 13,

567. Daou, J.N., and P. Vajda, 1992, Phys. Rev. B 45,

10907. Daou, J.N., and R. Viallard, 1972, in: Hydrogène dans

les Métaux, Vol. 1 (Seience et Industrie, Paris) p. 123.

Daou, J.N., A. Lueasson and P. Lueasson, 1976, Solid Stare Commtm. 19, 895.

Daou, J.N., P. Vajda, M. Biget, A. Lucasson and R Lueasson, 1977, Phys. Status Solidi a 40, 101.

Daou, J.N., R Vajda, A. Lueasson and P. Lueasson, 1980a, J. Phys. F 10, L305.

Daou, J.N., R Vajda, A. Lueasson and P. Lucasson, 1980b, Solid State Commun. 34, 959. Erratum: 35, 809.

Daou, J.N., M. Chiheb and P. Lucasson, 1981a, J. Less-Common Met. 79, 65.

Daou, J.N., P. Radhakrishna, R. Tur and R Vajda, 1981b, J. Phys. F 11, L263.

Daou, J.N., P. Vajda, A. Lucasson and E Lueasson, 1981e, J. Phys. C 14, 129.

Daou, J.N., R Vajda, A. Lueasson and P. Lueasson, 1981d, J. Phys. C 14, 3155.

Daou, LN., R Vajda, A. Lueasson and E Lucasson, 1981e, Solid State Commtm. 40, 261.

Daou, J.N., P. Radhakrishna, R Vajda and Y. Allain, 1983, J. Phys. F 13, 1093.

Daou, J.N., A. Lueasson, E Vajda and J.R Burger, 1984a, L Phys. F 14, 2983.

Daou, J.N., P. Vajda, E Radhakrishna and Y. Allain, 1984b, Solid State Commun. 52, 1051.

Daou, J.N., E Vajda, J.R Burger and A. Lueasson, 1986a, Phys, Status Solidi a 98, 183.

Daou, LN., P. Vajda, A. Lueasson and J.R Burger, 1986b, Phys. Status Solidi a 95, 543.

Daou, J,N., 13. Vajda, A. Lueasson, E Lueasson and J.P. Burger, 1986e, Philos. Mag. A 53, 611.

Daou, J.N., R Vajda and LE Burger, 1987, Solid Stare Commun. 64, 937.

Daou, J.N., E Vajda and J.P. Burger, 1988a, Phys. Rev. B 37, 5236.

Daou, J.N., R Vajda, J.P. Burger and D. Shaltiel, 1988b, Europhys. Lett. 6, 647. Erratum: 1989, 8, 587.

Daou, J,N., E Vajda, G. Hilseher and N. PilImayr, 1988e, J. Phys. (Paris) 49(Suppl.), C8-357.

Daou, J.N., J.E Burger and R Vajda, 1989a, Phys. Status Solidi b 154, 321.

Daou, J.N., R Vajda and J.P. Burger, 1989b, Solid State Commun. 71, 1145.

Daou, J.N., J.P. Burger, E Vajda, G. Chouteau and R. Tur, 1990, J. Phys.: Condens. Marter 2, 7897.

Daou, J.N., J.E Burger and E Vajda, 1992, Philos. Mag. B 65, 127.

Drulis, H., and K.P. Hoffmann, 1985, Z. Phys. Chem. NF 145, 11.

Drulis, H., M. Drulis and W. lwasieezko, 1988a, J. Less-Common Met. 141, 201.

Drulis, M., 1985, Z. Phys. Chem. NF 145, 19. Drulis, M., and Z. Bieganski, 1979, Phys. Status Solidi

a 53, 277. Drulis, M., and B. Stalinskl, 1982, Phys. Status Solidi

a 69, 385. Drulis, M., and B. Stalinski, 1989, Z. Phys. Chem. NF

163, 155. Drulis, M., J. Opyrehal and W. Borkowska, 1984,

J. Less-Common Met. 101, 211. Drulis, M., H. Drulis and B. Stalinsld, 1988b, J. Less-

Common Met. 141, 207.


Fairclough, J.EA., D.K. Ross and S.M. Bermington, 1993, in: Proc. lnt. Conf. on Metal-Hydrogen Systems, Uppsala, Sweden, 1992, Z. Phys. Chem. NE 179, 281.

Fedotov, V.K., VG. Fedotov, M.E. Kost and E.G. Ponyatovskii, 1982, Sov. Phys. Solid State 24, 1252.

Ferreira, R, G. Teisseron, E Vuillet, J.M. Gil, RJ. Mendes, A.R de Lima and N. Ayres de Campos, 1987, J. Less-Common Met. 130, 155.

Friedt, J.M., G.K. Shenoy, B.D. Dunlap, D.G. Westlake and A.T. Aldred, 1979, Phys. Rev. B 20, 251.

Fujimori, A., and L. Schlapbach, 1984, J. Phys. C 17, 341 and refereneës therein.

Gibbs, D., J. Bohr, J.D. Axe, D.E. Moncton and K.L. D'Amico, 1986, Phys. Rev. B 34, 8182.

Glinka, C.J., J.M. Rowe, J.J. Rush, G.G. Libowitz and A. Maeland, 1977, Solid State Commun. 22, 541.

Greis, O., E Knappe and H. Müller, 1981, J. Solid Stare Chem. 39, 49.

Gschneidner Jr, K.A., J. Tang, S.K. Dhar and A. Goldman, 1990, Physiea B 163, 507.

Gupta, M., 1978, Solid State Commun. 27, 1355. Gupta, M., and J.E Burger, 1980, Phys. Rev. B 22,

6074. Gygax, EN., A. Amato, I.S. Anderson, J.J. Rush and

A. Schenk, 1993, in: Proc. Int. Conf. on Metal- Hydmgen Systems, Uppsala, Sweden, 1992, Z. Phys. Chem. NF 179, 181.

Han, J.W., C.T. Chang, D.R. Torgeson, E.EW. Seymour and R.G. Barnes, 1987, Phys. Rev. B 36, 615.

Haschke, J.M., and M.R. Clark, 1975, High-Temp. Sei. 7, 152.

Herbst, G., and H. KronmüUer, 1981, Phys. Status Solidi a 66, 255.

Hunt, D.G., and D.K. Ross, 1976, J. Less-Common Met. 49, 169.

Ito, T., B.J. Beaudry, K.A. Gschneidner Jr and T. Takeshita, 1983, Phys. Rer. B 27, 2830.

Ito, T., S. Legvold and B.J. Beaudry, 1984, Phys. Rev. B 30, 240.

Iwasieezko, W., H. Drulis and R.M. Frak, 1992, J. Alloys & Compounds 180, 265.

Jacob, I., A. Wolf and M.H. Mintz, 1981, Solid State Commun. 40, 877.

Jensen, C.L., and M.E Zalesky, 1980, J. Less-Common Met. 75, 197.

Jensen, J., and R.A. Cowley, 1992, J. Phys.: Condens. Matter 4, 9673.

Jensen, J., and A.R. Mackintosh, 1991, Rare Earth Magnetism (Clarendon Press, Oxford).

Jones, RM.S., J. Southall and K. Goodhead, 1964, AWRE-Report 0-22/64 (Atomie Weapon Researeh Establishment).

Juckum, C., 1980, Ph.D. Thesis (University of Paris VI).

Jung, P., and R. Lässer, 1988, Phys. Rev. B 37, 2844. Kai, K., K.A. Gsehneidner Jr, B.J. Beaudry and D.T.

Peterson, 1989, Phys. Rev. B 40, 6591. Kaldis, E., E. Boroeh and M. Tellefsen, 1987, J. Less-

Common Met. 129, 57. Kamitakahara, W.A., and R.K. Crawford, 1982, Solid

State Commun. 41,843. Khatamian, D., and ED. Manchester, 1988, Bull. Alloy

Phase Diagrams 9, 252. Khatamian, D., and ED. Manchester, 1990, Bull. Alloy

Phase Diagrams 11, 90. Khatamian, D., C. Stassis and B.J. Beaudry, 1981,

Phys. Rev. B 23, 624. Klavins, E, R.N. Shelton, R.G. Barnes and B.J.

Beaudry, 1984, Phys. Rev. B 29, 5349. Knappe, R, and H. Müller, 1986, J. Less-Common

Met. 124, 263. Knorr, K., B.E.E Fender and W. Drexel, 1978, Z. Phys.

B 30, 265. Kulikov, N.J., 1985, J. Less-Common Met. 107, 111. Lässer, R., B. Lengeler, K.A. Gschneidner Jr and E

Palmer, 1979, Phys. Rev. B 20, 1390. Lea, K.R., M.J.M. Leask and W.E Wolf, 1962, J. Phys.

& Chem. Solids 23, 1381. Leisure, R.G, R.B. Schwarz, A. Migliori, D.R.

Torgeson, I. Svare and I.S. Anderson, I993, in: Proe. Int. Conf. on Metal-Hydrogen Systems, Uppsala, Sweden, 1992, Z. Phys. Chem. NF 179, 359.

Libowitz, G.G., 1972, Ber. Bunsenges. Phys. Chem. 76, 837 and rel. therein.

Libowitz, G.G., and A. Maeland, 1979, Hydrides, in: Handbook on the Physies and Chemistry of Rare Earths, Vol. 3, eds. K.A. Gschneidner Jr and L. Eyring (North-Holland, Amsterdam) ch. 26.

Libowitz, G.G., and J.G. Pack, 1969, 3. Chem. Phys. 50, 3557.

Lichty, L.R., R.J. Sehoenberger, D.R. Torgeson and R.G. Barnes, 1987, J. Less-Common Met. 129, 31.

Liehty, L.R, J.W. Han, R. Ibanez-Meier, D.R. Torgeson, R.G. Bames, E.EW. Seymour and C,A. Sholl, 1989, Phys. Rev. B 39, 2012.

Lueasson, A., R Vajda, J.E Burger and J.N. Daou, 1985, Solid State Commun. 54, 807.

Maeland, A.J., 1970, J. Chem. Phys. 52, 3952. Mansmann, W., and W.E. Wallace, 1964, J. Phys.

(Paris) 25, 454.

290 R VAJDA

Messer, C.E., and M.K. Park, 1972, J. Less-Common Met. 26, 235.

Metzger, T.H., P. Vajda and J.N. Daou, 1985, Z. Phys. Chem. NF 143, 129.

Mintz, M.H., D. Hierschler and Z. Hadari, 1976, J. Less-Common Met. 48, 241.

Müller, H., P. Knappe and O. Greis, 1979, Z. Phys. Chem. NF 114, 45.

Mustaehi, A., 1974, J. Phys. & Chem. Solids 35, 1447.

Ohki, C., M. Tada, Y.C. Huang, H. Uchida and H.H. Uchida, 1984, J. Less-Common Mer. 103, 103.

Ohki, C., H. Uchida and Y.C. Huang, 1989, Z. Phys. Chem. NF 163, 149.

Opyrchal, J., and Z. Bieganski, 1978, Solid State Commun. 26, 965.

Parshin, P.E, M.G. Zemlyanov, M.E. Kost, A.Yu. Rumyantsev and N.A. Chemoplekov, 1978, Inorg. Mater. 14, 1288.

Pebler, A., and W.E. Wallace, 1962, J. Phys. Chem. 66, 148.

Phua, T.T., B.J. Beaudry, D.T. Peterson, D.R. Torgeson, R.G. Barnes, M. Belhoul, G.A. Styles and E.EW. Seymour, 1983, Phys. Rev. B 28, 6227.

Pleschiutschnig, J., W. Schwarz, O. Blaschko, P. Vajda and J.N. Daou, 1991, Phys. Rev. B 43, 5139.

Rush, J.J., H.E. Flotow, D.W. Connor and C.L. Thaper, 1966, J. Chem. Phys. 45, 3817.

Saw, C.K., B.J. Beaudry and C. Stassis, 1983, Phys. Rev. B 27, 7013.

Schefer, J., P. Fischer, W. Hälg, J. Osterwalder, L. Schlapbach and LD. Jorgensen, 1984, J. Phys. C 17, 1575.

Schlapbach, L., 1992, Surface properties and activation, in: Hydrogen in Intermetallic Compounds II, ed. L. Schlapbaeh L., Vol. 67 of Topics in Applied Physics (Springer, Berlin) eh. 2.

Schlapbach, L., H.R. Ott, E. Felder, H. Rudigier, P. Thiry, J.E. Bonnet, Y. Petroff and J.P. Burger, 1986, J. Less-Common Met. 130, 239.

Schlapbach, L., J.P. Burger, J.E. Bonner, P. Thiry and Y. Petroff, 1987, Surf. Sci. 189/190, 747.

Schmitzer, C., G. Hilscher, P. Vajda and J.N, Daou, 1987, J. Phys. F 17, 865.

Schreiber, D.S., and R.M. Cotts, 1963, Phys. Rev. 131, 1118.

Senoussi, S., J.N. Daou, P. Vajda and J.P. Burger, 1987, J. Less-Common Met. 130, 55.

Shaked, H., D.G. Westlake, J. Faber and M.H. Mueller, 1984, Phys. Rev. B 30, 328.

Shaltiel, D., J.P. Burger, J.N. Daou, P. Vajda and A. Grayevsky, 1991a, Phys. Rev. B 43, 6022.

Shaltiel, D., H. Winter, E. Dormann, J.P. Burger, J.N. Daou, P. Vajda and A. Grayevsky, 1991b, J. Less- Common Mer. 172-174, 293.

Shinar, J., B. Dehner, B.J. Beaudry and D.T. Peterson, 1988, Phys. Rev. B 37, 2066.

Shinar, J., B. Dehner and BA. Beaudry, 1989, Z. Phys. Chem. NF 163, 591.

Shinar, J., B. Dehner, R.G. Barnes and B.J. Beandry, 1990, Phys. Rev. Lett. 64, 563.

Smimov, I.A., L.S. Parfen'eva, T.B. Zhukova, Kh.M. Kholmedov, V.S. Oskotski, I.N. Kulikova, V.A. Shaburov, L.G. Karpukhina, H. Drulis, M. Drulis and W. Iwasieczko, 1992, Sov. Phys. Solid Stare 34, 281.

Stierman, R.J., and K.A. Gschneidner Jr, 1984, J. Magn. & Magn. Mater. 42, 309.

Stuhr, U., D. Steinbinder, H. Wipf and B. Frick, 1993, in: Proc. Int. Conf. on Metal-Hydrogen Systems, Uppsala, Sweden, 1992, Z. Phys. Chem. NF 181, 1.

Sturdy, G.E., and R.N.R. Mulford, 1956, J. Am. Chem. Soc. 78, 1083.

Subramanian, RR., and J.E Smith, 1982, J. Less- Common Met. 87, 205.

Switendick, A.C., 1970, Solid State Commtm. 8, 1463.

Switendick, A.C., 1971, Int. J. Quantum Chem. 5, 459.

Switendick, A.C., 1972, Ber. Bunsenges. Phys. Chem. 76, 535.

Thome, D.K., K.A. Gsehneidner Jr, G.S. Mowry and J.E Smith, 1978, Solid State Commun. 25, 297.

Titcomb, C.G., A.K. Cheetham and B.E.E Fender, 1972, J. Phys. C 7, 2409.

Toguchi, K., M. Tada and Y.C. Huang, 1982, J. Less- Common Met. 88, 469.

Torgeson, D.R., J.W. Hart, C.T. Chang, L.R. Lichty, R.G. Bames, E.EW. Seymour and G.W. West, 1989, Z. Phys. Chem. NF 164, 853.

Udovic, T.J., J.J. Rush, I.S. Anderson and R.G. Barnes, 1990, Phys. Rev. B 41, 3460.

Udovic, T.J., JJ. Rush, N.E Berk and I.S. Anderson, 1992, Phys. Rer. B 45, 12573.

Udovic, T.J., J.L Rush, N.E Berk, I.S. Anderson, J.N. Daou, P. Vajda and O. Blaschko, 1993, in: Proc. Int. Conf. on Metal-Hydrogen Systems, Uppsala, Sweden, 1992, Z. Phys. Chem. NF 179, 349.

Vajda, P., and J.N. Danu, 1984, J. Less-Common Met. 101, 269.


Vajda, R, and J.N. Daou, 1991, Phys. Rev. Lett. 66, 3176.

Vajda, P., and LN. Daou, 1992a, Phys. Rer. B 45, 9749.

Vajda, P., and J.N. Daou, 1992b, Mod. Phys. Lett. B 6, 251.

Vajda, R, and J.N. Daou, 1993a, in: Proc. Int. Conf. on Metal-Hydrogen Systems, Uppsala, Sweden, i992, Z. Phys. Chem. NF 179, 403.

Vajda, R, and J.N. Daou, 1993b, The rare-earth hydrogen systems, in: Metal-Hydrogen Systems, Vol. 1, eds A. Aladjem and RA. Lewis (VCH, Weinheim) ch. 3a.

Vajda, R, and J.N. Daou, 1994, Phys. Rev. B, to be published.

Vajda, E, J.N. Daou and P. Moser, 1983a, J. Phys. (Paris) 44, 543.

Vajda, R, J.N. Daou, E Radhakrishna and G. Chouteau, 1983b, J. Phys. F 13, 2359.

Vajda, E, J.N. Daou, J.E Burger and A. Lucasson, 1985, Phys. Rer. B 31, 6900.

Vajda, E, J.N. Daou, J.R Burger, K. Kai, K.A. Gsehneidner Jr and B.J. Beaudry, 1986, Phys. Rev. B 34, 5154.

Vajda, E, J.N. Daou and J.R Burger, 1987a, Phys. Rev. B 36, 8669.

Vajda, R, J.N. Daou, J.R Burger, C. Schmitzer and G. Hilscher, 1987b, J. Phys. F 17, 2097.

Vajda, E, J.N. Daou, A. Lucasson and J.R Burger, 1987c, J. Phys. F 17, 1029.

Vajda, R, J.N. Daou and J.E Burger, 1989a, Z. Phys. Chem. NF 163, 637.

Vajda, R, J.N. Daou and J.R Burger, 1989b, Phys. Rev. B 40, 500.

Vajda, R, J.N. Daou, J.R Burger, G. Hilseher and N. Pillmayr, 1989e, J. Phys. Cond. Matter 1, 4099.

Vajda, R, J.E Burger and J.N. Daou, 1990a, Europhys. Lett. 11,567.

Vajda, R, J.N. Daou, R Moser and R Remy, 1990b, J. Phys.: Condens. Marter 2, 3885.

Vajda, R, J.N. Daou and J.R Burger, 1991a, J. Less- Common Met. 172-174, 271.

Vajda, R, J.N. Daou and J.R Burger, 1991b, J. Phys. Cond. Matter 3, 6267.

Vajda, R, J.N. Daou, R Moser and R Remy, 1991c, J. Less-Common Met. 173, 522; Solid State Commun. 79, 383.

Vajda, R, J.N. Daou and G. André, 1993, Phys. Rer. B, to be published.

Viallard, R., and J.N. Daou, 1972, in: Hydrogène dans les Métaux, Vol. 1 (Science et Industrie, Paris) p. 76.

Volkenshtein, N.V., E.V. Gatoshina, M.E. Kost and T.S. Shubina, 1983, Phys. Status Solidi b 117, K47.

Völkl, J., H. Wipf, B.J. Beaudry and K.A. Gschneidner Jr, 1987, Phys. Status Solidi b, 144, 315.

Vorderwisch, P., S. Hautecler and W. Wegener, 1980, J. Less-Common Met. 74, 117.

Waibel, F., A. Strauss, W. Potzel, EE. Wagner and G. Wortmarm, 1980, J. Phys. (Paris) 41(Suppl.), C1- 231.

Weaver, J.H., R. Rosei and D.T. Peterson, 1979, Phys. Rev. B 19, 4855.

Wegener, W., P. Vorderwisch and S. Hautecler, 1980, Phys. Status Solidi b 98, Kl71.

Wiesinger, G., and G. Hilscher, 1991, Magnetism of hydrides, in: Handbook of Magnetic Materials, Vol. 6, ed. K.H.J. Buschow (North-Holland, Amsterdam) ch. 6.

Zarnir, D., R.G. Barnes, N. Salibi, R.M. Cotts, T.T. Phua, D.R. Torgeson and D.T. Peterson, 1984, Phys. Rev. B 29, 61.

Zogal, O.J., 1987, J. Less-Common Met. 130, 187. Zogal, O.J., and R UHéritier, 1991, J. Alloys &

Compounds 177, 83. Zogal, O.J., Ch. Jäger, H. Döhler and B. Schnabel,

1984, Phys. Status Solidi a 82, K153.

Handbook on the Physics and Chemistry of Rare Earths VoL 20 edited by K.A. Gschneidner, Jr. and L. Eyring © 1995 Elsevier Science B.V.. All rights reserved

Chapter 138

MAGNETIC PROPERTIES OF INTERMETALLIC COMPOUNDS*

D. G I G N O U X a n d D. S C H M I T T

Laboratoire de Magndtisme Louis N~el, C.N.R.S., BP 166,

38042 Grenoble Cddex 9, France

C o n t e n t s

List of symbols and abbreviations 1. Introduction 2. 3d Magnetism

2.1. Onset of magnetism in Co- and Ni- based alloys

2.1.1. Collective electron metamagnetism (CEM)

2.1.1.1. The Wohlfarth- Rhodes model

2.1.1.2. RCo2 2.1.1.3. ThCo 5 2.1.1.4. Further CEM

systems 2.1,1.5, Strong

magnetoelastic effects

2.1. t .6. Spin fluctuation effects

2.1.1.7. A new model of CEM

2.1.2. Very weak itinerant ferromagnetism (VWIF)

2.1.3. Cobalt antiferromagnetism 2.2. 3d Magnetocrystalline anisotropy

2.2.1. Experimental characteristics 2.2.2. Theoretical interpretations

2.3. Instability and frustration of Mn magnetism in RMn 2 compounds

2.3.1. Topological frustration 2.3.2. Mn moment instability and

complex magnetic structures

* In memory of Remy Lemaire.

294 2.3.3. Large Mn anisotropy 322

295 2.3.4. Giant spin fluctuations 323

296 2.3.5. Theoretical approaches 325

2.4. Lanthanide-3d transition-metal 297 compounds where both carry a well

defined magnetic moment 327 298

2.4.1. General characteristics 327

298 2.4.2. Curie temperatures and 299 3d-4f exchange interactions 328 301 2.4.3. High-field magnetization

processes, 3d-4f interaction 302 and magnetocrystalline

anisotropy 331

3. 4f Magnetism 337

303 3.1. Crystal-field and exchange interactions in ferromagnetic compounds 338

304 3.2. Metamagnetism and associated phase diagrams 345

306 3.2.1, General considerations 345

3.2.1.1. Demagnetizing 308 field effects and 309 310 hysteresis 347 310 3.2.2. CEF metamagnetic systems 350

313 3.2.3. Quadrupolar metamagnetic systems 355

316 3.2.4. Ferromagnetic 316 metamagnetic systems 359

3.2.5. Weakly anisotropic 317 metamagnetic systems 363

293

294 D. GIGNOUX and D. SCHMITT

3.2.6. Spin-flip metamagnetic 5.3. Antiphase structure 409 systems: simple 5.4. Collinear and noncollinear structures 409 antiferromagnets 367 5.5. Commensurate and incommensurate

3.2.7. Modulated metamagnetic structures 409 systems 369 5.6. Equal-moment structure 410

3.2.8. Spin-flip metamagnetism: 5.7. Exchange interaction J(/j) and Fourier long-period commensurate transform J(q) 410 systems 373 5.8. Fan structure 410

3.2.9. Spin-slip metamagnetism: 5.9. Flopside structure 411 long-period commensurate 5. i 0. Frustration 411 systems 378 5.11. Helical structure 412

3.2.10. Complex multistep 5.12. Helifan 413 metamagnetism: long-period 5.13. Multiaxial structure 413 commensurate systems 380 5.14. Multistep metamagnetic process 413

3.2,11. Planar metamagnetic 5.15. Multi-Q structure (double, triple . . . . ) 413 systems 390 5.16. Quadrupolar moment 413

3.2.12. Multiaxial metamagnetic 5.17. RKKY (Ruderman, Kittel, Kasuya, systems 394 Yosida) exchange interaction 414

3.3. Quantitative analysis of 5.18. Single-Q structure 415 incommensurate magnetic systems 399 5.19. Spin-flip transition 415

4. Summary and conclusion 406 5.20. Spin-flop transition 415 5. Appendix: Definitions and/or descriptions of 5.21. Spin fluctuations 416

magnetic terms or phenomena 408 5.22. Spin-slips (or spin discommensura- 5.1. Antiferroquadrupolar and tions) 416

ferroquadrupolar ordering 408 5.23. Spin-reorientation transition 417 5.2. Amplitude-modulated structure 408 References 417

Lis t o f s y m b o l s a n d abb rev i a t i ons

a, b, e basis vectors of the unit cell J total kinetic moment operator

a*, b*, c* basis vectors of the reciprocal unit J1 exchange interaction between cell nearest neighbours

AM amplitude modulated Jz exchange interaction between B magnetic induction second-nearest neighbours

B~ crystal field parameters J(ij) exchange interaction between

C phase commensurate phase moments i andj CEF crystalline electric field J(q) Fourier transform of the exchange

interactions CEM collective electron metamagnetism

J(0) paramagnetic exchange parameter EM equal moment

k B Boltzmann constant F free energy

K reciprocal lattice vector FOMR first-order magnetic reorientation Gj tetragonal quadrupolar parameter K~ second-order anisotropy constant of

tmiaxial systems G2 trigonal quadrupolar parameter L orbital kinetic moment operator gj Land~ factor

LMTO linear muffin tin orbital H magnetic field

M chemical symbol for 3d transition 7-( Hamiltonian metals

I phase incommensurate phase M magnetization INS inelastic neutron scattering

MAGNETIC PROPERTIES OF INTERMETALLIC COMPOUNDS 295

M s component of the total kinetic Tt~ Nrel temperature moment TQ quadrupolar ordering temperature

M-NM magnetic-nonmagnetic T R spin reorientation temperature n, n bilinear exchange coefficient Ts F spin fluctuation temperature n(/?F) density of states at the Fermi level Tt, TI, T2, ... transition temperatures N a demagnetizing field factor TEC thermal expansion coefficient N number of moments per magnetic U Coulomb repulsion or exchange

unit cell energy NMR nuclear magnetic resonance VWIF very weak itinerant ferromagnetism O~ Stevens operators W bandwidth PF model periodic field model F i irreducible representation of a Q propagation vector of magnetic symmetry group

structure y electronic specific heat coefficient q vector of the reciprocal space eF Fermi energy R chemical symbol for rare earth, )~ spin orbit coupling constant

lanthanide ~ wavelength R i position of atom i #B Bohr magneton RKKY Ruderman-Kittel-Kasuya-Yosida ~tSR muon spin resonance RPA random phase approximation r incommensurate component of the S Stoner enhancement factor magnetic propagation vector S spin kinetic moment operator X magnetic susceptibility SCR self-consistent renormalization Z~) third-order paramagnetic T c Curie temperature susceptibility

1. Introduction

This chapter is devoted to the magnetic properties of rare earth intermetallic compounds investigated during the last fifteen years. The earlier works in this field have been described by Kirchmayr and Poldy (1979) in a previous chapter of this Handbook series (volume 2, chapter 14), During the last 15 years, research in magnetism can be characterized by a boom in the field o f rare-earth (R)-based materials, in part icular the metall ic ones. Currently, rare earth intermetallics are in a prominent situation not only from a fundamental point of view but also for the large number of technological applications, in part icular in the field o f permanent magnets. Rare-earth intermetallics play an important role in a large range o f current research fields, in particular those devoted to heavy fermions, valence fluctuations, Kondo lattices, magnetostrictive materials, permanent-magnet materials, spin glasses and random anisotropy systems. Since these aspects o f magnet ism in rare-earth intermetallics are treated elsewhere, they will not be discussed here. In this chapter we are mainly concerned with the basic properties of intermetall ic compounds with normal lanthanides, i.e. those with a well localized 4f shell. This means that most o f the Ce and Yb materials are excluded. Furthermore, rather than giving an exhaustive report on magnetic properties with many physical values reported


in tables, we prefer to emphasize what we consider to be the major steps in this field of research during the period under consideration.

This chapter is divided into two major parts. The first part is devoted to systems in which the obtained results led to a better knowledge of 3d magnetism. Four major aspects will be considered. First (sect. 2.1), the onset of magnetism in Co and Ni, in which the major part is devoted to the systems where collective electron metamagnetism has been observed. The understanding of the large 3d magnetocrystalline anisotropy of many intermetallic compounds is treated in sect. 2.2. In the cubic Laves phase RMn2, the instability of Mn magnetism together with the topological frustration of antiferromagnetic interactions lead to quite original properties which are at the origin of new physical concepts and theoretical approaches. The magnetic properties of these fascinating compounds are presented in sect. 2.3. The last section of this part is devoted to rare- earth-3d transition-metal compounds where both carry a well defined magnetic moment. These compounds generally are excellent materials for permanent-magnet applications, but only the last results obtained concerning their intrinsic properties are presented.

The second part of this chapter concerns the magnetic properties of compounds in which only the lanthanide atom is magnetic. After a description (sect. 3. I) of recent progress made in the quantitative knowledge of the main interactions (exchange and crystal field) in the small number of lanthanide-based series which are ferromagnetic, the main purpose of this part is devoted to the compounds which exhibit metamagnetic processes of quite different origins (sect. 3.2). Because of the long range and oscillatory character of the indirect RKKY exchange interaction the majority of these compounds order antiferromagnetically with complex magnetic-field-temperature phase diagrams often characterized by the competition between commensurate and incommensurate magnetic structures. Dramatic progress has been made in the knowledge of these systems during the last decade due to the improvement of experimental devices, the increasing number of single crystals of good quality and the evolution of theoretical models. Parallel to the experimental advances in this field, theoretical models have been proposed to quantitatively analyze these complex phase diagrams, in particular the incommensurate magnetic systems, which is the purpose of the last section (sect. 3.3) of this part.

In this chapter a large number of experimental results and theoretical approaches, already presented in previous review papers, are assumed to be known. The reader will find useful information in the reports on rare-earth-based intermetallic compounds by Buschow (1977a, 1979, 1980, 1988) and by Kirchmayr and Poldy (1979).

2. 3d Magnetism

The R-M systems, where M is a 3d transition metal, form an outstanding tool for the study of 3d band magnetism and in particular the interactions, instabilities and anisotropies of such magnetism. In the majority of cases, for a given M element, a series of compounds with different rare earths crystallize in the same crystallographic structure and thus have practically the same band structure. It is then possible to study the 3d magnetism under


several conditions depending on the rare earth (nonmagnetic or magnetic, isotropic or not, different sign of the magnetocrystalline anisotropy parameters . . . . ). Many studies are devoted to these systems and it is impossible to describe all the results obtained. We focus on the most original advances in 3d magnetism discovered in R-M intermetallic compounds during the last decade.

2.1. Onset of magnetism in Co- and Ni-based alloys

These compounds are formed by the association of the 3d band of the M element with the 5d band of R (4d for Y) with higher energy. The electronegativity difference between the constituents causes a transfer of 5d (4d) electrons towards the unfilled 3d band. Since the screening of the nuclear potentials by the electrons is modified, the two bands approach each other leading to 3d-5d (or 3d-4d) hybridized states (Cyrot and Lavagna 1979, Shimizu et al. 1984). The Fermi level of the compounds often lies in this region of the density of states. This itinerant description of 3d magnetism is the most appropriate for Co and Ni in which, due to the width of the 3d band, the Un(ev) product (U is the Coulomb repulsion or exchange energy between up and down spins, and n(eF) the density of states at the Fermi level) is smaller than unity (with Mn and Fe this ratio is closer to unity and accordingly magnetism is more localized). Starting from pure Ni or Co, the progressive increase of the R percentage leads first to a decrease of the density of states at the Fermi level n(eF). For a critical concentration range (around RCo2 for cobalt and RNi5 for nickel) alloys are close to the conditions required for the onset of magnetism (Stoner criterion) and magnetic instabilities can be observed, each behaviour strongly depending on the fine structure of n(e) near eF. However, resurgence of 3d magnetism appears for a slightly larger R amount and then disappears altogether as shown in fig. 1.

e--

~ 6 - o ~ g o ( .9 e , l

I I ~ . - _ _ I I + L a x C O l _ x

g • Yxcol-x 1.5 " , + ,-~

. -~ ~,',ec o Y x N , l _ x

~r , g, v I i i k )

1.0 ~+I m g o ...1

'I ~ +'

0.5 ~, ~; '

t, t - - , ~ o

~ c 9

0 0.1 0.2 0.3 0.4

t ~

5- u

c,4

I

+

0'.5 x ~-

Fig. 1. Mean value of the 3d moment as a function of the rare earth concentration in the compounds of the La-Co, Y-Co and Y-Ni systems (Gignoux and Schmitt 1991).


Three types of characteristic behaviours are mainly observed for R concentrations near or larger than the critical ones, namely collective electron metamagnetism (CEM), very weak itinerant ferromagnetism (VWIF) and Co antiferromagnetism.

2.1.1. Collective electron metamagnet i sm (CEM)

2.1.1.1. The Wohl far th-Rhodes model. Collective electron magnetism (CEM), predicted in 1962 by Wohlfarth and Rhodes (1962), refers to the transition from a nonmagnetic to a magnetic state when the field acting on the band is larger than a critical value HM. Using a Landau-type expansion of the magnetic free energy of the d-electrons, such as

F = A M 2 + B M 4 + C M 6 + . . . . M H , (1)

the theory led to the following expressions for the first lower-order coefficients

1 2] B-=-64n3(eF) 3n(eF------) - \ n(eF) J J ' (3)

where S = (1 - Un(eF)) -1 is the Stoner enhancement factor, n, n' and n" are the density of states and its first and second derivatives at the Fermi level. CEM occurs when the magnetization dependence of F has the upper variation shown in fig. 2a in zero field and it becomes the lower curve of this figure above the critical field HM. The corresponding expected low-temperature magnetization curve is shown in fig. 2b. The above formulae show that such a behaviour can occur when: (1) A is weakly positive, i.e. when the Stoner criterion for the onset of ferromagnetism is almost satisfied, and (2) B is negative, which implies another minimum for a nonzero value of M. This latter condition requires n"(eF) to be large enough, which means that the density of states at the Fermi level has a strong positive curvature.

The system is now a Pauli paramagnet in low field and the thermal and field dependences of its susceptibility are given by

[,7~2(.BH(EF) Rt(EF) 2 ) S3(Bt"(EF)_nt(EF)2"~H2 ] X = SXo 1 - - -~S T 2 + • + . . . (4 )

This formula shows that a maximum in the thermal variation of the susceptibility, having the same origin, is also predicted (fig. 3b). Because of this increase of the susceptibility with temperature, the shape of the magnetization curves changes with temperature; the magnetization discontinuity tends to decrease and even to disappear above a given temperature. The high magnetization state is then reached continuously (fig. 3a).

This behaviour, which was assumed only to occur on Co in RCo2, but had not been directly observed until the late seventies, has since clearly shown up in several rare- earth-transition-metal alloys. The best examples are RCo2 and ThCo5 which are presented below.

1 A - 4n,gF,---~ o , o t ) (2)

MAGNETIC PROPERTIES OF 1NTERMETALLIC COMPOUNDS 299

z~F (a)

H=0

HE

/ M =

M (b)

i

H~ H M H~

H

Fig. 2. Collective Electron Metamagnetism. (a) Variation of the difference between the free energy of the ferromagnetic and paramagnetic states as a function of magnetization at different fields; (b) variation of magnetization with increasing field (Barbara et al. 1988).

M~ (a)

0 H M I~

X (b)

T2 Fig. 3. Schematic representation of the Collective Electron Metamagnetism. (a) M vs. H at various temperatures; Co) thermal variation of the initial susceptibility (Gignoux et al. 1983).

2.1.1.2. RCo2. As shown in fig. 1, RCo2 compounds are at the limit o f the onset o f Co magnetism. In these cubic Laves-phase compounds Co atoms belong to one crystallographic site. With magnetic rare earths the compounds are ferromagnetic (with light lanthanides) or ferrimagnetic (with heavy lanthanides) and, below the Curie temperature, Co is magnetic with a moment close to I#B. Conversely in YCo2 and LuCo2, Co is nonmagnetic (Lemaire 1966). These latter compounds are enhanced Pauli


20

A 18 ol

v- 12

,.J

-~ ~o n

U8

~ 6

YCo2

...........

,6o 26o 36o TEMPERATURE (K)

Fig. 4. Thermal variation of the susceptibility of YCo 2 and LuCo 2 (Gignoux et al. 1983).

0.5

LJ

Y(C°I"xAtx)2 ' ~ ' J r-,..

4.2K ~ ~ - - ~ " 1 ¢,...~ O0'6

t/oo, I/t= 0,

0 10 20 30 B (T)

Fig. 5. Magnetization curves of Y(Col_xAlx)2 at 4.2 K

(Sakakibara et al. 1987).

z,o

T=IO K LuC° U

20 40 60 80 100 H(T)

Fig. 6. Magnetization curves of YCo 2 and LuCo 2 at 10 K in pulsed ultra-high magnetic field up to 94 T (Gignoux and Schmitt 1991, after Goto et al. 1990). The magnetization data measured in a long pulse field are also plotted as dots.

paramagnets but the field and thermal effects indicate the possibility o f CEM. Indeed, in YCo2 and LuCo2 the susceptibility exhibits a broad maximum around 230 K and 370 K, respectively (fig. 4). Moreover, at 4.2 K the superimposed susceptibility o f YCo2 increases by about 20% between 0 and 35 T (Bloch et al. 1975), whereas in LuCo2 this effect is much smaller (Schinkel 1978). Actually, CEM was not observed because this maximum magnetic field was smaller than the critical field HM o f the metamagnetic transition. With


magnetic rare earths the high magnetization state was reached owing to the molecular field contribution of the rare earth. Moreover, the first-order transition observed at the Curie temperature in some of these compounds, namely DyCo2, HoCo2 and ErCo2, has been ascribed to the collapse of the Co magnetic moment at this temperature (Lemaire 1966, Petrich and M5ssbauer 1968, Givord and Shah 1972). In 1977, polarized neutron diffraction studies on TmCo2 and HoCo2 carried out by Gignoux et al. (1977) showed that HM should be smaller than 100T (around 70T with Tin). From a theoretical point of view, the first calculations (Bloch et al. 1975) led to a much larger value of Hr~ (142 T). Later, more realistic band structure calculations led to H ~ values around 80 T (Cyrot et al. 1979, Yamada et al. 1985, 1987, Yamada and Shimizu 1985, 1990). In order to directly observe the metamagnetic transition in this system, a large effort was undertaken to depress the critical field by substitution effects, and in 1987 this was obtained by substituting a small amount of A1 for Co in YCo2 and LuCo2 (Sakakibara et al. 1987) where the transition occurs below 40 T (fig. 5). In the Y(Col-xFex)2 system, although less dramatic, the CEM has been observed for 0.04 ~< x <~ 0.07 (Yoshimura et al. 1987). Finally, the most dramatic event in this fascinating story occurred quite recently thanks to the availability of magnetic measurement up to 94 T: as shown in fig. 6 the metamagnetic transition was directly observed in YCo2 and LuCo2 around 70T (Goto et al. 1990) in rather good agreement with the values calculated and those experimentally determined with a magnetic rare earth.

2.1.1.3. ThCo5 (Givord et al. 1979). As shown previously with trivalent rare earths, the critical concentration for the onset of Co magnetism is achieved in the RCo2 compounds, but this limit is close to the RCo5 composition with tetravalent R such as Th or Ce. Although Th is not a rare earth, ThCo5 has the same hexagonal CaCus-type crystallographic structure as the RCo5 series. In these compounds Co atoms are located at two different crystallographic sites. Only those at the 2c site are ferromagnetic. Within the homogeneity range of the ThCo5 phase, the magnetic properties strongly depend on the composition. The Curie temperature increases from 410K for ThCo5 to 730K for Th0.92Co5.16 (Van der Goot and Busehow 1971). As sketched in fig. 7c (lower part), in the Co-poor compounds, the temperature dependence of the spontaneous magnetization and that of the superimposed susceptibility show a maximum near 200 K (Ganapathy et al. 1974). Below 100K, a transition towards a state of higher magnetization is induced by a large applied field (fig. 7c, upper part). Above the transition, the magnetization reaches a value close to that of the spontaneous magnetization in the Co-rich compounds. Study of these two magnetization states by polarized neutron diffraction (Givord et al. 1977, 1979) has shown that: (i) in the low magnetization state, the magnetic moment is lower by about 20% on the Co3g atoms (0.96gB) than on the Co2c ones (1.21/~B); (ii) in the state of high magnetization, magnetic moments are the same on both sites (1.58/~B); and (iii) on the crystal of low spontaneous magnetization, i.e. the compound with the exact ThCo5 stoichiometry, the maximum of the temperature dependence of the spontaneous magnetization and superimposed susceptibility originate from the Co3g atoms. It is therefore concluded that these atoms exhibit CEM.

302

M~ 4.2 K M~,~ 4.2 K

I i Hc--HM-HE

D. GIGNOUX and D. SCHMITT

total field 0 applied field H A H T 0 applied field H A

o ~ o ~r o

(a) (b) (c)

Fig. 7. Schematic field and temperature dependences of the spontaneous magnetization M s and the superimposed susceptibility of (a) Co 2c atoms, (b) Co 3g atoms and (c) ThCo 5. Abbreviations: HA, applied field; HE, exchange field on the Co 3g atoms due to the Co 2c atoms; HT=HB+HA, the total field acting on Co 3g atoms; HM, the critical field for metamagnetism for Co 3g atoms; Hc, experimental transition field in ThCo 5 (Gignoux et al. 1983).

The magnetic properties of ThCo5 are schematized in fig. 7. The Co2c atoms are ferromagnetic, they exhibit a spontaneous magnetization. The superimposed susceptibility is almost constant below room temperature and close to that in YCo5 (fig. 7a). Co3g atoms exhibit a large enhanced paramagnetism with a susceptibility maximum around 200 K and are close to the condition for CEM. Magnetization, which is induced on these Co3g atoms by the exchange field HE arising from Coac atoms, then exhibits a maximum at the same temperature as the susceptibility (fig. 7b). The exchange field is slightly lower than the critical field for CEM. The latter can be reached in the Co-poor compounds in an applied field (as is observed in the stoichiometric compound), and in the Co-rich compounds such as Th0.92C05.16 by an increase of the exchange field on the Co3g atoms, caused by statistical substitutions of Co dumbbells on Th atoms, as usually occurs in the RCo5 system.

2.1.1.4. Further CEM systems. Within the homogeneity range of the CeCo5 phase, in which Ce is tetravalent, Co atoms are in a high magnetization state. The exchange interactions can be reduced by replacing the cobalt atoms by nonmagnetic nickel atoms and in Ce(Co0.93Ni0.o7)5 the field dependence of magnetization exhibits the same transition at low temperature as in ThCo5 as a result of the CEM of one part of the Co atoms (Givord et al. 1983).

Figure 1 shows that Ni magnetism falls rapidly with the R content. It is then not surprising that within their homogeneity range, the magnetic properties of the weak Y2Nil7 ferromagnet strongly depend on the stoichiometry. In particular in Y2Ni16


the thermal variation of the spontaneous magnetization and the low-temperature field dependence of the magnetization, although less pronounced, are analogous to those of ThCo5 showing a CEM behaviour of one part of Ni atoms (Gignoux et al. 1980a).

2.1.1.5. Strong magnetoelastic effects. Besides their magnetic properties, large magnetoelastic effects associated with the transition between magnetic and nonmagnetic states of Co have been observed in RCo2 and derived compounds. In the early seventies, large and negative pressure effects were measured on the Curie temperatures of magnetic RCo2 (Bloch et al. 1971, Voiron and Bloch 1971) and on the susceptibility of YCo2 (Voiron et al. 1973). As well, all the RCo2 compounds show an Invar-like thermal expansion anomaly below their Curie temperature and the large observed positive magnetic contribution to the spontaneous volume expansion (fig. 8) was found to be proportional to the square of the Co magnetic moment (Minakata et al. 1976, Lee and Pourarian 1976). Such a M:(Co) dependence of the spontaneous volume magnetostriction was also observed in Gdl-xYxCo2 (Muraoka et al. t983, 1984) and Gd(Col_xNix)2 (Tanaka et al. 1980). Let us quote also that in the Y(Col-xAlx)a compounds with 0.095 ~ x ~<0.12 a large volume change associated with the metamagnetic transition has been observed (fig. 9). It is also found to be proportional to the square of the magnetization in both paramagnetic and ferromagnetic regions (Wada et al. 1988).

These magnetovolume effects can be treated theoretically in the framework of the itinerant electron model and were, up to recently, interpreted as a consequence of the kinetic energy cost arising from the splitting of the 3d band when passing from the nonmagnetic to the magnetic state of Co, this energy cost being then minimized by a volume expansion, the 3d energy bandwidth being highly dependent on the atomic separation. In a first approximation, the increase in kinetic energy and, accordingly, the volume change are proportional to the square of the magnetization. Self-consistent spin-polarized energy band calculations performed by Janak and Williams (1976) led to an overestimation of the volume change. Later a better account of the experimental

10

8

A

O

2

0 0

Spontaneous Magnetostriction of RCo 2

A GdCo 2 B TbCo 2 C Dy Co 2 D HoCo 2

" ~ . . , , ~ " ~ - ~ . E ErCo2

100 200 300 aO0 500 T(K)

Fig. 8. Temperature dependence of the magnetic contribution to the spontaneous volume magnetostriction of the RCo 2 compounds. The arrows indicate the Curie temperatures (Minakata et al. 1976).

304

15

10

5

~ 0 _J .J 5


Y(C°I' x AIx)'2 '

4 .2K x ~ = 0.0s5

x=OA05

~ i , i i 0 10 20 30

H (T) Fig. 9. Longitudinal magnetostriction curves of Y(COl_xAlx) 2 at 4.2K (Wada et al. 1988).

results has been obtained taking into account spin fluctuations (see Nakamura 1983 and references therein).

2.1.1.6. Spin fluctuation effects. It is well known that the Stoner (or Hartree-Fock) theory, which considers only individual excitations of electron-hole pairs with opposite spins, fails to take into account thermal effects of itinerant electron magnetism. Collective modes of spin fluctuations, particularly in nearly ferromagnetic (or antiferromagnetic) systems play a crucial role in thermal properties such as specific heat and magnetic susceptibility. For this purpose much attention has been paid to the RCo2 compounds to test the different itinerant-electron theories of magnetism. The first approach, using the random phase approximation (RPA) pointed out that spin fluctuations in the paramagnetic phase (paramagnons) induce a logarithmic dependence on temperature of the electronic specific heat coefficient 7 (Doniach and Engelsberg 1966, Berk and Schrieffer 1966) and lead to an enhancement of the coefficient of the T 2 term in the magnetic susceptibility (B6al-Monod and Lawrence 1980). These latter authors introduced a spin-fluctuation temperature TSF = kBeF/S, where eF is the Fermi energy, to show that the thermal effects have to appear at much lower temperatures than those expected in a model which takes into account the individual excitations only. x(T, H) has almost the same dependence as


in eq. (4) with respect to n", n' and n, but the coefficient of the T 2 term is proportional to S 3 instead of $2:

6 2 n--~F) l . Z ~ ) T2+~CH2+ ... (5)

where C is a coefficient which may be different from that in eq. (4) but which also depends on the band structure (B~al-Monod 1982). This model led to a better simultaneous quantitative account of field effect at low temperature and the susceptibility maximum of YCo2 and LuCo2. Later Misawa (1988) has shown that the thermal variation o f z was proportional to T 2 In T rather than T 2. It was pointed out by Brinkman and Engelsberg (1968) and by B6al-Monod et al. (1968) that the application of a high magnetic field quenches the spin fluctuations. This quenching has been evidenced in YCo2 and LuCo2 (fig. 10) from specific measurement where the y coefficient is reduced by a factor of 4% and 10% respectively in a field of 10 T (Ikeda et al. 1984, Ikeda et al. 1991 and references therein). Using a self-consistent renormalization (SCR) theory of spin fluctuations, a unified picture has been proposed of itinerant magnetism ranging from the localized limit, for which the spin fluctuations are localized in space, and the limit of weak itinerant ferromagnetism (or antiferromagnetism), for which spin fluctuations are localized in the reciprocal space (Moriya and Takahashi 1978, Moriya and Hasegawa 1980, Moriya 1991 and references therein). Among the results of this approach one can quote the quantitative description of the nuclear spin relaxation rate and the high-temperature susceptibility. The latter follows a Curie-Weiss law without localized moments and the Curie constant, which is then a measure of the spin fluctuations, is the sum of two contributions, C = Ct + CI, where Ct corresponds to transverse fluctuations of the localized limit and CI corresponds to longitudinal fluctuations of the itinerant limit. The ratio between the effective moment deduced from the Curie constant and the low-temperature saturation moment allows one to evaluate the preponderant nature of spin fluctuations. High-temperature susceptibility measurements performed on RCo2 allowed one to observe the Curie-Weiss behaviour and to derive the effective moments which are reported in fig. 11 as a function of the

1 4 t ~ i i ~ i i i

t3 Lu Co 2 ~

(35.0 ot.°/o Lu) ,,,~T,~6,~,"'J

~ , ~ . . ~ . . , e - ~ o 0 .00 T I0 ~@li~ i~,~ ^ " 2.50

8 x 9.98

7 1 i i i i i r / i

4 8 12 16 20 24 28 52 36 T2( K 2 )

Fig. 10. Heat capacity of LuC% at five magnetic fields (Ikeda et al. 1984).


z+ILu~ °2 l'%fflCo) spin only

7 3 o.

e_

tlt= t t "~ TmCo21 PrCo ~ NdCo~ Dy[o~

ErCo2 HoCo2 1

]

too

o

TbCo2

I I

CadCo2

200 300 t,00 T c (K) L

Fig. 11. The effective cobalt moments as a function of Curie temperatures in RCo 2 compotmds (Burzo and Lemaire 1992).

Curie temperature Tc (Burzo and Lemaire 1992). These Co effective moments are well above the saturation Co magnetic moment (~I#B) and steadily decrease from about 4#B in YCo2 and LuCo2 to about 2.6/~B in GdCo2 which has the largest Curie temperature. This decrease has been ascribed to the quenching of spin fluctuations by the internal field, as does an applied field, leading then to a decrease of the Curie constant. Finally it is worth noticing that the nuclear magnetic relaxation observed in YCo2 (Yoshimura et al. 1984) is well accounted for with the SCR theory of Moriya of spin fluctuations in weakly or nearly ferromagnetic metal.

2.1.1.7. A new model o f CEM. Up until now the CEM, in agreement with the prediction of Wohlfarth and Rhodes (1962), was ascribed to a special shape of the density of states near the Fermi level in systems where the Stoner criterion is almost satisfied. As shown above the large magnetovolume effects were considered as a consequence of the magnetic-nonmagnetic state transition. Band calculations were then performed in order to check if in the compounds which exhibit CEM the density of states had the expected shape (Yamada et al. 1984, 1985, 1987, Yamada and Shimizu 1985). Indeed, band calculations were performed in the tight binding approximation. From the deduced density of states and taking into account the effect of spin fluctuations, relevant parameters were found for RCo2 which fit the thermal variation of the susceptibility of YCo2 and LuCo2, and which lead to critical fields of the metamagnetic transition close to those later observed by Goto et al. (1990). Actually, given the rather large number of systems close to the onset of magnetism and exhibiting CEM, it is a little surprising that, in all


cases, the density of states presents a peculiar variation near the Fermi level. So in 1992, Duc et al. (1992) proposed a new approach to CEM. For any shape of the density of states this phenomenon would simply result from the interplay between the magnetic and elastic energies. Considering the variation of the bandwidth with volume, it is shown that the transition towards magnetism is determined by the balance between the elastic energy, which increases with volume, and the magnetic energy, which decreases when the volume increases, in the ferromagnetic phase. Assuming an elliptic density of states n(e) = ( 1 / ~ W 2 ) ~ W -'~ - e 2 (2W =bandwidth) in order to exclude the type of instability to which CEM was previously ascribed, the total energy in the Stoner model at 0 K is written as Etot = Eel + Elat, where Eel is the electronic energy,

rE+ rE- UM 2 Eel = e n(e) de + e n(e) de M H , (6) rv w 4It~3

and Elat the lattice energy:

Elat = Cg2 + K(22, (7)

with £2 = ( V - Vo)/Vo (Vo being the volume in the paramagnetic state) and K is the contribution to the elastic constant due to all terms other than the band contribution. C is determined by the condition

OEel para, ~c2--0 o ~ + c = 0. (8)

In the tight binding approximation the bandwidth decrease with the volume increase is given by W = W0 exp(-qf2), where q is of the order of 1 to 5/3 for 3d electrons. Under these conditions, when the filling of the band (about 9.6 3d electrons per atom) is such that the Stoner criterion is almost satisfied, one can have the variation of Etot with g2 shown in fig. 12, where the variation of the magnetization is also reported. In the presence of a field (exchange and/or applied) one obtains the evolution of the total energy shown in fig. 13a. A metamagnetie transition, associated with a large volume discontinuity, then occurs for a critical field (fig. 13b). For fillings of the d band smaller or larger than that necessary for CEM, ferromagnetic or paramagnetic states are stable, respectively. This is the reason why, for an excess of Co in ThCos, both Co sites are in the high magnetization state, the filling of the 3d band being smaller than in the stoichiometric compound. This model gives account for alloying effects in Y(Col-xAlx)2 where the volume increases with the A1 concentration, leading to a transition from Pauli paramagnetism to ferromagnetism for a critical concentration x ~ 0.13. At larger AI concentration, ferromagnetism disappears again due to the dilution of Co atoms by nonmagnetic A1. Note that in this model, metamagnetism cannot be expected in materials where K is too small or too large. This has been studied experimentally in Y(CoxAlyCuz)2 where, when ehoosing the A1 vs Cu concentration in order to maintain the band structure, it is found that by adding Cu


-2.003

-2.004

-2.005

-2.006

-2.007 -0.05

i i i 1

j -OM -Qc

I I ~ ¢ / I I

0

0.5

0.4

0.3

0.2

o.1

o 0.05 0.10 0.15 0.20

£2

Fig. 12. Calculated variations of the total energy and magnetization as a function of volume £2 for N=9.55, K=2.6eV, U=2.5eV and Wo=5eV after Due et al. (1992). N, number of d electrons per atom; K, contribution to the elastic constant due to all terms except the band contribution; U, exchange energy; 2Wo, bandwidth at £2=0.

-2.002 -2.004 -2.006

~-2 .008

-2.010

-2.012

-2.014 -2.016

0

2 0.05 0.10 0.15 0.20 0.25

0.5

3.4

0.3

9.2

0.1

b)

/ I

0 100 500

00"20[ °1°1[ 0.12[

2 f 0 200 400

, j H(T),

200 300 400 H (T)

Fig. 13. (a) Calculated total energy for the same parameters as in fig. 12, for different magnetic fields; (b) calculated curve M(H) for the same parameters (after Due et al. 1992).

the metamagnetic transition disappears (Due, unpublished). This can be attributed to the decrease o f K since Cu is very stiff. Finally let us note that similar models for nonmagnetic-magnetic transitions have been proposed for other systems where strong volume effects are observed, in particular in cerium heavy-fermion compounds (Lavagna et al. 1983, Ohkawa 1989).

2.1.2. Very weak itinerant ferromagnetism (VWIF) Whereas YNi5 is a Pauli paramagnet, the resurgence o f 3d magnetism observed in YNi3 (Gignoux et al. 1980b) and Y2Ni7 (Ballou et al. 1990b), as shown in fig. 1, must be associated with the fine structure o f n(e) in the region of 3d-4d hybridized states, such that n(eF) is large enough for the Stoner criterion to be fulfilled. Bulk magnetic properties are similar to those o f ZrZn2 o f which the behaviour can quite well be described within the model o f very weak itinerant ferromagnetism (Wohlfarth 1951). The magnetization is weak and strongly field dependent at all temperatures. The Arrott plots (M 2 versus H/M) show a linear variation, and the variation o f M2(H = O, T) as a function o f T 2 is also linear. However, contrary to ZrZn2, magnetization is not diffuse but localized at the Ni sites, as shown on the magnetization density map in YNi3 determined from polarized neutron diffraction experiments on a single crystal (fig. 14). This localization difference originates from the difference in the magnetic states in the band. Indeed, the magnetism in ZrZn2 is due to 4d electrons with a bonding character at the bottom o f the 4d band

MAGNETIC PROPERTIES OF INTERMETALLIC COMPOUNDS

@ Y o Ni

z, o 2Ni

,i

0 o Q @ o@ o@

c ax is o 0 o

~ o l o o l , 0 o 0 o

" @o • NilI~YI

N i I ~ *

0 1 y (a)

z

0.33: - - •

0.161 - -

0,082 i

L./

k ~ <-'_'-_=._-z'~ c , i~--~-~--. _-~,,-2. ~-L- , - 3~ 0.90

( -1.4o

• \ t t t ~ c . ~ ) ) ? l t - - - A - o.m

-> , ~ - -.. - C.'>"

:-... ~'i "~- ~ ~ ' - - 0.30

--0.45

0.5 y

( b )

309

Fig. 14. Magnetization density map in YNi 3 at 4.2 K (projection along the a axis of the hexagonal cell). The contours are in units of 10-'p,B/,~ 2 (Gignoux et al. 1980b).

while in YNi3 and Y2Ni7 the 3d electrons, which contribute to magnetism, lie at the top of the 3d band and have antibonding character.

2 .1 .3 . C o b a l t a n t i f e r r o m a g n e t i s m

In the LaCol_e (e=0.15) and La2Co3 compounds, although the La amount is larger than the critical concentration (RCo2) for the onset of magnetism, one observes a resurgence of magnetism characterized by an antiferromagnetic ordering with a large Nrel temperature (146 K and 315 K, respectively) (Gignoux et al. 1985). This resurgence as well as its antiferromagnetic character (quite unusual in a Co-based metallic system) can be understood in the light of the crystallographic structure of these compounds. In LaCol-e, La atoms form an ABAB-type hexagonal packing while Co atoms lie along chains parallel to the 6-fold axis. The Co-Co distance (2.36A) in a chain is much smaller than the distance between chains (4.89 A) and incommensurate with the c parameter of the La skeleton. Moreover weak correlations in Co positions manifest themselves between the chains. All this leads to the exciting phenomenon of quasi- unidimensionality of the Co lattice. This compound has a triangular magnetic structure with Co atoms, belonging to the same chain, ferromagnetically (Mco = 0.7 ~tB) coupled with their moment perpendicular to c. These chains are divided into three sublattices of which the magnetizations make an angle of 120 ° (fig. 15). Ferromagnetism inside a chain arises from the quasi-one-dimensional character of Co. As shown by Weinert and Freeman (1983), the large reduced dimensionality of linear chains gives rise to large moments and exchange values as compared to those of the bulk. The triangular magnetic


LaCo1_ E

\ /'A / 2V_:/-" V ! V

o[O ,ka

Fig. 15. Magnetic structure of LaCol_ ~. Moments of Co atoms of the same chain, which is parallel to the c axis, are parallel with each other (Gignoux et al. 1985).

structure between chains results from the frustration of negative interactions between neighbouring chains in a triangular (hexagonal) lattice. These interactions cannot arise from direct exchange which, on account of the large interchain distances, is expected to be negligible.

This unusual negative interaction in metallic Co systems must therefore originate from an indirect C o L a - C o exchange through the 3d-5d hybridization bearing strong analogy with superexchange in insulators. When the 3d magnetism is established, the 3d-5d hybridization induces a polarization of the 5d electrons. The system takes then advantage of a spin distribution which minimizes the 5d electron kinetic energy and gives rise to an antiferromagnetic coupling between chains. This indirect Co-La-Co negative exchange interaction is easily affected by exchange scattering due to RKKY interactions which polarize the 5d electrons in the vicinity of the 4f shells as it is shown by the change into collinear ferromagnetism when La is replaced by Pr or Nd (Ballou et al. 1986a,b). For La2Co3 the same interpretations of resurgence as well of antiferromagnetism work as the crystallographic structure can be described as a packing of alternating layers of Co and La characterized by a Co-Co distance in the layer much smaller than that from layer to layer.

2.2. 3d Magnetocrystalline anisotropy

2.2.1. Experimental characteristics Although crystalline electric field (CEF) coupling is much larger on 3d ions than on 4f ions, 3d metals and alloys are known to have a small magnetocrystalline anisotropy. This is particularly true in systems with cubic symmetry as can be observed in pure Fe and Ni, whereas anisotropy can be one order of magnitude larger in pure Co which is hexagonal and where the second-order phenomenological anisotropy constant Kl reaches 7.9x 10 5 J/m 3 at 4.2 K. This small anisotropy, compared to that of the lanthanide atom,


arises from the band structure which gives rise to a small number of states having a well- defined orbital character and from a quenching of the orbital moment in particular in cubic systems (Friedel 1969). As the magnetocrystalline anisotropy of itinerant electron systems is difficult to describe with a theoretical model starting from first principles on account of the great complexity of the collective character of the electronic states, the weakness of the 3d anisotropy in metallic systems was commonly admitted and there was no clear-cut knowledge of the mechanisms which indeed rule this anisotropy.

Contrary to pure 3d metal, in the early seventies evidence had emerged of a large 3d contribution to the uniaxial anisotropy in the hexagonal RCo5 compounds, in favour of the 6-fold axis. This magnetocrystalline anisotropy is of the same order of magnitude as that of the lanthanide at room temperature, giving rise to spin reorientation in compounds where the crystal field favours the basal plane as easy axis of the lanthanide. At low temperature the lanthanide anisotropy is larger than that of Co and, as exchange interaction dominates, magnetization is perpendicular to c. At high temperature the Co anisotropy overcomes that of the lanthanide and magnetization becomes parallel to c. This has been studied extensively in TbCos, NdCo5 and DyCo5 (Lemaire 1966, Ohkoshi et ak 1976, 1977). In YCos, from torque measurements on a single crystal, an anisotropy constant K I = 7.0 × 106 J/m 3 had been deduced (Klein et al. 1975), a value one order of magnitude larger than in pure cobalt. The main results concerning the magnetocrystalline anisotropy of this series, obtained after 1979, are the following:

(i) Polarized neutron diffraction studies on YCo5 (Schweizer and Tasset 1980) have shown a large orbital contribution to the Co magnetization (26% and 16% of the 2c and 3g sites, respectively). These authors then suggested that this could be the origin of the large magnetocrystalline anisotropy. Although only qualitative, nuclear magnetic resonance (NMR) studies on different RCo5 compounds later confirmed this large orbital contribution to the Co magnetism (Yoshie et al. 1985).

(ii) Magnetization measurements on a single crystal of YCos, shown in fig. 16, led to an anisotropy field of 140kOe at 300K (Alameda et al. 1981) whereas it is only 10kOe in pure Co, and to K1 =7.4x 10 6 J/nl 3 at 4.2K. Moreover this study has revealed a large anisotropy of the magnetization, between the c axis and the basal plane, which reaches 4% of the total magnetization at 4.2 K. Presented in the same paper (Alameda et al. 1981) a polarized neutron diffraction study on NdCos, below and above the spin reorientation temperature range, confirmed this result and showed that this anisotropy of the magnetization mainly arises from the 2c site.

Besides the RCo5 compounds, which have been particularly well studied, it has been found that many other R-3d compounds where the 3d atoms are magnetic, i.e. those rich in 3d, exhibit a large 3d magnetocrystalline anisotropy. This is particularly so in other uniaxial intermetallic compounds of the same type but with more complex crystallographic structure, such as R2MI7 (hexagonal and rhombohedral), R2M7 (rhombohedral), and the new material for permanent magnet applications R2M~4B (tetragonal). For instance, K1 reaches -3 .2x 106 J/m 3 in Y2Fel7 (Perkins and Nagel 1975), 2.3x 106 J/m 3 in Y2Co7 (Kakol et al. 1984), -7.9x106J/m 3 and 7.1xl06j/m 3 in Y2CoI4B and Y2FeI4B , respectively (Thuy et al. 1988). Actually the macroscopic anisotropy in these compounds


~ 6 o

4

Z

N

2

/

/ /

/ /

/ /

I

//C • JL .e. , a

.c / ' ~ Y Co., 4.2 K

I I I

5O 1OO 150

APPLIED MA6NETIC FIELD (KOel 200

Fig. 16. Variation of the magnetization in YCo5 at 4.2K in a field applied parallel and perpendicular to c (Alameda et al. 1981).

with several transition-metal sites results from the compromise between the different local anisotropies which can be very different and even of opposite sign. A method to determine the anisotropy constant of the different sites has been proposed by Thuy and Franse (1986). Combining the results of neutron diffraction studies on the preferential occupation of iron and cobalt atoms in the pseudobinary series Nd2(Fel-xCox)17 (Herbst et al. 1982), and the experimental bulk anisotropy data of the pseudobinary series Y2(Fel-xCox)17 (Perkins and Nagel 1975, Perkins and Str~issler 1977), Thuy and Franse (1986) have evaluated the contribution of the iron and cobalt atoms belonging to four inequivalent sites. They have later extended this method to other series. Such an approach allows for instance to understand why the bulk anisotropy of Y2Co17 (KI =-0 .5× 106 J/m 3) is much smaller than in the isomorphous Fe-based compound mentioned above. However the results, based on the assumption that the local anisotropies of iron or cobalt on each site are independent of x, must be considered with caution. Indeed, Thuy et al. (1988) concluded that in YCos the anisotropy constant of the Co at the 3g site was negative, i.e. opposite to that of the 2c site with the largest anisotropy, whereas the magnetization anisotropy, deduced from polarized neutron diffraction on NdCos (Alameda et al. 1981), Mco, IIc- Mco, ±c is positive for both sites.


In the cubic Laves phases RM2, the 3d atoms are at a site with a three-fold symmetry axis lying along one of the four (111) directions. In the RCo2 series NMR spectra have revealed a large and anisotropic orbital moment leading to a strong local anisotropy of each Co atom (Hirosawa and Nakamura 1982). However, because of the particular symmetry of this cubic structure, contributions from respective 3d atoms in the unit cell to the total anisotropy energy cancel each other, resulting in a relatively small anisotropy energy of the order of 104x J/m 3, as observed in GdCo2 (Gignoux et al. 1975). The same conclusions have been obtained for Mn from NMR studies and from the knowledge of the magnetic structures of the (Yl-xTbx)Mn2 compounds (Berthier et al. 1988).

Finally, it is worth noting the hexagonal RCoI_~ compounds (R = La, Pr, Nd), where the strong Co anisotropy is, contrary to that in YCos, in favour of the basal plane (Ballou and Lemaire 1988): the anisotropy constant K1, deduced from magnetization measurements on single crystals, is of the order of -13 x 106 J/m 3. NMR studies on these three compounds led in LaCo~-e to a relative orbital contribution of 30% to the Co magnetic moment (Ballou, unpublished). This confirms again that orbital magnetism is at the origin of the 3d magnetic anisotropy.

2.2.2. Theoretical interpretations

The origin of this large 3d anisotropy has been a puzzle until recently, and its understanding led, in the few last years, to a better knowledge of the 3d magnetism in metallic systems. As we will see below, this anisotropy arises precisely from the itinerant character of magnetic electrons (or holes), and its phenomenological approach, first proposed by Ballou and Lemaire (1988) and then more precisely developed by Pinettes and Lacroix (1993a) in the case of LaCol_E, has been confirmed "by band calculations in the case of YCos (Daalderop et al. 1992, Nordstrrm et al. 1992).

It is well known that magnetocrystalline anisotropy arises from spin-orbit coupling. However the sign and magnitude of this anisotropy depend on the orbital selection operated on the collective electron states before the spin-orbit coupling is switched on. Such a selection has two origins (see for instance Friedel 1969): (i) The first is analogous to what occurs in insulators or in 4f ions, and corresponds to the diagonal elements (the so called a overlap integrals) of the band Hamiltonian in the individual state representation; it gives rise to the well known crystal field effects. This effect is always rather small and cannot explain the large observed anisotropy. (ii) The second, properly itinerant, is due to the/3-type multi-centre resonance integrals, mixing the individual states and leading to electron energy dispersion, i.e., the bandwidth. A strong dependence of this dispersion on the azimuthal quantum number is to be expected for an atomic packing other than the compact ones. This latter situation is encountered in pure 3d metals. On the contrary, in the rare-earth-3d intermetallic compounds we are faced with a band structure with rather well-pronounced one-dimensional or two-dimensional character. This latter situation is precisely the one encountered in thin films on which band calculations, leading to similar conclusions as in the compounds we are interested in, have been performed (Bruno 1989).


YCo5 enters in this category whereas LaCol_e has a strongly pronounced one-dimensional character.

Let us consider for instance the case of hexagonal RCol-e. In these compounds Co atoms form chains parallel to c in which the Co-Co distance is much shorter than the distance between chains. One is faced with a quasi one-dimensional itinerant system. Then the dispersion of the 12, 0) states of 3d electrons, i.e. the 3z 2 - r 2 orbitals, which are elongated along c, is much larger than that of the 12, +2) states, i.e. the x 2 _y2 and xy orbitals. Taking into account band calculations within the local spin-density approximation of Weinert and Freeman (1983 ), Pinettes and Lacroix (1993 a) deduced the band structure sketched in fig. 17. The width of the d~2 band is ten times larger than that of the degenerate dxy and dx2_y2 bands, and twice as large as the degenerate dxz and dyz ones. Note that, due to the a integral, i.e. the crystal field, the center of the dxy and dx2_y2 band is lower than that of the other bands. The 3d band is almost filled up and the position of the Fermi level lies in states corresponding to orbitals with a prolate character. The application of spin-orbit coupling leads then to a strong basal-plane anisotropy in agreement with experiment. Note that the sign and magnitude of the anisotropy energy strongly depends on the position of the Fermi level. This is well illustrated in fig. 18 which shows the anisotropy constant K1 as a function of the number, n, of d electrons. In RCol_e, with the parameters used, one finds a negative Kl value about half that estimated experimentally, but the model is too simple to make a quantitative comparison. However this calculated anisotropy is still one order of magnitude larger than in pure Co. Figure 18 also shows the calculated anisotropy AL=L[I - L -L of the orbital moment as a function of the band filling n (number of 3d electrons per atom). It is worth noting the close connection between K1 and AL: the same relative amplitude, opposite signs when the band is less than half filled and the same sign when the band is more than half filled. This is quite consistent with experiment. The different signs for n < 5 and n > 5 arise from the fact that in the former case one considers electrons whereas in the latter one considers positive holes.

This phenomenological approach is less simple in the case of YCo5 where, opposite to the situation above, the cobalt chemical bonds have a strong planar character (in layers perpendicular to c). However it is easy to predict a situation opposite to that of the RCOl-e compounds: the dispersion of prolate states is much smaller than that of the dxy and dx2_y2 band. As the Fermi level is also near the top of the 3d band where the states have a 12,-4-2) orbital character, the system has a strong positive anisotropy constant. This has recently been studied quantitatively by ab initio calculation of the magnetocrystalline anisotropy and orbital magnetism in YCo5 using the LMTO (Linear Muffin Tin Orbital) method (Daalderop et al. 1992, Nordstrrm et al. 1992). As illustrated in fig. 19 one can see again the close connection between the anisotropy energy and the anisotropy of the orbital moment. Moreover, the lower part of the figure shows that, in agreement with experiment, the anisotropy of the 3g site is smaller than that of the 2c site.

In a very simplified way one can understand the link between anisotropy energy and orbital anisotropy. Indeed, the spin-orbit coupling of 3d electrons can be written as


"Z',

q

, / dxy and dx2_y 2 : 12,_+2>

dxz and dy z : I2,_+1>

_ ~ ' • dz2 : 12,0>

/ 1 " " ~ / S (a.u.)

EF

Fig. 17. Schematic density of states of 3d electrons in a quasi one dimensional itinerant system.

15

10

5 's -~ 0

=" -5

-10

40 ~-

20 ~ ,m

-20 g ._=

-40 ,4 <3

Fig. 18. Model of Co anisotropy in hexagonal RCoI_~: calculated anisotropy constant K~ and orbital moment anisotropy AL as a function of the band filling n (number of 3d electrons per atom) for U=0.3 V/~ and z l= -0 .4eV (Pinettes and Lacroix 1993a). U, Coulomb repulsion; gel, d,2 bandwidth; A, the crystal field parameter which splits the two planar orbitals from the three other orbitals. K~ is in Z2/W~ (per unit cell) whereas AL is in )./W1 [xJat, where ). is the spin-orbit coupling coefficient.

E o

0 o9

E

o.

2 _ J

-2 44

a) ~_C ... .(.~

~ "'%..'""

~ [~Jr r 46 48 50

-6 52

0

-5

-10 44

b)

2C "', /

."' "".. [

46 48 50 52 Bandfilling q

0 0

2- .--I

Fig. 19. Ab initio calculation of the magnetocrystalline anisotropy energy and anisotropy of the orbital angular momentum in YCo 5 using the LMTO method (Daalderop et al. 1992). (a) Magnetic anisotropy energy per 3d atom, AEn(q), versus bandfilling q. Solid curve, calculation including spin--orbit coupling together with orbital polarization; dotted curve, spin-orbit coupling only; dashed curve (referring to the right-hand axis), anisotropy of the orbital angular momentum per 3d atom (calculation includes orbital polarization); vertical line, actual number of valence electrons n; horizontal dashed line, experimental anisotropy energy. (b) Anisotropy of the orbital angular momentum per Co atom at the 2c site (dashed) and 3g site (dotted), in units of h/2:~, and the average anisotropy per Co atom (solid).


Eso = ). L . S with )~ < 0 for electrons (n < 5) and ~ > 0 for holes (n > 5). The anisotropy constant is

KI = Eso, ± - Eso, [I = ,~(L± - Lrl) S = -~. z ~ . S,

if one assumes that the spin is independent of the direction. Then KI is proportional to AL with the same sign for n > 5 and with opposite sign for n < 5. The large anisotropy in many R-3d intermetallic compounds arises from the large orbital moment and hence its large anisotropy.

In principle the Coulomb repulsion U between electrons depends on the orbitals occupied by the two electrons, and this could be important for the calculation of orbital effects. However it has been established that this has little effect on the anisotropy energy.

In conclusion, the large magnetocrystalline anisotropies in rare-earth-3d intermetallics arise from the orbitally selective 3d band energy dispersion due to the particular character of the 3d atoms surrounding, associated with the presence of the rare earth, this effect being much larger than the usual crystal field effects.

2.3. Instability and frustration of Mn magnetism in RMn2 compounds

It is well known that exchange interactions in metallic Mn-based systems are negative. Moreover, when two nearest neighbours of an atom can be nearest neighbours to each other (e.g. triangular lattices or atoms on the tops of a regular tetrahedron) one is faced with frustrated magnetic systems. Such a topological frustration occurs in the RMnl2, R6Mn23 and RMnz series. Among them, the RMnz compounds are especially fascinating because the Mn moment is close to the instability of band magnetism. So, magnetism is complex and presents exotic features which have attracted much attention during the last ten years and have been investigated by using macroscopic techniques (such as magnetization and thermal expansion measurements) as well as microscopic techniques (e.g. neutron and X-ray diffraction, nuclear magnetic resonance (NMR) and Mrssbauer measurements).

2.3.1. Topological frustration For light lanthanides or for heavy ones, that is for large or small R atoms (R = Pr, Nd or Er, Tm, Lu), the RMn2 compounds crystallize in the hexagonal C14 Laves phase. ThMn2 and ScMn: also crystallize in this C14 phase. For intermediate R atoms (R= Gd, Y, Tb, Dy) the RMn2 compounds crystallize in the cubic (f.c.c.) C15 Laves phase. A dimorphism is observed for R = Sm or Ho. As shown in fig. 20, in both structures Mn atoms are at the tops of regular tetrahedra. These tetrahedra are stacked in chains along the six-fold axis in the hexagonal phase and they are packed in the diamond arrangement, connected by sharing vertices, in the cubic structure. In both structures, the topology of the packing ensures that any antiferromagnetic ordering will be highly frustrated.


.... 0 q

, C 1 5 7

I . . . .

317

' - ~ C 14 o-- .-o 0

Fig. 20. Crystallographic structures of f.c.c. CI5 and hexagonal C14 Laves phases. Left, projection in (001) plane; right, stacking of Mn tetrahedrons.

2.3.2. Mn moment instability and complex magnetic structures A characteristic signature of the magnetic instability of manganese in the RMn2 intermetallics is well illustrated by the large magnetovolume anomalies observed (fig. 21) for some R atoms. In fact, as shown (Wada et al. 1987a and references therein, Shimizu 1985) through thermal expansion and NMR measurements (fig. 22), such anomalies occur depending upon the Mn-Mn interatomie distances. A critical distance (de = 2.66 A) for the onset of a Mn moment appears to exist, which allows us to divide the compounds into three different subsets of magnetic behaviours.

When the Mn-Mn distance is significantly lower than de, as in ScMnz, ErMn2 and HoMn2, Mn is nonmagnetic. ScMn2 is a Pauli paramagnet and its thermal expansion coefficient (TEC) is small. ErMn2 and HoMn2 exhibit ferromagnetic ordering characteristic of the rare-earth moment only (Feleher et al. 1965). The paramagnetic TEC is large but no volume discontinuity appears at TN. (The situation of HoMn2 is not quite clear and NMR seems to indicate that, depending on the preparation, some Mn sites could be magnetic.)

When the Mn-Mn distance is larger than de, as in PrMn2, NdMn2, SmMn2 and GdMn2, the Mn magnetism is well stabilized with large values of the Mn moment (about 2.7/~B). Magnetic Mn ordering is accompanied by a large volume discontinuity and a paramagnetic TEC is as large as in the compounds with Er and Ho. Collinear antiferromagnetic structures with moments parallel to [120] have been determined by neutron diffraction in PrMn2 (TN = I15K) and NdMn2 (TN = 104K). However, in the latter, below 50 K, some Mn moments and all Nd moments progressively rotate toward the [100] axis due to the magnetocrystalline anisotropy ofNd (Ballou et al. 1988a, Ouladdiaf 1986). The magnetic structure of GdMn2 bears some similarities [same propagation vector


J YMn2

I • P r M n 2

L

: 1 7 : - - _ - : ; .

c

1 , ' 2

. . . . d i t c t t ome te r

J ] J I ~ I

0 100 200 300 TEMPERATURE (N)

Fig. 21. Thermal expansion curves of RMn 2 obtained by X-ray diffraction measurements (circles) and dilatornetric measurements (dashed lines). Open and solid circles show the processes with decreasing and increasing temperature, respectively. Solid lines are guides for the eye (Wada et al. 1987a).

2 2 (3, 3, 0)] with the virgin magnetic structure of TbMn2 (Ouladdiaf 1986). The magnetic structure of SmMn2 is still unknown.

The most dramatic properties are observed in the other compounds, where Mn is close to the magnetic instability and where magnetism is very sensitive to external parameters such as temperature, pressure, magnetic field and alloying. When temperature is increased, YMn2 shows a first-order transition (with a large hysteresis) at TN accompanied with a giant volume drop of about 5%, which is ascribed to a substantial reduction of the Mn moment at TN. The TEC above TN is the largest of the series (50× 10 -6 K -1 at 300 K). The magnetic structure of YMn2, determined from neutron diffraction, is helimagnetic (fig. 23) with a long period (~380 ]~). On the other hand NMR spectra have shown that the helix is not regular but distorted owing to a large Mn magnetic anisotropy which favours


4

% zL ~3

2 o

:d. I

~2-

<J

0

(o)

Sc i . I

2.5 2.6

Fir

T

H o i m ,

d~n_t4 n Qt 4.2 K 2 "~,)

(b)

Tb{

so. I Er, H o 0 # ,

/ 2.5 2.6 2.7

I 2.8

k Nd Pr

I

2.8

! f f 6

2O

10

INTERATOMIC DISTANCE, d~r~M#t R.T. (~,)

Fig. 22. Variations of Mn moment, volume change at T~ and thermal expansion coefficient (TEC) with interatomic distance, dMn_Mn (Wada et al. 1987a). (a) Mn moment, /~Mn, at 4.2K in RMn 2 as a function of dMn_Mn; CO) volume change at T N (AV/V) at T= T~ (solid circles) and the average TEC between 200 K and 300 K (open circles) plotted against dMn-Mn at room temperature. Lal0 and La25 represent Y09oLao loMnz and Y0.75Lao 25Mn2, respectively.

one of the local two-fold axes (110) (Ballou et al. 1987). The substitution of a small amount of Sc for Y shrinks the lattice, leading to nonmagnetic Mn atoms (Nakamura et al. 1988a). In Y0.97Sc0.03Mn2 a complete paramagnetic state at 4.2 K has been observed and the absence of Mn moment has been confirmed by NMR. However, a large TEC, as in YMn2, is observed. For a Sc amount smaller than 2% the coexistence of the magnetic state with a Mn moment mMn ~ 2.7/UB and nonmagnetic state is observed. On the contrary, the substitution of La for Y expands the lattice and enhances the stability of the antiferromagnetism. In particular, in Y0.75La0.25Mn2 the volume discontinuity at TN is about 2% and the TEC at room temperature is 40× 10 --6 K -I, smaller values than in pure YMn2 (Nakamura et al. 1988b). In the Yl-xCexMn2 pseudo-binary alloys, the decrease of the cell volume with Ce content and the destruction of the magnetic ground state for x ~> 0.05 are surprising as Ce has a larger ionic volume than Y in both the 3+ and the


2N-I 2 ~ ~" /

O ,

~ J ~ + ~' ~ >?:

') > y /' /

! , . i .... !

0 ~ . I ..... . ............. ....,j

2N ! 2N+2

s

b I , / ~-/

b

Fig. 23. Magnetic structure of YMnz. Only Mn atoms are shown. (a) Collinear antiferromagnetic structure previously reported (Nakamura et al. 1983), open and solid circles represent Mn atoms with up and down spins, respectively. The propagation vector is Q = (0, 0,1); (b) helimagnetic structure deduced from neutron diffraction studies using a long wavelength. In the tetrahedron layers (solid lines) the antiferromagnetic arrangement is collinear as in (a). The propagation vector is Q=(r,0,1) with r=0.02. A and z~' are the two easy directions of Mn moments. Inset: in both models, the Heisenberg exchange interactions do not cancel between pairs of atomic layers 2N - 1,2N, but do cancel between pairs of atomic layers 2N, 2N + I. Magnetic structures are then formed of highly correlated layers of tetrahedra with weak coupling between these layers. (Ballou et al. 1987).

4+ state. This property has been ascribed to a strong hybridizat ion of the Ce-4f and M n - 3 d

bands (Monda l et al. 1992). In TbMn2, the magnet ic field structure in zero applied field is complex, with all

manganese atoms in the magnet ic state. However, a "mixed structure" wi th coexist ing magnet ic and nonmagne t i c M n atoms (fig. 24) is induced by an applied field of 4.5 T at 25 K or by chemical pressure induced by the subst i tut ion of smaller Fe atoms


Mn(lb)~ Mn(3d)~ Tb ~ Fig. 24. Magnetic structure of Tb0Vlno.96Fe0.04)2 below 30 K, or the S2-type structure of TbMn 2 induced by an applied field of 4.5 T at 25 K (Brown et al. 1992).

for a small amount (~4%) of Mn atoms as shown by neutron diffraction (Brown et al. 1992) and by M6ssbauer measurements (Oddou et al. 1993). In this magnetic structure, although all the Mn sites are chemically equivalent, only 25% of them bear a magnetic moment. Note that in TbMn2, as well as in YMn2, the variation of the N6el temperature with hydrostatic pressure reaches a huge value, namely -36 K/kbar (Voiron et al. 1990, Oomi et al. 1987).

DyMn2 is the first compound in which, in the absence of applied field, a mixed magnetic-nonmagnetic Mn state was evidenced by NMR (Yoshimura and Nakamura 1984, Yoshimura et al. 1986a). The magnetic structure, as determined from neutron diffraction (Ritter et al. 1991), is similar to that of TbMn2 in an applied field when considering the Mn sublattiee only.

Because thorium is tetravalent, the Mn-Mn distance in ThMn2 cannot be compared with dc determined for trivalent R elements; however in this compound, due to the larger filling of the 3d band, Mn is also close to the magnetic instability. ThMn2 orders antiferromagnetically at TN=ll5 K (Buschow 1977b) in a mixed structure, shown in fig. 25, in which magnetic Mn atoms form a triangular structure resulting from the topological frustration of antiferromagnetic interactions (D6portes et al. 1987a). Note that in all these mixed states the nonmagnetic Mn atoms are those which are subjected to a


In 2

Fig. 25. Projection into the basal plane of the ThMn 2 magnetic structure. Only Mn atoms of the 6h site are magnetic (Drportes et al. 1987a).

total field smaller than the critical value necessary to induce a magnetic state of higher energy. In particular, in ThMn2 the molecular field on nonmagnetic atoms is strictly zero. However the cancellation of Mn moment on some sites is really a nonmagnetic state and not a paramagnetic one which would have resulted from a simple cancellation of the field on localized moments. Indeed, the susceptibility does not increase at decreasing temperatures as expected for local moments in paramagnetic state in an applied field. Consequently the splitting of the local band is cancelled.

2.3.3. Large Mn anisotropy Although it cannot be measured directly because of the complex frustrated structures, a large local magnetocrystalline anisotropy of Mn moments has been shown in the RMn2 compounds. It manifests itself clearly in YMn2 and NdMn2. In the former, a quantitative analysis of the tilt of the moments with respect to a perfect helix, inferred from NMR and neutron diffraction experiments (Ballou et al. 1987), leads to a local anisotropy of the same order of magnitude as generally observed in uniaxial 3d intermetallics, in particular those containing cobalt (see sect. 2.2). In NdMn2 this anisotropy, of the same order of magnitude as that of Nd in the plane perpendicular to c, is responsible for the noncollinear magnetic structure observed at low temperature (Ballou et al. 1988a).


2.3.4. Giant spin fluctuations Most physical properties of the RMn2 series bear witness to the importance of spin fluctuations in these frustrated systems, which are dramatically enhanced in the compounds close to the Mn magnetic instability, in particular in YMn2. As cited above, the large volume change at TN and the large TEC above this temperature in this compound is ascribed to a substantial reduction of the Mn local moment mMn and then to its rapid recovery with temperature in the paramagnetic state. Indeed, a phenomenological theory of magnetovolume effects (Shiga 1981) has shown that the magnetic contribution to the TEC is proportional to the square amplitude of the local spin fluctuations or, in other words, the square of the local moment. The lattice contribution to the TEC has been taken as that of the Y(Mnl-xAlx)2 compounds for x > 0.1; there it has been established from different measurements (lattice parameter as a function of the AI content, NMR experiments, Yoshimura et al. 1986b) that mMn is stable and takes the maximum local value of about 3/~B which is temperature independent. From this weak contribution to the TEC, it has been possible to deduce the thermal variations of local spin fluctuations, i.e. (m2n), in the different RMn2 compounds. They are schematically shown in fig. 26. Curve (e) is the local moment limit (Y(Mnl_xAlx)2 compounds with x > 0.1, Shiga et al. 1987, Motoya et al. 1988) whereas, at the opposite, curve (a) is the Pauli paramagnetic type limit (ScMn2). In YMn2 the Mn moment, which reaches 2.7#B at low temperature, is reduced to about 1/tB just above TN and recovers to 2#B at room temperature. This result has been confirmed from neutron diffraction experiments below TN and from paramagnetic scattering measurements using polarized neutrons (D@ortes et al. 1987b, Freltoft et al. 1988). The results revealed that the amplitude of the local magnetic moment of Mn atoms drops by more than 30% at TN and then slowly increases with increasing temperature. Moreover, up to 6TN, the paramagnetie scattering was strongly enhanced about the staggered antiferromagnetic wavevector. The thermal variation of the magnetic susceptibility of YMn2 is also quite unusual (fig. 27) and its increase with temperature above TN is further evidence for the increase of the local spin-fluctuation amplitude with temperature. In the nonmagnetic Y0.97Sc0.03Mn2 compound, the TEC as large as in pure

/X ~c

-I V

(e__])

( PrMn~ Ndt,,tn , j - -F~- -~ , ts~Mr~2 '

~u t |GdMn 2

~ YMn2 ~(c)

( D ~ Mn 2 }HoMn) Er~4n-

) i~ xSC2xi, An

(O) ScMn 2

T EMPERATURE

"ID

Fig. 26. Schematic representation of the temperature variation of ( ~ 2 n ) of RMn2. Curve (a) shows the Pauli paramagnetic type and (e) the local moment limit. The type of spin fluctuations changes from (b) to (d) in RMn 2 with increasing dMn_Mn (Wada et al. 1987a).


i

x

...,.. x =0.05

e Xe ¢ 0 • • • • • t

; ..~" x=O.02 e * ~ e ' v = % 101 ee l e o • • 0• *"- • l e e • • l *

• J l • e • ~ o I o • - • I *= l . i ~ ' • • t,e

• %e, i • e • • • • e= I • • l e • . o e oe e

• % • = j o e . e • e e I • ~ e g * * * o e o , • = ~ * * .......... o.:..f.....

• ieoQ~ • \ ........ "x._AY

, I i I i I ~ I , I i

0 100 200 300 t~00 500 T (K}

Fig. 27. Temperature dependence of the susceptibility of Y(MnI_~Alx) 2 for 0 ~< x ~< 0.05. Arrows indicate heating and cooling processes (H= 8.28 kOe) (Shiga et al. 1987).

YMn2 is typical of a nearly antiferromagnet in which giant spin fluctuations are thermally excited (Wada et al. 1987a). In systems which are not so critical as YMn2 the jump of (m~n) at the ordering temperature and its thermal increase in the paramagnetic state are slightly smaller (curves b, d in fig. 26). Muon spectroscopy (~tSR) on YMn2 and related compounds (Y0.9Tb0.1Mn2, Y0.98Sc0.02Mn2 and TbMn2) confirmed that the dynamics of Mn magnetic moments in the paramagnetic state is typical for an itinerant system (Kalvius 1994). This measurement also confirmed the observation of Ballou et al. (1990a) that paramagnetic state and antiferromagnetic phase (spin-glass like) coexist within a certain temperature range above TN as an outcome of frustration.

Note finally that other physical quantities testify the importance of spin fluctuations in this frustrated series close to the itinerant magnetism instability: (i) The thermoelectric power in YMn2 shows an anomalous behaviour with temperature (Kamimura et al. 1987). (ii) The electric resistivity of this compound (Kamimura et al. 1987) follows a T 5/3 dependence up to 10 K in accordance with spin-fluctuation theory (Ueda and Moriya 1975). (iii) In YMn2 a pressure of 1.6 kbar is enough to suppress magnetic ordering, and the electronic specific-heat coefficient • reaches 160mJ/K 2 mol (Fisher et al. 1992). As well, in Y0.97Sc0.o3Mn2, which is also paramagnetic, y reaches 140mJ/K 2 mol (fig. 28) (Wada et al. 1987b). These values are very large among the 3d transition metals and compounds, particularly in comparison with YCo2 ( y ~ 18mJ/K 2 mol) which is close


oJ

E

E

16° I 1501 . . . .

1401 --~.." " "~" "~"- "Z. "- ''-- '''---" " "-~-" ........ ...-~...,-;-'-" ""

13C

12C

11C

100 ( Yo.97 SCo.o3) Mn 2

0 10 20 30 40 T 2 ( K 2 )

Fig. 28. Low-temperature specific heat of Y0mSc0.03Mnz in the form of C / T against T 2. The solid line has 7~w = 140 mJ/K 2 tool and 0D = 300 K (Wada et al. 1987b).

to the Co moment instability and with YNi2 (7 ~ 1.8 mJ/K 2 mol). These features bear resemblance to the heavy-fermion systems, such as UPt3 (Franse et al. 1985a).

2.3.5. Theoretical approaches The possibility of two magnetic states on Mn atoms in R M n 2 , depending on the lattice constant, has been discussed in 1988 by Yamada and Shimizu (1988) from band calculations within the tight-binding approximation. However the magnetic instability of highly frustrated crystallographic structures has been theoretically treated for the first time more recently (Ballou et al. 1991, 1992, Nunez-Regueiro et al. 1992a,b) in an approach which takes into account the four main experimental characteristics, namely: (i) the itinerant character of magnetism; (ii) the frustration of interactions; (iii) the magnetic instability; and (iv) the anisotropy of Mn sites. Since in the RMn2 compounds the R-R and R-Mn exchange interactions are one order of magnitude smaller than the Mn-Mn interactions, the theory is limited to the Mn lattice which is described using a Hubbard model, where the on-site Coulomb repulsion U is of the order of the bandwidth W, close to the magnetic-nonmagnetic (M-NM) instability. Due to the large Mn anisotropy, transverse fluctuations are neglected and only the longitudinal component of the local moment,/4 = (niT - nil 1, is considered. The effective Hamiltonian can then be mapped into a pseudo spin S = 1 Blume-Capel Hamiltonian:

7~ = A ~ S~ + ½ ~ Jij s iS / , (9) i i ~ j

where zl and Jo are related to the parameters of the Hubbard model. (Note that in the convention adopted in eq. (9), a positive Jij corresponds to a negative interaction and conversely). The M-NM transition can occur if A > 0 and then Si can take three


', : : ', 1 ', ', ; I I I I I p I t -

- 0 . 5 0.5 O2/J1

Fig. 29. Phase diagram at T = 0 of a two-dimensional triangular lattice using an effective Hamiltonian mapped into the pseudo spin S = 1 Blume-Capel Hamiltonian (Ballou et al. 1991). Open circles indicate nonmagnetic sites. The borderlines between the different phases are determined by the following: phases I and III, J2 = A - J ~ ; phases I and II, J2 =J1 /2 -A/3 ; phases II and III, J2 =zl/9; phases II and IV, J2 =-A/3. J l and J2 are nearest and second-nearest neighbour interactions, respectively. Note that following equation (9), positive values of J~ correspond to negative interactions and conversely.

values: Si = + 1 if the site has a magnetic moment/~i = : L / ~ , and S i = 0 if #i = 0, the latter corresponding to the ground state in the absence of exchange and/or applied field. Rather than introducing the complexity of the Laves phase RMn2 structure, a two dimensional triangular lattice has been used to model frustration. This Hamiltonian was studied by two different methods, i.e. Monte Carlo simulations and analytical calculations where correlations in the elementary magnetic cell are treated exactly. Both methods give the same phase diagram at low temperature. As shown in fig. 29 this model leads to a rich phase diagram that can be related to the different RMn2 compounds: (i) a nonmagnetic phase (phase I) where/~i = 0 at all Mn sites (ScMn2 and ErMn2); (ii) magnetic phases (phases III and IV) in which/~i ~ 0 at all Mn sites (YMn2 and NdMn2); and (iii) a new type of mixed magnetic phase (phase II, ThMn2 and DyMn2) in which, because of frustration, the molecular field at some Mn sites, but not all, is too small to compensate the energy A necessary to stabilize the moment. The field effect on these different phases is particularly interesting: generally several field-induced first-order transitions are obtained, even when starting from the nonmagnetic phase in zero field. Moreover, when applying the field on a fully magnetic phase, mixed intermediate phases appear (fig. 30). This characteristic is exactly that observed in TbMn2. It is worth noting that, in this model, a uniaxial anisotropy favouring an easy magnetization direction is essential in order for a mixed phase to be stabilized. Note that a recent ab initio band calculation in the ordered phase of ThMn2 gives a good prediction of the observed mixed structure in this compound (Uhl et al. 1993).

More recently, some states obtained within the above Blume-Capel (pseudo spin S = 1) model have been studied using a more realistic treatment of the Hubbard model which takes into account charge transfer and then does not fix an ad hoe value of the magnetic moments (Pinettes and Lacroix 1993b). This model confirms the results obtained with the pseudo spin S = 1 model, in particular it shows that the mixed phase can be stable


0 . 7 . =

z o m

I -

N F_0. UJ Z o <¢

0 . 2 5

5 10

APPLIED FIELD (uni ts of J1)

Fig. 30. Monte Carlo simulation for increasing magnetic field of a two dimensional triangular lattice, for A=J 1 and Jz =JJ2, corresponding to an antiferromagnetic phase in zero field (Ballou et al. 1992). Note that following equation (9), positive values of J~ correspond to negative interactions and conversely.

in the triangular lattice if." (i) U is not too large, and (ii) there is a large anisotropy. The introduction of spin fluctuations in this model allowed one to qualitatively study the thermodynamical properties of these systems. Depending on the temperature range studied, the random phase approximation (Pines and Nozi~res 1966, Landau and Lifshitz 1981) or the Murata-Doniach approximation (Murata and Doniach 1972) were used. The main results obtained are the following: (i) the large pressure-induced decrease of the ordering temperature mainly comes from the magnetic instability rather than the frustration; (ii) the specific-heat coefficient )~ of the paramagnetic phase seriously increases in the vicinity of an instability when the interactions are strongly frustrated. This result accounts for the much larger value of ~, in the paramagnetic phase of YMn2 (obtained by applied or chemical pressure) than in YCo2 where no frustration is associated with the instability.

2.4. Lanthanide-3d transition-metal compounds where both carry a well defined magnetic moment

2.4.1. General characteristics

As discussed at the beginning of this section, which is devoted to 3d magnetism, the magnetic moment of the 3d ions disappears when the rare-earth fraction is larger than a critical value which depends on the 3d element (fig. 1). Whereas this amount is small with Ni, it is much larger with Fe. So in rich 3d rare-earth-transition-metal alloys the 3d atoms are magnetic. Most of these alloys have tmiaxial structures (hexagonal, rhombohedral, tetragonal) which are derived from the hexagonal CaCu5 structure found in the RCo5


and RNi5 phases. They are of the type R2M17, R2M7, R]V[3, RMs. These alloys together with derived compounds such as the prominent R2M14B series and more recent interstitial compounds (nitrides, carbides . . . . ) are well known for their technological applications as permanent magnets. Several reviews devoted to these materials have been written in the last few years: Buschow (1988), Strnat (1988), Li and Coey (1991), and Franse and Radwanski (1993). Since permanent magnets are beyond the scope of this chapter, we will not discuss too much of the magnetic properties of these compounds. We would like only to,present some major steps made in the last fifteen years in the knowledge of intrinsic properties of these alloys in which the 3d element is mainly Fe, Co, or Ni. Long since, it is known that in these materials (Kirchmayr and Poldy 1979, and references therein):

(i) The ferromagnetic 3d-3d dominant interaction is at the origin of the large Curie temperatures which are well above room temperature.

(ii) The smaller antiparallel coupling between the lanthanide spin and that of the 3d element leads to ferromagnetic compounds for light lanthanides where J = [ L - S] and to ferrimagnetic compounds for heavy lanthanides where J = L + S .

(iii) The indirect 4f-4f exchange coupling is still one order of magnitude smaller than the previous one.

(iv) Spin reorientations are observed in some compounds as a result of the competition of the 3d and lanthanide magnetocrystalline anisotropies, the latter being preponderant at low temperature whereas the former dominates near the ordering tempera~tre.

2.4.2. Curie temperatures and 3d-4f exchange interactions The experimental determination of the parameters describing the main interactions, namely the exchange and the crystal field, has considerably progressed in the last decade. We will focus on the 3d-4f exchange interaction. This interaction can be written as

ERM ---- --nRMMRMM, (lO)

w h e r e M R and M M are the lanthanide and transition metal magnetizations, respectively, and nRM the relevant molecular field coefficient. Assuming that the 3d moment is of spin origin, the R and M spin magnetizations can be expressed as M s = yRMR and M s = MM, where YR = - 2 ( g j - 1 ) / g j . Expression (10) can then be rewritten as

_ ~S ~l~S ] 4 S ERM -- --ttRMZ,a R ~,~ M, (11)

where nSul(<O)=nr~M/),R is the negative molecular field coefficient between spin magnetizations.

In a given series of compounds (M fixed and R varied) the highest value of Tc always occurs in the Gd compound, where the spin is the largest of the lanthanides. This means, as is generally expected, that the R-M interaction occurs between spins and can be written as in eq. (11) (Belorizky et al. 1987). In a given series, due to the expected similarity of the lanthanide 5d band structure, it is usually assumed that npS M is constant.


Applying a ferrimagnetic molecular field treatment the following expression for the Curie temperature Tc has been derived by Nrel:

Tc = ½ [TM+ TRv/(TM - TR)2+4T~M] , (12)

where TM, TR and TRM represent the contributions to Tc arising from the M-M, R-R and R-M interactions, respectively, and are given by:

_ s 2 s ( 1 3 , 14) TM : nMMCM -- nMMCM, T~ = nr~CR = yRnr~RCr~,

= : (15)

where CM and CR are the Curie constant of the M and R sublattices, respectively. Concerning the M sublattice, the assumption of a Curie susceptibility is not obvious due to the itinerant character of the 3d magnetism. Actually experiments show that the temperature variation of the total susceptibility may be analyzed assuming XM = CM/T where CM has been measured for all the series considered. The above expression for TRM shows that TiM is proportional to the "de Gennes" factor of the lanthanide element, G(J )=(g j - 1)2j ( j+ 1). Assuming a constant value of nSM in a series, in general a satisfying correlation between the value of Tc and the de Gennes factor is found for heavy lanthanides compounds, but for light lanthanide compounds deviations from simple systematics are always observed, e.g., Buschow and van Stapele (1970) for RFe2, Pszczola and Krop (1986) for the iron series and Sinnema et al. (1984) for R2Fel4B. Basing on a careful and systematic study of n ~ of different series Belorizky et al. (1987) were the first to ascribe this deviation to substantial increase of the 3d-4f interactions towards the light lanthanides. Combination of the above equations (Belorizky et al. 1987) leads to

- 5-,/(re - r M ) ( r c - rR) (16) I~J[ V CRCM

In the series studied, TM was deduced from the value of Tc of compounds with nonmagnetic rare earths such as La and Lu, whereas TR was deduced from the ordering temperature of compounds with Ni where it is nonmagnetic. The results for the R2Fel4B and RCo2 series, shown in fig. 31 a, reveal a significant decrease of InSMI with increasing number of 4f electrons. Because of the spatial localization of the 4f shell the direct overlap between the 3d and 4f spins is rather small and Campbell (1972) suggested that the 3d-4f coupling is indirect and involves two stages, namely the 3d-5d and 5d-4f direct interactions. These interactions being distant dependent, they are expected to vary from compound to compound through dl=dRM -rso -r3d and d2 = rsd --r4f respectively, where dRM is the distance between R and M atoms and r3d, rsd and raf are the radii of the 3d, 5d and 4f shells, respectively. In their analysis Belorizky et al. (1987) have shown that the lanthanide contraction (associated with rsa) is ten times smaller than the corresponding contraction of the 4f shell (associated with raf ). As a result across a series, whereas the


t"¢3

5000

,.000

300C

200C

100

RCo 2 (*)

R 2 Fe14B (-)

( a )

O

o

t

La Ce Pr Nd PmSm Eu Gd Tb Dy Ho Er Tm Yb Lu

!

f,~

(b ) 1,3

1.25

1,2

Le Ce Pr Nd PmSm Eu Gd Tb Dy Ho Er Tm Yb Lu

Fig. 31. (a) Absolute value of n ~ in the R2Fel4B and RCo 2 series. (b) r4f-rsa across the 4f series (rsd is noted r R in the figure) (Belorizky et al. 1987).

variation of dz is negligible, there is a large increase of d2 as shown in fig. 3lb. As a consequence, the overlap of 5d and 4f wave functions decreases towards the heavy lanthanide ions.

The decrease of InSMI therefore originates from the increase of the difference between the spatial extent of the 4f and 5d electrons (see fig. 3 lb). It has been concluded that the change of the effective 3d--4f exchange interaction through the 4f series mainly originates


~00 [....,

c~

2O0

, t .

cePrNd

0

1

o°, *-[" l-.-. . .~R2Fel 7' R2Fe17C ",,, "- . . . . . ~ . R2Fe14B, R2FelC ".~ R Fe~ "°~-., 6 z~

O x • " " ",8. , lp"

, , "~-- .. R2Co17,RCo 5 " , , R2C°14B

"°-o R Co 2

o - - R2Ni17 i i , I , I i I

Sm 6d TboyHOEr Tmyb

R Fig. 32. Values of the exchange field Be~,e,M experienced by the 4f spin moment in a number of RnM m series. Solid circles, crosses and open circles are data obtained from magnetization studies, inelastic neutron scattering and from T c values, respectively. Broken lines are guides for the eye (after Radwanski et al. 1990).

from the change of the 4f-5d part. This variation of nSM is quite general and has been observed in other series, as shown in fig. 32 which reports (Radwanski et al. 1990) the exchange field on the rare earth due to the M atom P. = nRMMM) , s S (Bex, RM derived from different types of experiments.

2.4.3. High-field magnetization processes, 3 d - 4 f interaction and magnetocrystalline anisotropy

The analysis of high-field magnetization processes provided a quantitative determination of the different exchange and anisotropy parameters. In particular in fields up to 35 T it is possible to induce the noncollinearity of the R and M magnetizations in ferrimagnets and then to measure the 3d-4f exchange coupling although, due to the importance of this interaction, much larger fields (of the order of 200 T) are needed to reach the full ferromagnetic state even in compounds with small anisotropy such as those with Gd.

In a two-sublattice model, the phenomenological energy of a magnetic system in an external field Bo has been written as (Verhoef et al. 1989, 1990)

R ERM = EMa + E a - nRMMRMM - (MM + MR) Bo, (17)

where MM and MR are assumed to be constant in modulus. The first two terms represent the magnetocrystalline anisotropy of the two sublattices. The M sublattice is not affected by the applied field (all M moments are assumed to remain parallel) and, its intrinsic energy being conserved, it does not appear in the expression of the energy. Besides, the 4f-4f coupling is very weak and is thus neglected.

332 D. G1GNOUX and D. SCHMITT

o

8

, i , i , i ,

P ~ B

< ~ ~- MR ~ M M : r :~

M=IM M -MRI / ...........

I I I I I

B CPit i Blcp it

IApplied Magnetic Field 2

200

150 ~ W

g m

100 2

50

Fig. 33. Calculated field dependence of the resultant magnetic moment of a two-sublattice system without anisotropy, or for free to rotate single crystals when only one sublattice has a magnetoerystalline anisotropy (solid curve and left-hand scale). The dashed curve (right-hand scale) is the angle e, 180 ° - e being the angle between the magnetizations of the two sublattices; for this curve, M M was taken equal to 2M R and [nRMI equal to 0.5 kgT/A m 2. For the different field ranges the related sublattice moment configurations are indicated (Verhoef et al. 1990).

In ferrimagnetic systems without magnetocrystalline anisotropy, it can be readily deduced from the above expression of the energy that in a field region such as:

InRMI IMM --MR[ < B < InRMI IMM +MRI (18)

the magnetization curve is linear with a slope given by I1/nRM]. Below and above this field range, magnetization is constant and equal to IMM--MR[ and MM+MR respectively. Figure 33 shows an overview of the expected magnetization curve as a function of the applied field Bo together with the related configurations of the two sublattice moments. The field dependence of the angle e, by which the moment configuration deviates from a strict anti-parallel alignment, is shown as well in fig. 33. Actually the assumption of zero magnetocrystalline anisotropy is not realistic in compounds that are known to have a substantial anisotropy. However, in systems where it is assumed that only one sublattice has a magnetocrystalline anisotropy, it has been shown that the magnetization curves of single crystals (one spherical single crystal or a finely powdered polycrystalline sample) free to rotate in the applied field, follow quite well the above variation (fig. 33) when the field is sufficiently large (Verhoef et al. 1989). This arises because the anisotropy does not enter into the energy expression, due to the fact that the single crystals always orient their total magnetization along the applied field direction. The above assumption is satisfied in Gd-based compounds. With the other magnetic lanthanides it is assumed that it is the magnetic anisotropy of the 3d sublattice which is zero because, in most hard magnetic


70

60

2~

50 <:I:

40

' t I 1

Ho2Co: l 7 T = 4 , 2 K ::: :::::

o free single-crystallane sphere :::. 5: ̧ + f r e e p o i y c r y s t a i l i n e p o w d e r :/::::

.:::: ::

[ i

3 0 , I . , I I

0 ~0 2O 3O 8 IT]

40

Fig. 34. High-field magnetization curves at 4.2 K of a free single-crystalline sphere (open circles) and a free powder sample (crosses) of the Ho2Co17 compound (Verhoef et al. 1990). Dashed lines represent the experimental results of linearly-decreasing field pulses.

l

E

lO0

BO

60

40

20

o o 10 20

B [T]

:o .................................. :i!!!!!!!) . . . . .-1111'.'.11211..--'"

. . ." ' . , .v ' " . . - ' .,

. , . . , o .

H o 2 C o I 7 -

v Ho2Co14Fe 3 o E r 2 C o l 7 - - o E r 2 F e 1 7 o Dy2Co~ 7

t , [ , I ,

30 40

Fig. 35. High-field magnetization curves at 4.2 K of several R2M17 single-crystalline spheres that are free to orient themselves in the applied magnetic field (Verhoef et al. 1992).

R - M intermetallic compounds, it is known that the anisotropy of the 3d sublattice is smaller than the anisotropy o f the 4 f sublattice by at least one order o f magnitude. As illustrated in figs. 34 and 35, using this remarkable property the intersublattice interaction has been measured directly from the high-field magnetization curve in a large number of R - M ferrimagnets. Note in fig. 34 that there is a remarkable agreement between the magnetization curves performed on a free single crystalline sphere and a free powdered polyerystalline sample. This type of measurements is then particularly interesting because it allows a direct quantitative determination of nRM by using polyerystalline materials.


10 ..-7.

5

U c

s /

I C / I t - . . . . . .

GdC°3 ~ - - B /

Mc°

. . " ' / c [ B M~

. . . . . . . . . . . . . .. / Mco [ N ~ z / --

(b)

0 40 100 300 B(T) Fig. 36. Magnetization curves in the full-field range for the GdCo 3 ferrimagnet calculated with relevant parameters when the field is parallel and perpendicular to the c axis (Radwanski 1986). The moment configurations for the field of 250T applied parallel and for the field of 100T perpendicular to the easy hexagonal axis are shown.

In the above experiments the magnetization of the sublattice considered as anisotropic (a lanthanide with a nonzero orbital moment or 3d atoms in Gd-based compounds) remains parallel to its easy magnetization direction and no information about the magnetic anisotropy can be obtained. In case of fixed single crystals both moments are pushed out of their easy direction and therefore magnetization curves depend on the anisotropy as well as exchange interactions. Whereas in a simple uniaxial ferromagnet with only a single magnetic sublattice the magnetization curve along the hard axis depends only on the anisotropy constants, in ferri- or ferromagnetic systems, composed of different magnetic sublattices, the external field disturbs the magnetic configuration of the different sublattices. Expression (17) for the phenomenological energy still applies and has been used in order to analyze the magnetization processes along the different symmetry directions.

Two typical examples of the magnetization process for Gd-based compounds are reported in figs. 36 and 37 which show the calculation performed for GdCo3 (Radwanski 1986) and GdCo5 (Radwansld et al. 1992a) by using relevant parameters. For fields applied along the easy c direction the curves for both cases are similar, with the same characteristics as those of fig. 33 where the intermediate region corresponds to noncollinearity. Note that, due to the large intersublattice interaction, the forced ferromagnetic state is usually reached well above 100T. The magnetization processes along the hard axis of both examples are rather different and depend, in general, on the magnitude of the spontaneous magnetization of the ferrimagnetic system and on the strength of the intersublattice coupling. For large spontaneous magnetization and strong 3d-4f coupling, the hard-axis magnetization process is that of GdCo3 in which there is an


20

~o

3 0

"-~ 2 0

%

1 I I

. ' / " " l I l I i ]

) :tOO 2 0 0 3 0 0 '400

B (T)

D ~ D o a o O a D

A

A

A ~ A

0 - - ' I 0 I0

a Q

A

GdCo 5

,," J_c 4 . 2 K

I i I

20 30 B (T)

40

Fig. 37. Magnetization curves in the full field range for the GdCo 5 ferrimagnet calculated with relevant parameters when the field is parallel and perpendicular to the c axis (Radwanski et al. 1992a).

Fig. 38, Experimental magnetization curves for GdCo 5 at 4.2K measured for field parallel and perpendicular to the hexagonal c axis (Radwanski et al. 1992a).

intermediate state with magnetization close to that observed along the easy axis. In the other case the process is that of GdCo5 where, even in small field, the internal magnetic structure is modified and the magnetization continuously and almost linearly increases toward the forced ferromagnetic configuration. In particular, the apparent anisotropy field, i.e. the crossing of easy- and hard-axis magnetization curves, does not depend on anisotropy only but is a complex function of all the magnetic parameters. Such behaviour has been verified by magnetization experiments performed up to 35 T which clearly show the crossing of magnetizations along the easy and hard magnetization directions (fig. 38) (Radwanski et al. 1992a). The fit of the hard-axis magnetization curve yielded nRM and a value of the Co-anisotropy constant Kt close to that determined in YCos.

Let us focus now on compounds where the magnetic lanthanide has a nonzero orbital moment. The large lanthanide magnetocrystalline anisotropy is, in general, one order of magnitude larger than that originating from the 3d sublattice. Interesting magnetization processes are observed in the high-field region, in particular in ferrimagnetic hexagonal easy-plane systems. In most cases, due to the large number of parameters necessary to describe the magnetocrystalli,ne anisotropy of both sublattices in addition to the intersublattice coupling, the analysis of magnetization curves is a complex problem.

336

40

20


Ho2Coz 7

~ T = 4 . 2 K

Fig. 39. Magnetization curves for Ho2Co17 calculated within the two sublattice model in the full field range for fields applied along the a and b directions of the orthohexagonal cell ([100] and [120] axes of the hexagonal cell, respectively) of the basal plane (Radwanski et al. 1985, Franse and Radwanski 1993).

I I I I I I I V

Fig. 40. Different configurations of the R and M moments for a ferrimagnetic easy-plane hexagonal compound, when the field is applied parallel to the easy direction of this plane (after Franse et al. 1988).

However the task is simplified in easy-plane systems where the second-order anisotropy constant is large enough so that magnetic moments of both sublattices remain in the basal plane during the magnetization process, when the field is applied within this plane. In such a case, only the in-plane K anisotropy parameter of the lanthanide and nRM enter into the expression (17) used to analyze the magnetization curves. The in-plane anisotropy of the 3d sublattice can be considered as negligible. Calculated magnetization process, shown in fig. 39 for Ho2Co17 (Franse et al. 1985b), along the easy symmetry [120] direction of the basal plane exhibits three transitions before the collinear induced ferromagnetic state is reached. The intermediate states correspond to noncollinear magnetic structures associated with first-order magnetic reorientation (FOMR) as shown in fig. 40. For fields applied along the hard axis of the easy plane one expects only two transitions (fig. 39). This behaviour has been observed for the first time in Ho2Co17 for which, thanks to a 35 T high-field installation, the first transition of each symmetry axis of the easy plane was observed (fig. 41) (Franse et al. 1985b). More recently the second easy-axis transition has been observed at 44 T (Tomiyama et al. 1991) in good agreement with the calculated value (Radwanski et al. 1985). Such dramatic behaviour has also shown up in Dy2Col7 (Sirmema et al. 1986), Ho2Col4Fe3 (Sinnema et al. 1987) and TbCo5 (Ballou et al. 1989).

The exchange fields experienced by the 4f spin moment, i .e nSM , R = nSRMMM), nex, RM deduced from the different low-temperature high-field magnetization measurements are reported for different series in fig. 32. They agree quite well with the values determined


~0 Ho2COl 7

60 ; "

2O

10 20 30 H (T)

Fig. 41. The high-field magnetization curves for Ho2Co17 at 4.2 K measured Mong the three crystallographic directions (the [120] axis is the easy axis of the easy basal plane). Symbols: +, [100] axis; x, [120] axis; open circles, [001] axis; full lines are the calculated curves (after Sirmema et al. 1987).

from the Curie temperatures as described previously, which has ted to the same conclusion concerning the origin of the variation of nSM with the lanthanide element (Beiorizky et al. 1987).

3. 4f Magnet i sm

This part is devoted to rare-earth-based intermetallic compounds in which only the rare earth is magnetic. Due to the oscillatory and long-range RKKY interaction characteristic of these materials, in most cases there is a competition between positive and negative interactions. This competition leads, at low temperature, to frustrated magnetic structures, a majority of them being of antiferromagnetic type associated with complex magnetic-field-temperature diagrams characterized by the competition between magnetic incommensurability and commensurability. Moreover, crystal field effects play a crucial role not only in the magnetocrystalline anisotropy, thus leading in uniaxial compounds to either easy-axis or easy-plane systems, but also in the lanthanide moment itself when CEF leads to a nonmagnetic singlet ground state. Magnetization processes are often complex and of metamagnetic type. Therefore the major part (sect. 3.2) of this chapter is devoted to the large variety of metamagnetie processes found in these systems and to the associated phase diagrams. The number of ferromagnetic compounds is much smaller and our knowledge of the evolution of the CEF and exchange parameters in such materials


during the last decade is the subject of sect. 3.1. Finally in sect. 3.3. we present a short review of the advances in the analysis of incommensurate magnetic systems.

3.1. Crystal-fieM and exchange interactions in ferromagnetic compounds

The first studies devoted to the quantitative determination of the main interactions, namely exchange coupling and CEF, have been performed on simple cubic ferromagnets and a few antiferromagnets, in particular the RA12 and RNi2 series (simple cubic Laves phase structure), the RZn, RCd, RAg and RCu compounds (simple CsCl-type structure) and RSb series (NaCl-type structure). Due to the high symmetry there are only two CEF parameters, and inelastic neutron scattering (INS) experiments are generally sufficient for their determination. The paramagnetic exchange parameter J(0) is then obtained from the thermal variation of the paramagnetic susceptibility. In ferromagnets, where not enough information was obtained from inelastic neutron experiments, CEF and paramagnetic exchange parameters were refined from a joint analysis ofM vs H below Tc on single crystals along the symmetry axes and of the paramagnetie susceptibility. A rather good knowledge of these interactions had been obtained in the late seventies (Busehow 1980 and references therein, Waind et al. 1983 and references therein) and from that time many studies were devoted to the determination of the other interactions, which are smaller by one or two orders of magnitude, in particular quadrupolar interactions and magnetoelastic effects. These results have been gathered recently in an extensive review paper (Morin and Schmitt 1990). So these aspects of lanthanide intermetallie compounds will not be presented here.

For the lower symmetries the number of CEF parameters is larger: four and five in hexagonal and tetragonal symmetries, respectively, and more in other systems. It is then impossible to determine CEF parameters unambiguously from INS experiments only. When the number of parameters is not too large, in hexagonal and tetragonal compounds, they can be determined, together with J(0), only from a joint analysis of different experiments such as INS, magnetization measurement on single crystals, and specific heat. In compounds with low symmetry (orthorhombic, monoclinic, triclinie) such a task is illusory because of the large number of parameters to be determined. So the next step of this type of studies has been devoted to ferromagnetic compounds with hexagonal symmetry. In particular, much effort has directed towards the RNi5 series for the following reasons: (i) It is the only series of hexagonal compounds where only the lanthanide metal is magnetic and which are ferromagnetic for any lanthanide. (ii) The structure is simple (one lanthanide atom per unit cell at a high- symmetry hexagonal site). (iii) They are isomorphous with RCo5 in which characteristics of the lanthanide are difficult to determine because of the strong 3d contribution to magnetocrystalline anistropy and exchange interaction. The RNi5 compounds then offer the possibility of determining the lanthanide contribution to the anisotropy assuming that there is not much difference between RNi5 and RCos. (iv) Much work has been devoted to PrNi5 because, due to a nonmagnetic singlet CEF ground state and small exchange interactions, it does not order down to very low temperature and in fact has been


successfully used in nuclear adiabatic demagnetization experiments which have yielded end temperatures around 0.8 mK (Andres and Darack 1977).

In hexagonal ferromagnets the Hamiltonian acting on the R 3+ ion is the sum of the CEF contribution,

0 o + , 0 o 0 +,0o 6 6 "]"~CEF = B202 + B606, (19)

the Zeeman coupling with the effective magnetic field,

7-/Zee = gJ#BJ" Heft, (20)

and the exchange interaction,

7-/ex = -n(gj/zB) 2 {J) ' J , (21)

where n is the isotropic ferromagnetic exchange interaction related to J(0), the Fourier transform of the exchange interaction at Q=0. In RNis, although Ni is nonmagnetic its small induced contribution has been taken into account because it plays an important role in magnetic properties when the lanthanide contribution is small, i.e. at high temperature. This Ni polarization contributes in two ways: (i) by enhancing the internal (applied plus demagnetizing) field Hi and leading to an effective field Herr = Hi(1 + ~t), and (ii) by enhancing the exchange interaction between the lanthanide ions n = nRR + anRNi. Here a = ZNinltNi where Z~i is the exchange-enhanced susceptibility, and nRR and nRNi the molecular field constants between moments as defined in sect. 2.4 (Barthem et al. 1988).

Contrary to cubic compounds, the number of crystal field parameters is too large to be determined unambiguously from the fit of inelastic neutron scattering (INS) experiments on powder alone. Actually these four parameters, together with the lanthanide exchange interaction and the two parameters (ZNi and nRNi) describing the Ni contribution, were refined from a simultaneous analysis of the latter experiments and low-temperature magnetization processes along the three symmetry axes together with the anisotropy of the thermal dependence of the paramagnetic susceptibility measured on single crystals. Additional measurements such as specific heat were used to confirm the obtained parameters. Useful information has also been obtained from M6ssbauer spectroscopy (Gubbens et al. 1988). The different sets of parameters obtained have been proposed by Andres et al. (1979), Alekseev et al. (1980) and Reiffers et al. (1989) for PrNi5, Goremychkin et al. (1985a) and Barthem et al. (1989a) for NdNis, Ballou et al. (1988b) for SmNis, Gignoux et al. (1979) and Goremychkin et al. (1984) for TbNis, Aubert et al. (1981) for DyNis, Gignoux et al. (1979) and Goremychkin et al. (1985b) for HoNi5, Goremychkin et al. (1984), Radwanski et al. (1992b) and Zhang et al. (1994) for ErNis, and Barthem et al. (1989b) for TmNis.

The importance of analyzing the largest number of experiments is well illustrated in the case of ErNi5 in which a set of parameters has been proposed which gives good fits for INS, paramagnetic susceptibilities, the low-temperature magnetization curve along the


o 8

% v

"T

I 1 / /

/ /

/ /

/

Pr-Ni 5 I I I / /

i .-,- f / /

/ / / / / i/.,

, ' / ,,2,/

I ! 100 200 300 TEMPERATURE (K)

Fig. 42. Thermal variation of the reciprocal susceptibilities of PrNi5 parallel and perpendicular to c. Solid circles are the experimental values, solid lines are the calculated variations, and dashed lines are the variations corrected for the nickel contribution (Barthem et al. 1988).

easy [001] axis and the specific heat, but which fails to account for the very high field low- temperature curves along the [100] and [120] directions of the basal plane (see sect. 3.2.4). A rather different set of parameters was then found which accounts quite satisfactorily for all the experimental results. At this moment, from the comparison of the different sets of CEF parameters through the series it seems that the latest ones determined in compounds with Pr, Nd, Tb, Dy and Er are reliable whereas improvement can still be obtained for those of Sm, Ho and Tm compounds (Zhang et al. 1994).

The relative importance of Ni magnetism is the largest for the light lanthanides (Pr, Nd and Sm) and yields thermal variations of the paramagnetic susceptibilities quite different from that of the lanthanide ion alone as shown in fig. 42 for PrNis. The experimental susceptibilities parallel and perpendicular to [001], corrected for Ni contribution, follow the linear Curie-Weiss behaviour at high temperature with a slope corresponding to the effective moment of the R 3÷ ion. Note that the shift of the reciprocal susceptibilities parallel and perpendicular to the [001] direction corrected for the Ni contribution allows a first determination of the second-order CEF parameter (Boutron 1973) which generally is close to the value refined from all the experiments.

It is worth noting that the first direct measurement of the Zeeman splitting of the CEF levels by point-contact spectroscopy was done using PrNi5 (Reiffers et al. 1989). The significance of this experiment, illustrated in fig. 43, is that: (i) it has been possible to follow the transitions between levels when the field is applied successively along the three symmetry axes and (ii) transitions which were forbidden in zero applied


0.15 I 0 .27 I o.8s I 0.82 1.37

l { 15 0114

| ~ o.55 | 1.28 + 1 .28 ~ .

10 0.74 , J ,.--';f _

•

0.02 0.29

15 0.16 0.5(: 0 .48 0.7e 1.21 0. 1 .42

;

° ' 1 ' l 1(] ~ I 1.6(]

1 .89 2.87 2 .59 I

::D Q

..~E 1(] >. 0 uJ Z IJJ

.... L . _ +

0 1'o 1'8 2'0 M A G N E T I C FIELD ( T )

Fig. 43. Magnetic field dependence of the CEF energies obtained for PrNis~Cu point contacts for fields along the [100], [120] and [001] axes (different symbols are used for different contacts) after Reiffers et al. (1989). The solid curves are the calculated variations with the refined parameters. The sequence of the lowest CEF levels at zero field is F 3 (ground state), F 1 (38.3 K), F~ I~ (4I .6 K) and F 6 (42.2 K). The numbers are proportional to the calculated transition probabilities from the ground state at 10 T and 20 T and are given in the same order as the calculated energy levels. The dashed curves show the calculated energy of the first excited F t level with the CEF parameters given by Barthem et al. (1988). (Zero energy corresponds to the ground state).

field were observed. In part icular it has been possible to follow the field dependence o f the first excited F] CEF level whereas the transition from the ground state to this level cannot be observed directly in zero field. This experiment confirmed that the sets o f parameters previously determined were reasonably correct (Andres et al. 1979, Alekseev et al. 1980, Barthem et al. 1988) and at the same time allowed them to be refined. The knowledge o f CEF parameters allowed one to predict a highly original high-field magnetization behaviour arising from the existence of the nonmagnetic singlet ground state, namely transitions associated with the field-induced "crossing" and "anticrossing" o f the two lowest states along the [100] and [120] directions, respectively. In quantitative agreement with prediction, metamagnetic transitions have been observed at low temperature (T ~< 5K) from magnetization measurements in fields up to 38T; associated with "crossing" these become steeper and steeper as temperature decreases,


~: 15

©

5

0 0 20 40 60 80 O0

T(K)

Fig. 44. Specific heat of ErNis: black dots are the experimental points (Radwanski et al. 1992b), the solid line is the calculation with parameters given by Zhang et al. (1994).

whereas those associated with "anticrossing" are nearly temperature independent (Ball et al. 1992a) (see sect. 3.2.2).

In TbNis, in addition to the above quoted experiments, the spin waves and single-ion type magnetic excitations have been studied by inelastic neutron scattering at 4 K on a single crystal along the (q, 0, 0) and (0, 0, q) propagation directions (Gignoux and Rhyne 1986). One dispersive accoustic mode and two nondispersive modes were observed, from which J(q) along these two directions has been deduced; this resulted in improvement of the CEF parameters proposed earlier (Gignoux et al. 1979, Goremychkin et al. 1984).

As quoted above, in ErNi5 the latest set of parameters (Zhang et al. 1994) gives particularly good fits for all the experiments, in particular the low-temperature high-field magnetization measurements along the hard axes of the basal plane (see sect. 3.2.4) and the specific heat characterized by a large Schottky anomaly around 35 K (Radwanski et al. 1992b; fig. 44). The microscopic aspects of the magnetization processes along the [120] and [100] axes, calculated with the refined set of parameters, exhibit quite interesting features as shown in fig. 45: (i) There is a large decrease of the value of the Er moment during the rotation process from the easy c axis toward the applied field direction, the minimum value corresponding to the field at which moments become parallel to [120] and [100] (i.e. 19 T and 22 T), respectively. (ii) Above 22 T, the reduction of the magnetization measured in the basal plane (compared to that measured along [001]), arises from a huge anisotropy of the magnetization and not from the fact that moments would not be parallel to the applied field. As with the reduction of the Er moment during the rotation, this is a consequence of the fact that the moments in the basal plane are induced by the applied field.

As for ErNi5, the calculation with the refined parameters allows us to understand the magnetization processes. For instance, in NdNi5 (fig. 46), the anisotropy energy between the a ([100]) and b ([120]) axes (hatched area in the figure) is weak: a field of 11 kOe applied along b is large enough to align the moments in this direction. It is worth noting that in higher fields the magnetization difference between both axes arises from a large anisotropy of the magnetization which strongly increases with the field up to 130kOe and reaches 12% in 150kOe. When the field is applied along the hard


Z LU

~3

zL v 4-a C-

d )

E o

(19 (1) Ob (1)

q~ v

10

1 0 0

8 0

6 0

40

20

Q ~ ~ 0 Q 0 Q I Q Q ~ ~

ErNi 5

'I.4K

/

/

/

/

/

I ~ ~ I I

,o H// [120] . . . . . . -_

o ./. o~o~O~

/" ° ~" ~ H / / [ 1 0 0 ] 7 . f

/ / "

1 J I ; I I [ I i I I I I I

o ÷ * l a o * a e e * e a w m m * ~ o l

H//[120]

o o

. o ~o

® ® ®

10

H//[100] o

o

0 0 2 0 3 0 4 0

H ( T e s l a )

Fig. 45. ErNis: calculated field dependences of the moment amplitude (upper part) and of the angle between moments and the [001] axis (lower part) when the field is applied along the [120] and [100] axes of the hard plane. Dashed lines in the upper part represent the calculation of the moment amplitude when moments are forced to be either along [120] or [100] (after Zhang et al. 1994).

c axis, the observed variation o f the magnetization corresponds to a slow rotation o f the Nd moments associated with a gradual decrease o f their amplitude. Besides, in zero field the Nd moments are perpendicular to c and reach 2.01/ZB, in an internal field o f 150 kOe the moment amplitude is only 1.40/~B and moments still make an angle o f 29 ° with the field (Barthem et al. 1989a).

From these quantitative studies in this hexagonal series and earlier studies in cubic ferromagnetic compounds it has been possible to compare the exchange parameters along the series. As for the previously reported analysis o f the R - M exchange coupling, Belorizky et al. (1988) analyzed the R - R coupling in different series. The variation OfnRM in all the studied series had been ascribed to a variation o f the 4f -5d exchange interaction arising from the increasing distance between the 4 fand 5d shells going from light to heavy R elements. As the same 4 f -5d exchange interactions are involved in any metallic system containing magnetic R elements, it was natural to study the R - R interactions in systems where they are not masked by dominant R - M interactions, i.e. in the absence o f magnetic M atoms. The RA12, RZn and RNi5 series are quite suitable for such a study. As shown


% z 113 z

r n :3 .

._..,_____..-----J

~ - ~

l i b

NdNi 5 1.5K

M N d = 1.&.0 PB

HIIc ~°= 29" "

N d

L~MNd =2.01 PI~ 0 50 160 Hi(kOe ) 150

Fig. 46. Internal field (applied field corrected for the demagnetizing field) dependences of the magnetization at 1.5 K in NdNi 5. Black dots are the experimental values. Solid lines are the calculated variations (Barthem et al, 1989a).

5 000

4 000

I

~ " 3 ooo ~l ~

m ~

20OO \ \ \\ k\

U 1000

\

\

0 K I I I L o . C e Pr Nd,

~x \ \ \

\ ".

~ , ~ ~ O

I I I I I I I I I Sm Gal. Tb Dy Ho Er Tm

t

Lu

Fig. 47. Molecular field coefficients nSR in the RA12 (open circles), RZn (solid circles) and RNi 5 (open triangles) series (Belorizky et al. 1988).


in fig. 47 there is a large increase of the R-R interactions across a given series from heavy to light R atoms. This increase is still larger than for the R-M interactions (see figs. 31 and 32). In particular it has been observed that the increase of nSg is similar to that of (nSM) 2. Knowing that the ne, g coupling involves three stages, namely the 5d-4f, 5d-5d and again the 5d-4f interactions, the observed variation has the same origin as that of nSM and confirms that, according to Campbell (1972), the exchange interaction involving R atoms are essentially mediated by the 4f-5d exchange. The same conclusions have been derived from the analysis of the transferred hyperfine field at the nonmagnetic site like A1 and Zn in the RAI2 and RZn series (Belorizky et al. 1988 and references therein).

3.2. Metamagnetism and associated phase diagrams

The concept of metamagnetism has spread considerably over the last decades, since Kramers introduced the term for the original property of a first-order phase transition between a simple antiferromagnetic structure with a low magnetization and the induced ferromagnetic state with a high magnetization, this transition being induced by the application of a magnetic field (see ref. 1 in Stryjewski and Giordano 1977). First limited to such single-step phase transitions, this concept has been progressively extended to a lot of processes breaking antiferromagnetic structures, and more generally to all types of field-induced magnetic phase transitions (Date 1990, Gignoux and Schmitt 1991). The aim of this section is to present an extensive review of the different types of metamagnetic processes occurring in the rare-earth intermetallic compounds in which only the rare earth is magnetic (the metamagnetism associated with 3d magnetism is not considered here). For each process, a number of examples as large as possible will be provided for illustrating the particular physics involved or the particular balance between the different couplings giving rise to the metamagnetic behaviour. After some general considerations, each type of metamagnetic process will be widely developed by order of increasing complexity.

3.2.1. General considerations First we have to specify exactly what the term metamagnetism will signify in the following. We will consider as metamagnetie behaviour any anomaly occurring during the magnetization process of a given compound, compared to the "normal" behaviour of a magnetization curve exhibiting a downward curvature (usual paramagnetic or ferromagnetic system). Such an anomaly is characterized by an upward curvature present in a limited field range. Two main classes of metamagnetic transitions can then be distinguished (see fig. 48): (i) a step-like behaviour where the magnetization jumps more or less suddenly between two well defined plateaus: class (1); (ii) an S-shaped behaviour where the magnetization increases smoother than in class-(1) systems, showing only an inflexion point at a given critical field He: class (2). It can be noticed that class-(1) transitions are often, but not always, associated with a first-order transition, which is never the case for class-(2) transitions; moreover, class-(1) transitions are generally sharper as the temperature is lowered, and they often evolve at high temperature towards class-(2)


M M (a)

class (1)

(b)

2)

Hext Hext Fig. 48. Schematic representation of: (a) a discontinuous (class (1)), and Co) a continuous (class (2)) metamagnetic transition.

behaviour. More subtle particularities may occur in both classes: for class-(1) materials, the transition can be discontinuous or can present a portion with a finite slope as a function of the external (applied) magnetic field, and this will be related to demagnetizing field effects in the presence of hysteresis (see below); for class-(2) compounds, the magnetization curve may exhibit an angular point at the critical field, i.e. a discontinuity of the slope dM/dH at the transition, or keep a smooth variation in the whole field range. Note that this smooth behaviour may be intrinsic or due to faults or inhomogeneities in the sample. It is worth noticing that some compounds may present both types of metamagnetic transitions, on the same magnetization curve or at different temperatures.

The value of the transition field Hc generally depends on temperature, T, and sometimes on the direction of variation of the field (increasing or decreasing field). Moreover, some transitions may exist for one single direction of variation. By reporting the corresponding H - T values, more or less complex phase diagrams can be constructed, showing one or several distinct regions, each one associated with a particular spin structure, and separated by boundary lines which are generally first- or second-order transition lines (see fig. 49). In addition, these phase diagrams may exhibit several critical points on the transition lines, such as tricritical points (junction between first- and second- order transition lines), triple points (junction between three first-order transition lines) and critical or bicritical endpoints (end of a second- or first-order transition line) (Stryjewski and Giordano 1977). Numerous examples will be shown throughout this section. The general topology of a phase diagram together with its associated details will reflect the underlying microscopic properties at the origin of the metamagnetic behaviour. The two main ingredients playing an essential role in these phenomena are the anisotropy and the interionic interactions. The former property, i.e. the crystalline electric field (CEF) coupling, plays a fundamental role by constraining the magnetic moments to lie along a given direction (axial anisotropy), or within a given plane (planar anisotropy), or anywhere in space (weak anisotropy). A particular situation of axial anisotropy will occur when there are several equivalent noncollinear easy magnetization directions, as for example the two-fold axes in hexagonal or tetragonal symmetry, or the three-fold axes in cubic symmetry. The one-ion magnetoelastic coupling must be included in this first category, being considered as the strain derivative of the CEF itself. The second


H first order line " ~ , , , ~ tricrifical point

X \

triple point \ ' ,

bicritical • endpoint

I

second orderqine I

T Fig. 49. Schematic view of a H - T magnetic phase diagram with some critical points.

fundamental ingredient includes all types of interionic interactions, namely the isotropic or anisotropic bilinear exchange coupling and the two-ion quadrupolar coupling, as well as their possible strain dependence, i.e. the interionic magnetoelastic couplings. These two basic microscopic properties appear to be the essential characteristics of a metamagnet. Their relative importance as well as the sign of the different parameters involved will lead the considered compound to belong to one of the families described below, keeping in mind that, sometimes, there is no obvious frontier between two different behaviours, and that an observed transition can result from the combined action of several phenomena.

3.2.1.1. Demagnetizing field effects and hysteresis. Special attention must be paid to the distinction between internal and external (applied) magnetic field, in particular as far as a first-order transition is concerned. For an ellipsoidal sample, it is well known that the magnetization is uniform as a function of the applied field Hext, but actually the magnetic ions experience an effective internal field, Hi, instead of Hext:

H i = Hext - H d = Hext - N d M , (22)

w h e r e N d is the demagnetizing field factor depending on the shape of the sample and on the direction of application of the field. The presence of this demagnetizing field Hd has an important consequence in the case of a first-order transition (Stryjewski and Giordano 1977). Let us consider such a first-order magnetic transition for the critical internal field H~ and without any hysteresis (see fig. 50a). Actually this field is defined by the crossing of the Gibbs free energy variation for both magnetic states under consideration. The magnetization M then should jump discontinuously from MB to Mc when the internal field reaches the critical value H~ (vertical line BC in fig. 50a). In external field, the transition starts for the critical value HCxt = H c + NdMm However, the transition cannot proceed all at once, because an increase of M would lead to a decrease of Hi below the value required to induce the transition. The transition therefore must take


M

(a) ~ B D

A-

M

A'

(b) C;

J., C H i Hi

D'

Hexl

M (c) E C D

B A F

H~ H~ H i

M (d) E' C'

B ~ A ~ F'

D'

Hext

M (e) D F E

A

M (f) D' E ' !,'S

A'

Hext

M C (g) E

G B A F

D M (h) E ! C I _ _

G, I/ t A' F'

D'

Hi Hext

Fig. 50. Schematic representation of a first-order metamagnetic transition in internal (a, c, e, g) or external (b, d, f, h) field, and without hysteresis (a, b), with a large hysteresis (c, d, g, h) or with a small hysteresis (e, f); the distinction between (c, d) and (g, h) arises from the way the domain structure is modified during the transition (see text).


place gradually, any change 6M occurring only for the corresponding change 6He×t which keeps Hi constant, i.e.:

5M 1

6Hext Nd" (23)

The result is an inclined portion in the magnetization process as a function of the applied field (line WC t in fig. 50b), the slope corresponding to the reciprocal demagnetizing field factor 1/Nd. During this portion, the sample breaks into domains of the two phases coexisting at the first-order transition, a behaviour similar to the initial magnetization process of a ferromagnet below its Curie temperature. This mixed-phase region is then associated with all first-order transitions between states of different magnetization but without any hysteresis.

Let us consider now the case of a first-order magnetic transition with hysteresis. The crossing of the free energy of both states still defines the theoretical critical field H~. However, the magnetization does not jump for this critical field, but exhibits a hysteresis cycle between the two limits H u and H d (see fig. 50c). These fields correspond to the points where the change of magnetic configuration is initiated in increasing and decreasing field, respectively. This phenomenon arises when an energy barrier between both states prevents the system to carry out the transition at H~. The hysteresis width may range from small to relatively large values, as we will see in the following, depending on the origin of this barrier and on the temperature. The critical point H~ corresponds to the instability of the low-field state which may occur either within the whole sample or in some nucleation centers. In the former situation, and if the hysteresis is wide enough, the full system suddenly jumps from B to C on the cycle, experiencing a corresponding reduction of the internal field equal to Na(Mc-MB) . This is possible because point C corresponds to a state allowed for the system, i.e. a stable state. This results in a vertical portion WC p in the magnetization process in external field (fig. 50d). The inverse process occurs in decreasing field (lines EF and E~Ft). As a consequence, the hysteresis width AHC×t in external field is reduced compared to the theoretical value c u d Zk/-/i = (H i - H i ) in internal field:

AH~x t = AH~ - Nd(Mc - MB). (24)

In the case of a narrow hysteresis, namely AH~ smaller than N d ( M c - M s ) , the situation should be more complex, exhibiting both behaviours described above, and should lead to an unusual hysteresis cycle in external field, where the increasing critical field HeUt is lower than the decreasing one Hdxt (fig. 50e, f). Moreover, from the above considerations, it follows that a transition which follows the demagnetizing field factor in external field should always be associated with a first-order transition without hysteresis, while the existence of hysteresis should always produce a transition with vertical portions, at least in part. However this behaviour does not seem to be always the case in experiments, where transitions following the demagnetizing field factor in external field are often


associated with a strong hysteresis. This means that, generally, the sample does not transit at once, i.e. the domains where the high-field state is nucleated do not extend suddenly to the whole crystal: the transition occurs progressively as in the first case described above, within a finite external field range where the sample is in a mixed-phase state (fig. 50g, h). The nucleation centers around which the transition is initiated may be any fault, inhomogeneous region or antiferromagnetic domain wall. In this latter case, the situation is necessarily different by increasing or decreasing field since the magnetic structure itself can be very different on both sides of the transition. This difference can play an important role in the occurrence and width of the hysteresis. Finally, the effective critical field H u for example may be smaller than the theoretical value corresponding to the instability of the low-field state, because of the presence of these nucleation centers, following the same process as in ferromagnets with a hysteresis, where the coercive field is generally far below the anisotropy field.

3.2.2. CEF metamagnetic systems

The simplest systems where metamagnetism can occur are pure CEF ones, i.e. those where the CEF is the only interaction acting on the 4f shell. Indeed this single coupling is sufficient to induce field transitions under certain conditions of anisotropy and field direction. This effect was first predicted by Cooper (1966) for TmSb. This cubic compound exhibits a ['1 singlet as ground state, with a M j =4 main component. When an external field is applied along the hard magnetization direction [001], a crossing of F1 and of one of the levels issued from the F4 excited state (having a Mj = 5 component) is anticipated at about 40 T, giving rise to a step in the predicted magnetization becoming more and more pronounced as the temperature is lowered down to 0 K. A second crossing between F4 and one of the F~ 2) levels is predicted in still higher fields, resulting in a second step toward the saturated magnetization (Mj = 6). Due to the low availability of high magnetic fields at that time, this effect has not been observed experimentally 1.

Such a crossing of CEF levels has been observed several years later in Pr metal at a field of 31.5 T applied along the [001] hard direction of this double-hexagonal close-packed material (MeEwen et al. 1973). In this system, the ground state at both the cubic and hexagonal sites is a singlet, and the exchange interaction is undercritical so that there is no magnetic ordering down to very low temperatures. At 4.2 K and for a field of 31.5 T, the magnetization process along the hard direction exhibits a well-defined step (see fig. 51), which has been ascribed to a first-order transition on the hexagonal sites. The size of the magnetization jump is 2.08/~B per hexagonal site, and there is a noticeable hysteresis of about 0.2 T at 4.2 K, the transition being sharper and the hysteresis larger at lower temperature. This transition has been explained by the field-induced crossing of the F1 singlet ground state (Mj = 0) with the F3 excited level (Mj = 3 component) lying at about 50K above F1, in zero field. This has been confirmed later (Franse et al. 1990).

1 Note added in proof A field-induced metamagnetic transition associated to a CEF level crossing has been observed very recently in TmSb along the [001] direction, for a field of about 48T, in reasonable agreement with the theoretical predictions (Nimori et al. 1995).


o 2 c)

,-n ::::t.

F-..

Z LJ

C3 5 -

P £

o II10] . [001]

0

/ g

o

eeo O ~ o o e "

0

0 0

• • ° o

5

10

o o o

o o

• • s

1 I

2O 30 z.0 INTERNAL FIELD (TESLA

Fig. 51. High-field magnetization data for paramagnetic Pr metal at 4.2K along two different directions; note the hysteresis of the first order transition at 31.5T (after McEwen et al. 1973).

A still more interesting example is provided by the hexagonal compound PrNi5 in which two different types of CEF metamagnetic transition occur, namely a crossing of CEF levels along the [100] direction and an anticrossing along the [120] direction (Ball et al. 1992a). Indeed, in this paramagnet the ground state is the F3 singlet followed by another singlet F1 around 30 K and two doublets F~ 1) and F6 at about 50 K. When the magnetic field is applied in the basal plane, the energy of the first excited level decreases much faster than that of the ground state so that these two levels should cross for a given field. However, according to group theoretical considerations, the ground level I" 3 transforms into a F2 or 1"5 level under the application of a field along the [100] or [120] directions, respectively, while the first excited level keeps the Fl symmetry. It follows that the two levels actually cross each other in the first case, because they belong to different representations, while in the second case an anticrossing occurs because they both belong to the same representation (see fig. 52). This leads to a metamagnetic transition which becomes sharper and sharper in the first case when the temperature is lowered, finally reaching a stepwise behaviour at 0 K, while in the second case the transition remains smooth even at 0 K. Both transitions have been experimentally observed, for magnetic fields of 18.5 T and 12 T, respectively (fig. 53). It turns out that such behaviours (crossing or anticrossing) give useful information about the CEF level scheme because the value of the critical field of the metamagnetic transitions is directly related to the zero-field energy position of the excited level which crosses or anticrosses the ground state. This is particularly true in PrNis, where the composition of the 1̀ 1 excited level forbids one to observe directly a transition from the ground state by neutron spectroscopy in zero field. However, this transition becomes possible for nonzero magnetic field and has been actually observed by point-contact spectroscopy (see sect. 3.1, fig. 43) (Reiffers et al. 1989). This allowed one to slightly adjust the CEF parameters determined previously (Ball et al. 1992a).

In a general way, both types of CEF metamagnetic transitions occur when a non- or weakly magnetic ground state evolves into a stronger magnetic ground state as a function of the magnetic field, the continuous or discontinuous character of the transition depending on the symmetry of the levels, i.e. of the detailed composition in

352

4

3 E

-100

e~ -120

-140

-160

-180


I I I

PrNi s [1001

_ 0 . ~

" /~.~._¢~ 1.4K " - 4.2 K / ~ . ~ . . . .

, I i I m I i

0 10 20 30 Applied Field (Tesla)

I I !

PrNi , 54.2K ......~ ~ i - 2 " 0 i .... ,

. f 1.4K and 0.3K

- / -

~ ( c )

. _ _ ~ ~ F 1 [120] ]

10 20 30 40 Applied Field (Tesla)

Fig. 52. Calculated field variations of the magnetization and the energy of the first two CEF levels in PrNi 5 along both symmetry directions of the basal plane and at various temperatures; note the different behaviour of the metamagnetic transitions associated with the crossing or anticrossing of the levels (after Ball et al. 1992a).

Mj components. According to the sequence of the CEF levels and to the direction of the applied field, one or several successive stepwise transitions can be expected, associated with several successive levels crossings or anticrossings (Mrachkov and Leyarovski 1988). In fact, the metamagnetic behaviour should be present as soon as the CEF ground state eigenfunction does not include the Mj = J component as its major part, for the considered field direction. There always exists a direction fulfilling this condition, even possibly along the easy magnetization direction, although the corresponding critical fields often are much too high to be reached experimentally. In addition, as seen above, the sharpness of the metamagnetic behaviour increases when the temperature decreases, so that a low temperature is often needed to observe them. That explains why both examples where these transitions were observed (see above) are paramagnets, having a nonmagnetic singlet as ground state, because this particular CEF configuration more easily allows the exchange interaction to be undercritical with regard to the occurrence of magnetic ordering. A measurement at low temperature can then be made without being disturbed by the latter. However, one can imagine that the increasing availability of both high magnetic fields and low temperatures in the future will allow one to use these properties to get information about the CEF level scheme under magnetic field,


1

G o

3

i i i

PrNi 1.4K 5

t 1 2 0 ] / ' ~ i ................

/ .'° [100] J

f * ° ° °

/ j / ° , I , I , I q

PrNi 4.2K 5

° ° o

o° [lOO] o

[120]

# o

o o

o

o •

8 °

s

o e o e o *

I I I

10

[001]

O O

0 I , I 0 20 30 40

Applied Field (Tesla)

Fig. 53. High-field magnetization curves in PrNi 5 along the two main symmetry directions of the basal plane at 1.5 K and 4.2 K (after Ball etal . 1992a).

similarly as neutron spectroscopy does in zero field. Moreover, and as already mentioned by Cooper (1966), the field-induced transition is generally associated with an anomaly of the temperature dependence of the magnetic moment, namely the presence of a maximum which is particularly strong for a magnetic field just below the critical field: this effect is obvious when the successive isothermal curves in fig. 52 are considered. It can be noticed that this maximum is not always present on the susceptibility curve itself, i.e. in the zero-field limit, in particular in the case of a level crossing. However, when the susceptibility variation exhibits such a maximum, it is generally associated with a change of sign of the third-order magnetic susceptibility (Morin et al. 1988): below the temperature where this maximum occurs, the third-order susceptibility becomes positive, i.e. the initial magnetization process exhibits a positive curvature which is the signature of a metamagnetic transition in higher field.

Another interesting effect related to a CEF level crossing may appear in the presence of nonzero magnetic interactions and has been studied by Tsuneto and Murao (1971) in the case of a S = 1 system. R has been shown that, in the vicinity of the crossing point, small ferromagnetic exchange interactions may be at the origin of a field-induced second-order magnetic ordering. This can be explained as follows: within the mean-field picture, the usual magnetic ordering occurs when the initial susceptibility increases, by


M

M c

(a) /

H(T¢) H ° H~

M (b)

T<T ¢

Hc(T) H°c

AM

H. I

H

H ( T )

critical p ~ . ~ endpoint¢

metamagnetic transition line

first order transition line

I (c)

H

critical point endpoint

=

metamagnetic transition line

first order transition lines

l (d)

T T T T e ¢

Fig. 54. Schematic determination of the occurrence of a field-induced magnetic transition near a CEF level crossing (see text); (a) situation at the critical temperature To; (b) situation below T c. The slope of the straight line which defines the critical field Hc(T ) is 1/n. Temperature dependence of the critical field in the case of (c) ferromagnetic or (d) antiferromagnetic interactions.

decreasing temperature, above a certain threshold value proportional to the reciprocal exchange coefficient 1 /n . In the present case, the superimposed susceptibility at the crossing field diverges at 0 K so that, provided an applied field polarizes the system near this point, there exists also a critical temperature Tc where this susceptibility reaches the same threshold value 1 /n , resulting in a second-order transition (see fig. 54a). Below this temperature, the order parameter M experiences an additional variation AM compared to the expected field-induced dependence, for a critical field He(T) slightly smaller than He(T~) (fig. 54b). It is noted that the critical field Hc(Tc) includes a contribution of the ferromagnetic exchange coefficient n through the relation

Hc(Tc) o (25) = H e - n M c ,

where H ° is the metamagnetic critical field without interactions and Mc is the associated magnetization. This shift of the critical field is effective in fact over the whole temperature range of the transition. The corresponding temperature dependence of


He(T) is schematized in fig. 54c. Below the critical temperature To, a first-order transition line separates two ferromagnetic phases with different magnetization, while above Tc, the line corresponds to the normal metamagnetic field; this latter vanishes above a given temperature where there is no longer any metamagnetic transition due to the thermal effects on all the CEF levels. Note that this metamagnetic field is temperature independent, because it Js related to a level crossing which does not depend on temperature. In the case of predominant antiferromagnetic exchange interactions, the behaviour should be still more exotic, because the same effect should lead to a two-site ferromagnetic ordering below a critical temperature Tc and for a critical field He, where the antiferromagnetic component of the magnetization should follow the corresponding propagation vector maximizing J(q). A second transition line then should close this intermediate phase above the previous one (fig. 54d). Although such phenomena have not yet been observed experimentally, one can anticipate that the increasing availability of high magnetic fields together with low temperatures will allow us to confirm the above assumptions in the future. A possible example could be the PrNi5 compound, where a small ferromagnetic Coupling is present (see above in this section): such an effect should occur along the [100] direction (see fig. 52), but below a critical temperature Tc estimated to be about 1 K.

3.2.3. Quadrupolar metamagnetic systems The CEF interaction is not the only coupling able to induce metamagnetic processes within the paramagnetic phase. In fact, any coupling of rank 2 or higher may poten- tially produce metamagnetic transitions, through nonlinear effects on the magnetization. Among them, the best known is magnetoelastic coupling or, more generally, quadrupolar interactions. By using a perturbation theory, it has been shown that these latter provide an additional contribution to the third-order magnetic susceptibility X~ ) (Morin and Schmitt 1990). According to the sign of this term and to its magnitude compared to the pure CEF contribution (see above), the total third-order susceptibility may become positive, i.e. the initial curvature of the magnetization process may become positive, giving rise to the occurrence of a metamagnetic transition at a certain field. This transition can be either smooth, class (2), see sect. 3.2.1, when the quadrupolar coupling only speeds up slightly the "natural" magnetization process, or more discontinuous, class (1), when the strength of this coupling exceeds a critical value which depends on the magnetic and quadrupolar character of the CEF ground state.

Examples where the quadrupolar metamagnetic transition is of class (2) include mainly cubic compounds such as YmCu (Jaussaud et al. 1980), PrPb3 (Morin et al. 1982), TbP (Raffius and Krtzler 1983), DySb (Al~onard et al. 1984a), ErAI2 (del Moral et al. 1987), TmGa3 (Morin et al. 1987a) CeMg and CeZn (A16onard and Morin 1990). The predominance of cubic compounds is explained by the fact that for other symmetries the quadrupotar moment is already ordered by the crystal field; then the effects of magnetoelastic couplings are more difficult to be observed. In all these cubic compounds, the third-order magnetic susceptibility becomes positive in a limited


t o

bo

-5 0 5 10 15 20 25

r(K)

Fig. 55. Temperature variation of the third- order magnetic susceptibility for a magnetic field applied along a four-fold axis in cubic TmCu; solid lines are calculated taking into account the quadrupolar parameter Gj indicated (after Jaussaud et al. 1980).

temperature range above the ordering temperature, but its value remains quite weak. Therefore, the associated positive curvature of the magnetization process is barely visible on the curves themselves, and only a detailed analysis can provide a reliable value for X~ ) and thus a confirmation of the metamagnetic behaviour. As an example, fig. 55 shows the dependence of this third-order susceptibility in TmCu. In this compound, the metamagnetic transition occurs only along the four-fold axis, the corresponding quadrupolar parameter G1 = 10inK being positive and large enough. Along the other main symmetry direction, i.e. the three-fold one, the trigonal quadrupolar parameter G2 is negative, preventing the metamagnetic transition to appear. This is a general rule in lanthanide intermetallic compounds: the magnetic processes are anisotropic, at least in high field, therefore searching for a metamagnetic transition requires one to investigate successively each of the independent symmetry directions. In TmGa3, it turns out that the direction where a slight metamagnetie transition occurs just above the ordering temperature is the three-fold one, indicating that in this compound the trigonal quadrupolar coupling is involved in this behaviour. The same is true for the pnietide TbP. It is worth noting that the occurrence of this metamagnetic transition, i.e. of a positive third-order magnetic susceptibility, in the close vicinity of the magnetic ordering leads in principle to a first-order magnetic transition (Morin and Schmitt 1990). This is effectively the case for TmCu, TbP, DySb, CeMg and CeZn, all ordering antiferromagnetically within a first-order transition.

A more spectacular example is provided by the cubic compound TmZn (Morin et al. 1978) which exhibits a quadrupolar metamagnetic behaviour of class (1). This compound orders ferromagnetically at Tc = 8.1 K, but the quadrupolar interactions are large enough to induce a ferroquadrupolar ordering at the slightly higher temperature TQ = 8.55 K. Above this latter temperature, i.e. in the cubic paramagnetic phase, a single-step metamagnetic transition occurs along the [001] easy magnetization direction (see fig. 56). In this compound, the CEF ground-state triplet F~ 1) consists of a magnetic doublet with a dominant IMj = + 5 ) component and a nonmagnetic but strongly quadrupolar singlet having a main IMj = 6) character. In low field, the ground state arises from the doublet


6

A

O 5 \ :P

4 Z O )-- 3 <~ N

2

,< l [ 1

0 20 40 60 80 100 120 Fig. 56. Magnetization curves in cubic TmZn along the [001] direction at various temperatures: the inset shows the temperature dependence of the critical field (after Morin et al. 1978).

state within the triplet. The observed field-induced first-order transition takes place when the internal field exceeds the critical field necessary to induce the ferromagnetic ordering on the singlet component of the triplet, this phenomenon being strengthened by the quadrupolar character of this singlet together with the large positive quadrupolar coupling present in this compound (Morin and Schmitt 1990). Moreover, this first-order transition is replaced by a second-order one at a higher temperature, due to thermal averaging effects on the involved crystal-field levels. A similar behaviour exists in the isomorphous compound TmCd (A16onard and Morin 1979), although in this latter compound, the only phase transition is a ferroquadrupolar ordering which takes place at a lower temperature than in TmZn (TQ = 3.16 K). The temperature dependence of the metamagnetic critical field of both compounds leads to the phase diagram shown in fig. 57 (L/ithi et al. 1979). This kind of metamagnetic behaviour is characterized by a critical line starting from the ordering temperature and exhibiting a critical endpoint at the temperature where the third-order magnetic susceptibility becomes negative (these endpoints are out of scale in fig. 57).

A very specific type of metamagnetic transition related to the quadrupotar interactions occurs within the quadrupolar phase itself, i.e. when the quadrupolar moment is ordered but the magnetic moment is not. This was observed for example in CeAg, where the wide


2O Ta(K)

15

10

~.o

o

o TmZn

~ ~ T m C d

I I I

0 I 2 3 B (T)

Fig. 57. Magnetic phase diagram for TrnZn and TmCd; the critical fields are determined by magnetization (open circles), elastic constants (open triangles) and electrical resistivity (solid circles); solid lines are calculated (after Lfithi et al. 1979).

range of stability of this phase allowed a detailed investigation (Morin 1988). In this cubic compound, the ground state is a F8 quartet which splits into two doublets at TQ = 15.85 K due to the strong quadrupolar coupling associated with the tetragonal symmetry mode (<O °) is the order parameter). This cubic-tetragonal transition is accompanied by a huge tetragonal distortion due to a noticeable magnetoelastic coefficient (c/a- 1 ~ 1.7% at 1.5 K). The ferromagnetic interactions present in this compound lead to the ordering of the magnetic moments far below TQ, namely Te = 5.2 K. In the absence of any external stress, a strain domain structure takes place between Tc and TQ, i.e. three tetragonal domains are present, corresponding to the three equivalent four-fold directions of the initial cubic symmetry. When a magnetic field is applied along the [001] direction, it turns out that it is parallel to the local c axis for one domain but perpendicular to it for the two others. In this latter case, the field is then aligned with a local tetragonal a axis, and a sudden magnetization jump occurs as soon as the Zeeman and exchange energies are strong enough to destroy the initial quadrupolar ordering: at the corresponding critical field the a axis transforms into a c axis (see fig. 58). An additional nonreproducible hysteresis is associated with this strong metamagnetic behaviour, due to the actual repartition of the virgin sample into the three tetragonal domains. In the corresponding phase diagram, the critical field first increases between Tc and 10K, then decreases up to TQ. This anomalous behaviour has been explained by the different temperature dependences of the quadrupolar and bilinear energies: the latter, which decreases more rapidly than the former, requires an additional amount of external field to produce the transition in intermediate temperature range. Note that a similar metamagnetic behaviour also occurs within the ferromagnetic phase, i.e. below Te, the only difference being the presence of a spontaneous ferromagnetic component.


1.5

1.0

0.5

--0

- - /,-:." . / I :E ,~::'" / / 9 K I -

/ ~ J

0.5 - / ~ < : ; _ ..... _ . ~ . ~ . . . . . . . . "-:

l / / / / " ' " ----{0011 O~ ~ -'<'" ~ ----[101] q / / " " ' ' ----[1111 OI,// I 210 I LIo l 60 l__

H IkOe)

I I I [ I I t 1,5

/ / I 6K l / I ~ . ~ . . - - ~ , - - - - . . . . . ~1.0 /

/ . . . . - I . /"~.~-~. " ................... -_-_-:4~ / ...= . . < , , ~ . . t . . . . . . . . . . . . . . . ~ - - - - ~ . - [ ., .---.~ ~'~_.... . . . . . . . . ~ - - ~ 1 .-41.25

/2:: .... . ! t - j ~ as /..:"

1.0

0.75

).5

0 Fig. 58. Magnetization curves in the quadrupolar phase of cubic CeAg (after Morin 1988).

Another case of metamagnetism should occur in antiferroquadrupolar phases. In this case, only the quadrupolar moments are ordered, but within at least two different sublattices having a different local c axis. A sufficiently large magnetic field is then expected to destroy this antiferroquadrupolar arrangement, resulting in a metamagnetic transition. Unfortunately, only a few examples are known in the literature, namely CeB6, TmGa3 and PrPb3 (see Morin and Schmitt 1990). Moreover, the temperature range of the considered phase is very narrow in TmGa3: between 4.26 and 4.29 K, and the metamagnetic processes have been observed in fact within the antiferromagnefic phase, i.e. below 4.26K (see sect. 3.2.12). The case of CeB6 is complicated by the Kondo behaviour of the cerium ions, and the phase diagram suggests that a huge critical field is necessary to destroy the antiferroquadrupolar state (Effantin et al. 1985). In PrPb3, the ordering temperature is low (TQ=0.35K), but a preliminary magnetic measurement seems to indicate the expected metamagnetic behaviour around 7 T at 0.1 K (Morin 1993).

3.2.4. Ferromagnetic metamagnetic systems In both preceding sections, only paramagnetic systems were concerned, namely either strictly nonordered compounds or quadrupolarly ordered but still paramagnetic compounds. In the following sections we will focus on magnetically ordered systems. The first group considered includes different types of ferromagnetic compounds. In the majority


of cases, the metamagnetic behaviour is basically associated with crystal-field properties, namely a crossing or an anticrossing of CEF levels. The only complication arises from the presence of a ferromagnetic exchange field which implies that the magnetic moments are not always parallel to the applied magnetic field. Actually, in most cases, the metamagnetic process occurs along a hard magnetization direction, i.e. during the rotation of the moments from the easy axis toward the applied field. To our knowledge, there is no experimental evidence of CEF level crossing in a ferromagnet along an easy magnetization direction. Examples where such metamagnetic processes have been well studied included several cubic systems, such as the RZn and RA12 compounds. In ErZn (Te=20.6K), the moments are ordered along the [001] four-fold direction. When the magnetic field is applied along the [111] hard axis, the magnetization increases suddenly at a critical value He which depends on the temperature (He = 20 kOe at 4.2 K, Morin and Schmitt 1978). The associated jump in the magnetization is moderated (AM ~ 0.5/%/at), because the field-induced transition occurs at the end of the rotation process. In HoZn, the same behaviour is observed, but the metamagnetism takes place along the [111] direction at low temperature (below TR =23 K) and along the [I01] direction at high temperature, i.e. between TR and Te=74K (Morin and Schmitt 1978). This is related to the change of easy magnetization direction which occurs precisely at TR from the [101] axis toward the [111] axis. Here also, the jump of magnetization is small but relatively sudden, and the critical fields remain less than 10kOe. In ERA12 (To = 14K), the same behaviour occurs during the rotation of the moments from the [111] easy axis toward the [001] direction, albeit at a much larger critical field (~80kOe at 4.2K, Purwins et al. 1976). In DyA12 (Tc=64K), the metamagnetic transition observed along the [111] direction exhibits a clear first-order character with a noticeable discontinuous jump in the magnetization (AM ~ 3/% at 4.2K, Barbara et al. 1978). Such first- or second-order transitions have been widely studied and have been explained in the frame of a Hamiltonian which includes the effects of the magnetocrystalline anisotropy in the presence of an effective (applied plus exchange) magnetic field. In some cases, additional couplings have been considered, e.g. the quadrupolar coupling in ErZn and HoZn, but it is worth noting that the metamagnetic phenomena are basically related to the CEF anisotropy, i.e. to a strongly distorted dependence of the energy on the spatial position of the moments due to the high- order CEF terms.

The same is true in lower symmetry compounds, such as in hexagonal systems where, due to the uniaxial character of the anisotropy, the metamagnetic transitions can be more spectacular. In HoRu2 (To = 18K), the moments rotate suddenly at a critical field of about 15 kOe at 4.2 K from near the a easy axis towards the c direction, i.e. over almost 90 °, resulting in a magnetization jump of more than 6/tB (see fig. 59; Okamoto et al. 1985). As in cubic systems, the explanation of this phenomenon has been given in terms of a cross-over between the ground state and the first excited state, this latter evolving to a more and more magnetic state as the field increases along the hard magnetization direction. According to the exact composition of the CEF levels, this evolution may be more or less abrupt, as shown by the neighbouring compounds DyRu2 (Te = 30 K) and ErRu2 (Te = 8 K) where the metamagnetic transition is smoother


0

:?: m m.

10

B 6

4

2

0

. .m

"c H°Ru2

10 20 30

H,,.. (kOe)

40 50

Fig. 59. Magnetization curves of HoRu 2 at 4.2 K along the three main symmetry directions of the hexagonal cell. Solid lines are calculated curves including crystal field and exchange couplings (after Okamoto et al. 1985).

10

Z 8

LLI r f l

g6

0 0

' ' ' 1 ' ' ' ' 1 . . . . J ' ' '

~ " ErNi 5

/ " T=1.4K , , r r r i p r i i i r ] i i i 1 -

10 20 30 40

H(Tesla)

Fig. 60. Magnetization curves of ErNi s at 1.4 K along the three main symmetry directions of the hexagonal cell. Solid and dashed lines are calculated curves for two different sets of crystal field and exchange parameters (after Zhang et al. 1994).

at 4.2K than in HoRu2 (Andoh 1987). However, care should be taken to distinguish between a true second-order transition and a smooth transition arising from thermal effects. The relation between the sharpness of the transition and the exact composition of the CEF levels is emphasized in the other hexagonal compound ErNi5 (Zhang et at. 1994). In this latter compound (To = 9 K), most of the magnetic properties are well described by two different sets of CEF parameters which differ only by the nature of the second excited state lying at about 70 K above the ground state. This apparently minor difference actually leads to a drastically different behaviour on the magnetization curves along the [100] and [ 120] hard directions, the sharpness of the metamagnetic processes occurring in a high field (around 20 T) being strongly reduced for one set of parameters, in agreement with experiment (see fig. 60). This underlines the interest to use as much experimental information as possible to obtain a reliable determination of the crystal field.

The same behaviour as in HoRu2 is present in the orthorhombic compound HoGa, when the magnetic field is applied along the b hard magnetization direction (Shohata 1977). In other compounds of the same series, i.e. PrGa, NdGa, SmGa, TbGa and DyGa, the metamagnetic transition occurs along the easy axis and is accompanied with a hysteresis


d ~ I 0 . E

~. 5 b

• ~ ~ J 0 - 4 0 - 2 0

-5"

[SmGo ] - I0-

-15- i

C

20 o 4 0

Heft (kOe)

Y Fig. 61. Magnetization curves of SmGa at 4.2 K along the three main symmetry directions of the orthorhombie cell. Solid lines are guides for the eye (after Shohata 1977).

cycle and a remanent magnetization, indicative of domain-wall freezing by the large anisotropy energy. The coercive field depends on the lanthanide, ranging from less than 1 kOe (Pr, Nd) to 47kOe (Sin) (fig. 61). This kind of metamagnetic behaviour is not intrinsically related to microscopic properties but due to macroscopic effects associated with the dynamics of the ferromagnetic domains. In ErGa, the metamagnetic process observed along the a hard magnetization direction has a character different from that of the other compounds within the series, and has been interpreted as the signature of a noncollinear ferromagnetic structure (Shohata 1977). The same explanation is valid in the orthorhombic RNi series (Gignoux and Lemaire 1974). In these low-symmetry systems, the local easy axes are not all parallel to each other so that the magnetic lanthanide ions can be divided into two sublattices. Ferromagnetic interactions then result in a noncollinear (canted) moment arrangement, with both ferromagnetic and antiferromagnetie components. When the magnetic field is applied along this latter one, and if the magnetocrystalline anisotropy is large enough, a spin-flip mechanism may occur, corresponding to the reversal of the moments of one sublattice. This is the case of ErNi along the a axis, or of DyNi along the c axis (see fig. 62; Sato et al. 1986). Other types of moment reorganization may appear in low-symmetry compounds with more than one crystallographic site for the magnetic lanthanide ion, leading also to metamagnetic behaviour. For example, in rhombohedral HoNi3, the lanthanide atoms are divided in two sublattices with a different point symmetry and consequently a different ordered moment (9.3 and 7.9ktB at 4.2K along the b axis; Hashimoto 1988). Along the a and c axes, several steps have been observed on the magnetization processes, probably related to the


6 ~ i ~ ~ ~4.2K M c . . . . . . = -

I I bt; / ..-" "" "'56K

0 0 20 z,0 60 80

H ( k O e )

Fig. 62. Field dependences of the magnetization along the c axis in orthorhombic DyNi (after Sato et al. 1986).

existence of the two sites with different anisotropy, but the exact nature of the intermediate states has not been determined.

3.2.5. Weakly anisotropic metamagnetic systems The gadolinium-based antiferromagnetic compounds constitute special metamagnetic systems owing to their very weak magnetocrystalline anisotropy. Indeed, as the magnetic moments are nearly free to rotate in any direction, the magnetic behaviour under field reflects only the way the antiferromagnetic structure is destroyed, i.e. it characterizes the properties of the exchange interactions alone. However, in general a small anisotropy subsists (mainly of exchange origin), which fixes the zero-field orientation of the magnetic structure with regard to the lattice, and which is revealed in low field through a spin- flop metamagnetic transition. During this transition, there is typically a rotation of the moments toward a direction perpendicular to the applied field, without drastically changing the position of the spins relatively to each other. This occurs because, in most cases, the perpendicular susceptibility is larger than the longitudinal one. The associated metamagnetic field therefore is the critical field needed to overcome the residual lattice-related anisotropy. A good example is the orthorhombic GdCu6 compound (TN = 16K; Takayanagi et al. 1989), where the magnetization curves along the b and c axes exhibit small discontinuous steps around 3.5 T before varying linearly up to the saturated value reached at Hs = 24 T (see fig. 63). The absence of a transition along the a direction suggests a planar symmetry for the magnetic structure, for example a helical arrangement of the moments within the b-c plane, because it is the only direction for which all the moments are initially perpendicular to the applied field. In the case of a simple antiferromagnet, the spin-flop transition should occur along one single axis, namely parallel to the direction of the moments, at least in low-symmetry systems. If the symmetry is higher and if there are several equivalent directions for the antiferromagnetic

364

:x2

0 0


./ / ,

/ ' /

o<ioo 1.3K < . ~ / / /

b • ° ~ . / 7 - - 1 / / / . /"

-

/J 4- 8 12

Magnetic Field { T )

Fig. 63. Magnetization curves along each principal axis in the orthorhombic GdCu 6 compound at 1.3 K; note the spin- flop transition along the b and c axes (after Takayanagi et al. 1989).

structure, some spin-flop transitions may correspond to change in the magnetic domain configuration, i.e. without changing the local symmetry for the moments. A more detailed analysis of the magnetization processes as well as a good knowledge of the magnetic structure itself is then needed to fully explain the observed behaviours.

Once the perpendicular configuration is achieved, i.e. above the spin-flop transition, any anomaly on the magnetization curves will be associated with the destruction of the antiferromagnetic structure itself. It is worth noting that, for a simple antiferromagnet or a helical structure, the magnetization process is, in principle, strictly linear. Therefore, any observed metamagnetic transition will suggest a more complex structure or will be the signature of anisotropic exchange interactions. For example, in the orthorhombic GdCu2 compound (TN=42K; Borombaev et al. 1987), only a tiny lattice-related anisotropy exists as shown by the small differences between the three main axes, but the field-induced ferromagnetism is reached through two relatively sharp steps occurring at 68 and 95 kOe (see fig. 64). These steps have been interpreted as transitions from a spiral structure towards a ferrimagnetic structure and then to the induced ferromagnetic state. Although the magnetic structure is not precisely known, it can be anticipated

Z

[- .< b~

7 z ,<

GdCu2 F

4.2 K j 4 '

:::,,: ~ " : ' " I ""i"" C laXls I

50 100 750

APPLIED MAGNETIC FIELD (kOe)

Fig. 64. Magnetization curves along each principal axis in the orthorhombic GdCu2 compound at 4.2 K (after Borombaev et al. 1987).


6 Z

< 4

Z < 2

i i i

GdGa2 . /

/

/ : 1.5 K

c axis / / "

i / I I I

10 20 3 0

MAGNETIC FIELD ( T )

4 0 Fig. 65. High-field magnetization curve along the c axis in hexagonal GdGa~ at 1.5 K (after Ball 1993).

that it should be incommensurate, as observed in several neighbouring compounds within the RCu2 series (see sects. 3.2.8 and 3.2.10). However, the magnetic processes observed, as well as the specific heat variation (Luong et al. 1985), are not consistent with a spiral structure, at least in zero field. As described by Blanco et al. (1991a), the reduction of the height of the ~, anomaly at TN is well explained if a collinear (modulated) incommensurate structure is assumed rather than a helical one. It can therefore be assumed that the observed metamagnetic process is more complex than initially interpreted. The metamagnetic transitions may be also much more subtle than in GdCu2, as in the hexagonal GdGa2 compound, where several successive anomalies have been seen along each of the three main symmetry directions (see for example the c axis in fig. 65), a situation quite surprising in a gadolinium compound (Ball 1993). Below TN =22 K, this compound exhibits an incommensurate magnetic structure with propagation vector Q= (0.39, 0.39, 0). Thermodynamic considerations have shown that this structure is not helimagnetic but amplitude modulated, then antiphase at low temperature (Bouvier et al. 1991, Blanco et al. 1991 a). The anomalies in the magnetization processes manifest themselves either as small discontinuous steps with a possible hysteresis (AM ~ 0.2#B/Gd), or as a change of slope or curvature, and lead to a rather complex magnetic phase diagram (fig. 66). This complex behaviour has been attributed to slight modifications of the magnetic structure under field involving transitions from antiphase to different successive noncollinear (fan) structures, and suggests the presence of an anisotropie exchange coupling. In the cubic GdB 6 compound (TN = 15.4 K), apart from a spin-flop transition occurring at about 6 kOe along the four-fold axis and related to domain effects (Nozaki et al. 1980), small anomalous steps have been observed near the saturation field Hs =490 kOe. They have been explained by the local spin-flip of disordered Gd ions located at the B6 cluster site (Sugiyama et al. t988). Although they are not intrinsic, such disorder effects have to be kept in mind when considering small steps in the magnetization processes of these nearly isotropie systems.

Finally, in all the above examples single crystals were concerned, and the results along the various crystallographic directions have shown that, even if there are some minor differences between them, they all give the same principal features. As a


400

300

~ 200

100

0

8 0 . . . . i . . . . i , i , , • \ i

60- ~ L

40 ~~

G d G a 2 ~h . [ 0 0 1 ] 20 ~L,

" ",, 10 20 x

10 20 30 T(K)

30 Fig. 66. Magnetic phase diagram along the c axis in GdGa2; open circles correspond to the anomalies in the magnetization process. Note the small region near 4 K - 3 0 k O e (after Ball 1993).

consequence, measuring polycrystalline materials should already give a good picture of the main characteristics of the magnetization processes. For example, some metamagnetic transitions appear to be relatively smooth, as in GdNizSi2 and GdCu2Si2 (Barandiaran et al. 1988), in GdRu2Si2 (Czjzek et al. 1989) or in GdPt2Si2 (Gignoux et al. 1991c), while others are much sharper, as in GdMg under pressure (Liu et al. 1986)• In the hexagonal Gd2In compound, the Gd ions are at two different crystallographic sites, and two magnetic phases have been established below Tc = 187 K (McAlister 1984). Between Te and Tt = 99.5 K the compound is a ferromagnet, while below Tt the magnetic structure has been interpreted as being spiral, with an abrupt metamagnetic transition at 10 kOe, the amplitude of the magnetization jump being more than 5#B/Gd (see fig. 67). Moreover, the slope of the magnetization curve during the transition is close to the initial slope in the ferromagnetic phase (demagnetizing field factor), so that the transition should be nearly vertical once drawn as a function of the internal field. It has been suggested that this behaviour is due to the collapse of the spiral structure into a ferromagnetic one, i.e. a first-order field-induced transition with a change of the propagation vector.

ee

< eq F. ~a

z <

G d 2 I n 4.2 K o° . . . . . o o

oO°

o ° o o o o o ~o°°o o o

¢ o

° o o ° o° 140 K |

° oO° o

o o

° °° 288 K ]

. . . . ~°° o 5 I0 15 20

APPLIED MAGNETIC FIELD (kOe)

Fig. 67. Field dependence of the magnetization on polycrystalline GdEIn at several temperatures (after McAlister 1984).


It can be noticed that an analogous strong metamagnetic transition of similar amplitude had been previously observed in orthorhombic GdA1 (B~cle et al. 1970). In conclusion, it is clear that the absence of magnetocrystalline anisotropy in gadolinium compounds does not necessarily facilitate the understanding of magnetic behaviour under field. In fact, the situation is even more complicated because several types of coupling generally neglected should now be taken into consideration. Moreover, it should be noticed that a good determination of the magnetic structure remains important to describe the properties, and this has been done in Gd compounds by carrying out neutron diffraction experiments using a Gd isotope or at a very low wavelength ()~ ~ 0.5 A), because of the huge absorption cross-section of natural gadolinium in normal conditions. This explains the small number of such experiments in the literature. As a summary, the weak lattice-related anisotropy in these systems manifests itself by : (i) spin-flop transitions in low field to position the magnetic structure in the whole in a proper configuration relative to the magnetic field; (ii) small differences in the magnetization along the various crystallographic directions. Oppositely, the exchange-related anisotropy, even weak, deeply affects the way the magnetic structure is destroyed, resulting in magnetization processes often far from linearity.

3.2.6. Spin-flip metamagnetic systems: simple antiferromagnets In all of the lanthanide intermetallic compounds except those with gadolinium, the presence of a strong magnetocrystalline anisotropy favours an easy axis or an easy plane for the magnetic moments, according to the crystal symmetry and the sign of the related CEF parameters. As a consequence, in the case of an easy-axis anisotropy and in the presence of simple antiferromagnetic interactions, spin-flip metamagnetic transitions may occur when the magnetic field is applied along the direction of the moments. These transitions are characterized by a simple reversal of all the moments antiparallel to the field. The most spectacular case should correspond to simple antiferromagnets having a strong uniaxial anisotropy, e.g. hexagonal or tetragonal systems with a c easy axis, where the transition would be single-step from a low magnetization state toward a fully saturated state. It turns out that examples showing such behaviour are scarce in lanthanide intermetallic compounds, while several have been investigated for a long time in semimetals or insulators, such as the lanthanide phosphates or vanadates. With the increasing number of new compounds being studied using single crystals, in particular in ternary systems, such examples should be available in the future in lanthanide intermetallics.

Very surprisingly, spin-flip metamagnetic transitions showing two steps have been found in few simple antiferromagnets. For example, the body-centered tetragonal compound DyCo2Si2 orders below TN = 24 K within an antiferromagnetic structure with the propagation vector Q= (0, 0, 1), the magnetic moments being along the c direction. The sequence of the moments then is + - + - along the propagation vector, in zero field. At low temperature, the magnetization process along the same direction exhibits a two-step metamagnetic transition (see fig. 68), with an intermediate region between Hcl = 23 kOe


i i r I I L

I [o01] DyCo2Si2

12 I ~ o Dy HI/<O01> • Co 7 °'- ° ' -°-~ "~

10 * Si

8 4 1111

6 Uoo] ~_ 1111 ~,

FoO-OO- o -o - -o -o J T : 4 . 2 K

4 r I

t.lrl-Ii I°

i~. i i . J I I1"

0 " - T ~ ' ~ " M ' ' I I 0 20 40 60

He (kOe)

Fig. 68. Magnetization curves along and perpendicular to the c axis in the tetragonal compound DyCo2Si 2 at 4,2 K; the inset represents the zero field magnetic structure; dashed lines are calculated (after Iwata et al. 1990).

ErGo 2 / BK¢'~

4 8 12 16 20 24 28 APPLIED FIELD (kOe)

Fig. 69. Magnetization along the easy e axis in the hexagonal ErGa: compound at various temperatures (after Doukour6 and Gignoux 1982).

and He2 = 44 kOe where the magnetization reaches 5/~B/Dy, i.e. exactly one half of the saturated value (Iwata et al. 1990). This plateau suggests that one half of the moments antiparallel to the field have been flipped, and a sequence like + + + - for the moments along the c axis has been proposed and found consistent with molecular-field calculations involving four exchange parameters and crystal-field effects. The intermediate magnetic structure remains nevertheless to be confirmed by neutron diffraction under field 2. Another similar behaviour has been observed in the simple hexagonal compound ErGaa (Doukour6 and Gignoux 1982). In this latter compound, the zero-field magnetic structure is characterized by the propagation vector Q = (0,1, 0), the moments being perpendicular to the basal plane. When the field is applied along the direction of the moments, a two-step process occurs, the critical fields being here about 7 and 20 kOe while the value of the intermediate magnetization reaches one half of the saturated value, as in DyCo2Si2 (see fig. 69). In the intermediate phase, as shown by neutron diffraction on a single crystal, one half of the moments antiparallel to the field have been flipped, leading to a new magnetic cell four times larger than the crystallographic one, i.e. (2a, 2b, c) (see fig. 70). It is worth noting that this arrangement does not correspond to a new propagation vector such as Q = (0, ¼, 0) for example, but is actually the superposition of: (i) a triple-Q magnetic structure with the same propagation vector as in zero field, and (ii) a ferromagnetic component. The metamagnetic process of ErGa2 has been satisfactorily accounted for by

2 Note added in proof The intermediate magnetic structure of DyCoaSi 2 has been recently determined by neutron diffraction: it consists of ferromagnetic (111) planes with the sequence + + + - along the additional

- - I 1 1 propagation vector Q2- (i, i , i) (Shageoka et al. 1994).


\

I I 1 H < 6.8 kOe

E r G a 2

° E r

o Ga I 1

6 . 8 < H < 2 0 kOe

369

Fig. 70. Magnetic structures of ErGa 2 at 1.5 K in low field (left-hand side) and in the intermediate region (fight-hand side) (after Doukour6 and Gignoux 1982).

a simple model involving a huge uniaxiat anisotropy and exchange interactions between nearest and second-nearest neighbours in the plane perpendicular to c. The same situation seems to occurs also in the hexagonal compound CeZn5 (TN = 3.8 K). This compound crystallizes in another structure than ErGa2, but the lanthanide lattice is the same in both compounds, namely simple hexagonal, and the propagation vector is identical as well as the direction of the magnetic moments. Although magnetic measurements have been performed on a polycrystal, the same two-step metamagnetic behaviour as in ErGa2 has been observed, with surprisingly the same ratio between both critical fields (Gignoux et al. 1987). The same feature has been also reported by Kirchmayr and Poldy (1979) for the rhombohedral compound c~-ErA13 where the zero-field magnetic structure is reminiscent of that in ErGa2 (Weber 1977). Finally, it can be noticed that, if there are several equivalent directions for the magnetic moments, e.g. two-fold axes in the basal plane of tetragonal or hexagonal systems, or high symmetry axes in cubic systems, the situation of the simple antiferromagnets is more complicated, because several magnetic domains have to be considered, and spin-flop rather than spin-flip processes may then occur.

3.2.7. Modulated metamagnetic systems In the intermetallic compounds, the presence of conduction electrons allows the local exchange interaction between themselves and the 4f shell to propagate from one site to the other ones. This effective long-range RKKY-type indirect coupling is a common feature in all the lanthanide compounds. It often leads to the existence of magnetic structures more complex than ferromagnetic or simple antiferromagnetic. As a consequence, in the presence of long-range and frustrated exchange interactions, and in the case of an easy-


0.3

0 . ~ O.2

en

v

I oJ

O.lO

0J2

o~ 0.12

0:10

o.o6 0

TbNi2Si 2

"~,--;• ). HII [001]

k...,/ ' , , .~.T = 9 K H / j • ~ . . - " , i. " .... "'••••.•• •~

" " " "= T=IO K •• •- J 4~, ~'~. " • . • • 1 ~ : ~ - . . ..... ••.•...•

' "~'.; ~r • " ; - l l K • "" ~k "..k" - "-••..

.-/• ~. "~•o.•

;a "~ ~.~ %, • •,

• """,.~',,.. T=12 K '" '. ..,.,.,~_ ,'c-....

• % "'.•

-'a~..,,, T=13 K "'". • : '='t~,, --%

%.

~o ~o 8 H (kOe)

Fig. 71. Field derivatives of the magnetization curves of tetragonal TbNi2Si 2 along the c axis at various temperatures; the peak at 12 and 13 K indicates the metamagnetic critical field in the modulated phase (after Blanco et al. 1991b).

axis anisotropy, the magnetic moments may develop an incommensurate or long-period commensurate amplitude-modulated magnetic structure instead of a spiral one, being frozen along a single direction• This is particularly true near the ordering temperature TN if the Fourier transform of the exchange coupling, J(q), exhibits a maximum value for a vector Q not in a high-symmetry position in the Brillouin zone, i.e. Q ~ 0 and Q ~ (a )K, where K is a reciprocal lattice vector. In that case, the modulated structure is mainly sinusoidal, the growing of higher-order harmonics in the periodic structure occurring only at lower temperatures, on account of the squaring of the structure. The metamagnetism associated with such modulated structures is simple when the magnetic field is applied along the direction of the moments, exhibiting a single smooth transition of class (2) (see sect. 3.2•1)• However, it turns out that the anomaly on the magnetization curves is often hardly visible due to the proximity of TN. It is worth noting that Arrott plots (M 2 vs H/M) or plots of dM/dH vs H are generally a good way to amplify these anomalies. On the other hand, the magnetization processes at low temperatures are often much more spectacular, exhibiting much sharper anomalies (see the following sections), so that the study of the modulated phase is generally neglected• Thus, lanthanide metals as Er and Tin, where such an amplitude modulated phase exists immediately below TN and which have been considerably studied for more than 20 years, should exhibit this kind of metamagnetic transition. Finally, in the case of modulated systems


"r" ' - - m

v

8 . . . ° ~

H o A I G a / / c 6

•

4 1 . 5 K . :"

2 .

"" . . . . . . . " 6 K -

2 -

o 2 -

O_

. . . . .

0 . . o . - "

0 TJ.,.~ : " " . . . .

i i i

0 2 0 4 0 6 0 8 0

H ( k O e )

Fig. 72. Magnetization processes in hexagonal HoA1Ga at different temperatures along the c axis; note the modulated metamagnetic behaviour at 20K (after Gignoux et al. 1991b).

with a high crystallographic symmetry, e.g. a cubic symmetry with a modulation along the four-fold axes, a difficulty arises concerning the magnetic domains, because it is not obvious a priori whether the magnetic field favours the domain with moments parallel or perpendicular to itself. In uniaxial-type modulated systems, this problem does not occur.

More recently, the increasing number of lanthanide intermetallic compounds showing an incommensurate modulated structure, at least in a limited temperature range below TN, allowed these transitions to be observed. In particular, numerous tetragonal compounds having the ThCr2 Si2-type crystallographic structure order within an amplitude-modulated structure with their magnetic moments pointing along the c direction. This is the case for TbNi2Si2 between T t = 9 K and TN=15K, where the propagation vector is Q = (0.426, 0.574, 0), while, below Tt, the structure changes towards simple commensurate antiferromagnetie with Q =(0.5, 0.5, 0) (Blanco et at. 1991b). Depending on temperature, several different incommensurate phases are induced by a magnetic field applied along the c axis, but in the modulated phase, more precisely between 12 and 15 K, there is one single metamagnetic transition around 10-15 kOe, as is clearly seen in fig. 71. The isomorphous tetragonal compound PrCo2Si2 exhibits the same behaviour between Tt=17K and TN=30K (Sugiyama et al. 1992). In the simple hexagonal compound HoA1Ga, the magnetic structure is antiphase at low temperature, with the basic propagation vector Q=(½, ½, ½) together with its third harmonics 3Q=(0,0, ½), but, between Tt=18.5K and TN=31 K, an additional modulation of the moments appears along the c axis, with a periodicity of about 53 unit cells (Gignoux et al. 1991b). In this latter phase, a single metamagnetic transition occurs again, as shown in fig. 72. It is worth noting that the corresponding anomaly in the magnetization curves is smoothed by thermal effects. In the above examples as well as in the vast majority of the modulated systems, the high-temperature structure is not stable down to 0 K, because of entropy effects,


2 I I I q I I

"-" " . . . . . . . . t PrNi2Si2

.

Z - . . ~ [ 1 0 0 1

o 0 2 4 6 8

M A G N E T I C F I E L D ( T )

Fig. 73. Magnetization processes in tetragonal PrNizSi 2 at 1.5 K along and perpendicular to the c easy direction; note the cusp when the induced ferromagnetic state is reached along the c axis. Inset: corresponding phase diagram. Lines are calculated by using the periodic field model (after Blanco et al. 1992a).

\ / I 11 \ I ~ I I

I I I I t~ tl \~ I I \ /t ~, \ I

"-.,- J ~. . / x j '

\ / \ \~ ,t

ii X x

• /

, , / / ~ /

- - J x ~ \j

H=0 T

H=4 T

H=5 T

Fig. 74. Schematic representation of the magnetic structure of PrNi2Si 2 in various magnetic fields at 1.5 K; note the residual modulation at 5.8T, i.e. immediately below the cusp where it vanishes (after Blaneo et al. 1992a).


and the system transforms at an intermediate temperature into a more stable state, namely a magnetic structure with a shorter period. One exception may occur when the CEF ground state is a nonmagnetic state, as in tetragonal PrNi2Si2. In this compound, a sine-wave modulated structure occurs at TN =20K, the propagation vector being Q= (0, 0, 0.870) and the moments aligned along the c axis (Blanco et al. 1992a). This structure persists down to OK without changing its periodicity owing to the existence of a nonmagnetic CEF singlet as ground state well isolated from the excited levels. In these conditions it is possible to study the modulated phase down to low temperatures, and in particular the metamagnetic behaviour. In fig. 73, this latter manifests itself very clearly as a positive curvature in the magnetization curve along the c axis up to about He ~ 6 T where a cusp is observed. As depicted in fig. 74, this curvature corresponds to the progressive vanishing of the modulation in the applied field, and the observed cusp indicates precisely the completion of this evolution, i.e. the entrance into the induced ferromagnetic state. It should be noted that above He, the large residual superimposed susceptibility is reminiscent of the nonmagnetic character of the CEF ground state. The temperature dependence of the critical field leads to a very simple phase diagram having a single line of separation between the modulated phase and the induced ferromagnetic state (see inset of fig. 73). This diagram has been perfectly accounted for by using the periodic field model (see sect. 3.3), and by considering only the CEF parameters and the exchange coupling coefficients J(0) and J(Q).

3.2.8. Spin-flip metamagnetism: long-period commensurate systems

As noted above, in the presence of an uniaxial anisotropy, incommensurate magnetic structures are generally not stable at low temperature, and evolve or transform toward a structure with equal moments. Moreover, their periodicity often becomes locked onto the lattice, resulting in long-period commensurate (antiphase) structures (Gignoux and Schmitt 1993). This situation may lead to a particular spin-flip metamagnetism, namely a field-induced multistep behaviour. During this process, the magnetic moments antiparallel to the field are successively flipped, giving rise to successive steps in the magnetization curve, with intermediate plateaus which may remain relatively flat, at least at low temperature. The corresponding values of the magnetization are then directly related to the magnetic periodicity and to the number of moments which have been flipped. In the same way, the amplitude of the steps depends on this periodicity and must be a multiple of (2/N)Mo, where N is the number of moments per magnetic unit cell and Mo the value of each moment. Consequently, the steps are as much smaller as the magnetic periodicity is longer. Note that in the limit of a true incommensurate structure, the magnetization should then increase continuously. However, the various intermediate configurations are not all possible, due to free energy considerations, and the system may even change its propagation vector during the magnetization process to minimize this free energy. The simplest case corresponds to systems which keep the same propagation vector and where the magnetic periodicity is short. Examples are provided within the orthorhombic RCu2 series, through TbCu2 (TN = 55 K) and DyCu2 (TN = 31 K) (Lebech et al. 1987). At


b

b

(a)

(c) a

(b)

F

a (d)

Fig. 75. Various moment configurations projected on the ab plane when the magnetic field is applied along the a axis; the proposed sequences are (a)-(d) for TbC½ and (a)-(b)-(d) for DyCu 2.

low temperature, both compounds exhibit the same antiferromagnetic ordering, namely an antiphase structure with a basic propagation vector Q = (½, 0, 0), the moments being parallel to the a axis. As there are four lanthanide atoms in the unit cell, 12 magnetic moments, decomposed into four sublattices, have been considered to describe the possible structures in the presence of a magnetic field applied along the easy direction (Iwata et al. 1989). By using a self-consistent mean-field model, four possible configurations have been found (see fig. 75), their free energy varying with the field in a specific way which depends on the values of the exchange coefficients. The first configuration (fig. 75a) is the fully compensated antiphase structure, with a net magnetization equal to zero, observed in TbCu2 and DyCu2 in zero field. At each subsequent step (figs. 75b-d), 2 moments antiparallel to the field have been flipped, resulting in successive magnetization

1 2Mo, then Mo. Experimentally, it has been shown that the values equal to gMo, magnetization process along the a easy axis of TbCuz exhibits a single step at 19kOe (fig. 76), while a two-step metamagnetic process is observed in DyCu2 with critical fields of 16 and 19 kOe and an intermediate magnetization of about ½ of the saturated value (fig. 77). Therefore, the successive sequences of configurations (a) to (d) and (a) to (b) to (d) have been proposed to occur in TbCu2 and DyCu2, respectively, and appropriate exchange coefficients allow us to account for the observed single- or two-step behaviours (Iwata et al. 1988, Iwata et al. 1989). These proposed configurations need to be checked by means of neutron diffraction on a single crystal and in a magnetic field.

The above cases of TbCu2 and DyCuz are particularly pedagogical, because of the short magnetic periodicity (3 crystallographic unit cells) which leads to large jumps in the magnetization. Other examples where a similar behaviour has been proved are not common, because it requires neutron diffraction experiments in a magnetic


lo

8

0 6

<

Z 2

<

o

I

TbCu2

I I I

o I oOO o o o o o ¢ a

I i o

I

J

I 4 . 2 K I c

10 20 30 40 50

H (kOe)

~10 £

Z

~ 6 [.-, <

Z ~: 2

F

DyCu2 : . ."- '------- '-~a 1 2 I " 4.2 K j . 1

i b

20 40 60 H (kOe)

Fig. 76. Magnetization process along the three main symmetry directions at 4.2 K in orthorhombic TbCu2; lines are calculated (after lwata et al. 1987).

Fig. 77. Magnetization process along the three main symmetry directions at 4.2 K in orthorhombic DyCu2; lines are calculated (after Iwata et al. 1989).

field. Nevertheless, favorable cases should be compounds with a strong anisotropy and which do not exhibit any change of propagation vector within their ordered phase at zero field, meaning that their magnetic periodicity is very stable. The tetragonal compound CeA12Ga2 (TN = 8.5 K) seems to be in this situation (Gignoux et al. 1988). It orders with the propagation vector Q=(0,0, 6) , with moments aligned along the [110] direction, resulting at low temperature in a non-compensated antiphase structure with a net ferromagnetic component ~3Mo ~ 0. I#B (see fig. 78). Although a noticeable superimposed susceptibility is present on the magnetization curves, a clear plateau can be observed around 25 kOe in the basal plane, followed by a sharp step at a critical field He ~ 38 kOe. The values of the magnetization on both sides of this metamagnetic transition, i.e. roughly 0.5 and 0.9#B, suggest that two moments have been flipped between 0 and 25 kOe, and two others at He. Another example where the magnetic periodicity does not change within the ordered phase is provided by the hexagonal compound DyA1Ga (TN = 50 K; Gignoux et al. 1993). Moreover, the propagation vector is relatively simple, namely Q=(1, ½, 1), leading to the sequence ( + + + - - - ) , or (33), for the moments along Q. A few steps with large amplitude can then be expected in the magnetization process along the c easy axis, and are actually observed (fig. 79). It turns out that two well-defined plateaus are observed at low temperature, the first one corresponding to ~ of the saturated magnetization Mo = 9.67/z~, while the second one reaches ½Mo. These metamagnetic transitions lead to a phase diagram which exhibits a quite original feature (fig. 80). Although no neutron diffraction data are available for this compound, the comparison with the isomorphous compound HoAIGa (Ball et al. 1992b) allows us to assume that, in the first intermediate phase, region II, the magnetic cell is tripled along c, and that, among the 18 corresponding moments, two antiparallel moments have been flipped and one parallel moment has been "anti"-flipped. Apart from this region where the propagation vector has changed, all the remaining regions in fig. 80 were supposed to have the same fundamental propagation vector Q plus several harmonics nQ, depending on the location in the diagram: the region I' corresponds to an amplitude-

376

1.2

ID


12 K

0~

~0.2 "-a

I 0 o o I t + ,~ j ~ 1.5 K

" C A j~4" ~ K

0.B ~ . . . . . t "

i 1.5 K .:---,--: ....... : .... - i , i .... ", 0 10 20 30 /.0 50 60 70

Hezt ( k O e )

Fig. 78. Magnetization curves of tetragonal CeA12Ga 2 for the three main symmetry directions (after Gignoux et al. 1988).

modulated structure, the region I to a pure antiphase structure (Q, 3Q), the region I" to a field-induced non-compensated antiphase structure (Q, 2Q, 6Q). For this latter case, the sixth harmonics corresponds to the ferromagnetic component, and the sequence of the moments is (45) along Q. The original characteristic of this diagram consists in the presence of the bicritical endpoint B (see sect. 3.2.1), which arises because the phases

10 8

~ 6 Q

ca 4 v

~ 2

0 2

, \

MAGNETI~ PROPERTIES OF INTERMETALLIC COMPOUNDS

DyAIGa//c ~" 1 oc .,e,

1.4K

~ ~ , I n

20 40 60 80 100 120 140 H(kOe)

Fig. 79. Magnetization process along the c axis in

377

I I ~ I I

DyAIGa//c 8 0 60 ' ,~TN=50K

40 ' T T ~ ' ~ A B " ~

" II ! I' /

20~II , I , l ,- I ' I

0 10 20 30 40 50 60 Temperature(K)

Fig. 80. Magnetic phase diagram of DyA1Ga for the c direction. Note the absence of boundary between the antiphase region I, the modulated phase I' and the

hexagonal DyA1Ga; at 1.4 K, the first (second) plateau field-induced non-compensated antiphase region I 't, reaches ~ (3) of the saturated value (after Gignoux leading to the presence of the bicritical endpoint B et al. 1993). (after Gignoux et al. 1993).

I, I' and I '~ all have the same propagation vector: this critical point is reached when the thermal modulation of the moments is large enough to prevent a sudden flipping of the moments involved in the transition and to allow a continuous modification of their value. A single metamagnetic transition then remains at high temperature, associated with the vanishing of the modulated structure (see sect. 3.2.7). Therefore, the magnetic structure may continuously change between the different moment configurations I, I ~ and I", by moving around B without crossing any borderline.

Another example where the spin-flip character of the metamagnetic transition has been well established by a neutron diffraction experiment is provided by the simple hexagonal system PrGa2 (TN = 7.2 K), in a limited region of its phase diagram. At 1.5K and in zero field, this compound exhibits a non-compensated long-period commensurate antiphase structure, with the propagation vector Q = (4 , 4 , 0), the moments being aligned along the [100] axis of the basal plane (Ball et al. 1993a). Although this latter plane is expected to be nearly isotropic due to the hexagonal symmetry, the compound actually presents a uniaxial character along the [100] axis, at least as far as the low-field magnetization processes are concerned (H < 9kOe, see fig. 81). More precisely, it has been shown by a detailed neutron diffraction experiment on a single crystal that the first field-induced metamagnetic transition is of spin-flip type (Ball et al. 1994a). Below a critical field He ,.~2.3 kOe (phase II), the magnetic structure includes 27 moments, the sequence of which is (43)(321)(33)(43) along the [100] direction, i.e. it consists of 4 groups of seven moments (4 up, 3 down), with two faults over 28 sites, namely one inversion up-down in the second group and a missing up moment in the third group. The induced magnetic structure above He (phase III) corresponds to the vanishing of the first fault of the zero


=~

° . ~a e-

e~

0.~

I ' i I I ' ~,i

PrGa 2 ":*:

VI :~ _.~..v'~ ..~''; i

.".::::::J t ::/" ~ IV

p~" ..it ,~"~ III

' T I , I , I , I , I

I 2 4 6 8 10 II H (kOe)

i

12

Fig. 81. Low-field magnetization process along the [100] axis at 1.5 K in hexagonal PrGa2; the first transition at ~2.3 kOe (increasing field) is of spin-flip type, the other ones of spin-slip type; the propagation vector is Q = (4, ~, 0) in phases II and III, and Q=(-~, -~, 0) in phases IV and VI (after Ball et al. 1994a).

P r G a 2 T = I . 8 K

+ + - _ _

H = 4 kOe - Phase VI

+ + ~ - - _

S p i n - s l i p

+ + + + - _ _

H = 3 kOe - Phase HI

+ + + + - - - H = 0 kOe - Phase II

+ + + + - - -

+ + + @ - - _ + + ÷ . + + + + - _ _

' +I S p i n - f l i p

+ + + @ + + + + + + - _ _

F i r s t d e f a u l t S e c o n d d e f a u l t

Fig. 82. Low-field magnetic structures of PrGa2 at 1.8 K; note the successive spin-flip and spin-slip behaviours (after Ball et al. 1994a).

field structure, i.e. to a single spin-flip within the second block, without changing the magnetic periodicity (see fig. 82). Therefore, the resulting magnetization changes from 1 M o to 3 M o , where Mo = 3. I#B is the Pr magnetic moment, as observed experimentally. This spin-flip transition is associated with the growing of the 2Q and 4Q even harmonics in the neutron diffraction patterns, accompanied by the decrease in intensity o f the odd harmonics. It is worth noting that the other transitions are not pure spin-flip ones, and this will be discussed in the next section.

3.2.9. Spin-slip metamagnetism: long-period commensurate systems The spin-slip concept is now well established since the detailed original investigation of the magnetic structures o f holmium and erbium by X-ray scattering studies (Gibbs et al. 1985, Gibbs et al. 1986). In both hexagonal metals, the magnetic propagation vector depends on the temperature through a succession of lock-in transitions on commensurate


3

B (T}

2

0 '

i I

I0 20 30

Ho

40

T{K)

Fig. 83. Phase diagram of hexagonal holmium metal at 2 K with a magnetic field applied along the c axis; note the successive values of the propagation vectors illustrating the spin-slip behaviour (after Jehan et al. 1992).

values close to each other. The formation of these spin-slips is principally driven by the competition between the exchange coupling, favouring the formation of an incommensurate structure, and the crystal field interaction, which favours a commensurate structure. More precisely, there is a tendency for the basal-plane component of the magnetic moments to lock close to the easy axes within the hexagonal plane, resulting in periodic defects (spin slips) instead of a regular rotation of the spiral order. Although pure lanthanide metals are not the main purpose of this review, it is interesting and important to present some details about this spin-slip phenomenon and the associated H - T phase diagrams, because it is associated with a remarkable renaissance in the study of the magnetic structures of the heavy lanthanides (Jensen and Mackintosh 1992). Furthermore, this phenomenon is quite similar to the behaviour found in numerous lanthanide intermetallics (see the following sections). In holmium for example, it has been shown by neutron diffraction at low temperature that the application of a magnetic field along the c hard axis produces a resurgence of the propagation vectors observed at higher temperature (see fig. 83). The sequence of the successive propagation vectors underlines the slight rearrangement of the magnetic structure occurring at each spin-slip transition, i.e. the small step-like increase of its periodicity. A similar behaviour has been observed in erbium (Lin et al. 1992). All these effects have been mainly deduced from X-ray or neutron diffraction, because of the sensitivity of these experiments with regard to the magnetic periodicity. In the past few years these spin-slip transitions have been observed in other types of measurements such as heat capacity, ac susceptibility and electrical resistivity of erbium (see Pecharsky et al. 1993 and references therein).


A recent example where spin-slip behaviour has been clearly seen is provided by the intermetallic hexagonal compound PrGa2 in its low-field magnetization process. The difference with the above case of pure lanthanide metals arises in the tmiaxial character of PrGa2 in low field while the spiral part of the structure was concerned in Ho and Er. Apart from the first field-induced transition between phases II and III, attributed to a spin-flip mechanism (see previous section), it has been demonstrated by neutron diffraction that the other transitions occurring below 9 kOe are of spin-slip type (Ball et al. 1994a). More precisely, the well-defined plateau observed by decreasing field between 6 and 2 kOe (see fig. 81, Phase VI) has been shown to correspond to a magnetic periodicity of exactly seven unit cells, i.e. Q = ( 4 , 4 ,0 ) , where the second fault in the sequence of magnetic blocks has disappeared (see fig. 82). Moreover, this periodicity appears by increasing field at around 4 kOe and subsists up to 8 kOe (Phase IV), the width of the associated neutron diffraction peaks varying in the same field range and being related to the large superimposed susceptibility observed on the magnetization curve. This behaviour has been explained by the difficulty for the system to establish a perfect long-range periodicity of seven cells, possibly due to defects in the crystal.

3.2.10. Complex multistep metamagnetism: long-period commensurate systems This section extends the simple metamagnetic behaviours described in the previous sections for compounds having an uniaxial symmetry to more complex systems: these also have a strong easy-axis anisotropy, but exhibit several different propagation vectors as a function of temperature. As a consequence, the magnetization processes at low temperature along the easy axis generally show a multistep metamagnetic behaviour, mixing spin-flip, spin-slip mechanisms and/or more drastic changes of the magnetic structure, resulting in more or less complex H - T phase diagrams. An increasing number of lanthanide intermetallic compounds has been shown to belong to this category, but only a few of them have been thoroughly investigated by means of detailed magnetic and neutron diffraction measurements on single crystals. A wealthy family is the body- centered tetragonal ThCr2Si2-type system where a strong magnetocrystalline anisotropy often confines the magnetic moments along the c high-symmetry axis. Among this family, PrCo2Si2 has been particularly thoroughly investigated. This compound orders at TN = 30 K within a long-period commensurate structure with Q1 = (0, 0, 7) (Shigeoka et al. 1987). As the temperature is lowered, a first-order transition occurs at T2 = 17 K, the new propagation vector being Q2- 13 - (0 , 0, ~) , while the periodicity locks below T1 = 9 K into a simple antiferromagnetic structure with Q3 =(0, 0, 1). High-field magnetization measurements performed at 1.3 K have shown a four-step metamagnetic behaviour along the c axis, the value of the net magnetization at each step being a fractional multiple, namely ~ 3 2 and 1, of the saturated value of Mo = 3.2#B/Pr (see fig. 84; Fujii 14' 14' 9 and Shigeoka 1990). These intermediate magnetization values are consistent with field- induced magnetic structures corresponding to the same successive propagation vectors Q2 and Q1 as those stabilized at higher temperature. This has been confirmed by a neutron diffraction study in pulsed high magnetic field (Motokawa et al. 1992). The temperature

MAGNETIC PROPERTIES OF INTERMETALLIC COMPOUNDS 38i

5 "-2

rn

v

I

I

PrCo2Si 2

T=1.3 K

Hc 2 Hc~

I I .

~ r O0 10

i

Hc~,

H a II c - a x is

Ha.Lc -axis

2'0 3'0 Ha (T)

Fig. 84. High-field magnetization curves along the c and a axes at 1.3 K in tetragonal PrCozSi2; the dashed line is calculated by using a simple incommensurate mean field model (after Fujii and Shigeoka 1990).

variation of the critical fields leads to a characteristic phase diagram where the high- temperature phases extend toward the low-temperature and high-field region by turning around the origin (fig. 85). A simplified incommensurate exchange field model was first proposed by Date (1988) to explain this behaviour by successive spin-slip and spin-flip transitions. A more elaborate model was then developed by Iwata (1990), within the mean field approximation, and taking into account a realistic shape for the Fourier transform J(q) of the exchange interactions along the whole c* direction. This function is maximum for q = Q1 with a weak variation between Ql and Q3. The free energy of several moment configurations has then been calculated in a self-consistent way and the experimental features of the multistep metamagnetic process could be well reproduced, in particular the small third step at 89 kOe interpreted as a transition between Qz = 7 and Qz = 3 It is worth noting that all the values for the propagation vectors and the net magnetizations differ only

15

B

10

Be

PrCo2Si2 x ×

A A

5 - A

Be1" • x

o . TT T2

0 10 T(K)

J

20

N \

\ \

\ \

\

! m

TN

30

Fig. 85. Magnetic phase diagram ofPrCo2Si 2 along the c axis determined by high-field neutron diffraction studies; the open circles, solid circles, open triangles, and crosses show the successive phases with Qz = 1, 0.926, 0.777 and 0, respectively (after Nojiri et al. 1991).


% :3_

v

:E

..-" H.[O01] TbNi2Si 2 ,

T=I.5K

H~' 'Hf • . . . , . . . , . ~

2'0 '

• . . . . • .

, . • . " " . ,

H,EllO!

HIl[lO0]

i

0 40 6'0 H(kOe) 80

Fig. 86. Magnetization processes at 1.5 K in tetragonal TbNi2Si2 along the 3 main symmetry directions (after Blanco et al. 1991b).

slightly between both models, and correspond to very slight differences in the free energy. However, the main features of the observed behaviour are well understood. A similar situation has been seen in the neighbouring compound NdCo2Si2 where the sequence of propagation vectors is Q = (0, 0, 1) for T < 15 K, Q = (0, 0, 0.928) between 15 and 24 K and Q=(0,0,0.785) between 24K and TN=32K (Shigeoka et al. 1988). Low-field magnetization measurements at 4.2 K have revealed the first two metamagnetic transitions which can be presumably associated with the resurgence of the two high-temperature propagation vectors, the last transition being expected at a much higher magnetic field. The isomorphous compound NdCo2Ge2 exhibits only two magnetic phases in zero field, i.e. Q=(0,0,1) below 10K and Q=(0,0,0.75) between 10K and TN=28.5K (Vinoharova et al. !991). Magnetization measurements performed on a polycrystal show at least 3 sharp metamagnetic steps at low temperature, suggesting also the existence of a complex phase diagram.

A second analogous compound has been well studied, in particular by neutron diffraction under field on a single crystal, namely TbNi2Si2. This compound belongs to the same family as PrCo2Si2, and orders at TN = 15 K within a modulated structure with

1 0) and 17 = 0.074, while a first-order transition occurs at Tt = 9 K toward Q1 = ( l - T , ~+z,

a simple antiferromagnetic structure with Q2 = (½, 1 ~,0) (Blaneo et al. 1991b). At low temperature, a three-step metamagnetic process takes place along the easy c axis, with two well defined plateaus (see fig. 86). The temperature variation of the metamagnetic critical fields leads to the complex phase diagram shown in fig. 87. The various intermediate phases have been investigated by neutron diffraction. Once again, both field-induced phases at low temperature reveal a resurgence of an incommensurate or long-period commensurate propagation vector close to Q1, namely Q3 - (21- - r , 1 + 1;, 0) and 17 = 0.104, the difference between phases III and IV arising from the relative magnitude of all its associated high-order harmonics. Moreover, the high-temperature phase V exhibits


o TbNi2Si2 40 F ~ * ~ H II [00 I]

-r-

H/~

30 ]~-

20 Ill

1 0

o ~ 4 5 8 ~o ~2 ~ T(K)

Fig. 87. Magnetic phase diagram of TbNi2Si 2 along the c axis; phase F is induced-ferromagnetic, phase I is amplitude modulated, phase II is simple antiferromagnetic, phase III is long-period commensurate, phase IV is complex amplitude modulated and zone V is a complex magnetic phase (after Blanco et al. 1991b).

a complex behaviour with the presence of several propagation vectors of the type 1 1 ( 3 - r, ~ + 3, 0), with values of r ranging from 0.025 to 0.104 according to the field and

the temperature. It is noted that an independent investigation of the same compound by another group (Shigeoka et al. 1992a) led to a slightly more complex situation: there the magnetization process at low temperature exhibited two additional intermediate steps, and the neutron diffraction experiment gave another sequence for the propagation vectors (fig. 88). The corresponding full magnetic phase diagram seems then more complex, with at least 9 intermediate phases. Note however that the observed values of the propagation vector always are on the same symmetry line of the Brillouin zone, with r ranging between 0 and 0.125. This behaviour appears as a typical example of a spin-slip behaviour (see sect. 3.2.9) or more generally a devil's staircase, and the slight differences between both single crystals emphasize the coexistence of several similar magnetic phases within the same reduced free energy range.

Apart from the above examples found in the tetragonal systems with Co and Ni, other compounds of the same family present similar metamagnetic behaviours, however they have been much less investigated. In the series with Ru, TbRu2Si2 exhibits a single propagation vector Q=(0.23, 0, 0) below TN =56 K. Its magnetization process at 4.2K shows a two-step metamagnetic behaviour with a strong hysteresis (fig. 89; Shigeoka et al. 1992b). Neutron diffraction under field has revealed an increase of the second harmonics (0.46, 0, 0) below the first critical field, and the appearance of the new vector (0.23, 0.23, 0) in the intermediate region. A field-induced transition from a single- Q toward a double-Q structure seems then to occur in this compound, the new vector

384

10

8

~ 6

~r 2


( o ) T = I . 3 K TbNi~

0

b)

l,J 0.I

0 * = "

0 2

- - I c

14. ' I ' (~ -T , ~ - ~ , 0)

6 8 10 H ( Testa )

10

• 6 R

2

0 0

TbRu2 Si 2

T = 4 . 2 K ~ 0 1 ~

10 20 30 40 50 Ha ( k O e )

60

Fig. 89. Magnetization process at 4.2 K along the main symmetry axes oftetragonal TbRu2Si 2 (after Shigeoka

Fig. 88. (a) Magnetization process at 1.3 K along et al. 1992b). the a and c axes in TbNi2Si2; (b) field dependence of the propagation vector as determined by neutron diffraction (after Fujii and Shigeoka 1990).

possibly resulting from the coupling between both equivalent basic vectors (0.23, 0, 0) and (0, 0.23, 0). In the same series, NdRu2Si2 develops two different magnetic structures below TN = 24 K: an amplitude-modulated structure with Qt = (0.13, 0.13, 0) above 10 K, and a ferromagnetic structure below this temperature. The magnetization curves along the easy c direction exhibit ferromagnetic behaviour below 10K, and a single-step or a two-step metamagnetic process with low critical fields above 10K (fig. 90; Shigeoka et al. 1990). Due to the presence of the ferromagnetic phase at low temperature, which is not completely surprising due to the proximity of Q1 and Q = 0, the corresponding magnetic phase diagram should be quite original and rather different from that observed in the previous examples. This is effectively the case for the isomorphous compound NdRu2Ge2, although only polycrystalline materials have been investigated (Ivanov et al. 1992b). In this compound, two successive magnetic phases are present in zero field: below 10K the magnetic arrangement is ferromagnetic, while between 10K and TN = 17 K the structure is amplitude modulated with two wavevectors Q1 = (0.12, 0.12, 0) and Q2 = (0.19, 0.05, 0.125), the moments always being parallel to the c axis (Ivanov et al. 1992a). A metamagnetic process is observed only in the incommensurate phase, leading to a magnetic phase diagram exhibiting a single antiferromagnetic region completely surrounded by the spontaneous or induced ferromagnetic phase (fig. 91). Other tetragonal lanthanide intermetallic series seem to be worth studying using single crystals, since polycrystals already exhibit magnetization curves with a sharp metamagnetic behaviour. For example, the compound TbRh2Si2 orders at TN = 94 K in a simple antiferromagnetic structure, with Q=(0,0 ,1) , while its magnetization process at 4.2K seems to show a three-step metamagnetic behaviour (Szytuta et al. 1992). On account of the large number


5

v

~r

NdRu2Si2

co>'T: ~+.+ ; ~ ¢ . - o - - - + , - - + ~ - - e . - - + + ¢,,--,,e-0-¢-

< 0 0 1 >

< 1 0 0 > < 1 1 0 >

. , i

c) 'T= l~ K ' 3

I

0 ~ L 20 4.0

H~

(b) T:'12 K' o__..-0

i i i

(el) T=29 K'

i i r i i

0 20 /+0 ( kOo )

6 0

Fig. 90. Magnetization process at various temperatures and along the main symmetry axes in tetragonal NdRuzSi 2 (after Shigeoka et al. 1990).

T(K)T~"~ P ____..o-----~

F 10

N d R u 2 G e 2

I I I I -

8 lo H(kOe)

Fig. 91. Magnetic phase diagram of NdRu2Ge 2 obtained on a polycrystal; AF refers to the modulated phase, P and F to the para- and ferromagnetic phases, respectively. Note that the borderline between P and F has no physical meaning, both phases being ferromagnetic (induced or spontaneous) (after Ivanov et al. 1992b).

o f compounds having this tetragonal crystallographic structure and a c easy magnetization direction, numerous new results can be expected in the future.

The other very simple crystallographic structure having a strong uniaxial character is the hexagonal structure. However, few complex antiferromagnefic systems with this symmetry and a c easy axis have been thoroughly investigated. One recent example is provided by the simple A1B2-type compound HoA1Ga, which has been extensively studied by magnetization and neutron diffraction measurements on a single crystal. As quoted above (see sect. 3.2.7), this compound exhibits two different magnetic phases in zero field (Gignoux et al. 1991b): (i) an antiphase one below Tt = 18.5K, characterized by the basic vector Q 1 - I i 1 - ( 3 , 3, 2) and its third harmonics 3Ql =(0,0 , ½); (ii) an amplitude


9 A

o "r

:::L 6

o o

60

¢ 50 O v

'1- 40

30

20

10

I I I

] I -

~tPI -~ \~ ~ ~/ / / c axis t(

~ ~ T : I . / G a

/ = ~ - ~ , I ~ , ~ I , , , I ~ ~

20 40 60 80 H(kOe)

Fig. 92. Magnetization process at 1.7 K in hexagonal HoA1Ga along the c axis and associated magnetic structures as determined by neutron diffraction in fields of 0, 30 and 48 kOe; A, B and C denote lines of moments [3n,3n, z], [3n+l,3n+l,z] and [3n+2,3n+2,z], respectively (n integer) (after Ball et al. 1992b).

. . . . I . . . . I . . . . I . . . .

"15 "to HoAIGaJ/c 2Ql " 2Q2 ' 2Q2 X

.m \ ~\ f°-o'Q~'2Q, \ ,. \

~ , 3 ) ~Tt :185K I I i TN:31K

lo 20 30 T(K) 40

Fig. 93. Magnetic H-T phase diagram of HoA1Ga for the c direction; the propagation vectors observed by neutron diffraction are shown for each measured point (solid squares); the hatched region indicates the progressive vanishing of the low- temperature periodicity associated with Q~ (see text) (after Ball et al. 1992b).

modulated structure between Tt and TN = 31 K with the single incommensurate vector Q2 = (½, ½, 0.481). It is worth noting that no anomaly could be detected by specific heat or susceptibility experiments at Tt; only neutron diffraction allowed us to determine the temperature of this transition. At low temperature, a three-step metamagnetic process is observed along the c axis (see fig. 92), with a hysteresis decreasing in increasing field, the two intermediate magnetizations reaching ~ i and ½ of the full moment. From the temperature dependence of the critical fields (see fig. 72, sect. 3.2.7), a magnetic phase diagram has been constructed (see fig. 93). It shows three ordered regions, the magnetic structures of which have been determined by neutron diffraction on a single crystal (Ball et al. 1992b). The first intermediate phase (Phase III) is characterized by: (i) the vanishing of the 3Q1 harmonics; (ii) the growing of the even harmonics 2Q1 and 6Q1 = Q0 = (0, 0, 0), this latter corresponding to the ferromagnetic component; (iii) the appearance of new propagation vectors, namely (0, 0, 1) and (½, ½, ½). The smallest common vector able to


generate the observed ones being (½, ½, ~), a magnetic cell three times larger than the zero- field one and containing 18 moments has been considered. As shown in fig. 92, in the corresponding structure, a single line B (or equivalently C) is involved: along this line, a flipping of 32- of the initially antiparallel moments and an "antiflipping" of ½ of the parallel moments has occurred, in agreement with the value of the net magnetization. The second field-induced state at 1.7 K is characterized by the flipping of all the remaining antiparallel moments of line B, the magnetic unit cell recovering the same size as at zero field, i.e. it includes 6 moments. However, this structure does not appear fully consistent with the apparent absence of borderline detected by magnetic measurements within Phase II (Gignoux et al. 1991b), since the other extremity of this phase is associated with an incommensurate propagation vector. Effectively, such borderline has been determined by neutron diffraction, although the transition is not as strong as expected (see the hatched region in fig. 93). In fact, a broadening of the diffraction peaks at 1.7 K and 48 kOe is already present and suggests that a perfect arrangement with wavevector Q1 and its even harmonics is not fully achieved within this limited region, but presents faults reminiscent of the high-temperature propagation vector and illustrating the competition between both commensurate and incommensurate periodicities.

Another crystal symmetry showing complex multistep metamagnetism is the or-

thorhombic symmetry. In the RCu2 series, HoCuz, ErCu2 (Hashimoto et at. 1979) and more particularly NdCu2 exhibit a metamagnetic behaviour. In this latter compound, four successive antiferromagnetic phases have been detected in zero field below TN = 6.3 K, and magnetoresistance as well as magnetization measurements have revealed a quite complex phase diagram along the b easy direction, showing numerous antiferromagnetic and ferrimagnetic phases (see fig. 94; Svoboda et al. 1992). In the isomorphous

3

0 i

o

I I I

2 4 6 T [K]

I

a M v s T 0 R v s H D C y s T

N d C u 2

i [ - . i

8 10

Fig. 94. Proposed magnetic phase diagram of orthorhombic NdCu2 along the b axis, deduced from magnetization, magnetoresistance and specific heat measurements, A, antiferromagnetic phases; F, ferrimagnetic phases; P, paramagnetic phases. (After Svoboda et al. 1992.)


120

100

cD _~ 80

80

"I--

ZZ

~0

20

0 0 0

z

P r Z n 2

t

o H~

o H~

O

O

0 0 ® ® ® 0 ® 0

• 8g i ~ i 0 - -

00 5 10 15 20 25

T(K)

Fig. 95. Magnetic phase diagram in orthorhombic PrZn 2 along the three main symmetry axes; a is the easy axis, and c is the least favoured axis (after Kaneko et al. 1992b).

. . . . i , , , , i . . . . i

0 , :

o-oxi5 o ~ o ~ O -

O0 50 100 150 H (kOe)

Fig. 96. Magnetization processes of orthorhombic CeZn~ at low temperature along the three main symmetry axes (after Yamashita et al. 1987).

RZn2 series, several more or less sharp metamagnetic transitions have been observed along the three different symmetry axes of NdZn2 (Kitai et al. 1990) and DyZn2 (Abe et al. 1992). The same is true in PrZn2 for which the magnetic phase diagram has been determined for the three main symmetry directions (fig. 95; Kaneko et al. 1992b). This


80

0 60

o a

40 .2

2 0

I I i I t [ I t

_ _ - * - - ~ . ~ . . . ~ CeZn z

b a x i s

j I

2 4 6 8 Temperature (K)

Fig. 97. Magnetic phase diagram of CeZn2 along the b easy direction (after Gignoux et al. 1992).

diagram suggests the existence of two zero-field magnetic phases, but no experimental data is available at the present time. The simple antiferromagnet CeZn2 (TN = 7 K) appears to be much more anisotropic than the other compounds of the same series, and exhibits a three-step metamagnetic behaviour along the single b easy axis (see fig. 96). The associated phase diagram is shown in fig. 97. Comparison with the substituted compound Ce(Zn0.9Cu0.1)2, which exhibits a similar behaviour and which has been investigated by neutron diffraction in magnetic fields using a single crystal (Gignoux et al. 1992), suggests that both intermediate phases correspond to the successive flipping of blocks of moments according to a magnetic periodicity first tripled, then doubled along the c axis. These changes of magnetic cell are consistent with the values of the net magnetization in

1 and ½ of the saturation magnetization. Within the other orthorhombic both phases, i.e. g series RCu6, the NdCu6 compound appears as a complex metamagnetic system below TN = 6.1 K (Takayanagi et al. 1991). In zero field, up to three incommensurate magnetic phases have been found in a narrow temperature range below TN, the associated transition temperatures being successively 5.83, 5.74 and 5.58 K, and all having a propagation vector of the type (0, r, 1) (Mitsuda et al. 1991), while below 5.58 K the simple antiferromagnetic structure with Q=(0, 0, 1) is stabilized. The magnetization process at 1.3 K along the b easy axis shows four successive sharp metamagnetic transitions with noticeable hysteresis (see fig. 98). It is noted that the hysteresis is anomalous for the last two transitions, the critical fields being lower in increasing field than in decreasing field (see sect. 3.2.1). Furthermore, the large superimposed susceptibility in the first plateau can be resolved into two different phases with an additional intermediate step by lowering the temperature down to 0.6 K. The low-field corresponding phase diagram has been determined by high-resolution specific-heat measurements under field (see fig. 99). As often observed, the incommensurate phases of the low-field and high-temperature region seem to replace the simple antiferromagnetic one at high field and low temperature, but this fascinating compound clearly needs a lot of additional investigations to be well understood, in particular the determination of the structures of the numerous field-induced


:Z

]E

NdCue t HRb-axis 2.0 1.3K TI

f 1.0 I a

i[l //" JJ / j ~

~ / " / " c L , r ...- / .

t > j 0 50 100 I50

M'agne'tic Field ( kOe )

~ 5 . 0 ~

4.0

2 3.0 o

.~ 2.0 m

~ 1.0

/ E / ~ H//b

4.5 5 5.5 6 6.5 Temperature [K]

Fig. 99. Magnetic phase diagram of NdCu 6 along the b axis deduced from specific heat measurements (after Takayanagi et al. 1991).

Fig. 98. Magnetization curves at 1.3 K in orthorhombic NdCu 6 along the three main symmetry directions. Note the peculiar hysteresis associated with the last two transitions (after (Jnuki et al. 1986).

magnetic phases. As a conclusion of this long section devoted to the complex multistep metamagnetic behaviour of compounds having a strong uniaxial-type anisotropy, one may still expect a large number of new experimental results in the future, from magnetization measurements as well as neutron diffraction experiments performed on single crystals, allowing us to determine the microscopic aspects of the related complex phase diagrams.

3.2.11. Planar metamagnetic systems The previous section has shown the variety of behaviours which can be observed in uniaxial lanthanide systems having their magnetic moments confined along the high- symmetry direction in the presence of incommensurate magnetic structures. Much less spectacular and a priori more complex are the same systems where the crystal field anisotropy fixes the moments to remain perpendicular to this direction. Indeed, the one- dimensional character of the possible structures has to be replaced by a two-dimensional problem, which either can be isotropic or may reveal new features related to the in- plane anisotropy. Again, although the pure lanthanide metals are not the main subject of this review, it is worth making a few remarks about them, on account of the recent remarkable renaissance in the study of their magnetic structures in various conditions of field and temperature (Mackintosh and Jensen 1992). Most of the new features were revealed in high-resolution studies with both X-rays and neutrons, performed using high- quality single crystals. First, new types of magnetic structures have been identified during the magnetization process of a helical structure with a magnetic field applied in the plane of the helix, as in Ho metal (Jensen and Mackintosh 1990). These helifan structures do not


require specific anisotropic interactions, and occur between the distorted helix observed in low field and the fan configuration present in high field. Secondly, as described above (see sect. 3.2.9), spin-slip transitions have been observed as a function of field or temperature, resulting from the in-plane anisotropy of Ho for example (Jensen and Mackintosh 1992). Finally, the presence of several equivalent symmetry directions in the plane may also favour multiple-Q magnetic structures as in Nd metal for example, which exhibits a fascinating hierarchy of 1Q, 2Q, 3Q and 4Q structures below its Nrel temperature TN = 19.9K, and where more than 10 phases have been revealed in its complex phase diagram (McEwen and Zochowski 1990). Some of these phases are characterized by the appearance of subharmonics of the fundamental modulation wavevector and present some analogy with the helifan structure quoted above.

As a general rule, the existence of several equivalent easy directions within the basal plane of planar intermetallic lanthanide systems allow the magnetic moment configurations to become non-collinear during the magnetization processes. Such canted magnetic structures noticeably multiply the number of possible magnetic phases. From this point of view, the most favourable symmetry is the hexagonal one, showing 6 possible directions for the moments. In this context, the RGa2 series appears particularly promising to be studied, several compounds of this series exhibiting at least one incommensurate magnetic phase together with an easy axis within the basal plane. For example, the PrGa2 compound, which presents a low-field behaviour being of Ising-type along its [100] easy direction at low temperature, as described above (see sects. 3.2.8, 3.2.9), recovers a planar behaviour at higher fields and/or higher temperature, as shown in fig. 100 (Ball et al. 1993a). The associated metamagnetic process is characterized by a two-step behaviour along the [100] direction, and a three-step one along the [120] hard direction of the basal plane, in the field range 10-15kOe. Moreover, the intermediate phases present a large superimposed susceptibility, a feature which seems to be quite general in these planar processes. This feature can be definitely associated with the noncollinear arrangement of the moments and their ability to rotate more or less continuously within

3.2

~ 2.4 = / 1.5K

• ~ 1.6

130 10 20 30 40 50 613 70 80 H (kOe)

Fig. 100. Magnetization curves of hexagonal PrGa~ at 1.5 K along the three main symmetry directions. Note the large superimposed susceptibility of the high-field intermediate phases along the [100] and [120] axes (above 10kOe) (after Ball et al. 1993a).


3 Z

= 2

' [ 1 2 0 ] ' I

Ol NdGa 2

/~.~ 1.5 K

. . . .

. . . . . . . " t I i I i

0 20 40 60 80 H (kOe)

Fig. 101. Magnetization curves of hexagonal NdGa 2 at 1.5 K along the three main symmetry directions. Note the large superimposed susceptibility of the intermediate phases along the [100] and [120] axes (after Ball et al. 1994b).

the basal plane. In addition, it can be seen that during such rotations, the moments may be temporarily locked into intermediate easy directions. A preliminary neutron- diffraction experiment in this high-field phase at 1.5 K along the easy axis has shown the resurgence of the incommensurate propagation vector Q = (0.148, 0.148, 0.023) which characterizes the high-temperature phase of this compound in zero field (between 3.5 K and TN = 7.2 K). The resulting H - T magnetic phase diagrams of PrGa2 along both directions [100] and [120] of the basal plane then include 5 and 6 distinct phases, respectively. In the neighbouring compound NdGa2 (TN = 9.5 K), the situation is quite similar. This compound exhibits two different incommensurate magnetic structures in zero field (Ball et al. 1992c), and a multistep metamagnetic behaviour along both directions of the basal plane (see fig. 101). Again, the intermediate phases exhibit a superimposed susceptibility which is still larger than in PrGa2, and the corresponding phase diagrams include 4 (6) distinct regions along the [120] ([100]) directions (Ball et al. 1994b). The compound CeGa2 as well as its derived solid solutions Ce(Gal-xAlx)2 exhibits also planar metamagnetic properties, with the presence of ferromagnetic and incommensurate magnetic structures in their H - T phase diagrams (Takahashi et al. 1988, Jerjini et al. 1988, Frrmy et al. 1989). However, the most complex system of the RGa2 series is certainly DyGa2, where three successive magnetic phases have been observed in zero field (Gignoux et al. 1991a). Below 6.1 K, the structure is simple antiferromagnetic, the propagation vector being Q=(0, ½,0). Between 6.1 K and' TN = 11 K, the structure is incommensurate (amplitude modulated) with Q=(2r, ½- r, 0) and 3=0.134. Within the modulated phase, there is an additional spin reorientation transition at 8.7 K, the easy magnetization direction being the [120] and the [100] axis below and above this temperature, respectively. At low temperature, the magnetization processes show a particularly complex multistep metamagnetic behaviour, with numerous field-induced transitions when the magnetic field is applied in the basal plane, suggesting a great number of intermediate magnetic phases (see fig. 102). Some transitions are very sharp, while others are more subtle. A hysteresis is associated with almost all transitions, their


10

8

~ 6

0

oi 0

20 40 60 80 H(kOe)

Fig. 102. Magnetization curves of hexagonal DyGa 2 at 1.5K along the three main symmetry directions; b represents the [120] easy direction and a the [100] hard direction in the basal plane (after Gignoux et al. 1991a).

7O

60 ©

• "v 50

4O

30

2O

10

Oo

I I I I ' I ' |

4 DyGa2 II b

'~ ¢" 'VIII - \

" t I X " ,

2 4 T(K) 6T1 8 T2 10 TN 12

Fig. 103. Magnetic phase diagram of DyGa2 along the [120] axis; the magnetic structure is simple antiferromagnetic below T~ and amplitude modulated between T Z and TN (after Gignoux et al. 1991a).

amplitude decreasing with increasing field. Some intermediate phases are present only in decreasing field. Although the general features of the curves are similar for both directions in the basal plane, they slightly differ in detail, and lead to quite complicated magnetic phase diagrams (see fig. 103 for the [120] axis). Very likely, all the observed field- induced transitions are associated with a mixing of the different types of metamagnetism (spin-flip, spin-flop, change of periodicity, . . . ), but only an extensive neutron study will allow us to determine all the microscopic aspects of these phase diagrams. It is worth noting that there are only a few examples of planar multistep systems available up to now in other symmetries than the hexagonal one, this latter remaining the most favourable. One orthorhombic compound however, namely Ce3Sn7 (TN=5.1 K), exhibits a two-step metamagnetic process along the c easy axis (Fillion et al. 1992). The small discontinuous field-induced transitions have been explained by the occurrence of various intermediate


canted magnetic structures in the (a, c) plane, and these latter have been determined by using polarized and nonpolarized neutron scattering.

3.2.12. Multiaxial metamagnetie systems

In the previous sections, a single axis or a single plane was involved in the metamagnetic processes, the symmetry of the anisotropic lanthanide systems being of uniaxial type. This last section is devoted to the systems where the whole space will be concerned, i.e., where the equivalent symmetry directions for the moments do not all belong to the same plane. This is the case of the cubic symmetry. The first example of metamagnetism associated with this symmetry can be found in cubic NaCl-type lanthanide pnictides, where some compounds exhibit, in an applied field, canted intermediate structures similar to the "topside" antiferromagnetie structure evidenced in HoP (Fischer et al. 1985). An early example is provided by DySb (Everett and Streit 1979), but similar behaviours have been also reported in other pnictides, such as HoSb (Brunet al. 1980), HoAs and HoBi (Hulliger 1978) and DyBi (Hulliger 1980). This latter compound undergoes a first- order transition at TN = 11.2 K into a simple antiferromagnetic structure [Q = (½, ½, ½)] with magnetic moments aligned along the [001] direction. Under the application of a magnetic field along the three main cubic symmetry directions, i.e. [100], [110] and [111], there is in each case an abrupt metamagnetic transition, the corresponding critical fields being approximately in the ratio 2:x/~:v~, and the resulting intermediate magnetizations reaching respectively ½, l/x/2 and l/v/3 of the saturated value (see fig. 104). A second and last step occurs at a slightly higher field along the four-fold axis, while no further transition could be seen up to 200 kOe for the two other directions. All the relative values of the critical fields and intermediate magnetizations are consistent with the "topside" structure where the moments are oriented along two orthogonal (100) directions, keeping the same propagation vector (bi-axial structure). This behaviour requires first a strong anisotropy favouring the four-fold axes, and secondly strong negative two-ion quadrupolar interactions in order to stabilize such a canted structure (K_im and Levy 1982). A biquadratic coupling was also found to be important to explain the similar two-step metamagnetic processes observed in the S-state isomorphous compound EuSe (Fukuma et al. 1985).

A strong antiferroquadrupolar coupling has been also shown to be fundamental to explain the spontaneous triple-Q magnetic structures observed at low temperature, as well as the occurrence of well-defined field-induced multi-axis magnetic structures in some other simple cubic CsCl-type systems, such as DyCu and DyAg (Morin et al. 1990). The compound DyCu orders at TN--62.8K within a simple antiferromagnetic structure characterized by the propagation vector Q = (½, ½, 0). A thorough study of its magnetoelastic properties, in particular the absence of any spontaneous magnetostriction at low temperature in spite of a large magnetoelastic coupling, led to the conclusion that the cubic symmetry is preserved in the ordered phase by developing a triple-Q structure with magnetic moments pointing along the four three-fold symmetry directions of the unit cell (A16onard et al. 1984b). This configuration is favoured by the existence of a negative


M(p B)

9

8

7

6

5

4

3

2

1

0 0

2"

• . . ,

l : ;

, j , : " . . • f~

20 40

• [ l O O ]

[110]

[111]

DyBi

1 5 K

i I I

60 80 J Fig. 104• Magnetization curves in cubic H (kO) DyBi at 1.5 K (after Hulliger 1980)•

z O

U 7- Lu 2 z O ,<

12 8

50

4.2KK _ _ _ _ ~

I I

0 100 150 200 INTERNAL FIELD (kOe)

Fig. 105• Magnetization curves in cubic DyCu along the [111] direction; the drawn magnetic structures correspond to the configuration on both sides of the metamagnetic transition (after Al@onard et al. 1984b).

quadrupolar coupling for the appropriate trigonal symmetry, because of the corresponding noncollinear mutual arrangement of the associated quadrupolar components. This multi- axis configuration then appears particularly rigid with regard to the field effects, leading to the existence of very sharp steps defining one or several well-defined plateaus in the magnetization processes along the three main cubic symmetry directions (see fig. 105 along the [111] axis for example). Several mechanisms occur during these metamagnetic


120

80

v

U " r -

40

0 30

I I I i i I t I

~ , . ! DyCu

H//r.o 01]

• • ~ d_.N.N • ,..x ÷~././ \ dT

• @ \ \÷~o

¢ % °

I I I I I I ~'

40 50 60 TEMPERATURE (K)

Fig. 106. Magnetic phase diagram in DyCu for a four-fold direction; in the representation of the structures, the arrows correspond to the magnetic moments, the ellipsoids to the quadrupolar moments (after Morin et al. 1990).

10' t111 ] j

y j 0

0 0 ' ' o' 100 200 3 0 400

H (kOe)

Fig. 107. High-field magnetization curves in cubic DyAg at 4.2K along the three main symmetry directions (after Morin et al. 1989).


transitions: some magnetic moments may flip preferentially along their own direction in order to preserve the same quadrupolar energy (the quadrupolar moment is invariant during such spin-flip transitions), or the triple-Q structure may be replaced by a double- Q one, the moments being along (111) or (101) directions. Only at the very end of the process, the magnetic moments leave a high-symmetry direction and rotate progressively toward the applied field. This leads to the existence of phase diagrams which are specific for each symmetry direction, as shown in fig. 106 for the [001] axis. The case of the isomorphous compound DyAg is similar albeit more complex. Indeed, this compound exhibits successively: (i) the same low-temperature structure as in DyCu below T1 = 47.4 K; (ii) a double-Q structure between T1 and T2 = 49 K; (iii) an amplitude- modulated structure having the incommensurate propagation vector Q=(½-r , ½,0), with 7:~0.07 between T2 and TN=56K (Morin et al. 1989). As a consequence, the magnetization processes along the three cubic symmetry directions present some additional features (see fig. 107). In addition to the large metamagnetie transitions near 100 kOe analogous to those observed in DyCu, there exists a succession of several other smaller steps in very high field, in particular along the [101] and [111] directions. From the general behaviour described in the previous sections, it can then be assumed that these high-field transitions are likely related to the resurgence of the incommensurate periodicity existing in zero field close to TN. The corresponding phase diagrams then should exhibit numerous field-induced magnetic phases. Multistep metamagnetic transitions are also observed in several other isomorphous compounds presenting both antiferromagnetic bilinear coupling and negative quadrupolar interactions favouring multi-axis (multi-Q) structures, such as PrZn and NdZn (Morin and Pierre 1975), PrAg (Morin and Schmitt 1982), PrCd (Al~onard and Morin 1984), and ErAg and HoAg (Kaneko et al. 1992a).

Antiferroquadrupolar interactions are also present in other cubic systems, as in the lanthanide hexaborides, where they drive the antiferroquadrupolar state occurring in CeB6 at 3.3K (Effantin et al. 1985). In the neighbouring compound PrB6, an incommensurate double-Q magnetic structure occurs through a first-order process at TN =6.9 K, characterized by the propagation vector Q= (¼- r, ¼, ½) with r =0.05, while it is replaced below Tt = 3.9 K by a commensurate double-Q structure through a lock-in process of Q on the value (¼, ¼, ½) (Morin et al. 1991). Here the breaking of the multi- Q structure by a magnetic field leads only to weak anomalies in the magnetization curves, but they have been confirmed by neutron diffraction experiments. These transitions allow us to construct phase diagrams which reveal how strong the quadrupolar interactions are through the weakness of the field dependence of the commensurate-incommensurate transition temperature. The last examples of cubic systems where multistep metamagnetic transitions related to antiferroquadrupolar interactions have been seen are provided by the AuCu3-type cubic compounds TmGa3 and Ndin3. In both compounds, the lanthanide lattice is simple cubic as in DyAg and DyCu or in the lanthanide hexaboride. In TmGa3, two first-order transitions occur at TN =4.26 K and TQ = 4.29 K, corresponding to antiferromagnetic and antiferroquadrupolar orderings, respectively (Morin et al. 1987b). In the low-temperature phase, the negative quadrupolar coupling associated with the trigonal symmetry favours a multiaxial triple-Q spin arrangement, identical to the low-


a3

"5"

o o o o O O o o o A o o j o o ~ )

ooo o • • , . ; : : * o

T= 1 , 5 ° 4 , ' " • "5K o • • e."

J o "

o O O ° . o o° ¢

H#c1113 I o , "

d°

:o" :°o

• o

o

~*oo o °

I0 2'0 3'0 z,'O 5~0 6'0 H (kOe)

70 Fig. 108. Magnetization processes for a [111] magnetic field direction in cubic TmGa3 (after Morin et al. 1987b).

temperature structure of DyCu and DyAg (see above). It follows that the magnetization processes are also similar, with for example a two-step metamagnetic behaviour along the [111] direction (see fig. 108). The three magnetic phase diagrams corresponding to the main symmetry directions are similar to each other, except for the values of the critical fields (see fig. 109 for the three-fold axis). Owing to the range of these critical fields, which are smaller than in the Dy compounds, neutron diffraction has been performed on a single crystal allowing us to determine the intermediate phases, which have a bi-axial or a quadri-axial character. The case of Ndln3 has been less studied but it presents an analogous behaviour. This compound exhibits three successive transitions at Tl = 4.65 K, T2 = 5.13 K and TN = 5.9 K, and a multistep metamagnetic behaviour has been observed at low temperature along the three symmetry directions (Czopnik et al. 1985). The first two transitions at T] and T2 are first-order and are related to a change of the magnetic structure. A recent neutron diffraction investigation on a single crystal has proved that both high-temperature phases are incommensurate, with Q= (½, ½, r) and l:=0.017 and 0.037 below and above T2, respectively, while the low-temperature phase is simple antiferromagnetic with Q - 1 _(~, 1, 0), the moments pointing along a four- fold axis at any temperature (Amara et al. 1994). Detailed magnetic measurements have also revealed the existence of very complex magnetic phase diagrams along the three symmetry axes, with numerous intermediate structures, some of them being triple-Q while others are characterized by the resurgence of the incommensurate periodicity. Again in this compound as in all the compounds described in this section, the competition between: (i) a strong magnetocrystalline anisotropy with several equivalent directions in the crystal, (ii) large antiferromagnetic interactions, and (iii) a noticeable antiferroquadrupolar coupling, is very likely at the origin of the complex multistep metamagnetic behaviour observed, through the stabilization of multi-axis magnetic structures.


i

Hc2

15

TIO

I r I

o 2 ; 7 TEMPERATURE (K)

Fig. 109. Magnetic phase diagram of TmGa s for a magnetic field along a three-fold direction (atter Morin et al. 1987b).

3.3. Quantitative analysis of incommensurate magnetic systems

During the last decade the theoretical approach of the complex magnetic phase diagram, resulting from the competition of magnetic interactions in systems with strong magnetocrystalline anisotropy, has attracted much attention. In particular theoretical models focused on the transition between commensurate (C) and incommensurate (I) phases, and on the properties of the incommensurate phase.

A model which has been widely used is the axial next-nearest neighbour Ising (ANNNI) model (Bak 1982 and references therein, Bak and von Boehm 1980, Selke and Duxbury 1984). It considers a simple spin-½ Ising variable, S = 4-1. The magnetic arrangements are described as a stacking of ferromagnetic planes (this means one propagation vector perpendicular to the planes) in which a positive interaction J0 between nearest neighbours is considered. Along the propagation vector an interaction J l > 0 and J2 < 0 between nearest and next-nearest neighbours is assumed. On the basis of this model, phase diagrams have been determined by using different methods, in particular Monte Carlo techniques and various mean-field theories. The most prominent results are illustrated in figs. 110 and 111 which show the ([Jz/Jl[, T) phase diagram constructed on the basis of a self-consistent mean-field calculation, and the wavevector versus temperature calculated for J2/J1 =-0.6, respectively. In fig. 110 dark areas indicate high-order commensurate phases with incommensurate phases in-between. Note that, at the ordering temperature,

z (the the wavevector changes continuously from q=0 at the Lifshitz point to q--~ + + - - phase) for -J2/Jl --* oc. At T=0 on the other hand the system can have only two states, i.e. q = 0 fo r - J2 / J l < 0.5 and q = ~ for-J2/J1 > 0.5. (In fact the existence of only two possibilities at low temperature arises because of the severe limitation concerning


i I l I ' -I PN

I

FN It, 9

i I , ! ~I i I I I 0.2 0 .4 0 .6

-J2/Ja

Fig. 110. Mean-field phase diagram for the 3D Ising model with competing interactions (Bak 1982). The dark areas indicate high-order C phases with I phases in-between (incomplete devil's staircase). P is the Lifshitz point.

I I tit,

0 . 2 5

0 . 2 0

0 .15

0

219 - 311t. -

115

3116 - - 2111

2111" - 3117

I 1 6

T c

1 t Fig. 111. Propagation vector versus t, temperature as calculated by Bak (1982)

for J2/Jl = -0.6.

the signs o f J l and J2 and because longer-range interactions are neglected.) As shown in fig. 111, the periodicity thus changes as the temperature is lowered, leading to the so called "devil's staircase" behaviour. It has also been shown that, in addition to C and I phases, there are chaotic structures which are at least metastable (Bak 1982 and references therein). These theoretical studies allowed us to discover new quite exciting physical concepts and to qualitatively account for experimental results, but, because of their great simplifications, they fail to explain the experimental observations in any exact detail.


5 ,.,.2 ~ 2 : :k

2._

1

T = 4 . 2 K

S o o lOO

I

200 H ( k O e )

i

300

Fig. 112. Comparison between experimental (solid line) and calculated (dashed line) metamagnetic process for PrCo2Si 2 at 4.2K (Iwata 1990).

In order to explain the complex phase diagram of CeSb and CeBi (Rossat-Mignod et al. 1983, Chattopadhyay et al. 1986), Date (1988) considered an Ising spin chain immersed in a sinusoidally modulated exchange field. This model is less restrictive concerning the sign and range of exchange interactions, however it is not self-consistent and, surprisingly, the q dependence of the Fourier transform of the exchange interactions J(q) is not considered, but instead an additional energy term of the type V(q-qe) 2 is introduced. In spite of these simplifications, the phase diagram of some compounds such as CeSb, CeBi, PrCo2Si2 (Shigeoka et al. 1987, 1989) and UPdln (Sugiura et al. 1990) were sketched by this model.

Much more realistic is the approach of Iwata (1990). Within the mean-field approximation Iwata considers the q dependence of d(q) and solves the problem self- consistently in the same way as will be described in more detail in a more recent model presented below. The only limitation is that the CEF ground state is the Jz =1~/) doublet, the higher-energy CEF levels being ignored, leading then to an Ising-like system. The model then can be applied in systems with large uniaxial anisotropy imposing only one direction for magnetic moments. These conditions are fulfilled in PrCo2Si2, where a remarkable quantitative account of the H-T phase diagram, in particular the multistep low-temperature metamagnetic process (figs. 112, 113) and the temperature dependence of the propagation vector in zero applied field (see sect. 3.2.10). The q dependence of J(q) along the [001] direction has been determined to account for these properties. Later the complicated phase diagram of CeBi has been satisfactorily interpreted within the framework of the same model (Iwata et al. 1991).

Recently, a more realistic and more general model has been proposed, and has been successfully applied to describe the magnetic properties (e.g. magnetization processes, magnetic susceptibility, phase diagram, specific heat . . . . ) of several frustrated magnetic systems with any periodicity (commensurate as well as incommensurate) and any moment direction (collinear as well as noncollinear structures) (Blanco et al. 1991a, 1992a,

402

(cl) H<lOkOe, Q=l,rn=0.

LI! i


(b) lOkOe<~H<37kOe, Q=13/14, m=l/14.

T T T T I I T T T T ] T I ] I t [ L L L L L L L L i L L

(c) 37 kOe<_H< 89kOe, Q=7/9, m=2/9.

I tl ] 1] 111]T ._. I t [ L LL I

(d) 89kOe<H<123kOe, Q=3/4, rn=l/Z.,.

T TT TT I t t

(e) 123kOe_<H, Q=0, m=l.

U!

Fig. 113. PrCo2Si2: predicted arrangements of the Pr moments in various magnetic fields (Iwata 1990). Notations Q and m represent the propagation vector and reduced magnetization, respectively.

Ball et al. 1993a). This self-consistent periodic field (PF) model is based on an N-site Hamiltonian, N being the number of magnetic ions over one period of the magnetic structure. This Hamiltonian can be written as

N N N N 7-g = ~ ~(i) 1 ' ~'CEV + ~ ~-/g) + ~ ~'~(B) + 2 ~ (M(i)) H(i) x. (26)

i=1 i=I i=1 i=1

In this expression, the first term is the CEF coupling from which the anisotropy originates. This term has generally two effects: (i) it may provide either a preferential (easy) direction for the magnetic moments, leading to the occurrence of an amplitude-modulated structure at TN, or a weak or easy-plane anisotropy, leading to a helical structure, or even a mixing of both; (ii) by mixing the 4f wave functions, the CEF term, by raising the (2J + 1)-degeneracy of the ground-state multiplet, then may produce either a magnetic or a nonmagnetic level as the ground state (in the latter case a modulated magnetic structure can be stable down to 0 K as observed in PrNi2Si2, see sect. 3.2.7) (Blanco et al. 1992b).

The second term, 7-/z, is the Zeeman coupling -H.M(i) between the 4f magnetic moment M(i)=- gj/tBar(i) at site i and the internal magnetic field H . The third term, ~B, is the isotropic bilinear interaction -Hex(i)'M(i) written in the mean-field approximation as a function of the effective exchange field acting on the ith site:

Hex(i) = (gj~tB) -2 ~ J(ij) (M(j)) = ~ Hn~g~ einQg' . (27) j=xi n


The second part of this equation arises from the periodicity of magnetic structure which leads to a Fourier expansion of the magnetic moments:

(M(j)) = Z MnQ e inQ/~j (28) n

which defines the basic propagation vector Q of the magnetic structure. Therefore it follows that the exchange field is also periodic with the same periodicity as M, the Fourier harmonics I-InO. being related in a simple way to the corresponding harmonics nnQ of the magnetic moments through the Fourier transform J(q) of the interionic exchange interaction J ( ij):

HnQ = ( g J / 2 B ) - 2 J(nQ) MnQ. (29)

This equation shows that the periodic shape of the exchange field does not necessarily follow that of the magnetic moment, depending on the relative values of the successive couplings J(nQ). The last term in eq. (26) is a correction term necessary due to the mean- field treatment. From the self-consistent diagonalization of the Hamiltonian for the N ions over one magnetic period, one can calculate: (i) the magnetic moment of each ion at any temperature and in any internal magnetic field; (ii) the specific heat at any temperature.

The parameters which enter in the Hamiltonian are the CEF parameters and the J(nQ)'s. The former, as well as J(0), can be determined in the paramagnetic state from a joint analysis of a set of experimental results such as inelastic neutron scattering on powder, thermal dependences of paramagnetic susceptibilities and field dependences of magnetization measured on a single crystal, and specific heat. Moreover, J(Q) at TN is given by

(gJIZB) 2 J(Q)- Zo(TN~' (30)

where Z0 is the susceptibility without interaction which can be calculated as soon as CEF parameters are known. The other J(nQ) coefficients are adjustable parameters (their determination would require the analysis of the magnetic excitations measured by inelastic neutron scattering on single crystal in order to obtain J(q) over the whole Brillouin zone). In fact the role of J(Q) is preponderant (in particular higher-order terms have no effect in sine-wave modulated and helical states) and it has been shown that the knowledge of CEF parameters and of J(0) and J(Q) was generally enough to account quite satisfactorily for the magnetic properties below TN.

From parameters determined in the paramagnetic state, the PF model has been successfully applied in the analysis of the magnetic properties below TN of the tetragonal PrNi2Si2 (Blanco et al. 1992a,b) and TbNi2Si2 (Blanco et al. 1992c), and the hexagonal HoA1Ga (Ball et al. 1993a, Zhang 1992) and PrGa2 (Ball et al. 1993c, Ball 1993) compounds, as illustrated in figs. 73 (sect. 3.2.7), 114 and 115. It is worth noting that


6O

~" 50 O

,,~ 40

30

20

10

0

. . . . . . . . ~ HoA1Ga [001]

II ,. - ' X

iIi I • . . i ' "\

r '~\ T=18.5K t TN=31K

3Q,'Q, = I "\t; Q2 =

, , , ' , , , t . . . .

10 20 30 40 T(K)

Fig. 114. Boundaries of the phase diagram of the hexagonal HoA1Ga compound along the easy [001] axis (Ball et al. 1993b, Zhang 1992). Dots are experimental points. Solid lines are calculations with the PF model• Bound- aries of phase III are not accounted for by the model because this phase is described with several noncollinear propagation vectors.

1 6 , , , , i . . . . i , , , , .

. . . . z=u2 "'i ~% ... . . . . . . . . . . . . . . .5 14 ~fz=7/47 ,' ''~101 ~ 1 :

• t'c=1/44, / A',~" 8[ ~ 7 1-

) 1o " . . . . I ;

c~ 2 P r G a . / , 2

0 5 10 15 Temperature (K)

Fig. 115. Low-temperature variation of the magnetic contribution to the specific heat in PrGa2 (Ball et al. 1993c). The solid line results from calculation with the PF model (AM structure). For comparison the simple antiferromagnetic case (EM structure) is also drawn (dashed line). Inset: corresponding variation of the entropy.

the PF model does not apply only for collinear structures but also for noncollinear arrangements such as those expected in easy-axis systems when the field is applied perpendicular to the easy axis, for instance in PrNi2Si2 (Blanco et al. 1992a). Indeed, the model allowed one to discuss the magnetization processes observed in GdGa2, in particular the possibility of field-induced helical-to-fan structure transition (Ball 1993). As well, in PrGa2, which is easy-plane, metamagnetic processes involving domain effects and noncollinear field-induced structure have been fruitfully discussed, thanks to this model (Ball 1993; fig. 116).

An interesting capability of the PF model concerns the microscopic description of the phase diagrams, in particular the intermediate magnetic phases. Indeed, the PF model may allow one to understand, in some cases, the occurrence of these new magnetic configurations. As explained above, the periodicity of the exchange field follows that of the magnetic moments. However, while in the majority of situations these latter keep a constant magnitude over the whole magnetic unit cell at low temperature (antiphase structure), the same is not true for the exchange field itself, through eq. (29). Some magnetic sites, namely those situated near the nodes of the modulation, then experience a reduced exchange field, so that the corresponding magnetic


"F E12ol - : " < . . .

0 0 20 40 60 80 H (kOe)

2o

O E

10

u

T/T N

Fig. 117. Calculated magnetic contribution to the specific heat as a function of

Fig. 116. Field dependence of the magnetization in hexagonal the reduced temperature T / T N for (a)fer- PrGa 2 compound along the [120] direction at 5 K (Ball et al. 1993c, romagnetic and (b) AM structures. The Ball 1993). The circles are experimental; the solid line is calculated exchange parameters are: (a) J(0) = 10; by the PF model for the D3o- and Dgo-domains (see references). (b) J (Q)=10 (arbitrary units) (Blanco Several noncollinear configurations for the magnetic moments are et al. 1991a). also shown. Inset: initial moment configurations of the domains with respect to the applied field for the calculations.

moments will be flipped preferentially by an applied magnetic field, resulting in a one- step metamagnetic transition. Typical examples are provided by the spin-flip transition observed in low field and at low temperature in PrGa2 (see fig. 82, sect. 3.2.8), or in TbNizSi2 (Blanco et al. 1992c).

Another remarkable result obtained by the PF model concerns the thermodynamical properties of the incommensurate or long-period commensurate systems. Indeed, it has been shown that, in the case of a single-Q magnetic structure, the specific-heat discontinuity AC at TN of a system having an amplitude-modulated (AM) structure is only two third of that present in a compound with an equal-moment (EM) structure, i.e. a ferromagnetic, a simple antiferromagnetic or a helimagnetic compound (fig. 117; Blaneo et al. 1991a). This noticeable reduction occurs because of the modulated distribution of the magnetic moments and accordingly of their internal energy just below TN. In the case of a double-Q or a triple-Q structure, it can be easily extrapolated that the reduction is still stronger, the ratio CAM~GEM then reaching (2)2 or (2)3, respectively. This unique feature, first derived in Gd-based systems (Blanco et al. 1991a), has been extended later to compounds in the presence of CEF effects (Blanco et al. 1992a). In these latter compounds however, the analysis is more complex and requires first a good knowledge of the CEF parameters. The second important consequence of the magnetic modulation on the thermodynamical properties is the dependence of the slope of C at TN on the ratio J(3Q)/J(Q) for AM systems. In particular, under certain conditions, this slope may become negative, leading to the original feature that a maximum of specific heat must occur at a temperature below TN. It follows that the whole shape of the specific heat variation below TN is affected by the modulation, and more specifically by the relative amplitude of the successive J(nQ) parameters (fig. 118). These original results throw a new light on the experimental temperature dependences of specific heat found in the literature, in particular in Gd-based compounds (Bouvier et al. 1991 and references


2c

O E

-~ 1C

i

d ...,.,,.. . . . . .f -.&.

. . - - C -S 1

T/T N

Fig. I 18. Calculated magnetic contribution to the specific heat for various sets of exchange parameters (J (Q) = 10

for all curves): (a) J(3Q) = -8 , J(5Q) = 8; (b) J(5Q) = 8; (c) J(3Q) = 8; (d) J(3Q) = 8, J(5Q) = 8 (arbitrary units) (Blaneo et al. 1991a).

therein). They should be quite useful to choose between a helical, i.e. EM, and an AM structure near TN, from specific heat data.

One aspect of the low-temperature metamagnetic processes of easy-axis compounds with large anisotropy concerns the hysteresis of the transitions which present the following features: (i) The experimental as well as the calculated hysteresis decrease when temperature is increased due to thermal effects as shown in the case of HoA1Ga (Ball et al. 1993a). (ii) From the analysis of the relative amplitude of the hysteresis of the three metamagnetie steps observed in the Zn-rich Ce(Znl-xCux)2 compounds it has been concluded that hysteresis arises from the energy barrier associated with the exchange interactions and not with the anisotropy (Gignoux et al. 1992). (iii) The calculated hysteresis, in particular at low temperature, is much larger than the observed one. This last point, which is still a puzzle, could be due to: (1) the crossing of the energy barrier through thermal fluctuations; (2) the effect of higher-order J(nQ) harmonics not taken into account in the calculation; and/or (3) a true distribution of exchange fields larger than the calculated one due to the true incommensurability of the analyzed structure or to the existence of defects.

In conclusion, the self-consistent PF model is a powerful tool for the analysis of a large variety of long-period magnetic structures, collinear (antiphase, amplitude-modulated) as well as noncollinear (helix, fan . . . . ). In the examples presented above this model is limited to single-Q (and obviously to its harmonics and Q =0) systems but it can be extended without problem to the case of multi-Q systems.

4. Summary and conclusion

This survey shows the extreme wealth of information and unusual behaviour of rare-earth intermetallics in magnetism, including itinerant 3d magnetism in addition to localized 4f magnetism. During the last fifteen years crucial advances were obtained thanks to experiments of higher performances (in particular magnetization measurements in intense magnetic field and neutron diffraction experiments) and the simultaneous evolution of the theoretical approaches.


Concerning 3d magnetism, during this period the most dramatic results, to our feeling, have been obtained on: (i) collective electron metamagnetism; (ii) 3d magnetocrystalline anisotropy; and (iii) the simultaneous effects of topological frustration and magnetic instability as observed in the fascinating RMn2 series. This latter topic is expected to have still further interesting experimental as well as theoretical developments in the future, not only for the cubic RMn2 series but also for other Mn series such as the tetragonal RMn2Si2 compounds for instance.

Important improvements have also been obtained in the knowledge of the compounds where both 4f and 3d magnetism are well established. These compounds, rich in 3d elements, are of special interest not only for their fundamental aspects but also for their technological applications, in particular as permanent magnets and magnetostrictive materials. The complex magnetization processes in intense field as measured on single crystals allowed a better knowledge of the main interactions involved, namely exchange couplings and magnetocrystalline anisotropies. Further useful information will surely be obtained in still larger applied fields, large enough to break the large exchange coupling between the 3d and 4f sublattices.

In the intermetallic compounds where only the rare-earth element is magnetic, a large number of metamagnetic behaviours of quite different origins (crystal field, quadrupolar interactions and/or frustration of bilinear exchange interactions) have shown up, and the often complex magnetic phase diagrams have been determined in some compounds. In most cases these metamagnetic processes are rather well understood and quantitatively analyzed. If we take into account the metamagnetic processes characterizing 3d magnetism in the above compounds, one can tell that metamagnetism is the most common feature encountered in lanthanide-based intermetallic compounds. At this moment, a large number of studies are devoted to the determination of complex magnetic phase diagrams for a large number of compounds where the frustration of RKKY-type exchange interactions associated with crystal-field anisotropy frequently leads to incommensurate high-temperature structures which compete with low-temperature commensurate ones. The number of systems where the microscopic aspects of the phase diagrams have been investigated is rather limited, and a special effort should be made in this direction. Simple uniaxial compounds, in particular those with hexagonal and tetragonal structures, have been studied most extensively. Accurate magnetization measurements and neutron diffraction in magnetic field on single crystals would allow us in the future to obtain a better knowledge of this type of systems, in particular the easy-plane ones where the phase diagrams are more complex than in easy-axis systems, due to the degeneracy of the easy magnetization direction. Special attention will also need to be paid to the weakly anisotropic Gd-based systems, in particular with respect to their microscopic magnetic structures which have not, so far, been studied due to the large neutron absorption of Gd. Finally let us note that, for each compound where L ~ 0, a good knowledge of the crystal-field parameters is needed in order to perform an accurate quantitative analysis of the complex magnetic properties in the ordered magnetic state.


5. Appendix: Definitions and/or descriptions of magnetic terms or phenomena

5.1. Antiferroquadrupolar and ferroquadrupolar ordering

In a form analogous to the bilinear exchange coupling between magnetic dipoles, a two- ion coupling between 4f quadrupoles O~ (see quadrupolar moment) is possible and has been found in several rare-earth intermetallic compounds. As an example, if we restrict ourselves to the single component m--0 among the five quadrupolar components, this coupling between two ions (i and j) can be written as

~Q = -K(ij) O°(i) O°(j).

A ferroquadrupolar (antiferroquadrupolar) coupling, i.e. K(ij) > 0 (< 0), favours electronic distributions on sites i and j such that their quadrupoles have their local z axes parallel (perpendicular). When the magnitude of this interionic coupling is large enough, compared to the bilinear exchange coupling, ordering of the 4f quadrupoles can occur without simultaneous magnetic ordering. Such quadrupolar ordering has only been observed in few experimental situations (see Morin and Schmitt 1990). Couplings K(ij) which are predominantly positive lead to a ferroquadrupolar ordering where all quadrupoles are aligned (fig. 119a). On the contrary, if the K(ij) are mainly negative, an

, antiferroquadrupolar arrangement will be obtained (fig. 119b).

0@@@@ Ferroquadrupolar ordering

(a)

Antiferroquadrupolar ordering

(b) Fig. 119. Schematic representations of (a) ferroquadrupolar and (b) antiferroquadmpolar orderings.

5.2. Amplitude-modulated structure

The simplest amplitude-modulated structure is the collinear sine-wave modulated structure, illustrated in fig. 74 (sect. 3.2.7) in the case of PrNi2Si2, in which the moment at site i is given by

M(ri) = M0 cos(Q • ri + (9).


Such structures are stabilized at TN when: (i) the magnetocrystalline anisotropy is strong and uniaxial so that the moment always remains parallel to the easy axis; (ii) the Fourier

1 1 (this transform J(q) of the magnetic interactions is maximum for Q ~ 0, ~K or ~K latter situation is particular because it can lead either to modulated or to equal-moment structures, see Gignoux and Schmitt 1993), where K is a reciprocal lattice vector. The periodicity associated with the propagation vector Q is then usually long-period or incommensurate.

In this type of structure, the moment of a large number of atoms is reduced. When the intrinsic magnetic moment, in presence of crystal field, is well defined, amplitude- modulated magnetic structure is not stable at low temperature, especially at OK. It transforms into a structure with equal moments (ferromagnetic, simple antiferromagnetic, antiphase, helicoidal). However, when in the absence of applied or exchange field, the ground state is a nonmagnetic singlet, the magnetic moment at 0 K is induced by the field and an amplitude-modulated magnetic structure can be stable down to very low temperature.

5.3. Antiphase structure

An antiphase magnetic structure is a collinear structure with equal moments which can be described with a long-period commensurate or incommensurate (see under commensurate, incommensurate structures) propagation vector Q and its harmonics. If Q is incommensurate or commensurate, Q=(p/q)K with q even, the resulting magnetization is zero; the antiphase structure is said to be compensated. In case of one magnetic atom per unit cell, if Q is commensurate with q odd, there is a small resulting magnetization; the antiphase structure is said to be uncompensated. Examples of antiphase structures are shown in figs. 82 (sect. 3.2.8) and 113.

5.4. Collinear and noncollinear structures

A collinear (noncollinear) structure has all magnetic moments parallel (not parallel). Noncollinear and multiaxial have the same meaning.

5.5. Commensurate and incommensurate structures

The magnetic periodicity is commensurate when the propagation vector can be written as Q = ( p / q ) K where p and q are integer. This means that the magnetic periodicity is q times the crystallographic one.

An incommensurate magnetic periodicity has a propagation vector which can be written as Q = rK with r ~p/q.


5.6. Equal-moment structure

In contrast with amplitude-modulated structures, the magnetic moments in equal- moment structures all have the same amplitude; this includes ferromagnetic, simple antiferromagnetic, antiphase, helical or triangular structures.

5.7. Exchange interaction J (ij) and Fourier transform J (q)

The exchange energy, which is of electrostatic origin, between magnetic moments at sites i and j can be written as follows:

(i) For lanthanides: E U =-J ( i j ) (J(i)) (J(j)), where J(i) and J(j) are the total angular momenta.

(ii) For 3d atoms: E O. =-J(ij) (S(i)) (S(j)), where S(i) and S(j) are the spin momenta. J(i) [or S(i)] is proportional to the magnetic moment M(i), and according to the sign of J(ij) this interaction favours either parallelism or antiparallelism of magnetic moments.

The Fourier transform of this interaction,

J(q) = Z J(ij) exp[iq(rj - ri)], j ¢ i

is a useful function. In particular, it can be shown that the Q vector of the reciprocal space for which J(q) is maximum defines the propagation vector, i.e. the magnetic periodicity, of the system just below the ordering temperature.

5.8. Fan structure

When a helimagnetic structure is submitted to a field applied along one direction of the plane of the moments, for a field larger than a critical value the structure becomes a fan structure (fig. 120). The regular rotation of the moment in the helimagnetic arrangement

I

/ /

i+4

i+l

k ~ i i+5 \ \

Fig. 120. Schematic representation of a fan structure.


transforms into a sine wave oscillation of the moments about the field direction between two maximum values of the angle (+0M and --0M). At OK, moments have the same amplitude and their angle with field direction are such that Oi = 0M sin(Q • ri + 0).

5.9. Flopside structure

The word "topside structure" has been introduced to characterize a biaxial magnetic structure observed in the cubic HoP compound (Fischer et al. 1985). As shown in fig. 121 the propagation vector is Q=(½, l l g, g) and the structure is formed as a stacking of ferromagnetic planes with their moments successively parallel to two different edges of the cube. This structure originates from the degeneracy of the easy (100) magnetization direction and the compromise between ferromagnetic bilinear exchange interactions and antiferroquadrupolar interactions. This structure observed in zero field in HoP can be induced by a field in other compounds such as DySb (Everett and Streit 1979).

Fig. 121. Flopside magnetic structure of the HoP cubic compound.

(b)

Fig. 122. A simple picture of the frustration: (a) if two moments are antiparallel in order to satisfy the negative interaction (J < 0), the direction of the third cannot be antiparallel to both of the others; (b) under certain conditions the system finds a compromise through a triangular magnetic structure.

5.10. Frustration

In magnetism, this word is generally used for magnetic structures in which the interatomic magnetic interactions are not all satisfied. A schematic example is given by three magnetic moments at the corners of an equilateral triangle (fig. 122a) or by four magnetic moments at the comers of a regular tetrahedron. If the nearest neighbours are antiferromagnetically coupled (J(ij)< 0), any magnetic arrangement is frustrated, i.e. cannot simultaneously satisfy all the couplings. The resulting structure should then be a compromise such as that shown in fig. 122b, in which the moments make an angle of 2Jr/3 (triangular structure). Helimagnetic or amplitude modulated structures are typical examples of such frustrated arrangements. Most compounds with antiferromagnetic interactions are frustrated. This generally occurs in rare-earth intermetallics on account of the RKKY long-range and oscillatory character of the exchange interactions.


5.11. Hel ical structure

In a helical or helimagnetie structure, as sketched in fig. 123, the magnetic moment at site i is given by

M(ri) = M [u cos(Q • ri) + v sin(Q • ri)],

where Q is the propagation vector, while u and o are perpendicular unit vectors defining the plane P in which the moments remain parallel. This structure can then be described as a stacking of collinear ferromagnetic planes perpendicular to Q. From plane to plane the moments o f each plane rotate in plane P o f the same angle. The propagation vector Q is generally long-period or incommensurate. Such structure can be stabilized when the magnetocrystalline anisotropy imposes the moments to lie in plane P and when the anisotropy in the plane is small (for instance hexagonal systems). Note that in numerous compounds Q is perpendicular to the plane P. When the propagation vector lies in the plane P o f the moments, the structure is also called cycloidal. Classical examples o f helimagnetic structures are found in MnAua, MnO2 and in the lanthanide metals such as Tb, Dy and Ho.

<Z-_-_

Fig. 123. Helical structure.

Fig. 124. The helifan (3/2) structure in Ho at 50K. The moments lie in planes normal to the c-axis and their relative orientations are indicated by arrows. A magnetic field of 11 kOe is applied in the basal plane, and moments with components respectively parallel and antiparallel to the field are designated by solid and open arrowheads. This component of the moments has a periodicity which is 3/2 that of the corresponding helix, and the helicity of the structure changes regularly (after Jensen and Mackintosh 1992).

HelifQn (3/2)

i'


5.12. Helifan

When a magnetic field is applied in the plane of a helical structure, an intermediate phase can be stabilized in a small field range before the fan structure is reached, this latter closing progressively toward the ferromagnetic state. This intermediate phase is called the helifan structure. Such a phase has been recently discovered in Ho (fig. 124) and Dy from a careful neutron diffraction investigation (Jensen and Mackintosh 1992).

5.13. Multiaxial structure

See under collinear and noncollinear structure.

5.14. Multistep metamagnetic process

At low temperatures, a large number of compounds exhibit magnetization processes called multistep metamagnetic processes, characterized by more than one metamagnetic transition. Such behaviour is illustrated in figs. 68, 69, 72, 79, 81, 84, etc.

5.15. Multi-Q structure (double, triple, . . . )

A multi-Q structure is necessarily described with different propagation vectors:

M(ri) = ~ MnQj exp(inQjrg). n,j

In many multi-Q structures (in particular double and triple-Q structures) all Qj are equivalent in reciprocal space and can be deduced from one another through point- symmetry operations. They form a so-called star. The structure is then multiaxial with equal moments. Such structures are often observed in cubic systems on account of the high degeneracy of the symmetry axes. Note that Qi and Qj can be considered as different only if Qi - Qj =~ K, where K is a reciprocal lattice vector. For more details about multi- Q structures see for instance Rossat-Mignod (1986).

5.16. Quadrupolar moment

The charge distribution of the electrons of the 4f shell can be expanded in successive harmonics. The lowest-order terms of this expansion, i.e. the second-order ones, are the 5 components of the quadrupolar moment. For a charge distribution associated with a state


In) = gt(1, 2 , . . . , i , . . . , n) of the n electrons of the 4f shell of a lanthanide ion these 5 (for m = 1 to 5) components are given by:

Cm ~ f ~*(1, . . . , i, . . . , n ) f m(ri) ktt(1, . . . , i, . . . , n)d3ri, i=1

where the C m are constants and the fm are

f l ( r ) = 3z 2 - r z, f2(r) = x 2 _y2, f3(r ) --- xy, f4( r ) =yz, f s ( r ) = zx.

As the In) state is a linear combination of [ J , Mj) states characterizing the total kinetic momentum, so called Stevens Equivalent Operators have been introduced to calculate these component. For instance, the first component can be rewritten as

C1 ~ I/-/*(1, . . . , i, . . . , n ) ( 3 z ~ - r 2) tp(1 . . . . . i . . . . , n)d3ri = C'aj (u Io°l u), i=1

where C' is a constant, aj is the second-order so called Stevens coefficient characteristic of the 4f shell of the considered lanthanide atom and 020 =3Jz 2 - J ( J + 1) is an operator acting on the ~/, M j ) states. In terms of operators used in a hamiltonian this quadrupolar component can be written as C'ajO °. The operators associated with the otherfi functions are

0 2 = j2 x _,12, Pxy = l(JxJy -JyJx) , Pyz = l ( jyJz -JzJy) , Pzx = l(JzJx -JxJz) .

A positive value of the C'aj {u I0° I u) component of the quadrupole corresponds to a distribution of the 4f electrons elongated along the z axis (prolate shape). On the contrary a negative value of C laJ (u IO°1 u) corresponds to an pancake-like distribution (oblate shape).

Relevant references are Hutchings (1964), Schrnitt (1986), Morin and Schmitt (1990).

5.17. RKKY (Ruderman, Kittel, Kasuya, Yosida) exchange interaction

This term concerns the long-range and oscillatory character of the bilinear exchange interaction between lanthanide magnetic moments in a metallic compound. Due to the localization of the 4f shell, this interaction is not direct, as is the case between 3d shells of transition metals such as Fe, Co or Ni, but indirect. This means that it is mediated through the polarization of the conduction electron. This interaction between lanthanide atoms is much smaller than the direct interaction in 3d metal, leading to ordering temperatures in the former one order of magnitude smaller than in pure Fe, Co or Ni. On account


of the itinerant character of conduction electrons, the effective interionic interaction is long-range and oscillatory. This leads to a Fourier transform of this interaction as

J(q) = Z J(ij)exp[iq(rj - ri)], j ~ei

where J(ij) is the exchange interaction between atoms i and j , which frequently has a maximum for a non-simple value of Q. The magnetic structure, at least near the ordering temperature, is then long-period-commensurate or incommensurate with the corresponding propagation vector Q.

Relevant references are Ruderman and Kittel (1954), Kasuya (1956), Yosida (1957) and Coqblin (1977).

5.18. Single-Q structure

In the single-Q structure the magnetic moments can be described with a unique propagation vector Q and possibly its harmonics:

M(ri) = Z MnQ exp(inQ • ri). n

There is a large variety of single-Q antiferromagnetic structures: (sine-wave) amplitude- modulated, antiphase, simple antiferromagnetic, helimagnetic, etc.

5.19. Spin-flip transition

In compounds with large uniaxial anisotropy, when the field H is applied along the easy axis of an equal-moment collinear antiferromagnetic structure, the magnetization process (of metamagnetic type) involves, for H > He, the flipping of all or part of the moments antiparallel to the field which then become parallel to the latter (fig. 125). The concept of spin-flip transition was first introduced by Nrel to interprete the metamagnetism of this type of compounds. In some cases the metamagnetic behaviour involves simultaneously spin-flip and anti spin-flip processes (see for instance Gignoux et al. 1993).

H<Hc H>Hc

M 2 M1 M 2 M1 - - ~ 2 ~ . . . . ~ _ _ _ ~ _ _

Fig. 125. Spin-flip transition. M t and M z schematize the directions of the two sublattices involved.

5.20. Spin-flop transition

In compounds with small magnetocrystalline anisotropy, when the field is applied along the moment direction of a collinear antiferromagnetic structure, for a critical field Hc


H<Hc H>Hc

Fig. 126. Spin-flop transition. M1 and M 2 schematize the directions of the two sublattices involved.

the moments take the magnetic configuration schematized in fig. 126. The concept o f spin-flop transition was first introduced by N6el to account for this type o f transition. For larger fields the moments progressively rotate towards the field direction.

5.21. Spin fluctuations

This quite general concept is used to specify any shift (in time and space) between the instantaneous value o f magnetic moments and their mean value given by the molecular field approximation and the Boltzmann statistics. Spin fluctuations can be individual and/or collective. In the latter case processes such as spin waves or paramagnons are considered and many models have been developed to interprete experiments with these

concepts.

5.22. Spin-slips (or spin discommensurations)

The concept o f spin-slips or discommensurations was first introduced to explain the

observed lock-in transitions in the magnetic spirals o f lanthanide metals such pure Ho and Dy in terms o f simple commensurate structures (fig. 127). More generally this term can be used to characterize structures which present periodic faults in a simple sequence o f magnetic moments. For instance, let us consider, in an Ising chain, a sequence o f 4 moments up followed by 3 moments down (this is found in some compounds). The propagat ion vector is ~. In certain regions of H-T space the propagation vector is slightly

o b

Fig. 127. Self-consistent mean-field calculations of periodic structures in Ho. Each circle represents the magnitude and direction of the ordered moment in a specific plane, relative to the size of the moment at absolute zero (10/~B), indicated by the length of the horizontal lines. The orientation of moments in adjacent planes is depicted by the positions of the neighbouring circles. (a) The 12-layer zero-spin-slip structure at 4 K. The open circle in the centre indicates the ferromagnetic component in the cone structure; (b) the 1 l-layer one-spin-slip structure at 25 K. The bunched pairs of moments are disposed asymmetrically with respect to the easy axis in the vicinity of the spin slip (after Jensen and Mackintosh 1992).


different, for instance 4 instead of 4 . This indicates the presence of a fault each four sequences.

The term spin-slip transition is used to characterize the change from one discommen- suration to another. It is generally associated with a metamagnetic transition of small amplitude in the magnetization process and a small shift o f the propagation vector, as in PrGa2 (fig. 81) at 1 ,5K in fields smaller than 9kOe (Ball et al. 1994a).

Relevant references are Gibbs et al. (1985), Cowley and Bates (1988), Jensen and Mackintosh (1992), Gibbs et al. (1986) and Bohr et al. (1986).

5.23. Spin-reorientation transition

This term specifies all transitions with temperature (or even pressure) which involve a change in the magnetization direction associated with a symmetry change. These transitions can be of first or second order. Many compounds exhibit such spin reorientations. For instance, in the cubic HoZn compound the magnetization, which is along a two-fold axis below 25K, aligns, through a first-order transition, along a three-fold axis above 2 5 K (Morin and Schmitt 1990). As well, in the hexagonal TbCo5 compound, magnetization is along the six-fold axis below 390K and in the basal plane above 440 K. Between these two temperatures a progressive rotation takes place (Lemaire 1966). Under an applied magnetic field spin-reorientation transitions are more specific phenomena in a sense that, when the applied field is not parallel to the initial magnetization, a rotation of the latter always occurs. In that case, spin-reorientation transitions, generally of first order, characterize drastic acceleration o f such rotation process. Such transitions, called FOMR (first-order magnetization reorientation), are frequently observed in lanthanide-3d intermetallics such as Ho2Co17 and Dy2COl7 (Franse and Radwanski 1993). Field-induced spin reorientations have been reviewed by Asti (1990).

References

Abe, S., T. Kaneko, M. Ohashi, Y. Nakagawa and T. Kitai, 1992, J. Magn. & Magn. Mater. 104-107, 1403.

Alameda, J.M., D. Givord, R. Lemaire and Q. Lu, 1981, J. Appl. Phys. 52, 2079.

Alekseev, P.A., A. Andreeff, H. Griessmann, L.P. Kaun, B. Lippold, W. Matz, I.P. Sadikov, O.D. Christyakov, I.A. Markova and E.M. Savitskii, 1980, Phys. Status Solidi b 97, 87.

A16onard, R., and E Morin, 1979, Phys. Rev. B 19, 3868.

Al~onard, R., and E Morin, 1984, J. Magn. & Magn. Mater. 42, 151.

A16onard, R., and P. Morin, 1990, L Magn. & Magn. Mater. 84, 255.

A16onard, R., P. Morin, D. Schmitt and E Hulliger, 1984a, J. Phys. F 14, 2689.

A16onard, R., P. Morin and J. Rouchy, 1984b, J. Magn. & Magn. Mater. 46, 233.

Amara, M., R.M. Gal~ra, R Morin, T. Veres and P. Burlet, 1994, J. Magn. & Magn. Mater. 130, 127.

Andoh, Y., 1987, J. Phys. Soc. Jpn. 56, 4075. Andres, K., and S. Darack, 1977, Physiea B 86-88,

1071. Andres, K., S. Darack and H.R. Ott, 1979, Phys. Rev.

B 19, 5475. Asti, G., 1990, in: Ferromagnetic Materials, Vol. 5, eds


K.H.J. Buschow and E.P. Wohlfarth (North-Holland, Amsterdam) ch. 5, p. 397.

Aubert, G., D. Gignoux, B. Hermion, B. Michelutti and A. Nait-Saada, 1981, Solid State Commtm. 37, 741.

Bak, P., 1982, Rep. Prog. Phys. 45, 587. Bak, P., and J. von Boehm, 1980, Phys. Rev. B 21,

5297. Ball, A.R., 1993, Thesis (University of Grenoble)

unpublished. Ball, A.R., D. Gignoux, EE. Kayzel, D. Schmitt and

A. de Visser, 1992a, L Magn. & Magn. Mater. 110, 337.

Ball, A,R., D. Gignoux, D. Schmitt, EY. Zhang and M. Reehuis, 1992b, J. Magn. & Magn. Mater. 110, 343.

Ball, A.R., D. Gignoux and D, Schmitt, 1992e, Physica B 180-181, 58.

Ball, A.R., D. Gignoux and D. Schmitt, 1993a, J. Magn. & Magn. Mater. 119, 96.

Ball, A,R., D. Gignoux, D. Sehmitt and EY. Zhang, 1993b, Phys. Rev. B 47, 11887.

Ball, A.R., D. Gignoux, A.E Murani and D. Schmitt, 1993c, Physica B 190, 214.

Ball, A.R., D. Gignoux, D. Sehmitt, EY. Zhang and P. Burlet, 1994a, J. Magn. & Magn. Mater. 130, 317.

Ball, A.R., D. Gignoux, J. Rodriguez Fernandez and D. Sehmitt, 1994b, J. Magn. & Magn. Mater. 137, 281.

Ballou, R., and R. Lemaire, 1988, J. Physique 49, C8-523.

Ballou, R., D. Gignoux, R. Lemaire, R. Mendia- Monterroso and J. Schweizer, 1986a, J. Magn, & Magn. Mater. 54-57, 499.

Ballou, R., D. Gignoux, B. Gorges and R. Lemaire, 1986b, J. Magn. & Magn. Mater. 54-57, 497.

Ballou, R., J. Ddportes, R. Lemaire, Y. Nakamura and B. Ouladdiaf, 1987, J. Magn. & Magn. Mater. 70, 129.

Ballou, R., J. Ddportes, R. Lemaire and B. Ouladdiaf, 1988a, J. Appl. Phys. 63, 3487.

Ballou, R., VM.T.S. Barthem and D. Gignoux, 1988b, Physica 149B, 340.

Ballou, R., B. Gorges, R. Lemaire, H. Rakoto and J.C. Ousset, 1989, Physica B 155, 266.

Ballou, R., J. Ddportes, R. Lemaire, R Rouault and J.L. Soubeyroux, 1990a, J. Magn. & Magn. Mater. 90-91, 559.

Ballou, R., B. Gorges and P. Molho, 1990b, J. Magn. & Magn. Mater. 84, L1.

Ballou, R., C. Lacroix and M.D. Nunez-Regueiro, 1991, Phys. Rev. Lett. 66, 1910.

Ballou, R., B. Ouladdiaf, P.J. Brown, M.D. Nunez- Regueiro and C. Lacroix, 1992, Phys. Rev. B 45, 3158.

Barandiaran, J.M., D. Gignoux, D. Schmitt, J.C. Gomez-Sal, J. Rodriguez Fernandez, P. Chieux and J. Schweizer, 1988, J. Magn. & Magn. Mater. 73, 233.

Barbara, B., M. Rossignol and P. Bak, 1978, J. Phys. C 11, L183.

Barbara, B., D. Gignoux and C. Vettier, 1988, in: Lectures on Modern Magnetism, ed. Li Yifa (Springer, Heidelberg) ch. 10.

Barthem, V.M.T.S., D. Gignoux, A. Nait-Saada and D. Schmitt, 1988, Phys. Rev. B 37, 1733.

Barthem, V.M.T.S., D. Gignoux, A. Nait-Saada, D. Schmitt and A. Takeuchi, 1989a, J. Magn. & Magn. Mater. 80, 142.

Barthem, V.M,T.S., D, Gignoux, D, Schmitt and G. Creuzet, 1989b, J. Magn. & Magn. Mater. 78, 56.

Bdal-Monod, M.T., 1982, Physiea B 109-110, 1837. B~al-Monod, M.T., and J.M. Lawrence, 1980, Phys.

Rev. B 21, 5400. B~al-Monod, M.T., S.K. Ma and D.R. Fredkin, 1968,

Phys. Rev. Lett. 22, 929. B~cle, C., R. Lemaire and D. Paccard, 1970, J. Appl.

Phys. 41, 855. Belorizky, E., M.A. Frdmy, J.P. Gavigan, D. Givord

and H.S. Li, 1987, J. Appl. Phys. 61, 3971. Belorizky, E., J.P. Gavigan, D. Givord and H.S. Li,

1988, Europhys. Lett. 5, 349. Berk, N., and J.R. Schrieffer, 1966, Phys. Rev. Lett.

17, 433. Berthier, Y., J. D~portes, M. Horvatic and P. Rouault,

1988, J. Phys. (Paris) 49, C8-261. Blanco, J.A., D. Gignoux and D. Schmitt, 1991a, Phys.

Rev. B 43, 13145. Blanco, J.A., D. Gignoux, D. Schmitt and C. Vettier,

1991b, J. Magn. & Magn. Mater. 97, 4. Blanco, J.A., D. Schmitt and J.C. Gomez-Sal, 1992a,

J. Magn. & Magn. Mater. 116, 128. Blanco, J.A., D. Gignoux and D. Sehrnitt, 1992b, Phys.

Rev. B 45, 2529. Blanco, J.A., D. Gignoux and D. Schmitt, 1992c, Z.

Phys. B 89, 343. Bloch, D., E Chaissd, E Givord, J. Voiron and E.

Burzo, 1971, J. Phys. (Paris) 32, Clq559. Bloeh, D., D.M. Edwards, M. Shimizu and J. Voiron,

1975, J. Phys. F 5, 1217.


Bohr, J., D. Gibbs, D.E. Moncton and K.L. D'Amico, 1986, Physica A 140, 349.

Borombaev, M.K., R.Z. Levitin, A.S. Markosyan, VA. Reimer, E.V. Sinitsyn and Z. Smetana, 1987, Sov. Phys.-JETP 66, 866.

Boutron, P., 1973, Phys. Rev. 7, 3226. Bouvier, M., P. Lethuillier and D. Schmitt, 1991, Phys.

Rev. B 43, 13137. Brinkman, W.E, and S. Engelsberg, 1968, Phys. Rev.

169, 417. Brown, P.J., B. Ouladdiaf, R. Ballou, J. D@ortes and

A.S. Markosyan, 1992, J. Phys.: Condens. Matter 4, 1103.

Brtm, T.O., EW. Korty and J.S. Kouvel, 1980, L Magn. & Magn. Mater. 15-18, 298.

Bruno, R, 1989, Phys. Rev. B 39, 865. Burzo, E., and R. Lemaire, 1992, Solid State Commun.

84, 1145. Buschow, K.H.J., 1977a, Rep. Prog. Phys. 40, 1179. Busehow, K.H.J., 1977b, Solid State Commun. 21,

1031. Buschow, K.H.J., 1979, Rep. Prog. Phys. 42, 1373. Buschow, K.H.J., 1980, in Ferromagnetic Materials,

Vol. 1, ed. E.P. Wohlfarth (North-Holland, Amster- dam) oh. 4, p. 297.

Buschow, K.H.J., 1988, in: Ferromagnetic Materials, Vol. 4, eds E.P. Wohlfarth and K.H.J. Buschow (North-Holland, Amsterdam) ch. 1, p. 1.

Buschow, K.H.J., and R.P. van Stapele, 1970, J. Appl. Phys. 41, 4066.

Campbell, I.A., 1972, J. Phys. F 2, L47. Chattopadhyay, T., P. Burlet and J. Rossat-Mignod,

1986, J. Magn. & Magn. Mater. 54--57, 503. Cooper, B.R., 1966, Phys. Lett. 22, 244. Coqblin, B., 1977, The Electronic Structure of Rare-

Earth Metals and Alloys: the Magnetic Heavy Rare- Earths (Academic Press, New York).

Cowley, R.A., and S. Bates, 1988, J. Phys. C 21, 4113.

Cyrot, M., and M. Lavagna, 1979, J. Phys. (Paris) 40, 763.

Cyrot, M., D. Gignoux, E Givord and M. Lavagna, 1979, J. Phys. (Paris) 40, C5-171.

Czjzek, G., V. Oestreich, H. Schmidt, K. Latka and K. Tomala, 1989, J. Magn. & Magn. Mater. 79, 42.

Czopnik, A., N. Iliew, B. Stalinski, C. Bazan, H. M~idge and R. Port, 1985, Physica B 130, 259.

Daalderop, G.H.O., RJ. Kelly and M.EH. Schuurrnans, 1992, J. Magn. & Magn. Mater. 104--107, 737.

Date, M., 1988, J. Phys. Soc. Jpn. 57, 3682. Date, M., 1990, J. Magn. & Magn. Mater. 90-91, 1.

del Moral, A., M.R. Ibarra, LS. Abell and LED. Montenegro, 1987, Phys. Rev. B 35, 6800.

D@ortes, J., R. Lemaire, B. Ouladdiaf, E. Roudaut and E Sayetat, 1987a, J. Magn. & Magn. Mater. 70, 191.

Drportes, J., B. Ouladdiaf and K.R.A. Ziebeck, 1987b, J. Magn. & Magn. Mater. 70, 14.

Doniach, S., and S. Engelsberg, 1966, Phys. Rev. Lett. 17, 750.

Doukourr, M., and D. Gignoux, 1982, J. Magn. & Magn. Mater. 30, I 11.

Duc, N.H., D. Givord, C. Lacroix and C. Pinettes, 1992, Europhys. Lett. 20(1), 47.

Effantin, J.M., J. Rossat-Mignod, R Butler, H. Bartholin, S. Kunii and T. Kasuya, 1985, J. Magn. & Magn. Mater. 47-48, 145.

Everett, G.E., and P. Streit, 1979, J. Magn. & Magn. Mater. 12, 277.

Felcher, G.R, L.M. Corliss and L.M. Hastings, 1965, J. Appl. Phys. 36, 1001.

Fillion, G., E Givord, P. Lejay, E. Ressouche, J. Schweizer and A. Stunault, 1992, Physica B 180- 181, 142.

Fischer, E, A. Furrer, E. Kaldis, D. Kim, J.K. Kjerns and P.M. Levy, 1985, Phys. Rev. B 31, 456.

Fisher, R.A., R. Ballou, J.P. Emerson, E. Leli~vre- Berna and N.E. Phillips, 1992, Int. J. Mod. Phys. B 7, 830.

Franse, J.J.M., and R.J. Radwanski, 1993, in: Handbook of Magnetic Materials, Vol. 7, ed. K.H.J. Buschow (North-Holland, Amsterdam) ch. 5, p. 307.

Franse, J.J.M., A.A. Menovsky, A. de Visser, C.D. Bredl, U. Gottwich, W. Lieke, H.M. Mayer, U. Rauchschwalbe, G. Sparn and E Steglich, 1985a, Z. Phys. B 59, 15.

Franse, LJ.M., ER. de Boer, RH. Frings, R. Gersdoff, A.A. Menovsky, EA. Muller, R.J. Radwanski and S. Sinnema, 1985b, Phys. Rev. B 31, 4347.

Franse, J.J.M., N.R Thuy and N.M. Hong, 1988, J. Magn. & Magn. Mater. 72, 361.

Franse, J.J;M., R.J. Radwanski and R. Verhoef, 1990, J. Magn. & Magn. Mater. 81,299.

Freltoft, T., P. Brni, G. Shirane and K. Motoya, 1988, Phys. Rev. B 37, 3454.

FrOmy, M.A., D. Gignoux, D. Schmitt and A. Takeuchi, 1989, J. Magn. & Magn. Mater. 82, 175.

Friedel, J., 1969, in: The Physics of Metals, 2. Elec- trons, ed. J.M. Zeeman (Cambridge University Press, Cambridge) ch. 8.

420 D. GIGNOUX and D, SCHMITT

Fujii, H., and T. Shigeoka, 1990, J. Magn. & Magn. Mater. 90-91, 115.

Fukauna, H., T. Komatsubara, T. Suzuki, E. Kaldis and T. Kasuya, 1985, J. Phys. Soc. Jpn. 54, 3067.

Ganapathy, E.V., W.E. Wallace and R.S. Craig, 1974, in: Proc. l lth Rare Earth Research Conf., eds J.M. Hoschke and H.A. Eick (USAEC, Oak Ridge, TN) p. 430.

Gibbs, D., D.E. Moncton, K.L. D'Amico, J. Bohr and B.H. Grier, 1985, Phys. Rev. Lett. 55, 234.

Gibbs, D., J. Bohr, J.D. Axe, D.E. Moncton and K.L. D'Amico, 1986, Phys. Rev. B 34, 8182.

Gignoux, D., and R. Lemaire, 1974, Solid State Commun. 14, 877.

Gignoux, D., and J.J. Rhyne, 1986, J. Magn. & Magn. Mater. 54-57, 1179.

Gignoux, D., and D. Schmitt, 1991, J. Magn. & Magn. Mater. 100, 99.

Gignoux, D., and D. Schmitt, 1993, Phys. Rev. B 48, 12682.

Gignoux, D., E Givord and R. Lemaire, 1975, Phys. Rev. B 9, 3878.

G-ignoux, D., E Givord and W.C. Koehler, 1977, Physiea B 86-88, 165.

Gignoux, D., A. Nait-Saada and R. Perrier de la Bathie, 1979, J. Phys. (Paris) 40, C5-188.

Gignoux, D., R. Lemaire and P. Molho, 1980a, J. Magn. & Magn. Mater. 21, 119.

Gignoux, D., R. Lemaire, P. Molho and E Tasset, 1980b, J. Magn. & Magn. Mater. 21, 307.

Gignoux, D., E Givord, R. Lemaire and E Tasset, 1983, J. Less-Common Met. 94, 1.

Gignoux, D., R. Lemaire, R. Mendia-Monterroso, J.M. Moreau and J. Schweizer, 1985, Physiea B 130, 376.

Gignoux, D., D. Schmitt and M. Zerguine, 1987, J. Magn. & Magn. Mater. 66, 373.

Gignoux, D., D. Schmitt and M. Zerguine, 1988, J. Phys. (Paris) 49, C8-433.

Gignoux, D., D. Schmitt, A. Takeuchi and EY. Zhang, 1991a, J. Magn. & Magn. Mater. 97, 15.

Gignoux, D., D. Schmitt, T. Takeuchi, EY. Zhang, C. Rouchon and E. Roudaut, 1991b, J. Magn. & Magn. Mater. 98, 333.

Gignoux, D,, R Morin and D. Schmitt, 1991c, J. Magn. & Magn. Mater. 102, 33.

Gignoux, D., E Morin, J. Voiron and P. Burlet, 1992, Phys. Rev. B 46, 8877.

Gignoux, D., D. Schmitt, J. Voiron, EY. Zhang, E. Bauer and G. Schandy, 1993, J. Alloys & Compounds 191, 139.

Givord, D., L Laforest and R. Lemaire, 1977, Physica B 86--88, 204.

Givord, D., J. Laforest and R. Lemaire, 1979, J. Appl. Phys. 50, 7489.

Givord, D., J. Laforest, R. Lemaire and Q. Lu, 1983, J. Magn. & Magn. Mater. 31-34, 191.

Givord, E, and LS. Shah, 1972, Comptes Rendus 274, 923.

Goremychkin, E.A., E. Mtihle, P.G. Ivanitskii, V.T. Krotenko, M.V. Pasechnik, V.V. Slisenko, A.A. Vasilkevich, B. Lippold, O.D. Chistyakov and E.M. Savitskii, 1984, Phys. Status Solidi b 121, 623.

Goremychldn, E.A., E. Mtihle, I. Natkaniec, M. Popescu and O.D. Christyakov, 1985a, Sov. Phys. Solid State 27, 1195.

Goremychkin, E.A., E. Miihle, B. Lippold, O.D. Christyakov and E.M. Savitskii, 1985b, Phys. Status Solidi b 127, 371.

Goto, T., T, Sakakibara, K. Murata, H. Komatsu and K. Fukamichi, 1990, J. Magn. & Magn. Mater. 90&91, 700.

Gubbens, EC.M., A.M. Van der Kraan and K.H.J. Buschow, 1988, J. Magn. & Magn. Mater. 76-77, 187.

Hashimoto, Y., 1988, 1. Phys. (Paris) 49, C8-421. Hashimoto, Y., H. Fujii, H. Fujiwara and T. Okamoto,

1979, J. Phys. Soc. Jpn. 47, 67. Herbst, J.H., J.J. Croat, R.W. Lee and W.B. Yelon,

1982, J. Appl. Phys. 53, 250. Hirosawa, S., and Y. Nakamura, 1982, J. Magn. &

Magn. Mater. 25, 284. Hulliger, E, 1978, J. Magn. & Magn. Mater. 8, 183. Hulliger, F., 1980, J. Magn. & Magn. Mater. 15--18,

1243. Hutehings, M.T., 1964, Solid State Physics, Vol. 16

(Academic Press, New York) p. 227. Ikeda, K., K.A. Gschneidner Jr, R.J. Stierman, T.-W.E.

Tsang and O.D. McMasters, 1984, Phys, Rev. B. 29, 5039.

Ikeda, K,, S.K. Dhar, M. Yoshizawa and K.A. Gschneidner Jr, 1991, J. Magn. & Magn. Mater. 100, 292.

Ivanov, V., L. Vinokurova and A. Szytuta, 1992a, J. Magn. & Magn. Mater. 110, L259.

Ivanov, V., L. Vinokurova, A. Szytuta and A. Zygmunt, 1992b, J. Magn. & Magn. Mater. 114, L225.

Iwata, N., 1990, J. Magn. & Magn. Mater. 86, 225. Iwata, N., T. Kimura, T. Shigeoka and Y. Hashimoto,

1987, J. Magn. & Magn. Mater. 70, 279. Iwata, N., T. Kimura, T. Shigeoka and Y. Hashimoto,

1988, J. Magn. & Magn. Mater. 73, 79.


Iwata, N., Y. Hashimoto, T. Kimura and T. Shigeoka, 1989, J. Magn. & Magn. Mater. 81, 354.

Iwata, N., K. Honda, T. Shigeoka, Y. Hashimoto and H. Fujii, 1990, J. Magn. & Magn. Mater. 90-91, 63.

Iwata, N., M. Nishikawa and T. Shigeoka, 1991, J. Magn. & Magn. Mater. 99, 209.

Janak, J.E, and A.R. Williams, 1976, Phys. Rev. B 14, 4199.

Jaussaud, C., P. Morin and D. Schmitt, 1980, J. Magn. & Magn. Mater. 22, 98.

Jehan, D.A., D.E McMorrow, R.A. Cowley and G.J. Melntyre, 1992, L Magn. & Magn. Mater. 104.107, 1523.

Jensen, J., and A.R. Mackintosh, 1990, Phys. Rev. Lett. 64, 2699.

Jansen, J., and A.R. Mackintosh, 1992, J. Magn. & Magn. Mater. 104-107, 1481.

Je~jini, M., M. Bonnet, P. Burlet, G. Lapertot, J. Rossat-Mignod, J.Y. Henry and D. Gignoux, 1988, J. Magn. & Magn. Mater. 76-77, 405.

Kakol, Z., H. Figiel and K. Turek, 1984, IEEE Trans. Mug. MAG-20, 1605.

Ka/vius, G.M., 1994, Hyp. Int. 84, 249. Kamimura, H., J. Sakurai, Y. Komura, H. Nakamura,

M. Shiga and Y. Nakamura, 1987, J. Magn. & Magn. Mater. 70, 145.

Kaneko, T., S. Abe, S. Sakurada, H. Yoshida, G. Kido and Y. Nakagawa, 1992a, J. Magn. & Magn. Mater. 104.107, 1401.

Kaneko, T., T. Kitai, S. Abe, M. Ohashi and Y. Nakagawa, 1992b, Physica B 177, 295.

Kasuya, T., 1956, Progr. Theor. Phys. 16, 45. Kim, D., and P.M. Levy, 1982, J. Magn. & Magn.

Mater. 27, 257. Kirchmayr, H.R., and C.A. Poldy, 1979, in: Handbook

on the Physics and Chemistry of Rare Earths, Vol. 2, eds K.A. Gschneidner Jr and L. Eyring (North- Holland, Amsterdam) oh. 14, p. 55.

Kitai, T., T. Kaneko, S. Abe, S. Tomiyoshi and Y. Nakagawa, 1990, L Magn. & Magn. Mater. 90-91, 55.

Klein, H.P., A. Menth and R.S. Perkins, 1975, Physiea B 80, 153.

Landau, L., and E. Lifshitz, 1981, Statistical Physics (Pergamon Press, Oxford).

Lavagna, M., C. Lacroix and M. Cyrot, 1983, J. Phys. F 13, 1007.

Lebech, B., Z. Smetana and V. Sima, 1987, J. Magn. & Magn. Mater. 70, 97.

Lee, E.W., and E Pourarian, 1976, Phys. Status Solidi a 33, 483.

Lemaire, R., 1966, Cobalt 32, 132. Li, H.S., and J.M.D. Coey, 1991, in: Handbook of

Magnetic Materials, Vol. 6, ed. K.H.J. Buschow (North-Holland, Amsterdam) ch. 1, p. 1.

Lin, H., M.E Collins, T.M. Holden and W. Wei, 1992, J. Magn. & Magn. Mater. 104-107, 1551.

Liu, W.L., M. Kurisu, H. Kadomatsu and H. Fujiwara, 1986, J. Phys. Soc. Jpn. 55, 33.

Luong, N.H., J.J.M. Franse and TD. Hien, 1985, J. Phys. F 15, 1751.

Liithi, B., R. Sommer and R Morin, 1979, J. Magn. & Magn. Mater. 13, 198.

Mackintosh, A.R., and J. Jensen, 1992, Physica B 180-181, 1.

McAlister, S.E, 1984, J. Phys. F 14, 2167. MeEwen, K.A., and S.W. Zochowski, 1990, J. Magn.

& Magn. Mater. 90-91, 94. McEwen, K.A., G.J. Cock, L.W. Roeland and A.R.

Mackintosh, 1973, Phys. Rev. Lett. 30, 287. Minakata, R., M. Shiga and Y. Nakamura, 1976,

J. Phys. Soc. Jpn. 41, 1435. Misawa, S., 1988, Physica B 149, 162. Mitsuda, S., H. Yoshizawa, N. Wada, Y. (3nuki and I".

Komatsubara, 1991, J. Phys. Soe. Jpn. 60, 1428. Mondal, S., S.I-I. Kllcoyne, R. Cywinski, B.D.

Rainford and C. Ritter, 1992, J. Magn. & Magn. Mater. 104-107, 1421.

Morin, R, 1988, J. Magn. & Magn. Mater. 71, 151. Morin, R, 1993, private communication. Morin, R, and J. Pierre, 1975, Phys. Status Solidi a

30, 549. Morin, R, and D. Schmitt, 1978, J. Phys. F 8, 951. Morin, P., and D. Sehmitt, 1982, Phys. Rev. B 26,

3891. Morin, R, and D. Schmitt, 1990, in: Ferromagnetic

Materials, Vol. 5, eds K.H.J. Buschow and E.P. Wohlfarth (North-Holland, Amsterdam) ch. 1, p. 1.

Morin, P., J. Rouehy and D. Schrnitt, 1978, Phys. Rev. B 17, 3684.

Morin, P., D. Schmitt and E. de Lacheisserie, 1982, J. Magn. & Magn. Mater. 30, 257.

Morin, P., J. Rouchy, M. Giraud and A. Czopnik, 1987a, J. Magn. & Magn. Mater. 67, 95,

Morin, R, M. Giraud, P. Burlet and A. Czopnik, 1987b, J. Magn. & Magn. Mater. 68, 107.

Morin, P., J. Rouchy and D. Sctunitt, 1988, Phys. Rev. B 37, 5401.


Morin, R, J. Rouchy, K. Yonenobu, A. Yamagishi and M. Date, 1989, J. Magn. & Magn. Mater. 81,247.

Morin, E, J. Rouchy, D. Schmitt and E. de Laeheisserie, 1990, J. Magn. & Magn. Mater. 90-91, 105.

Morin, E, S. Kunii and T. Kasuya, 1991, J. Magn. & Magn, Mater. 96, 145.

Moriya, T., 1991, J. Magn. & Magn. Mater. 100, 261. Moriya, T., and H. Hasegawa, 1980, J. Phys. Soc. Jpn.

48, 1490. Moriya, T., and Y. Takahashi, 1978, J. Phys. Soc. Jpn.

45, 397. Motokawa, M., H. Nojiri and 5(. Endoh, 1992, Physica

B 177, 279. Motoya, K., T. Freltoft, R B6ni and G. Shirane, 1988,

Phys. Rev. B 38, 4796. Mrachkov, J., and E. Leyarovski, 1988, Physica B 150,

404. Mttraoka, Y., M. Shiga and Y. Nakamura, 1983,

J. Magn. & Magn. Mater. 31-34, 121. Muraoka, Y., H. Okuda, M. Shiga and Y. Nakarnura,

1984, J. Phys. Soc. Jpn. 53, 331. Murata, K.K., and S. Doniach, 1972, Phys. Rev. Lett.

29, 285. Nakamura, H., Y. Kitaoka, K. Yoshimura, Y. Kohori,

K. Asayama, M. Shiga and Y. Nakamura, 1988a, J. Phys. (Pads) Colloq. 49, C8-257.

Nakamura, H., H. Wada, K. Yoshimura, M. Shiga, Y. Nakamura, J. Sakurai and Y. Komura, 1988b, J. Phys. F 18, 981.

Nakamura, Y., 1983, J. Magn. & Magn. Mater. 31-34, 829.

Nakamura, Y., M. Shiga and S. Kawano, 1983, Physica B 120, 212.

Nimori, S., G. KJdo, D.X. Li, Y. Haga and T. Suzuki, 1995, J. Magn. & Magn. Mater. 140-144, to appear.

Nojiri, H., M. Uchi, S. Watamura, M. Motokawa, H. Kawai, Y. Endoh and T. Shigeoka, 1991, J. Phys. Soc. Jpn. 60, 2380.

NordstrOm, L., M.S.S. Brooks and B. Johansson, 1992, J. Magn. & Magn. Mater. 104-107, 1942.

Nozaki, H., T. Tanaka and Y. Ishizawa, 1980, J. Phys. C 13, 2751.

Nunez-Regueiro, M.D., C. Lacroix and R. Ballou, 1992a, Phys. Rev. B 46, 990.

Nunez-Regueiro, M.D., C. Lacroix, R. Ballou and E. Leli~vre-Bema, 1992b, J. Magn. & Magn. Mater. 104-107, 285.

Oddou, J.L., C. Jeandey, R. Ballou, J. D6portes and B. Ouladdiaf, 1993, Solid State Commun. 85, 419.

Ohkawa, EJ., 1989, Solid State Commun. 71,907.

Ohkoshi, M., H. Kobayashi, T. Katayama, M. Hirano and T. Tsushima, 1976, AlP Conf. Proc. 29, 616.

Ohkoshi, M., H. Kobayashi, T. Katayama, M. Hirano and T. Tsushima, 1977, Physica 86--88B, 195.

Okamoto, T., H. Fujii, Y. Andoh and H. Fujiwara, 1985, J. Magn. & Magn. Mater. 52, 208.

()nuki, Y., K. Ina, M. Nishihara, T. Komatsubara, S. Takayanagi, K. Kameda and N. Wada, 1986, J. Phys. Soc. Jpn. 55, 1818.

Oomi, G., T. Terada, M. Shiga and Y. Nakamura, 1987, J. Magn. & Magn. Mater. 70, 137.

Ouladdiaf, B., 1986, Thesis (University of Grenoble) unpublished.

Peeharsky, V.K., K.A. Gsehneidner Jr and D. Fort, 1993, Phys. Rev. B 47, 5063.

Perkins, R.S., and H. Nagel, 1975, Physica B 80, 143. Perkins, R.S., and S. Str~issler, 1977, Phys. Rev. B 15,

477. Petrieh, G., and R.L. M6ssbauer, 1968, Phys. Lett. A

26, 403. Pines, D., and P. Nozi~res, 1966, The Theory of

Quantum Fluids, Vol. I (Benjamin, New York). Pinettes, C., and C. Lacroix, 1993a, J. Magn. & Magn.

Mater. 123, 153. Pinettes, C., and C. Lacroix, 1993b, Solid State

Commun. 85, 565. Pszczola, J., and K. Krop, 1986, J. Magn. & Magn.

Mater. 59, 95. Purwins, H.G., E. Walker, B. Barbara, M. Rossignol

and A. Furrer, 1976, J. Phys. C 9, 1025. Radwanski, R.J., 1986, Physica B 142, 57. Radwanski, R.J., J.J.M. Franse and S. Sinnema, 1985,

J. Phys. F 15, 969. Radwanski, R.J., J.J.M. Franse and R. Verhoef, 1990,

J. Magn. & Magn. Mater. 83, 127. Radwanski, R.J., J.J.M. Franse, EH. Quang and EE.

Kayzel, 1992a, J. Magn. & Magn. Mater. 104-107, 1321.

Radwanski, R.J., N.H. Kim-Ngan, EE. Kayzel, J.J.M. Franse, D. Gignoux, D. Schmitt and F.Y. Zhang, 1992b, J. Phys.: Condens. Matter 4, 8853.

Raffius, G., and J. K6tzler, 1983, Phys. Lett. A 93, 423.

Reiffers, M., Y.G. Naidyuk, A.G.M. Jansen, P. Wyder, I.K. Yanson, D. Gignoux and D. Schmitt, 1989, Phys. Rev. Lett. 62, 1560.

Ritter, C., S.H. Kilcoyne and R. Cywinski, 1991, J. Phys.: Condens. Matter 3, 727.

Rossat-Mignod, J., 1986, in: Neutron Scattering in Condensed Matter Research, eds K. Skold and D.L. Price (Academic Press, New York).


Rossat-Mignod, J., E Burlet, S. Quezel, J.M. Effantin, D. Delacote, H. Bartholin, O. Vogt and D. Ravot, 1983, J. Magn. & Magn. Mater. 31-34, 398.

Ruderman, M.A., and C. Kittel, 1954, Phys. Rev. 96, 99.

Sakakibara, T., T. Goto, K. Yoshimura, M. Shiga, Y. Nakamura and K. Fukamichi, 1987, J. Magn. & Magn. Mater. 70, 126.

Sato, K., Y. Yosida, Y. Isikawa and K. Moil, 1986, J. Magn. & Magn. Mater. 54-57, 467.

Schinkel, C., 1978, J. Phys. F 8, L87. Schmitt, D., 1986, J. Phys. (Paris) 47, 677. Schweizer, J., and E Tasset, 1980, J. Phys. F 10, 2799. Selke, W., and RM. Duxbury, 1984, Z. Phys. B 57,

49. Shiga, M., 1981, J. Phys. Soc. Jpn. 50, 2573. Shiga, M., H. Wada, H. Nakamura, K. Yoshimura and

Y. Nakamura, 1987, J. Phys. F 17, 1781. Shigeoka, T., N. Iwata, H. Fujii, T. Okamoto and Y.

Hashimoto, 1987, J. Magn. & Magn. Mater. 70, 239.

Shigeoka, T., N. Iwata, Y. Hashimoto, Y. Andoh and H. Fujii, 1988, J. Phys. (Paris) 49, C8-431.

Shigeoka, I"., H. Fujii, K. Yonenobu, K. Sugiyama and M. Date, 1989, J. Phys. Soc. Jpn. 58, 394.

Shigeoka, T., M. Saeki, N. Iwata, T. Takabatake and H. Fujii, 1990, J. Magn. & Magn. Mater. 90-91, 557.

Shigeoka, T., H. Fujii, M. Nishi, Y. Uwatoko, T. Takabatake, I. Oguro, K. Motoya, N. Iwata and Y. Ito, 1992a, J. Phys. Soc. Jpn. 61, 4559.

Shigeoka, T., S. Kawano, N. Iwata and H. Fujii, 1992b, Physica B 180-181, 82.

Shigeoka, T., A. Gamier, D. Gignoux, D. Schmitt, EY. Zhang and R Buffet, 1994, J. Phys. Soc. Jpn. 63, 2731.

Shimizu, K., 1985, J. Phys. Soc. Jpn. 54, 1154. Shimizu, M., J. Inoue and S. Nagasawa, 1984, J. Phys.

F 14, 2673. Shohata, N., 1977, J. Phys. Soe. Jpn. 42, 1873. Sinnema, S., R.J. Radwanski, JJ.M. Franse, D.B. de

Mooij and K.H.J. Buschow, 1984, J. Magn. & Magn. Mater. 44, 333.

Sinnema, S., J.J.M. Franse, A.A. Menovsky and R.J. Radwanski, 1986, J. Magn. & Magn. Mater. 54-57, 1639.

Sinnema, S., J.J.M. Franse, R.J. Radwanski, A.A. Menovsky and ER. de Boer, 1987, J. Phys. F 17, 233.

Stmat, K.J., 1988, in: Ferromagnetic Materials, Vol. 4, eds E.P. Wohlfarth and K.H.J. Buschow (North- Holland, Amsterdam) ch. 2, p. 131.

Stryjewski, E., and N. Cfiordano, 1977, Adv. Phys. 26, 487.

Sugiura, E., K. Sugiyama, H. Kawanaka, T. Taka- batake, H. Fujii and M. Date, 1990, J. Magn. & Magn. Mater. 90-91, 65.

Sugiyama, K., Y. Koyoshi, S. Kunii, T. Kasuya and M. Date, 1988, J. Phys. Soc. Jpn. 57, 1762.

Sugiyama, K., K. Yonenobu, M. Date, T. Shigeoka and H. Fujii, 1992, Physica B 177, 275.

Svoboda, P., M. Divis, A.V. Andreev, N.V. Baranov, M.I. Bartashevich and P.E. Markin, 1992, J. Magn. & Magn. Mater. 104-107, 1329.

Szytuta, A., R.J. Radwanski and ER. de Boer, 1992, J. Magn. & Magn. Mater. 104-107, 1237.

Takahashi, M., H. Tanaka, T. Satoh, M. Kohgi, Y. Ishikawa, T. Miura and H. Takei, t988, J. Phys. Soc. Jpn. 57, 1377.

Takayanagi, S., Y. ()nuki, K. Ina, T. Komatsubara, N. Wada, T. Watanabe, T. Sakakibara and T. Goto, 1989, J. Phys. Soe. Jpn. 58, 1031.

Takayanagi, S., N. Wada, Y. ()nuki and T. Komatsub- ara, 1991, J. Phys. Soc. Jpn. 60, 975.

Tanaka, Y., I". Tsuchida and Y. Nakamura, 1980, J. Phys. Soc. Jpn. 48, 1092.

Thuy, N.P., and J.J.M. Franse, 1986, J. Magn. & Magn. Mater. 54-57, 915.

Thuy, N.P., J.J~M. Franse, N.M. Hong and R.D. Hien, 1988, J. Phys. (Paris) 49, C8-499.

Tomiyama, F., M. Ono, M. Date, A. Yamagishi, R. Verhoef, F.R. de Boer, LJ.M. Franse and X.P. Zhong, 1991, J. Appl. Phys. 69, 5539.

Tsuneto, T., and T. Mumo, 1971, Physiea 51, 186. Ueda, K., and T Moriya, 1975, J. Phys. Soc. Jpn. 39,

605. Uhl, M., L. Sandratskii and J. KObler, I993, Int. J.

Mod. Phys. 7, 1027. Van der Goot, A.S., and K.H.J. Buschow, 1971, Phys.

Status Solidi a 5, 665. Verhoef, R., F.R. de Boer, J.J.M. Franse, C.J.M.

Denissen, T.H. Jacobs and K.H.J. Busehow, 1989, J. Magn. & Magn. Mater. 80, 41.

Verhoef, R., R.J. Radwanski and JJ.M. Franse, 1990, J. Magn. & Magn. Mater. 89, 176.

Verhoef, R., S. Sinnema, P.H. Quang and JJ.M. Franse, 1992, J. Magn. & Magn. Mater. 104-107, 1325.

Vinokurova, L., V. Ivanov and A. Szytuta, 1991, J. Magn. & Magn. Mater. 99, 193.


Voiron, J., and D. Bloch, 1971, J. Phys. (Paris) 32, 949.

Voiron, J., J. Beille, D. Bloch and C. Vettier, 1973, Solid State Commun. 13, 201.

Voiron, J., R. Ballou, J. D6portes, R.M. Gal~ra and E. Leli~vre-Bema, 1990, J. Appl. Phys. 69, 5678.

Wada, H., H. Nakamura, K. Yoshimura, M. Shiga and Y. Nakamura, 1987a, J. Magn. & Magn. Mater. 70, 134.

Wada, H., H. Nakamura, E. Fukami, K. Yoshimura, M. Shiga and Y. Nakamura, 1987b, J. Magn. & Magn. Mater. 70, 17.

Wada, H., K. Yoshimura, G. Kido, M. Shiga, M. Mekata and Y. Nakamura, 1988, Solid State Commun. 65, 23.

Waind, ER., I,S. MacKenzie and M.A.H. McCausland, 1983, J. Phys. F 13, 1041.

Weber, K., 1977, Physiea B 86--88, 91. Weinert, M., and A.J. Freeman, 1983, J. Magn. &

Magn. Mater. 38, 23. Wohlfarth, E.E, 1951, Philos. Mag. 42, 374. Wohlfarth, E.E, and E Rhodes, 1962, Philos. Mag. 7,

1817. Yamada, H., and M. Shimizu, 1985, J. Phys. F 15,

L175. Yamada, H., and M. Shimizu, 1988, J. Phys. (Pads)

49, C8-247. Yamada, H., and M. Shimizu, 1990, J. Magn. & Magn.

Mater. 90&91, 703.

Yamada, H., J. Inoue, K. Terao, S. Kanda and M. Shimizu, 1984, J. Phys. F 14, 1943.

Yamada, H., J. Inoue and M. Shimizu, 1985, J. Phys. F 15, 169.

Yamada, H., T. Tohyama and M. Shimizu, 1987, J. Magn. & Magn. Mater. 70, 44.

Yamashita, M., M. Kurisu, H. Kadomatsu, I. Oguro and H. Fujiwara, 1987, J. Phys. Soe. Jpn. 56, 32.

Yoshie, H., M. Shiga and Y. Nakamura, 1985, J. Phys. Soe. Jpn 54, 1116.

Yoshimura, K., and Y. Nakamura, 1984, J. Phys. Soe. Jpn, 53, 3611.

Yoshimura, K., T. Shimizu, M. Takigawa, H. Yosuoka and Y. Nakamttra, 1984, J. Phys. Soe. Jpn. 53, 503.

Yoshimura, K., M. Shiga and Y. Nakamura, 1986a, J. Phys. Soc. Jpn. 55, 3585.

Yoshimura, K., M. Takigawa, H. Yasuoka, M. Shiga and Y. Nakamura, 1986b, J. Magn. & Magn. Mater. 54-57, 1075.

Yoshimura, K., Y. Yoshimoto, M. Mekata, T. Sakakibara and T. Goto, 1987, J. Magn. & Magn. Mater. 70, 147.

Yosida, K., 1957, Phys. Rev. 106, 893. Zhang, EY., 1992, Thesis (University of Grenoble)

unpublished. Zhang, EY., D. Gignoux, D. Schmitt, J.J.M. Franse,

EE. Kayzel, N.H. Kim-Ngan and R.J. Radwanski, 1994, J. Magn. & Magn. Mater. 130, 108.

A U T H O R I N D E X

Aarts, J., s e e Steglich, F. 6 Abe, S. 388 Abe, S., s e e Kaneko, T. 388, 397 Abe, S., s e e Kitai, T. 388 Abell, J.S., s e e del Moral, A. 355 Abeln, A. 212, 229, 252, 271,273, 276, 277 Abeln-Heidel, A., s e e Arons, R.R. 271,273 Aehard, J.C., s e e Rossat-Mignod, J. 62 Adachi, G. 140, 170-172 Adachi, G., s e e Arakawa, T. 144 Adachi, G., s e e Sakaguchi, H. 169-172 Adaehi, G., s e e Shirai, H. 172 Adams, RE, s e e Hubberstey, P. 140 Affrossman, S. 143 Affrossman, S., s e e Gimzewski, J.K. 137 Aguilera-Granja, E 122 Ahmed-Mokhtar, N. 127 Ahn, C.C., s e e Johnson, R.W. 178 Aidun, J.B. 132 Aknetey, A . , s e e McMinn, R. 134 Aksela, H., s e e Chorkendorff, I. 114 Aksela, S., s e e Chorkendorff, I. 114 A1-Bassam, T.S., s e e Hussain, A . A . A . 134 Alameda, J.M. 145, 311,312 Alameda, J.M., s e e Dieny, B. 165 Albert, L., s e e Gasgnier, M. 132 Albessard, A.K., s e e Aoki, H. 76-78 Albessard, A.K., s e e Ebihara, T. 42, 44-46, 48,

49, 51 Albessard, A.K., s e e Onuki, Y. 74-78, 80 Aldred, A.T., s e e Friedt, J.M. 282 Alekseev, P.A. 339, 341 Al~onard, R. 355, 357, 394, 395, 397 Aliotta, C.E, s e e Ronay, M. 185 Allain, Y., s e e Daou, J.N. 216, 268, 269 Allay, L., s e e Bosca, G. 132 Allen, C.W. 174 Allen, J.W. 115 Allen, J.W., s e e Heeht, M.H. 131 Allen, J.W., s e e Johansson, L.I. 115, 131 Allen Jr, S.J. 186, 187 Allen Jr, S.J., s e e Palmstrom, C.J. 186 Allenspach, R., s e e Landolt, M. 124 Allenspach, R., s e e Taburelli, M. 124 Allibert, C.H. 153

425

Alvarado, S.E 131 Alvarado, S.E, s e e Weller, D. 122-124 Amara, M. 398 Amaral, V.S., s e e Freitas, P.P. 185 Amato, A. 94, 95 Amato, A., s e e Gygax, EN. 232 Amato, A., s e e Rossat-Mignod, J. 81 Ambroth, K.E., s e e Krost, A. 188, 189 Andersen J.N. 115, 116 Andersen J.N., s e e Nilsson, A. 116 Andersen J.N., s e e Stenborg, A. 117 Andersen O.K. 12 Anderson Anderson Anderson Anderson Anderson Anderson Anderson Anderson Andoh, Y.

I.S. 216, 233, 234 I.S., s e e Berk, N.E 232 I.S., s e e Carmelli, G. 232 I.S., s e e Gygax, EN. 232 I.S., s e e Leisure, R.G. 232 I.S., s e e Udovie, T.J. 234, 235, 243 O.K., s e e Jepson, J. 22 P.W. 3

361 Andoh, Y., s e e Okamoto, T. 360, 361 Andoh, Y., s e e Shigeoka, T. 382 Andr6, G. 227, 230, 281 Andr6, G., s e e Vajda, P. 259, 275, 281,282 Andreeff, A., s e e Alekseev, P.A. 339, 341 Andreev, A.V., s e e Svoboda, P. 387 Andres, K. 339, 341 Andrews, B., s e e Li, D. 123 Angadi, M.A. 133 Angadi, M.A., s e e Ashrit, EV. 133 Annapoorni, S. 168 Antepenko, R.J. 142 Antepenko, R.J., s e e Holloway, D.M. 142 Anthony, T., s e e Coulman, D. 166 Anthony, T.C. 168 Antomangeli, F., s e e Sigrist, M. 126, 128 Aoki, H. 63~55, 76-78 Aoki, H., s e e Crabtree, G.W. 62-64 Aoyama, A. 166 Apai, G., s e e Mason, M.G. 114 Apostolov, A.V 126, 127 Arakawa, T. 144 Arbman, G.O., s e e Koelling, D.D. 12 Arko, A.J. 31, 33

426 AUTHOR INDEX

Arons, R.R. 210, 267, 271,273, 277-279, 281 Arons, R.R., s e e Bohn, H.G. 277 Asano, A., s e e Kubo, Y. 14, 36, 37 Asano, H. 91 Asayama, K., s e e Nakamura, H. 319 Ashrit, P.V. 133 Ashrit, EV., s e e Angadi, M.A. 133 Aso, K . , s e e Hashimoto, S. 168 Assmus, W., s e e Hunt, M. 81, 82 Asti, G. 417 Atzrnony, U., s e e Venkert, A. 179 Aubert, G. 339 Awano, H., s e e Katayama, T. 166 Axe, J.D., s e e Gibbs, D. 268, 378, 417 Aylesworth, K.D. 146, 150, 151 Aylesworth, K.D., s e e Shan, Z.S. 158 Aylesworth, K.D., s e e Strzeszewski, J. 151 Ayres de Campos, N., s e e Ferreira, P. 260

Baba, K. 188 Baba, K., s e e Nakamura, O. 118, 125 Baberschke, K. 122 Baberschke, K., s e e Farle, M. 122, 123 Babldn, G.V., s e e Gonchar, EM. 118 Babkin, G.V., s e e Lozovyi, Ya.B. 119 Bacburin, V.I. 125 Bacon, EM. 141 Baczewski, L.T. 159, 161 Baczewski, L.T., s e e Piecuch, M. 159, 161 Badia, E 157 Badia, E, s e e Ferrater, C. 158 Baenziger, C., s e e Eick, H.A. 110 Baer, Y., s e e Lang, J.K. 115 Baer, Y., s e e Moser, H.R. 130-132 Baihe, M., s e e Zhao, Z.B. 152 Baillif, P., s e e Gasgnier, M. 109 Bak, R 399, 400 Bak, P., s e e Barbara, B. 360 Ball, A.R. 342, 351-353, 365, 366, 375, 377,

378, 380, 386, 391,392, 402-406, 417 Ballou, R. 308, 310, 313, 317, 319, 320, 322,

324-327, 336, 339 Ballou, R., s e e Brown, P.J. 321 Ballou, R., s e e Fisher, R.A. 324 Ballou, R., s e e Nunez-Regueiro, M.D. 325 Ballou, R., s e e Oddou, J.L. 321 Ballou, R., s e e Voiron, J. 321 Bannai, E., s e e Ishizawa, Y. 31-33, 35 Barandiaran, J.M. 366 Baranov, N.V.., s e e Svoboda, R 387 Barbara, B. 67, 299, 360 Barbara, B., s e e Gratz, E. 87 Barbara, B., s e e Kaindl, G. 117 Barbara, B., s e e Lethuillier, R 48

Barbara, B., s e e Purwins, H.G. 360 Barbara, B., s e e von Molnar, S. 178, 180 Bardolle, J., s e e Gasgnier, M. 109 Bareham, H., s e e Corner, W.D. 126 Barnes, R.G. 216 Barnes, R.G., s e e Barnfather, K.J. 237 Barnes, R.G., s e e Belhoul, M. 277 Barnes, R.G., s e e Borsa, E 237 Barnes, R.G., s e e Han, J.W. 233 Barnes, R.G., s e e Klavins, P. 215, 221,225, 226,

229 Barnes, R.G., s e e Lichty, L.R. 232, 233,244 Barnes, R.G., s e e Phua, T.T. 237 Barnes, R.G., s e e Shinar, J. 251,253, 255 Barnes, R.G., s e e Torgeson, D.R. 233 Barnes, R.G., s e e Udovic, T.J. 234 Barnes, R.G., s e e Zamir, D. 256 Barnfather, K.J. 237 Barski, A., s e e Rossi, G. 130 Bartashevich, M.I., s e e Svoboda, E 387 Barth, J., s e e Gerken, F. 115, 131 Barth, J., s e e Johansson, L.I. 181 Barth, J., s e e Kammerer, R. 115 Barthem, VM.T.S. 339 341,343,344 Barthem, V.M.T.S., s e e Ballou, R. 339 Bartholin, H., s e e Effantin, J.M. 31,359, 397 Bartholin, H., s e e Rossat-Mignod, J. 62, 401 Bashev, V.E, s e e Tkach, V.I. 110 Bashkin, I.O. 225, 231 Bastow, T.J.M., s e e Barnes, R.G. 216 Bates, S., s e e Cowley, R.A. 417 Bauer, E. 128 Bauer, E., s e e Gignoux, D. 375, 377, 415 Bauer, E., s e e Gratz, E. 87 Bauer, E., s e e Kolaczkiewicz, J. 122 Bauer, E., s e e Stenborg, A. 116, 117 Bauer, G., s e e Krost, A. 188, 189 Bauer, R.S., s e e Allen, J.W. 115 Bauman, E, s e e Haussler, P. 118 Bazan, C., s e e Czopnik, A. 398 B6al-Monod, M.T. 304, 305 Beatfie, A.G. 241 Beaudry, B.J. 112, 217, 219, 234, 245 Beaudry, B.J., s e e Borsa, E 237 Beaudry, B.J., s e e Corner, W.D. 126 Beaudry, B.J., s e e Gschneidner Jr, K.A. 112 Beaudry, B.J., s e e Ito, T. 229, 268, 269 Beaudry, B.J., s e e Kai, K. 229, 241,252, 256 Beaudry, B.J., s e e Khatamian, D. 216, 219 Beaudry, B.J., s e e Klavins, P. 215, 221,225, 226,

229 Beaudry, B.J., s e e Phua, T.T. 237 Beaudry, B.J., s e e Saw, C.K. 216, 219 Beaudry, B.J., s e e Shinar, J. 251,253, 255, 257

AUTHOR INDEX 427

Beaudry, B.J., s e e Vajda, R 220, 236, 243, 245 Beaudry, B.J., s e e V611d, J. 233 Beavis, L.C. 142 Becker, M.E, s e e Choe, G. 163 B~cle, C. 367 Beille, J., s e e Voiron, J. 303 Belhoul, M. 277 Belhoul, M., s e e Phua, T.T. 237 Belorizky, E. 328-330, 337, 343-345 Benham, M.J., s e e Bennington, S.M. 234, 269 Bermington, S.M. 234, 269 Bennington, S.M., s e e Fairclough, J.EA. 219 Benoit, A. 52 Berendschot, T.T.J.M., s e e van der Meulen, H.E

81 Berger, L., s e e De Luca, J.C. 180 Berghaus, A., s e e Farle, M. 123 Berk, N. 304 Berk, N.E 232 Berk, N.E, s e e Anderson, I.S. 234 Berk, N.E, s e e Udovic, T.J. 234, 235 Bertel, E., s e e Netzer, EP. 108, I 11, 143, 144 Berthier, Y. 313 Besenicar, S., s e e Hole, J. 150 Besnus, M.J. 74 Bieganski, Z. 229, 282-284 Bieganski, Z., s e e Drulis, M. 241,252 Bieganski, Z., s e e Opyrchal, J. 278 Biget, M., s e e Daou, J.N. 219 Birecki, H., s e e Anthony, T.C. 168 Bischof, R. 214, 217, 271,273, 279 Bischoff, E., s e e Knoch, K.G. 152 Bittner, H., s e e Oesterreicher, H. 137 Biyadi, K., s e e Bras, J. 147 Bj6rneholm, O., s e e Stenborg, A. 117 Blancard, C. 112, 114 Blancard, C., s e e Gasgnier, M. 132 Blancard, C., s e e Sarpal, B.K. 112 Blaneo, J.A. 365, 370-373, 382, 383, 401-406 Blasehko, O. 215, 219, 220, 234 Blasehko, 0 . , s e e Andr6, G. 227, 230, 281 Blaschko, 0 . , s e e Pleschiutschnig, J. 234 Blaschko, O, s e e Udovie, T.J. 234, 235 Bloch, D. 300, 301,303 Bloch, D., s e e Voiron, J. 303 Block, J.H., s e e Melmed, A.J. 118, 119 Boespflug, E.R, s e e Harris, J.M. 177 Boeva, O.A. 136, 143, 240 Boeva, O.A., s e e Zhavoronkova, K.N. 136 Boffa, G., s e e Taborelli, M. 124 Bohdziewicz, A. 184 Bohn, H.G. 277 Bohr, J. 417 Bohr, J., s e e Gibbs, D. 268, 378, 417

Boltich, E.B., s e e Cheng, S.E 155 B6ni, P., s e e Freltoft, T. 323 B6ni, R, s e e Motoya, K. 323 Bonnet, J.E. 219, 225, 240 Bonnet, J.E., s e e Anderson, I.S. 216, 233 Bonnet, J.E., s e e Daou, J.N. 219, 245 Bonnet, J.E., s e e Schlapbach, L. 252, 257, 265,

266 Bonnet, M., s e e Jerjini, M. 70, 392 Borgensen, P. 180 Borkowska, W., s e e Drulis, M. 282 Boroch, E. 221,225, 226 Boroch, E., s e e Kaldis, E. 225 Borombaev, M.K. 364 Borsa, E 237 Bosca, G. 132 Boucherle, J.X., s e e Barbara, B. 67 Boucherle, LX., s e e Benoit, A. 52 Boukraa, A. 275, 282-285 Boukraa, A., s e e Ratishvili, I.G. 227 Boulesteix, C. 108 Boulet, R.M. 52 Bouten, RC.R, s e e Buschow, K.HJ. 108 Boutron, P. 340 Bouvier, M. 365, 405 Braaten, N.A. 178 Bracconi, R 137 Brag, J., s e e Anthony, T.C. 168 Braicovich, L., s e e Carbnne, C. 124, 158 Bran&, N.B. 5 Brar, N.S. 132 Bras, J. 147 Braun, H.E, s e e Kuboth, M. 185 Brearley, W., s e e Surplice, N.A. 143 Br~chignac, C. 114 Bredl, C.D. 70, 90 Bredl, C.D., s e e Franse, J.J.M. 325 Bredl, C.D., s e e Gratz, E. 87 Bredl, C.D., s e e Steglich, E 6 Brinkrnan, W.E 305 Briones, E, s e e Martinez, B. 146 Brooks, J.W. 182 Brooks, M.S.S., s e e Nordstr6m, L. 313, 314 Brouder, C. 159, 165 Brouder, C., s e e Guilmin, E 165 Brousseau, B., s e e Frandon, L 128-130 Brousseau-Lahaye, B. 128, 129 Brown, L.M., s e e Colliex, C. 132 Brown, L.M., s e e Gasgnier, M. 130 Brown, RJ. 321 Brown, RJ., s e e Ballou, R. 325, 327 Broyer, B., s e e Rayane, D. 114 Brun, T.O. 394 Bruno~ E 313

428 AUTHOR INDEX

Bruson, A., s e e Brouder, C. 159 Bryan, S.I. 179 Bucher, E., s e e Jayaraman, A. 7 Buevoz, J.L., s e e Barbara, B. 67 Burger, J.P. 229, 238, 243, 251,252, 257-261,

268, 271,273, 275-277, 283, 285 Burger, J.P., s e e Blaschko, O. 219, 234 Burger, J.P., s e e Daou, J.N. 213, 217, 219, 220,

225, 229, 233, 238, 239, 241,243-246, 248, 251,252, 255, 258, 262, 264, 267, 269, 271, 273, 277-279, 283

Burger, J.E, s e e Gupta, M. 243, 256 Burger, J.P., s e e Lucasson, A. 241,243, 251,252 Burger, J.P., s e e Schlapbach, L. 252, 257, 265,

266 Burger, J.P., s e e Senoussi, S. 271,273, 277, 279 Burger, J.P., s e e Shaltiel, D. 285 Burger, J.P., s e e Vajda, P. 213, 220, 227, 229,

230, 233, 236-238, 243-246, 251,256-259, 262, 267-271,273,275, 277-281

Buffet, P., s e e Amara, M. 398 Burlet, E, s e e Ball, A.R. 377, 378, 380, 417 Burlet, P., s e e Chattopadhyay, T. 401 Buffet, P., s e e Effantin, J.M. 31,359, 397 Burlet, P., s e e Gignoux, D. 389, 406 Buffet, P., s e e Jerjini, M. 70, 392 Burlet, P., s e e Morin, E 397-399 Burlet, P., s e e Rossat-Mignod, J. 62, 401 Buffet, P., s e e Shigeoka, T. 368 Burmistrova, O.P. 119 Burzo, E. 108, 144, 306 Burzo, E., s e e Bloch, D. 303 Buschow, K.H.J. 4, 108, 156, 177, 296, 321,328,

329, 338 Busehow, K.H.J., s e e Coene, W. 152 Buschow, K.H.J., s e e Gubbens, P.C.M. 339 Buschow, K.H.J., s e e Sirmema, S. 329 Buschow, K.H.J., s e e Van der Goot, A.S. 301 Busehow, K.H.J., s e e Verhoef, R. 331,332 Buxbaum, R.E. 141

Cable, J.W., s e e Arons, R.R. 273, 277 Cabuad, E, s e e Rayane, D. 114 Cadieu, EJ. 145, 155, 156 Cadieu, EJ., s e e Kamprath, N. 155 Cadieu, F.J., s e e Liu, N.C. 155 Cadieu, EJ., s e e Stadelmaier, H.H. 155 Cahuzae, Ph., s e e Br~chignac, C. 114 Callaway, J. 9 Camley, R.E. 159, 163 Camley, R.E., s e e LePage, J.G. 159 Campagna, M., s e e Alvarado, S.E 131 Campagna, M., s e e Hillebrecht, F.U. 63 Campagna, M., s e e Weller, D. 122, 124

Campbell, I.A. 329, 345 Cannelli, G. 232 Cantelli, R., s e e Cannelli, G. 232 Capellen, J., s e e Gschneidner Jr, K.A. 112 Carbone, C. 124, 158 Carlier, E, s e e Br6chignae, C. 114 Carlin, R.L. 271,275, 277, 281,282, 284, 285 Caro, P., s e e Dexpert-Ghys, J. 137 Caro, P., s e e Gasgnier, M. 132, 146, 160 Carter, C.B., s e e Zhu, J.G. 186 Castaing, B., s e e Goy, P. 25 Caulet, J. 187 Caulet, J., s e e Guivarc'h, A. 187 Caulet, J., s e e Le Corre, A. 187, 188 Cendlewska, B. 184 Cendlewska, B., s e e Bohdziewicz, A. 184 Cern~,, S, 143 Cern~,, S, s e e Boeva, O.A. 136, 143, 240 CereS,, S., s e e Smutek, M. 136 Cerri, A. 125, 140 Chaiss6, E, s e e Bloch, D. 303 Chang, C.L., s e e den Boer, M.L. 115, 130 Chang, C.T., s e e Han, J.W. 233 Chang, C.T., s e e Torgeson, D.R. 233 Chang, S., s e e Franciosi, A. 132 Chang, S., s e e Raisanen, A. 132 Chang, S., s e e Wall, A. 132 Chang, Y.S., s e e Parks, R.D. 181 Chapman, J.W. 126 Chapman, S.B. 92, 94, 95 Chassaing, G., s e e Sigrist, M. 126, 128 Chattopadhyay, T. 401 Chattopadhyay, T., s e e Rossat-Mignod, J. 62 Chaumont, J., s e e Mathevet, J.P. 180 Chee, K.T. 128, 129 Cheetham, A.K., s e e Titcomb, C.G. 225 Chen, D.Y. 132 Chen, EL., s e e Sakamoto, Y. 182 Chen, J.K., s e e Ramesh, R. 150, 151 Chen, K., s e e Cadieu, EJ. 156 Chen, N,, s e e Rau, C. 123 Chen, X., s e e Ma, E. 143 Cheng, S.E 155 Chang, S.E, s e e Demczyk, G.B. 155 Cherifi, K. 160 Chernoplekov, N.A., s e e Parshin, EP. 243 Chieux, E, s e e Barandiaran, J.M. 366 Chiheb, M. 219, 221,225, 227 Chiheb, M., s e e Daou, J.N. 219, 234 Chirico, R.D., s e e Carlin, R.L. 275, 281 Chistyakov, O.D., s e e Goremyehkin, E.A. 339,

342 Chizhov, P.E. 134 Chizhov, P.E., s e e Kostygov, A.N. 134

AUTHOR INDEX 429

Chizhov, RE., s e e Morozov, Yu.G. 134 Chlebeck, H.G., s e e Curzon, A.E. 110 Choe, G. 163 Chorkendorff, I. 114, 116 Chorkendorff, I., s e e Andersen, J.N. 115, 116 Chorkendorff, I., s e e Nyholm, R. 116 Chorkendorff, I., s e e Onsgaard, J. 116, 117, 127,

129, 131 Chouteau, G., s e e Burger, J.E 268 Chouteau, G., s e e Daou, J.N. 269 Chouteau, G., s e e Vajda, E 268, 269 Chowdhury, M.R. 229, 237 Christensen, N.E., s e e Zwieknagl, G. 14, 77, 78 Christyakov, O.D., s e e Alekseev, RA. 339, 341 Christyakov, O.D., s e e Goremyehkin, E.A. 339 Ciszewski, A. 118 Clark, M.R., s e e Haschke, J.M. 231 Claus, H., s e e Carlin, R.L. 271,277 Cochet-Muchy, D. 151 Cock, GJ., s e e McEwen, K.A. 350, 351 Coene, W. 152 Coey, J.M.D. 108, 178 Coey, J.M.D., s e e Li, H.S. 328 Cofield, M.L., s e e Shin, S.C. 160 Colliex, C. 117, 128-130, 132, 137 Colliex, C., s e e Brousseau-Lahaye, B. 128, 129 Colliex, C., s e e M a n o u b i , T. 132 Collins, M.E, s e e Lin, H. 379 Connerade, J.R 111, 112, 114, 115 Connerade, J.P., s e e Blancard, C. 112, 114 Connerade, J.R, s e e Esteva, JM. 131, 132 Cormerade, J.R, s e e Sarpal, B.K. 112 Cormor, D.W., s e e Rush, JA. 243 Contreras, M.C., s e e Alameda, J.M. 145 Cooper, B.R. 350, 353 Coqblin, B. 415 Cordero, E 232 Cordero, E, s e e Cannelli, G. 232 Corliss, L.M., s e e Feleher, G.R 317 Comer, W.D. 126 Comer, W.D., s e e Smith, R.L. 126 Cosier, J., s e e Hill, R.W. 39 Cotts, R.M., s e e Schreiber, D.S. 236, 237 Cotts, R.M., s e e Zamir, D. 256 Coulman, D. 166 Cowgill, D.F. 141 Cowgill, D.E, s e e Bacon, EM. 141 Cowley, R.A. 417 Cowley, R.A., s e e Jehan, D.A. 379 Cowley, R.A., s e e Jensen, J. 268 Cox, RA., s e e Lang, J.K. 115 Cox, S.RJ., s e e Chowdhury, M.R. 229, 237 Crabtree, G.W. 62-64 Crabtree, G.W., s e e Aoki, H. 63~55

Crabtree, G.W., s e e Arko, A.J. 31, 33 Crabtree, G.W., s e e Johanson, W.R. 52, 53 Crabtree, G.W., s e e Joss, W. 33, 34, 36 Crabtree, G.W., s e e Koelling, D.D. 4 Crabtree, G.W., s e e 0nuki, Y. 33-37, 91-93, 95 Craig, R.S., s e e Ganapathy, E.V 301 Craig, R.S., s e e Nasu, S. 40 Craig, R.S., s e e Smith, H.K. 137 Cmwford, R.K., s e e Kamitakahara, W.A. 243 Creeelius, G., s e e Wertheim, G.K. 115 Creuzet, G., s e e Barthem, V.M.T.S. 339 Croat, J.J., s e e Herbst, J.H. 312 Croft, M. 181 Croft, M., s e e Lu, F. 181 Cromer, D.T. 174 Cromer, D.T., s e e Larson, A.C. 87 Cromer, D.T., s e e Liberman, D. 9, 21 Cukier, M. 128, 129, 131 Curzon, A.E. 110, 120, 133-135, 137, 143 Curzon, A.E., s e e Rajora, O.S. 133 Curzon, A.E., s e e Singh, O. 134 Cyrot, M. 297, 301 Cyrot, M., s e e Lavagna, M. 308 Cywinski, R., s e e Mondal, S. 320 Cywinski, R, s e e Ritter, C. 321 Czjzek, G. 366 Czopnik, A. 47, 398 Czopnik, A., s e e Morin, P. 355, 397-399

Daalderop, G.H.O. 313-315 Daane, A.H., s e e Gschneidner Jr, K.A. 112 Dadiani, T.O. 188 Dadiani, T.O., s e e Dzhabua, Z.U. 188 Dadiani, T.O., s e e Glurdzhidze, L.N. 188 Dai, D.S., s e e Fang, R.Y. 157 d'Ambrumenil, N., s e e Stieht, J. 81 D'Amico, K.L., s e e Bohr, J. 417 D'Amieo, K.L., s e e Gibbs, D. 268, 378, 417 Daniel-Szab6, J., s e e Dudks, L 120 Danielou, R. 216 Daou, J.N. 212, 213, 216, 217, 219-221,225,

229, 233, 234, 238, 239, 241,243-248, 251-253, 255, 258, 261, 262, 264, 267-269, 271,273, 275, 277-279, 283, 284

Daou, J.N., s e e Andre, G. 227, 230, 281 Daou, J.N., s e e Blaschko, O. 215, 219, 220, 234 Daou, J.N., s e e Bonnet, J.E. 219, 225, 240 Daou, J.N., s e e Boukraa, A. 275, 282-285 Daou, J.N., s e e Burger, J.P. 229, 238, 243, 251,

252, 257-261,268, 271,273, 275-277, 283, 285 Daou, J.N,, s e e Chiheb, M. 221,225, 227 Daou, J.N., s e e Danielou, R. 216 Daou, LN., s e e Lucasson, A. 241,243, 251,252 Daou, J.N., s e e Metzger, T.H. 236

430 AUTHOR INDEX

Daou, J.N., s e e Pleschiutschnig, J. 234 Daou, J.N., s e e Schmitzer, C. 236, 248, 268 Daou, J.N., s e e Senoussi, S, 271,273, 277, 279 Daou, J.N., s e e Shaltiel, D. 285 Daou, J.N., s e e Udovic, T.J. 234, 235 Daou, J.N., s e e Vajda, P. 210, 213,219, 220, 227,

229, 230, 232, 233, 236-238, 243-246, 251, 253-260, 262, 263, 265, 267-271,273, 275, 277-285

Daou, J.N., s e e Viallard, R. 240 Daraek, S., s e e Andres, K. 339, 341 Dariel, M.E, s e e Shikhmanter, L. 179, 181 Dariel, M.R, s e e Venkert, A. 179 Darmon, J.M., s e e Bosca, G. 132 Dartyge, E., s e e Brouder, C. 159, 165 Dartyge, E., s e e Guilmin, R 165 Das, S.K. 190 Das, S.K., s e e Suryanarayanan, R. 189 Date, M. 345, 381,401 Date, M., s e e Morin, R 396, 397 Date, M., s e e Shigeoka, T. 401 Date, M., s e e Sugiura, E. 401 Date, M., s e e Sugiyama, K. 7, 365, 371 Date, M., s e e Tomiyama, E 336 David, J., s e e Bosca, G. 132 Davis, R.E, s e e Mason, M.G. 114 de Boer, ER., s e e Franse, J.J.M. 336 de Boer, ER., s e e Meyer, R.T.W. 51 de Boer, ER., s e e Sinnema, S. 336, 337 de Boer, ER., s e e Szytuta, A. 384 de Boer, ER., s e e Tomiyama, E 336 de Boer, ER., s e e Verhoef, R. 331,332 de Frutos, M., s e e Br~chignac, C. 114 de Haas, W.J. 27 de Lacheisserie, E., s e e Morin, R 355, 394, 396 de Lima, A.E, s e e Ferreira, R 260 De Luea, J.C. 180 de Mooij, D.B., s e e Coene, W. 152 de Mooij, D.B., s e e Sinnema, S. 329 De Rosa, E, s e e Allen Jr, S.J. 186, 187 de Visser, A., s e e Ball, A.R. 342, 351-353 de Visser, A., s e e Franse, J.J.M. 325 de Visser, A., s e e van der Meulen, H.E 81 de Vroomen, A.R., s e e van Deursen, A.J.R 33,

34, 36 Degtyareva, V.E, s e e Kostygov, A.N. 134 Dehner, B., s e e Shinar, J. 251,253, 255, 257 Dejauque, J., s e e Bras, J. 147 del Moral, A. 355 Delaeote, D., s e e Rossat-Mignod, J. 401 Deleroix, R, s e e Baezewski, L.T. 159, 161 Deleroix, P., s e e Brouder, C. 159 Delcroix, P., s e e Piecueh, M. 159, 161 Delley, B . , s e e Moser, H.R. 130-132

Demczyk, B.G., s e e Cheng, S.E 155 Demczyk, G.B. 155 den Boer, M.L. 115, 130 den Boer, M.L., s e e Murgai, V. 129, 130 den Boer, M.L., s e e Parks, R.D. 181 Denda, A., s e e Kojima, T. 169 Denda, A., s e e Uchida, H. 169, 170 Denissen, C.J.M., s e e Verhoef, R. 331,332 D~portes, J. 321-323 D6portes, J., s e e Ballou, R. 317, 319, 320, 322,

324 D6portes, J., s e e Berthier, Y. 313 D6portes, J., s e e Brown, EJ. 321 D6portes, J., s e e Oddou, J.L. 321 D6portes, J., s e e Voiron, J. 321 Devlin, E., s e e McGuiness, P.J. 148 Dexpert, H., s e e Gasgnier, M. 132 Dexpert-Ghys, J. 137 Dhar, S.K., s e e Gschneidner Jr, K.A. 6, 52, 264 Dhar, S.K., s e e Ikeda, K. 305 Dianoux, A.J., s e e Barnfather, K.J. 237 Dickinson, P.H., s e e Webb, D.J. 162 Dieny, B. 165 Dijkman, W.H. 70, 72 Dimmock, J.O. 12 Divis, M., s e e Svoboda, P. 387 Dobbertin, D.C., s e e Marshall, A.N. 164 D6hler, H., s e e Zogal, O.J. 237 Dokadze, E.V., s e e Dadiani, T.O. 188 Dokadze, E.V., s e e Dzhabua, Z.U. 188 Dokadze, E.V., s e e Glurdzhidze, L.N. 188 Domke, M. 114, 115 Doniach, S. 304 Doniach, S., s e e Murata, K.K. 327 Donovan, E, s e e Cherifi, K. 160 Donovan, P.E., s e e McMinn, R. 134 Dormann, E., s e e Shalfiel, D. 285 Doukour6, M. 368, 369 Dowben, P.A. 124 Dowben, P.A., s e e LaGraffe, D. 124 Dowben, P.A., s e e Li, D. 123 Drexel, W., s e e Knorr, K. 225, 243, 277 Drulis, H. 225, 256 Drulis, H., s e e Drulis, M. 241,252, 263, 275,

285 Drulis, H., s e e Iwasieczko, W. 225 Drulis, H., s e e Smirnov, I.A. 25t, 264 Drulis, M. 241,243, 252, 258, 263, 273, 275,

277-279, 282, 285 Drulis, M., s e e Bieganski, Z. 229, 282 Drulis, M., s e e Drulis, H. 225 Drulis, M., s e e Smirnov, I.A. 251,264 Due, N.H. 307, 308 Dud~s, J. 118, 120

AUTHOR INDEX 431

Dudfis, J., s e e Jinos, S. 120 Dufour, C., s e e Cherifi, K. 160 Dunlap, B.D., s e e Friedt, J.M. 282 Dunlap, B.D., s e e Koelling, D.D. 4 Durand, J., s e e Baczewski, L.T. 159, 161 Durand, J., s e e Malterre, D. 182 Durand, J., s e e Piecuch, M. 159, 161 Duxbury, RM., s e e Selke, W. 399 Dzhabua, Z.U. 188 Dzhabua, Z.U., s e e Dadiani, T.O. 188 Dzhabua, Z.U., s e e Glurdzhidze, L.N. 188

Eastman, D.E., s e e Kaindl, G. 117 Eaton, G.H., s e e Chowdhury, M.R. 229, 237 Ebe, H., s e e Ishida, A. 188 Ebihara, T. 42, 44-46, 48, 49, 51 Ebihara, T., s e e Umehara, I. 47-51 Ebihara, T., s e e Onuki, Y. 74-78, 80 Ebisawa, T., s e e Uehida, H. 169, 170 Eeher, C.J., s e e Koestler, C. 150, 151 Edelstein, A.S., s e e Johanson, W.R. 52, 53 Edwards, D.M., s e e Bloch, D. 300, 301 Efendiev, E.G. 187 Effantin, J.M. 31,359, 397 Effantin, J.M., s e e Rossat-Mignod, J. 62, 401 EgelhoffJr, W.E 116, 131 Egelhoff Jr, W.E, s e e Tibbetts, G.G. 116 Eguchi, T., s e e Kuwano, N. 182, 184 Eichner, S., s e e Rau, C. 124 Eick, H.A. 110 el Mandouh, Z.S., s e e Mahmoud, S. 118, 127 Elbicki, J.M., s e e Cheng, S.E 155 Eley, D.D. 136, 140 Ellegaard, 0 . , s e e Onsgaard, J. 116 Ellinger, EH. 110 Elyutin, A.V, s e e Savrin, V.D. 109 Emerson, J.P., s e e Fisher, R.A. 324 Endoh, D. 92, 93 Endoh, Y., s e e Hosoito, N. 158 Endoh, Y., s e e Motokawa, M. 380 Endoh, Y., s e e Nojiri, H. 381 Engelhardt, M.A., s e e Jaswal, S.S. 151 Engelsberg, S., s e e Brinkman, W.E 305 Engelsberg, S., s e e Doniach, S. 304 Eremenko, Z.V, s e e Savrin, V.D. 109 Eriksson, B., s e e Andersen, J.N. 116 Eriksson, B., s e e Nilsson, A. 116 Ernst, G., s e e Blaschko, O. 219, 220 Erskine, J.L., s e e Li, D. 123 Eschenfelder, A.H. 108 Esteva, J.M. 131, 132 Esteva, J.M., s e e Blancard, C. 112, 114 Esteva, J.M., s e e Gasgnier, M. 132 Esteva, J.M., s e e Sarpal, B.K. 112

Esteva, J.M., s e e Thole, B.T. t 14 Etourneau, J., s e e Kasaya, M. 6 Evans, J., s e e Hughes, D.T. 182 Everett, G.E. 394, 411 Eyring, L. 108 Eyring, L., s e e Eick, H.A. 110 Eyring, L., s e e Felmlee, T.L. 110

Faber, J., s e e Shaked, H. 271,275, 281-284 Fabian, D.J., s e e Gimzewski, J.K. 137 Fagot, M., s e e Bras, J. 147 Fairclough, J.P.A. 219 F/ildt, A. 115, 116 Falicov, L.M. 4 Fang, R.Y. 157 Fantner, E.J., s e e Krost, A. 188, 189 Farle, M. 122, 123 Farle, M., s e e Baberschke, K. 122 Farr, LEG., s e e Hirst, J.R. 182 Farraut, S., s e e Corner, W.D. 126 Fawcett, E. 26 Fedorus, A.G., s e e Gonchar, V.V 119 Fedotov, V.G., s e e Fedotov, V.K. 225 Fedotov, V.K. 225 Feh6r, A., s e e Dudfis, J. 118, 120 Feh~r, A., s e e J~inos, S. 120 Felcher, G.P. 317 Felder, E., s e e Schlapbach, L. 252, 257 Feldman, W.L., s e e Lowe, W.P. 125 Felmlee, T.L. 110 Felsch, W., s e e Brouder, C. 165 Felsch, W., s e e Guilmin, P. 165 Fender, B.E.E, s e e Knorr, K. 225, 243, 277 Fender, B.E.E, s e e Titcomb, C.G. 225 Fernengel, W., s e e Rodewald, W. 152, 153 Ferrater, C. 158 Ferrater, C., s e e Badia, E 157 Ferreira, P. 260 Ferro, R., s e e Rossi, D. 184 Fidler, J. 150, 152, 153, 155, 174 Fidler, J., s e e Knoch, K.G. 152 Fidler, J., s e e Parker, S.EH. 153 Figiel, H., s e e Kakol, Z. 311 Fillion, G. 393 Fillion, G., s e e Lethuillier, E 48 Finstad, T.G., s e e Palmstrom, C.J. 186, 187 Fischer, P. 394, 411 Fischer, R, s e e Schefer, J. 225, 273, 277 Fisher, R.A. 324 Fisher, R.A., s e e Amato, A. 94, 95 Fisk, Z., s e e Arko, A.J. 31, 33 Fisk, Z., s e e Joss, W. 33, 34, 36 Fisk, Z . , s e e van Deursen, A.J.R 33, 34, 36

432 AUTHOR INDEX

Flanagan, T.B., s e e Sakamoto, Y. 182 Flanagan, T.B., s e e Takao, K. 182 Flodstr6m, A., s e e Johansson, L.I. 181 Flodstr6m, A., s e e Kammerer, R. 115 Flodstr6m, A.S., s e e Gerken, E 115 Flotow, H.E., s e e Rush, J.J. 243 Flouquet, J., s e e Amato, A. 94, 95 Flouquet, J., s e e Benoit, A. 52 Flouquet, J., s e e Rossat-Mignod, J. 81 Flouquet, J., s e e van der Meulen, H.R 81 Fontaine, A., s e e Brouder, C. 159, 165 Fontaine, A., s e e Guilmin, P. 165 Forester, D.W. 168 Forester, D.W., s e e Schelleng, J.H. 167 Forester, D.W., s e e Vittoria, C. 168 Forgan, G.M. 26 Forker, M. 231 Forsyth, H., s e e McGuiness, P.J. 148 Fort, D., s e e Chapman, J.W. 126 Fort, D., s e e Hirst, J.R. 182 Fort, D., s e e Pecharsky, V.K. 379 Fraisse, R., s e e Ahmed-Mokhtar, N. 127 Frak, R.M., s e e Iwasieczko, W. 225 Franceschi, E. 179 Franciosi, A. 132 Franciosi, A., s e e Mason, M.G. 114 Franciosi, A., s e e Raisanen, A. 132 Franciosi, A., s e e Wall, A. 132 Franck, O., s e e Melmed, A.J. 118, 119 Franqois, J.C., s e e Sigrist, M. 126, 128 Frandon, J. 128-130 Frandon, J., s e e Brousseau-Lahaye, B. 128, 129 Frankenthal, R.E 168 Frankenthal, R.P., s e e van Dover, R.B. 168 Franse, J.J.M. 325, 328, 336, 350, 417 Franse, J.J.M., s e e Luong, N.H. 90, 365 Franse LJ.M., s e e Radwanski, R.J. 331,334-336,

339 342 Franse J.J.M., Franse J.J.M., Franse J.J.M., Franse J.J.M., Franse J.J.M.,

343 361 Franse J.J.M., Franz W., s e e

Fraustc ER.

s e e Sinnema, S. 329, 336, 337 s e e Thuy, N.P. 311,312 s e e Tomiyama, E 336 s e e Verhoef, R. 331-333 s e e Zhang, EY. 339, 340, 342,

s e e van der Meulen, H.P. 81 Steglich, E 6 168

Fraymonville, R., s e e Krost, A. 188, 189 Fredkin, D.R., s e e B~al-Monod, M.T. 305 Freeman, A.J., s e e Rath, J. 22 Freeman, A.J., s e e Weinert, M. 309, 314 Freeman, A.J., s e e Wu, R. 122 Freitas, EP. 185 Freltoft, T. 323

Freltoft, T., s e e Motoya, K. 323 Fr~my, M.A. 392 Fr6my, M.A., s e e Belorizky, E. 328-330, 337 Frick, B., s e e Stuhr, U. 237 Friedel, J. 311,313 Friedt, J.M. 282 Friedt, J.M., s e e Shinjo, T. 158 Frigerio, J.M. 177 Ffigerio, J.M., s e e Martin, M. 177 Frings, P.H., s e e Franse, J.J.M. 336 Fromm, E., s e e Wulz, H.G. 136, 169 Fuertes, J.E, s e e Alameda, J.M. 145 Fuggle, J.C., s e e Esteva, J.M. 131, 132 Fuggle, J.C., s e e Thole, B.T. 114 Fujii, A., s e e Isikawa, Y. 85 Fujii, H. 380, 381,384 Fujii, H., s e e Hashimoto, Y. 387 Fujii, H., s e e Iwata, N. 368 Fujii, H., s e e Okamoto, T. 360, 361 Fujii, H., s e e Shigeoka, T. 380, 382-385, 401 Fujii, H., s e e Sugiura, E. 401 Fujii, H., s e e Sugiyama, K. 371 Fujii, T., s e e Inoue, A. 166 Fujimaki, Y., s e e Ebihara, T. 48, 49, 51 Fujimaki, Y., s e e Umehara, I. 47-51, 70-72 Fujimori, A. 265 Fujimori, H. 159 Fujimori, N., s e e Kamiguchi, 3(. 159 Fujimura, S., s e e Yamamoto, H. 151, 152 Fujimura, T., s e e Endoh, D. 92, 93 Fujimura, T., s e e Goto, T. 33, 34 Fujimura, T., s e e Settai, R. 87-89 Fujimura, T., s e e Suzuki, T. 31, 33, 91 Fujita, T., s e e Satoh, K. 5, 94 Fujita, T., s e e Onuki, Y. 87 Fujiwara, H., s e e Hashimoto, Y. 387 Fujiwara, H., s e e Liu, W.L. 366 Fujiwara, H., s e e Okamoto, T. 360, 361 Fujiwara, H., s e e Yamashita, M. 388 Fujiyasu, H., s e e Ishida, A. 188, 189 Fukada, A., s e e Umehara, I. 70-72 Fukada, A., s e e Onuki, Y. 87 Fukami, E., s e e Wada, H. 324, 325 Fukamichi, K., s e e Gambino, R.J. 180 Fukamichi, K., s e e Goto, T. 300, 301,306 Fukamichi, K., s e e Sakakibara, T. 300, 301 Fukuhara, T. 74-76 Fukuma, H. 394 Fulde, E 14, 26 Fuller, M.L., s e e Larsen, J.W. 169, 171 Furrer, A., s e e Fischer, E 394, 411 Furrer, A., s e e Purwins, H.G. 360 Furukawa, M., s e e Sakamoto, Y. 182 Furukawa, Y., s e e Komatsubara, T. 31

AUTHOR INDEX 433

Galera, R.M. 33 Gal6ra, R.M., s e e Amara, M. 398 Gal6ra, R.M., s e e Voimn, J. 321 Galoshina, E.V, s e e Volkenshtein, N.V. 271 Gambino, R.J. 180 Gambino, R.J., s e e De Luca, J.C. 180 Gambino, R.J., s e e Pickart, S.J. 178 Gambino, R.J., s e e yon Molnar, S. 178, 180 Ganapathy, E.V. 301 Gao, Q.Z., s e e Kitazawa, H. 41-43 G a o , W . M . , s e e Huang, G.X. 150 Gamier, A., s e e Shigeoka, T. 368 Garrison, K.C., s e e Allen Jr, S.J. 186, 187 Garrisson, K.C., s e e Palmstrom, C.J. 186 Gasgnier, M. 108-110, 118, 120, 126, 130, 132,

137, 144-146, 150, 155, 156, 160, 163, 167, 175, 177, 184, 190

Gasgnier, M., s e e Brousseau-Lahaye, B. 128, 129 Gasgnier, M., s e e Colliex, C. 117, 128-130, 132,

137 Gasgnier, M., s e e Curzon, A.E. 134 Gaukler, K.H., s e e Reiehl, R. 111, 131 Gauth~, B., s e e Cukier, M. 128, 129, 131 Gavigan, J.P., s e e Belorizky, E. 328-330, 337,

343-345 Geballe, T.H., s e e Toxen, A.M. 163 Geballe, T.H., s e e Webb, D.J. 162, 163 Gehring, G.A., s e e Langford, H.D. 33 Gellman, A., s e e Jaffey, D.M. 116, 179 Gerken, E 115, 131 Gerken, E, s e e Johansson, L.I. 181 Gerken, E, s e e Kammerer, R. 115 Gersdorf, R., s e e Franse, J.J.M. 336 Ghijsen, J., s e e Andersen, J.N. 115, 116 Gibbs, D. 268, 378, 417 Gibbs, D., s e e Bohr, J. 417 Gibson, M.T., s e e Gimzewski, J.K. 137 Gignoux, D. 83, 85, 297, 299-303, 308-310,

313, 339, 342, 345, 362, 366, 369, 371, 373, 375-377, 385, 387, 389, 392, 393, 406, 409, 415

Gignoux, D., s e e Aubert, G. 339 Gignotlx, D., s e e Bail, A.R. 342, 351-353, 375,

377, 378, 380, 386, 391,392, 402-406, 417 Gignoux, D., s e e Ballou, R. 310, 339 Gignoux, D., s e e Barandiaran, LM. 366 Gignoux, D., s e e Barbara, B. 299 Gignoux, D., s e e Barthem, V.M.T.S. 339-341,

343, 344 Gignoux, D., s e e Blaneo, J.A. 365, 370, 371,382,

383, 401-403, 405, 406 Gignoux, D., s e e Cyrot, M. 301 Gignoux, D., s e e Doukour6, M. 368, 369 Gignoux, D., s e e Fr6my, M.A. 392 Gignoux, D., s e e Jerjini, M. 70, 392

Gignoux, D., s e e Radwanski, R.J. 339, 342 Gignoux, D., s e e Reiffers, M. 339-341,351 Gignoux, D., s e e Shigeoka, T. 368 Gignoux, D., s e e Zhang, EY. 339, 340, 342, 343,

361 Gil, J.M., s e e Ferreira, R 260 Gilchrist, H.L., s e e Allen Jr, S.J. 186, 187 Gilchrist, H.L., s e e Palmstrom, C.J. 186 Gimzewski, J.K. 137 Ginsberg, M.J., s e e Grady, D.E. 132 Giordano, N., s e e Stryjewski, E. 345-347 Giraud, M., s e e Morin, E 355, 397-399 Girouard, EE., s e e Ashrit, RV. 133 Girouard, EE., s e e Chee, K.T. 128, 129 Givord, D. 301,302 Givord, D., s e e Alameda, J.M. 311, 312 Givord, D., s e e Belorizky, E. 328-330, 337,

343-345 Givord, D., s e e Dieny, B. 165 Givord, D., s e e Due, N.H. 307, 308 Givord, E 301 Givord, E, s e e Bloeh, D. 303 Givord, E, s e e Cyrot, M. 301 Givord, E, s e e Fillion, G. 393 Givord, E, s e e Gignoux, D. 83, 85, 299-302, 313 Glinka, C.J. 243 Glinski, M., s e e Kletowski, Z. 41-43 Glurdzhidze, L.N. 188 Glurdzhidze, L.N., s e e Dadiani, T.O. 188 Glurdzhidze, L.N., s e e Dzhabua, Z.U. 188 Goldman, A., s e e Gsehneidner Jr, K.A. 264 Goltros, W. 188 Gomez-Sal, J.C., s e e Barandiaran, J.M. 366 Gomez-Sal, J.C., s e e Blanco, J.A. 372, 373, 401,

403-405 Gonchar, EM. 118 Gonehar, V.V. 119 Gond6, Y. 167 Gond6, Y., s e e Suezawa, Y. 167 Goodhead, K., s e e Jones, P.M.S. 217 Goremychkin, E.A. 339, 342 Gorges, B., s e e Ballou, R. 308, 310, 336 Gorodetskii, D.A. 118, 119 G6seiafiska, I., s e e Ratajezak, H. 157 Goto, T. 33-35, 6 5 , 6 6 , 300, 301,306 Goto, T., s e e Endoh, D. 92, 93 Goto, T., s e e O n u l d , Y . 7

Goto, T. , s e e Sakakibara, T. 300, 301 Goto, T., s e e Settai, R. 52, 53, 60, 61, 65, 87-89 Goto, T., s e e Suzuki, T. 31, 33, 34, 91 Goto, Z, s e e Takayanagi, S. 363, 364 Goto, T., s e e Yoshimura, K. 301 Gottwich, U., s e e Franse, J.J.M. 325 Goy, P. 25

434 AUTHOR INDEX

Grady, D.E. 132 Graham Jr, C.D., s e e Tang, W. 150 Grant, W.A. 167 Gratz, E. 87 Grayevsky, A., s e e Shaltiel, D. 285 Greene, L.H., s e e Lowe, W.P. 125 Greis, O. 221,225, 231 Greis, O., s e e Mfiller, H. 225 Grepstad, J.K., s e e Bmaten, N.A. 178 Grey, F., s e e Andersen, J.N. 115, 116 Grieb, B. 152 Grieb, B., s e e Knoch, K.G. 152, 153 Grier, B.H., s e e Gibbs, D. 378, 417 Griessmann, H., s e e Alekseev, P.A. 339, 341 Groiss, C., s e e Fidler, J. 153 Gr6ssinger, R. 153 Grozdev, K.I., s e e Apostolov, A.V. 126, 127 Grundy, R.J., s e e Parker, S.EH. 153 Griitter, P. 148 G~tter, P., s e e Heinzelmann, H. 148 Gsehneidner Jr, K.A. 6, 25, 52, 72, 112, 118,

135, 264 Gsehneidner Jr, K.A., s e e Beaudry, B.J. 112 Gsehneidner Jr, K.A., s e e Corner, W.D. 126 Gsehneidner Jr, K.A., s e e Hungsberg, R.E. 70 Gsehneidner Jr, K.A., s e e Ikeda, K. 305 Gsehneidner Jr, K.A., s e e Ito, T. 229 Gselmeidner Jr, K.A., s e e Kai, K. 229, 241,252,

256 Gschneidner Jr, K.A., s e e Lgsser, R. 265 Gsehneidner Jr, K.A., s e e Pecharsky, V.K. 379 Gschneidner Jr, K.A., s e e Stierman, R.J. 246, 271 Gschneidner Jr, K.A., s e e Tang, J. 70, 72 Gsehneidner Jr, K.A., s e e Thome, D.K. 236, 241,

246, 247, 252 Gschneidner Jr, K.A., s e e Vajda, E 220, 236, 243,

245 Gsehneidner Jr, K.A., s e e Vglkl, J. 233 Gu, B.X. 145 Gu, B.X., s e e Homburg, H. 145 Gubbens, EC.M. 339 Gudat, W., s e e Alvarado, S.E 131 Gudat, W., s e e Hillebreebt, EU. 63 Gudat, W., s e e Weller, D. 122, 124 Guesnais, B., s e e Caulet, J. 187 Guesnais, B., s e e Le Corre, A. 187 Guilmin, E 165 Guilmin, E, s e e Brouder, C. 159, 165 Guivarc'h, A. 187 Guivarc'h, A., s e e Cadet, J. 187 Guivarc'h, A., s e e Le Corre, A. 187, 188 Gunnarsson, O. 15 Gt~ntherodt, H.-J., s e e Grtitter, E 148 Gantherodt, H.-J., s e e Heinzelmann, H. 148

Guo, G.Y. 14, 69 Guo, Y., s e e Li, H. 185 Gupta, M. 243, 256 Gupta, S.C. 132 Gupta, Y.M. 132 Gupta, Y.M., s e e Brar, N.S. 132 Gupta, Y.M., s e e Chen, D.Y. 132 Gupta, Y.M., s e e Gupta, S.C. 132 Gustafsson, T., s e e Johansson, L.I. 131 Guy, C.N., s e e yon Molnar, S. 178 Gygax, EN. 232 Gyorgy, E.M., s e e Hellman, E 165 Gyorgy, E.M., s e e Lowe, W.P. 125 Gyorgy, E.M., s e e van Dover, R.B. 168

Habu, K., s e e Sato, N. 160, 164 Habu, K., s e e Yamauehi, K. 160 Haekemer, M., s e e Czopnik, A. 47 Hadari, Z., see Mintz, M.H. 213, 240 Hadjipanayis, G.C., s e e Aylesworth, K.D. 146,

150, 151 Hadjipanayis, G.C., s e e Jaswal, S.S. 152 Hadjipanayis, G.C., s e e Strzeszewski, J. 144, 151 Haensel, R., s e e Niemann, W. 114 Haga, Y., s e e Nimori, S. 350 Haga, Y., s e e Ozeki, S. 65, 66 Haga, Y., s e e Takeda, N. 65, 67 Hagstr6m, S.B.M., s e e Allen, J.W. 115 Hagstr6m, S.B.M., s e e Johansson, L,I. 131 Hahn, H., s e e Li, Z. 110 Hakkens, E, s e e Coene, W. 152 H~ilg, W., s e e Schefer, J. 225, 273, 277 Hall, G., s e e Croft, M. 181 Hall, G., s e e Lu, E 181 Halpem, H.A., s e e Pickart, S.J. 178 Harnaker, M.C., s e e Huang, C.Y. 185 Hart, J.W. 233 Han, J.W., s e e Lichty, L.R. 232, 244 Hart, J .W. , s e e Torgeson, D.R. 233 Handstein, A., s e e Moch, Th. 178 Hanke, W., s e e Falieov, L.M. 4 Hansen, P. 180 H a n y u , T. , s e e Miyahara, T. 129, 130 Hanzawa, K., s e e Yamada, K. 5 Hara, K., s e e Harada, T. 157 Hara, K., s e e Yamashita, S. 155 Harada, T. 157 Harbecke, B., s e e Krost, A. 188, 189 Harima, H. 14, 29, 32, 33, 72, 73, 81, 82, 89, 92,

94 Harima, H., s e e Kubo, Y. 14, 36, 37 Harima, H., s e e Sakai, O. 60, 61, 63, 64 Harris, I.R., s e e Brooks, J.W. 182 Harris, I.R., s e e Hirst, J.R. 182

AUTHOR INDEX 435

Harris, I.R., s e e Hughes, D.T. 182 Hien, R.D., s e e Thuy, N.P. 311, 312 Harris, I.R., s e e McGuiness, EJ. 148 Hien, T.D., s e e Luong, N.H. 90, 365 Harris, I.R., s e e Smith, D.A. 182 Hierschler, D., s e e Mintz, M.H. 213, 240 Harris, J.M. 177 Higo, S., s e e Kuwano, N. 182, 184 Hartmann, M. 180 Hill, H.H. 3, 10 Hartmann, M., s e e Hansen, P. 180 Hill, R.W. 39 Haschke, J.M. 231 Hillebrecht, EU. 63 Hasegawa, A. 22, 32, 39-43, 52-58, 60, 61, Hilscher, G., s e e Daou, J.N. 248, 251,269

67~69 Hilscher, G., s e e Schmitzer, C. 236, 248, 268 Hasegawa, A., s e e Harima, H. 92, 94 Hilscher, G., s e e Vajda, E 245, 246, 268-270 Hasegawa, A., s e e Kitazawa, H. 41-43, 60, 63 Hilscher, G., s e e Wiesinger, G. 210 Hasegawa, A., s e e Kletowski, Z. 41-43 Hilton, P., s e e Reinders, P.H.E 30 Hasegawa, A., s e e Yamagami, H. 13, 75, 77-79, Himpsel, EJ., s e e Reihl, R. 122

84-86 Hirano, M., s e e Ohkoshi, M. 311 Hasegawa, H., s e e Moriya, T. 305 Hirosawa, S. 313 Hashimoto, S. 168 Hirosawa, S., s e e Yamamoto, H. 151, 152 Hashimoto, Y. 362, 387 Hirst, J.R. 182 Hashimoto, Y., s e e Iwata, N. 368, 374, 375 Hoareau, B., s e e Rayane, D. 114 Hashimoto, Y., s e e Shigeoka, T. 380, 382, 401 Hoffmann, K.E, s e e Drulis, H. 256 Hastings, L.M., s e e Felcher, G.E 317 Hohenberg, R 14 Hauser, J.J. 118, 125 Holc, J. 150 Haussler, E 118 Holden, T.M., s e e Lin, H. 379 Hautecler, S., s e e Vorderwisch, E 243 Holloway, D.M. 142 Hautecler, S., s e e Wegener, W. 234 Holloway, D.M., s e e Antepenko, R.J. t42 Hawkes, C.M., s e e Owen, G. 179 Holloway, D.M., s e e Harris, J.M. 177 Hay, C.M. 179 Homburg, H. 145 Hayakawa, Y., s e e Fujimori, H. 159 Homburg, H., s e e Gu, B.X. 145 Hayakawa, Y., s e e Kamiguchi, Y. 159 Homma, H. 119 Hecht, M.H. 131 Homma, H., s e e Yang, K.A. 119 Hecht, M.H., s e e Egelhoff Jr, W.E 131 Honda, K., s e e Iwata, N. 368 Hedge, H., s e e Cadieu, EJ. 156 Honda, S. 164 Hedge, H., s e e Kamprath, N. 155 Hong, M., s e e Kwo, J. 119 Heinzelmann, H. 148 Hong, M., s e e van Dover, R.B. 168 Heinzelmarm, H., s e e Grfitter, P. 148 Hong, N.M., s e e Franse, J.J.M. 336 Heitmann, H. 168 Hong, N.M., s e e Thuy, N.E 311, 312 HelIman, E 165 Horikoshi, H. 173 Henig, E.-Th., s e e Grieb, B. 152 Horikoshi, H., s e e Takeda, S. 173 Henig, E.-Th., s e e Knoch, K.G. 152, 153 Hormes, J., s e e Blancard, C. 112, 114 Hennion, B., s e e Aubert, G. 339 Hormes, J., s e e Sarpal, B.K. 112 Henry, J.Y., s e e Jerjini, M. 70, 392 Horn, S., s e e den Boer, M.L. 115, 130 Henry La Blanehetais, Cb., s e e Dexpert-Ghys, J. Horn, S., s e e Murgai, V. 129, 130

137 HSrnstr6m, S.E., s e e Johansson, L.I. 181 Henry La Blanchetais, Ch., s e e Gasgnier, M. 1 4 6 , Horvatic, M., s e e Berthier, Y. 313

160 Hoshi, Y. 168 Herbst, G. 233 Hoshi, Y, s e e Naoe, M. 168 Herbst, J.H. 312 Hosoda, N. 136 Heremans, J., s e e Salamanca-Young, L. 189 Hosoda, N., s e e Uehida, H. 169 Herman, F. 9 Hosoito, N. 158 Herring, C. 19 Hosoito, N., s e e Mibu, K. 158 Herses, N., s e e Richter, H.J. 187 Hosoito, N., s e e Shinjo, T. 158 Hewson, A.C., s e e Wasserman, A. 35 Hosoito, N., s e e Yoden, K. 158 Hickox, C.E., s e e Bacon, EM. 141 Hrossman, S.A., s e e Gimzewski, J.K. 137 Hidber, H.-R., s e e Grfitter, R 148 Hua, H.C., s e e Huang, G.X. 150 Hidber, H.-R., s e e Heinzelmann, H. 148 Huang, C.Y. 185

436 AUTHOR INDEX

Huang, G.X. 150 Huang, Y.C., s e e Ohki, C. 239, 240 Huang, Y.C., s e e Toguchi, K. 240 Huang, Y.C., s e e Uchida, H. 169 Huang, Y.S. 179 Huang, Y.S., s e e Murgai, V. 129, 130 Hubberstey, P. 140 Hughes, D.T. 182 Hukin, D.A., s e e Hill, R.W. 39 Hull, G.W., s e e Allen Jr, S.J. 186, 187 Hulliger, F. 394, 395 Hulliger, F., s e e A16onard, R. 355 Hulliger, E, s e e Aoki, H. 63-65 Hulliger, E, s e e Crabtree, G.W. 62-64 Hungsberg, R.E. 70 Hunt, D.G. 243 Hunt, M. 81, 82 Hunt, M., s e e Chapman, S.B. 92, 94, 95 Hunt, M., s e e Satoh, K. 42, 44, 48, 51 Hussain, A.A.A. 134 Hutchings, C.W., s e e Li, D. 123 Hutchings, M.T. 414 Hiitten, U., s e e Forker, M. 231 Hwang, C., s e e Li~ D. 123

Iandelli, A., s e e Palenzona, A. 182 Ibanez-Meier, R., s e e Liehty, L.R. 232, 244 Ibarra, M.R., s e e del Moral, A. 355 Ichikawa, T., s e e Tsunashima, S. 163 Idczak, E. 128 Iga, E, s e e Settai, R. 87-89 Iga, E, s e e Sugiyama, K. 7 Ignatiev, A . , s e e Onsgaard, J. 111 Ignatiev, A., s e e Tougaard, S. 111, 126, 128 Ikeda, H., s e e 0nuki, Y. 95 Ikeda, K. 305 Ikeda, K., s e e Gsctmeidner Jr, K.A. 25 Ikeda, M., s e e Harada, T. 157 Ikematsu, M., s e e Inoue, A. 166 Iliew, N., s e e Czopnik, A. 398 Iliew, N., s e e Kletowski, Z. 52 tlyasov, T.M., s e e Efendiev, E.G. 187 Ina, K., s e e ()nuki, Y. 90-93, 390 Ina, K., s e e Takayanagi, S. 363, 364 Inokuchi, S., s e e Numata, T. 156 Inomata, K., s e e Sahashi, M. 156, 174 Inoue, A. 166 Inoue, J., s e e Shimizu, M. 297 Inoue, J., s e e Yamada, H. 301,306 Ishida, A. 188, 189 Ishii, H., s e e Baba, K. 188 Ishli, H., s e e Miyahara, T. 129, 130 Ishii, H., s e e Nakamura, O. 118, 125 Ishii, H., s e e Takeda, K. 133

Ishii, T. 3 Ishikawa, Y., s e e Takahashi, M. 70, 392 Ishiwatari, T., s e e Naoe, M. 168 Ishizawa, Y. 31-33, 35 Ishizawa, Y., s e e Nozaki, H. 365 Isikawa, Y. 85 Isikawa, Y., s e e Maezawa, K. 83, 84, 86, 90 Isikawa, Y., s e e Sato, K. 362, 363 Isikawa, Y., s e e Onuki, Y. 83, 84, 86 Ito, T. 229, 268, 269 Ito, Y., s e e Shigeoka, T. 383 Itoh, T., s e e Uchida, H. 169, 170 Ivanitskii, P.G., s e e Goremychkin, E.A. 339, 342 Ivanov, V. 384, 385 Ivanov, V., s e e Vinokurova, L. 382 Iwamura, E. 150 lwasieczko, W. 225 Iwasieczko, W., s e e Drulis, H. 225 Iwasieczko, W., s e e Smirnov, I.A. 251,264 Iwata, N. 368, 374, 375, 381,401,402 lwata, N., s e e Shigeoka, T. 380, 382-385, 401 Izumi, E, s e e Asano, H. 91

Jaccard, D., s e e Amato, A. 94, 95 Jaccard, D., s e e Rossat-Mignod, J. 81 Jacob, I. 241 Jacobs, T.H., s e e Coene, W. 152 Jacobs, T.H., s e e Verhoef, R. 331,332 Jacoud, J.L., s e e Rossat-Mignod, J. 81 Jaffey, D.M. 116, 179 J~iger, Ch., s e e Zogal, O.J. 237 Jan, J.-P. 39, 40 Jan, J.-P., s e e Boulet, R.M. 52 Janak, J.E 303 Jang, Y.-R., s e e Min, B.I. 36 J~nos, S. 120 J~nos, S., s e e Dud~s, J. 120 Jansen, A.G.M., s e e Reiffers, M. 339-341,351 Jaswal, S.S. 151, 152 Jaswal, S.S., s e e Shan, Z.S. 164 Jaussaud, C. 355, 356 Jayanetti, J.K.D., s e e Kamprath, N. 155 Jayaraman, A. 7 Jeandey, C., s e e Oddou, J.L. 321 Jehan, D.A. 379 Jennings, J.R. 179 Jennings, J.R., s e e Bryan, ST 179 Jennings, J.R., s e e Hay, C.M. 179 Jeunings, J.R., s e e Nix, R.M. 179 Jennings, J.R., s e e Owen, G. 179 Jensen, C.L. 245 Jensen, J. 266, 268, 379, 390, 391,412, 413, 416,

417

AUTHOR INDEX 437

Jensen, J., s e e Fulde, P. 26 Jensen, J., s e e Mackintosh, A.R. 390 Jepson, J. 22 Jerjini, M. 70, 392 Jezequel, G., s e e Quemerais, A. 127, 129 Jiang, S., s e e Li, H. 185 Jin, C., s e e Rau, C. 123 Jin, H., s e e Pan, S.M. 175 Johanson, W.R. 52, 53 Johansson, B. 111, 115 Johansson, B., s e e Johansson, L.I. 181 Johansson, B., s e e Nordstr6m, L. 313, 314 Johansson, B., s e e Rosengren, A. 111 Johansson, L.I. 115, 131, 181 Johansson, L.I., s e e Allen, J.W. 115 Johansson, L.I., s e e Gerken, E 115 Johansson, L.I., s e e Hecht, M.H. 131 Johansson, L.I., s e e Kammerer, R. 115 Johbettoh, H., s e e Hasegawa, A. 22, 54-57 Johnson, D.A. 109, 112 Johnson, R.L., s e e Andersen, J.N. 115, 116 Johnson, R.W. 178 Johnson, W.B., s e e Frausto, RR. 168 Johnson, W.L., s e e Schwarz, R.B. 180 Jones, D.W., s e e Chapman, J.W. 126 Jones, D.W., s e e Corner, W.D. 126 Jones, I.R, s e e Smith, D.A. 182 Jones, RM.S. 217 Jordan, R.G. 182 Jordan, R.G., s e e Corner, W.D. 126 Jorgensen, J.D., s p e Schefer, J. 225, 273, 277 Joss, W. 33, 34, .,6 Joss, W., s e e Aoki, H. 63-65 Joss, W., s e e Crabtree, G.W. 62-64 Joss, W., s e e Muller, T. 35, 36 Joung, K.O., s e e Carlin, R.L. 275, 281 Juckum, C. 213, 219, 225, 245 Judd, R.W., s e e Nix, R.M. 179 Julien, L.S., s e e Miller, R.E 118, 126, 127 Jung, R 220, 221,244, 245 Jung, Th., s e e Grfitter, R 148 Jungblut, R., s e e Carbone, C. 124, 158

Kaehel, I"., s e e Carbone, C. 124, 158 Kadomatsu, H., s e e Liu, W.L. 366 Kadomatsu, H., s e e Yamashita, M. 388 Kadowaki, K. 5 Kagami, S., s e e Nakamura, T. 162 Kagawa, M., s e e Takeda, N. 67 Kai, K. 229, 241,252, 256 Kai, K., s e e Vajda, E 220, 236, 243,245 Kaindl, G. 115, 117 Kaindl, G., s e e Domke, M. 114, 115 Kajiura, M. 157

Kakizaki, A., s e e Ishii, T. 3 Kakol, Z. 311 Kakuno, K., s e e Gond6, Y. 167 Kakuno, K., s e e Suezawa, Y. 167 Kaldis, E. 225 Kaldis, E., s e e Bischof, R. 214, 217, 271,273,

279 Kaldis, E., s e e Boroch, E. 221,225, 226 Kaldis, E., s e e Fischer, E 394, 411 Kaldis, E., s e e Fukuma, H. 394 Kalvius, G.M. 324 Kameda, K., s e e Onuki, Y. 90, 390 Kamiguchi, Y. 159 Kamiguchi, Y., s e e Fujimori, H. 159 Kamimura, H. 324 Kamitakahara, W.A. 243 Kammerer, R. 115 Kammerer, R., s e e Gerken, E 115 Kamprath, N. 155 Kamprath, N., s e e Liu, N.C. 155 Kanash, O.K., s e e Gonchar, VV 119 Kanayama, T., s e e Tsukahara, S. 167 Kanda, S., s e e Yamada, H. 306 Kandasamy, K. 137, 140 Kandasamy, K., s e e Surplice, N.A. 135, 137, 139 Kaneko, K., s e e Niihara, T. 168 Kaneko, M., s e e Hashimoto, S. 168 Kaneko, T. 388, 397 Kaneko, T., s e e Abe, S. 388 Kaneko, T., s e e Kitai, T. 388 Kanski, J. 131 Kappler, J.R, s e e Besnus, M.J. 74 Karim, D., s e e Arko, A.J. 31, 33 Karnatak, R.C., s e e Blancard, C. 112, 114 Karnatak, R.C., s e e Connerade, J.R 111, 112,

114, 115 Karnatak, R.C., s e e Esteva, J.M. 131, 132 Karnatak, R.C., s e e Gasgnier, M. 132 Karnatak, R.C., s e e Sarpal, B.K. 112 Karnatak, R.C., s e e Thole, B.T. 114 Karpukhina, L.G., s e e Smirnov, I.A. 251,264 Kasaya, M. 6 Kasaya, M., s e e Settai, R. 87-89 Kasaya, M., s e e Sugiyama, K. 7 Kass, W.J. 142 Kass, W.J., s e e Beavis, L.C. 142 Kasuya, M., s e e Ebihara, T. 48, 49, 51 Kasuya, T. 3, 13, 59, 60, 63-65, 415 Kasuya, T., s e e Effantin, J.M. 31,359, 397 Kasuya, T., s e e Fukuma, H. 394 Kasuya, T., s e e Galera, R.M. 33 Kasuya, T., s e e Goto, T. 33, 34 Kasuya, T., s e e Harima, H. 32, 33 Kasuya, T., s e e Kitazawa, H. 41-43, 60, 63, 65

438 AUTHOR INDEX

Kasuya, T., s e e Kwon, Y.S. 65, 67 Kasuya, T., s e e Morin, E 397 Kasuya, T., s e e Ozeki, S. 65, 66 Kasuya, T., s e e Sakai, O. 60, 61, 63, 64 Kasuya, T., s e e Settai, R. 60, 61, 65 Kasuya, T., s e e Sugiyama, K. 7, 365 Kasuya, T., s e e Suzuki, T. 33, 34 Kasuya, T., s e e Takahashi, H. 62 Kasuya, T., s e e ()nuki, Y. 7 Katayama, T. 166 Katayama, T., s e e Ohkoshi, M. 311 Kato, H., s e e Ishii, T. 3 Kato, T., s e e Maezawa, K. 83, 84, 86 Kaun, L.E, s e e Alekseev, P.A. 339, 341 Kavecansk), V, s e e Dudfis, J. 118, 120 Kawabata, H., s e e Uchida, K. 178 Kawaguchi, K., s e e Yoden, K. 158 Kawahata, T. 136 Kawai, H., s e e Nojiri, H. 381 Kawai, S., s e e Ishizawa, Y. 31-33, 35 Kawanaka, H., s e e Sugiura, E. 401 Kawano, S., s e e Nakamura, Y. 320 Kawano, S., s e e Shigeoka, T. 383, 384 Kayzel, EE., s e e Ball, A.R. 342, 351-353 Kayzel, EE., s e e Radwanski, R.J. 334, 335, 339,

342 Kayzel, EE., s e e Zhang, EY. 339, 340, 342, 343,

361 Kazimierzki, M., s e e Bohdziewicz, A. 184 Kelly, EJ., s e e Daalderop, G.H.O. 313-315 Kerley, N., s e e Reinders, EH.E 30 Ketterson, J.B., s e e Arko, A.J. 31, 33 Ketterson, J.B., s e e Windmiller, L.R. 30 Khanudova, Kh.Kh., s e e Varkanova, R.G. 142 Kharlamockhin, E.S., s e e Bachurin, V.I. 125 Khatamian, D. 215, 216, 219 Khatsernova, E.L., s e e Linetski, Ya.L. 153 Kholmedov, Kh.M., s e e Smirnov, I.A. 251,264 Kido, G., s e e Kaneko, T. 397 Kido, G., s e e Nimori, S. 350 Kido, G., s e e Ozeki, S. 65, 66 Kido, G., s e e Wada, H. 303,304 Kikuchi, M., s e e Kurosawa, Y. 42, 44, 51 Kikuchi, M., s e e Umehara, I. 53-58 Kilcoyne, S.H., s e e Mondal, S. 320 Kilcoyne, S.H., s e e Ritter, C. 321 Killoran, N., s e e Reinders, EH.E 30 Kim, D. 394 Kim, D., s e e Fischer, E 394, 411 Kim-Ngan, N.H., s e e Radwanski, R.J. 339, 342 Kim-Ngan, N.H., s e e Zhang, EY. 339, 340, 342,

343, 361 Kimura, T., s e e Iwata, N. 374, 375 King, C.A. 76, 78

Kipling, S.J., s e e Bryan, S.I. 179 Kirchmayr, H.R. 295, 296, 328, 369 Kirchmayr, H.R., s e e Burzo, E. 108, 144 Kirchmayr, H.R., s e e Gr6ssinger, R. 153 Kiriyama, H., s e e Numata, T. 156 Kisker, E., s e e Carbone, C. 124, 158 Kita, E., s e e Umemura, S. 159 Kitai, T. 388 Kitai, T., s e e Abe, S. 388 Kitai, T., s e e Kaneko, T. 388 Kitano, K., s e e Takeda, S. 173 Kitano, Y., s e e Komura, Y. 174 Kitaoka, Y., s e e Nakamura, H. 319 Kitazawa, H. 41-43, 60, 61, 63, 65 Kitazawa, H., s e e Kasuya, T. 13, 59, 60, 63-65 Kittel, C., s e e Ruderman, M.A. 3,415 Kjems, J.K., s e e Fischer, P. 394, 411 Klaasse, J.C.E, s e e Meyer, R.T.W. 51 Kiatt, K.H., s e e Bracconi, E 137 Kiavins, E 215, 221,225, 226, 229 Klein, H.E 311 Kletowski, Z. 41-43, 52 Knappe, E 225 Knappe, E, s e e Greis, O. 221,225, 231 Knappe, E, s e e Mfiller, H. 225 Knezo, D., s e e Dudfis, J. 120 Knoch, K.G. 152, 153 Knoch, K.G., s e e Fidler, J. 152, 153 Knoch, K.G., s e e Grieb, B. 152 Knorr, K. 225, 243,277 Kobayashi, H., s e e Ohkoshi, M. 311 Kobayashi, K.L.I., s e e Gerken, E 131 Kobayashi, T., s e e Sagasaki, M. 166 Koehler, W.C., s e e Gignoux, D. 301 Koelling, D.D. 4, 12, 13, 52, 55 Koelling, D.D., s e e Norman, M.R. 7, 55, 64 Koestler, C. 150, 151 Kofoed, J., s e e Chorkendorff, I. 116 Kohgi, M., s e e Takahashi, M. 70, 392 Kohn, W. 12, 14 Kohn, W., s e e Hohenberg, E 14 Kohori, Y., s e e Nakamura, H. 319 Kojima, T. 169 Kolaczkiewicz J. 122 Kolaczkiewicz J., s e e Bauer, E. 128 Kolar, D., s e e Holc, J. 150 Komatsu, H., s e e Goto, T. 300, 301,306 Komatsubara Komatsubara Komatsubara Komatsubara Komatsubara Komatsubara Komatsubara

T. 31 T., s e e Asano, H. 91 T., s e e Endoh, D. 92, 93 T., s e e Fukuma, H. 394 T., s e e Ishii, T. 3 T., s e e Maezawa, K. 90 T., s e e Mitsuda, S. 389

AUTHOR INDEX 439

Komatsubara, T., s e e Satoh, K. 5, 94 Komatsubara, T., s e e Sumiyama, A. 4 Komatsubara, T., s e e Suzuki; T. 91 Komatsubara, T., s e e Takayanagi, S. 90, 94, 363,

364, 389, 390 Komatsubara, T., s e e Takeda, N. 65, 67 Komatsubara, T., s e e Tanaka, K. 65, 66 Komatsubara, T., s e e 0nuki, Y. 33-37, 87-93,

95, 390 Komura, Y. 173, 174 Komura, Y., s e e Horikoshi, H. 173 Komura, Y., s e e Kamimura, H. 324 Komura, Y., s e e Nakamura, H. 319 Komura, Y., s e e Takeda, S. 173 Konc, M., s e e Dudfis, J. 120 Kondo, J. 4 Korringa, J. 12 Korty, EW., s e e Brun, T.O. 394 Kosak, M.M. 118, 120 Kosevich, R.M., s e e Lifshitz, I.M. 27 Koshizuka, N., s e e Suzuki, Y. 162 Kost, M.E., s e e Bashldn, I.O. 225, 231 Kost, M.E., s e e Fedotov, V.K. 225 Kost, M.E., s e e Parshin, EE 243 Kost, M.E., s e e Volkenshtein, N.V. 271 Kostygov, A.N. 134 Kostygov, A.N., s e e Chizhov, EE. 134 Kostygov, A.N., s e e Morozov, Yu.G. 134 K6tzler, J., s e e Raffius, G. 355 Kou, X.C., s e e Gr6ssinger, R. 153 Kouvel, J.S., s e e Brun, T.O. 394 Kovanagi, T., s e e Koyama, M. 165 Kowalczyk, A., s e e Ratajczak, H. 157 Kowalewski, J., s e e Czopnik, A. 47 Kowalsky, W., s e e Kunze, U. 133 Koyama, M. 165 Koyoshi, Y., s e e Sugiyama, K. 365 Kozlovskii, L.V. 134, I36 Kozlowski, G., s e e Huang, C.Y. 185 Krause, L.J., s e e Carlin, R.L. 271,275, 277, 282,

284, 285 Krewenka, R., s e e Gr6ssinger, R. 153 Krexner, G., s e e Blaschko, O. 215, 219, 220, 234 Krill, G., s e e Brouder, C. 159, 165 Krill, G., s e e Guilmin, R 165 Krill, G., s e e Malterre, D. 182 Krishna, E, s e e Verma, A.R. 172 Krishnan, R. 166 Kristensson, D.K., s e e F~ldt, A. 115 Krizek, J. 126, 127 Kronmiiller, H., s e e Fidler, J. 152, 153 Kronmfiller, H., s e e Herbst, G. 233 Kronmfiller, H., s e e Knoch, K.G. 152 Kronmiiller, K., s e e Knoch, K.G. 152, 153

Krop, K., s e e Pszczola, J. 329 Krost, A. 188, 189 Krotenko, V.T., s e e Goremyehkin, E.A. 339, 342 Kiibler, J., s e e Niksch, M. 38, 39 Kfibler, J., s e e Sficht, J. 81 K~ibler, J., s e e Uhl, M. 326 Kubo, Y. 14, 36, 37 Kuboth, M. 185 Kuentgens, U., s e e Blancard, C. 112, 114 Kuentgens, U., s e e Sarpal, B.K. 112 Kuji, T., s e e Sakamoto, Y. 182 Kulikov, N.J. 243 Kulikova, I.N., s e e Smirnov, I.A. 251,264 Kumar, R. 136, 137 Kunii, S., s e e Effantin, J.M. 31,359, 397 Kunii, S., s e e Galera, R.M. 33 Kunii, S., s e e Goto, T. 33, 34 Kunii, S., s e e Komatsubara, T. 31 Kunii, S., s e e Morin, P. 397 Kunii, S., s e e Suglyama, K. 365 Kunii, S., s e e Suzuki, 1". 31, 33, 34 Kunz, C., s e e Gerken, E 115, 131 Kunze, U. 133 Kurisu, M., s e e Liu, W.L. 366 Kurisu, M., s e e Yamashita, M. 388 Kurosawa, Y. 42, 44, 51 Kurosawa, Y., s e e Maezawa, K. 83, 84, 86 Kurosawa, Y., s e e Satoh, K. 89, 90 Kurosawa, Y., s e e Umehara, I. 53-58 Kurosawa, Y . , s e e ()nuki, Y. 83, 84, 86-89,

91-93, 95 Kuruzar, D.L., s e e Allen, C.W. 174 Kusuda, T., s e e Honda, S. 164 Kusuya, T., s e e Komatsubara, T. 31 Kuwano, N. 182, 184 Kuzmenko, V.M. 118, 121, 122 Kwo, J. 119 Kwok, W.K., s e e C)nuki, Y. 33-37, 91-93, 95 Kwon, Y.S. 65, 67 Kwon, Y.S., s e e Kitazawa, H. 65 Kwon, Y.S., s e e Ozeki, S. 65, 66 Kwon, Y.S., s e e Settai, R. 60, 61, 65 Kwon, Y.S., s e e Takeda, N. 65, 67 Kwon, Y.S., s e e Tanaka, K. 65, 66

Labarta, A., s e e Badia, E 157 Labarta, A., s e e Martinez, B. 146 Lacerda, A., s e e van der Meulen, H.E 81 Lacroix, C., s e e Ballou, R. 325-327 Lacroix, C., s e e Due, N.H. 307, 308 Lacroix, C., s e e Lavagna, M. 308 Lacroix, C., s e e Nunez-Regueiro, M.D. 325 Lacroix, C., s e e Pinettes, C. 313-315, 326 Lacy, S.E., s e e Amato, A. 94, 95

440 AUTHOR INDEX

Laesser, R., s e e Bracconi, R 137 Laforest, J., s e e Givord, D. 301,302 LaGraffe, D. 124 LaGraffe, D., s e e Dowben, RA. 124 Lambert, R.M., s e e Bryan, S.I. 179 Lambert, R.M., s e e Hay, C.M. 179 Lambert, R.M., s e e Jaffey, D.M. 116, 179 Lambert, R.M., s e e Jennings, J.R. 179 Lambert, R.M., s e e Nix, R.M. 179 Lambert, R.M., s e e Owen, G. 179 Lambrecht, A., s e e Carlin, R.L. 271,277 L a n , J., s e e Fang, R.Y. 157 Landau, L. 327 Landolt, M. 124 Landolt, M., s e e Cerri, A. 125, 140 Landolt, M., s e e Mauri, D. 122 LandoR, M., s e e Taborelli, M. 124 Lang, J.K. 115 Langell, M.A., s e e Jaswal, S.S. 151 Langford, H.D. 33 Lapertot, G., s e e Jerjini, M. 70, 392 Lapierre, E, s e e Amato, A. 94, 95 Larsen, J.W. 169, 171 Larson, A.C. 87 Larson, A.C., s e e Cromer, D.T. 174 LSsser, R. 265 L~ser, R., s e e Jung, E 220, 221,244, 245 Latka, K., s e e Czjzek, G. 366 Laubschat, C., s e e Domke, M. 114, 115 Lanbschat, C., s e e Kaindl, G. 115, 117 Laubschat, C., s e e Schneider, W.D. 118 Laughlin, D.E., s e e Cheng, S.E 155 Laughlin, D.E., s e e Shen, Y. 175 Lavagna, M. 308 Lavagna, M., s e e Cyrot, M. 297, 301 Lawrence, J.M. 40 Lawrence, J.M., s e e B6al-Monod, M.T. 304 Lazarev, B.G., s e e Kuzmenko, VM. 118 Lazarides, B., s e e Ahmed-Mokhtar, N. 127 Le Corre, A. 187, 188 Le Corre, A., s e e Caulet, J. 187 Le Corre, A., s e e Guivarc'h, A. 187 Le Corre, Y., s e e Krishnan, R. 166 Lea, K.R. 273 Leask, M.J.M., s e e Lea, K.R. 273 Lebech, B. 373 Lecrosnier, D., s e e Le Corre, A. 187 Lee, E.W. 303 Lee, R.W., s e e Herbst, J.H. 312 Lee, S.T., s e e Mason, M.G. 114 Legeler, B., s e e Seitz, E. 67~59 Legvold, S., s e e Ito, T. 268, 269 Lehmann, P., s e e Besnus, M.J. 74 Leiberich, A., s e e Lu, E 181

Leisure, R.G. 232, 236 Lejay, P., s e e Fillion, G. 393 Lejay, P., s e e Rossat-Mignod, J. 81 Lejay, E, s e e van der Meulen, H.R 81 Leli~vre-Bema, E., s e e Fisher, R.A. 324 Leli~vre-Berna, E., s e e Nunez-Regueiro, M.D.

325 Leli~vre-Berna, E., s e e Voiron, J. 321 Lemaire, R. 299, 301,311,417 Lemaire, R., s e e Alameda, J.M. 311,312 Lemaire, R., s e e Ballou, R. 310, 313, 317, 319,

320, 322, 324, 336 Lemaire, R., s e e Burzo, E. 306 Lemaire, R., s e e B&le, C. 367 Lemaire, R., s e e D~portes, J. 321,322 Lemaire, R., s e e Gignoux, D. 83, 85, 299, 300,

302, 303, 308-310, 313, 362 Lemaire, R., s e e Givord, D. 301,302 Lemonnier, J.C., s e e Quemerais, A. 127, 129 Lengeler, B., s e e Hisser, R. 265 LePage, J.G. 159 Lethuillier, R 48 Lethuillier, P., s e e Bouvier, M. 365, 405 Levitin, R.Z., s e e Borombaev, M.K. 364 Levy, EM., s e e Fischer, E 394, 411 Levy, EM., s e e Kim, D. 394 Leyarovski, E., s e e Mrachkov, J. 352 UH&itier, R, s e e Zogal, O.J. 221,225 Li, D. 123 Li, D.X., s e e Nimori, S. 350 Li, E, s e e Li, L. 152 Li, H. 185 Li, H.D., s e e Ma, E. 143 Li, H.S. 328 Li, H.S., s e e Belorizky, E. 328-330, 337,

343-345 Li, L. 152 Li, Z. 110 Lian, K.C., s e e Allen, C.W. 174 Liberman, D. 9, 21 Libowitz, G.G. 210, 212, 214, 229, 240, 251,

255, 256 Libowitz, G.G., s e e Glinka, C.J. 243 Lichty, L.R. 232, 233, 244 Lichty, L.R., s e e Torgeson, D.R. 233 Lieder, M., s e e Forker, M. 231 Lieke, W., s e e Franse, J.J.M. 325 Lieke, W., s e e Gratz, E. 87 Lieke, W., s e e Steglich, F. 6 Li~nard, A., s e e Alameda, J.M. 145 Lifshitz, E., s e e Landau, L. 327 Lifshitz, I.M. 27 Ligeon, E., s e e Danielou, R. 216 Lii, Z.Y. 156

AUTHOR INDEX 441

Lilienfeld, D.A., s e e Borgensen, P. 180 Lin, H. 379 Lin, Z., s e e Li, L. 152 Lindau, I., s e e Allen, J.W. 115 Lindau, I., s e e EgelhoffJr, W.E 131 Lindau, I., s e e Hecht, M.H. 131 Lindau, I., s e e Johansson, L.I. 115, 131 Lindau, I., s e e Rossi, G. 130 Lindau, I., s e e Yeh, J.J. 130 Linetski, Ya.L. 153, 174 Lippold, B., s e e Alekseev, RA. 339, 341 Lippold, B., s e e Goremychkin, E.A. 339, 342 Lippold, B., s e e Moth, Th. 178 Liu, B., s e e Ebihara, T. 48, 49, 51 Liu, B.X., s e e Ma, E. 143 Liu, N.C. 155 Liu, N.C., s e e Kamprath, N. 155 Liu, N.C., s e e Stadelmaier, H.H. 155 Liu, W.L. 366 Liu, Z.X., s e e Fang, R.Y. 157 Livesay, B.R., s e e Larsen, J.W. 169, 171 Lloyd, D., s e e Owen, G. 179 Loboda, VB. 120, 134, 137 Lochoshvili, T.S., s e e Dadiani, T.O. 188 Lochoshvili, T.S., s e e Glurdzhidze, L.N. 188 Loebich Jr, O. 182 Loebich Jr, O., s e e Jordan, R.G. 182 Loier, C., s e e Dexpert-Ghys, J. 137 Loisel, B., s e e Quemerais, A. t27, 129 Longuet-Higgins, H.C. 32 Lonzarich, G.G. 69, 70, 76-78 Lonzarich, G.G., s e e King, C.A. 76, 78 Lonzarich, G.G., s e e Taillefer, L. 26 Lord, D.G., s e e Parker, S.EH. 153 Loretto, M.H., s e e Brooks, J.W. 182 Loucks, T.L. 12, 20 Lousa, A., s e e Badia, E 157 Lousa, A., s e e Ferrater, C. 158 Lowe, W.R 125 Lozovyi, Ya.B. 119 Lozovyi, Ya.B., s e e Gonchar, EM. 118 Lu, E 181 Lu, E, s e e Croft, M. 181 Lu, Q., s e e Alameda, J.M. 311, 312 Lu, Q., s e e Givord, D. 302 Lu, Q.Z., s e e Huang, G.X. 150 Lfibcke, M. 114 Lfibcke, M., s e e Niemann, W. 114 Lubitz, R, s e e Forester, D.W. 168 Lubitz, E, s e e Schelleng, J.H. 167 Lubitz, R, s e e Vittoria, C. 168 Lucasson, A. 241,243,251,252 Lucasson, A., s e e Burger, J.E 243, 251,252, 271,

275, 285

Lucasson, A., s e e Daou, J.N. 213, 219, 220, 229, 233, 238, 239, 241,243-245, 247, 248, 251, 252, 268, 269

Lucasson, A., s e e Vajda, P. 213,220, 227, 233, 244-246

Lucasson, E, s e e Daou, J.N. 219, 220, 233,234, 244, 245, 247, 268, 269

Lucifiski, T., s e e Ratajczak, H. 157 Lundqvist, B.I., s e e Gunnarsson, O. 15 Luong, N.H. 90, 365 Ltithi, B. 357, 358 Ltithi, B., s e e Niksch, M. 38, 39 Luttinger, J.M. 11 Lynch, D.W., s e e Weaver, J.H. 127 Lysenko, A.B., s e e Tkach, VI. 110

Ma, E. 143 Ma, R.Z., s e e Pan, S.M. 175 Ma, R.Z., s e e Zhao, Z.B. 152 Ma, S.K., s e e B~al-Monod, M.T. 305 Machii, Y., s e e ()nuki, Y. 87 MacKenzie, I.S., s e e Waind, RR. 338 Mackintosh, A.R. 390 Mackintosh, A.R., s e e Jensen, J. 266, 379, 390,

391,412, 413, 416, 417 Mackintosh, A.R., s e e McEwen, K.A. 350, 351 Mgdge, H., s e e Czopnik, A. 398 Maeland, A., s e e Glinka, C.J. 243 Maeland, A., s e e Libowitz, G.G. 210, 214, 240 Maeland, A.J. 243 Maeno, Y., s e e Satoh, K. 5, 94 Maezawa, K. 83, 84, 86, 90 Maezawa, K., s e e Fukuhara, T. 74-76 Maezawa, K., s e e 0nuki, Y. 83, 84, 86, 91-93, 95 Mahmoud, S. 118, 127 Maienschein, J.L. 140 Maier-Komor, E 125 Maines, R.G., s e e Jayaraman, A. 7 Maita, J.R, s e e Fawcett, E. 26 Malinowski, M.E. 141 Malozemoff, A.R, s e e De Luca, J.C. 180 Malterre, D. 182 Malzfeldt, W . , s e e Niemann, W. 114 Manchester, ED., s e e Khatamian, D. 215, 216 Mancini, E 184 Mancini, E, s e e Huang, C.Y. 185 Mandel, T., s e e Dornke, M. 114, 115 Manedov, A.I., s e e Efendiev, E.G. 187 Mangin, Ph., s e e Cherifi, K. 160 Manoubi, T. 132 Manoubi, T., s e e Coltiex, C. 132 Mansmann, W. 231 Maple, M.B., s e e Falicov, L.M. 4 Maple, M.B., s e e Huang, C.Y. 185

442 AUTHOR INDEX

Maranzana, EE., s e e Buschow, K.H.J. 4 Marazza, R., s e e Rossi, D. 184 March, N.H., s e e Callaway, J. 9 Marchal, G., s e e Baczewski, L.T. 159, 161 Marchal, G., s e e Brouder, C. 159, 165 Marchal, G., s e e Cherifl, K. 160 Marchal, G., s e e Guilmin, P. 165 Marchal, G., s e e Malterre, D. 182 Marchal, G., s e e Piecuch, M. 159, 161 Mariko, H., s e e Nakamura, T. 162 Marinero, E.E. 166 Markandeylu, G., s e e Annapoorni, S. 168 Markin, P.E., s e e Svoboda, R 387 Markosyan, A.S., s e e Borombaev, M.K. 364 Markosyan, A.S., s e e Brown, P.J. 321 Markova, I.A., s e e Alekseev, P.A. 339, 341 Marshall, A.N. 164 Marshall, A.N., s e e Webb, D.J. 163 Mfirtensson, N., s e e Andersen, J.N. 116 Mfirtensson, N., s e e Hillebrecht, EU. 63 M~rtensson, N., s e e Kaindl, G. 115, 117 Mfirtensson, N., s e e Nilsson, A. 116 ML,'tensson, N., s e e Stenborg, A. 117 Martin, M. 177 Martin, M., s e e Frigerio, J.M. 177 Martinez, B. 146 Martinez, B., s e e Badia, E 157 Martinez, B., s e e Ferrater, C. 158 Martynyuk, A.V., s e e Gorodetskii, D.A. 119 Maruno, S., s e e Sakamoto, I. 73, 74 Mason, M.G. 114 Massov, A., s e e Br&hignac, C. 114 Masuda, H., s e e Suzuki, Y. 162 Materlik, G. 112 Mathevet, J.R 180 Matsubara, K., s e e Koyama, M. 165 Matsuda, R., s e e Suzuki, A. 166, 168 Matsui, H., s e e Goto, T. 65, 66 Matsumoto, H., s e e Huang, C.Y. 185 Matsuttra, S., s e e Ishida, A. 188, 189 Mattheiss, L.E 21, 22 Matthew, J.A.D. 132 Matthew, J.A.D., s e e Netzer, EE 108 Matz, W., s e e Alekseev, RA. 339, 341 Mauri, D. 122 Mauri, D., s e e Cerri, A. 125, 140 Maurice, V. , s e e Melmed, A.J. 118, 119 Mayer, H.M., s e e Franse, J.J.M. 325 MeAlister, S.R 366 McCausland, M.A.H., s e e Waind, ER. 338 McEwen, K.A. 350, 351,391 McGuiness, RJ. 148 McGuire, T.R., s e e Coey, J.M.D. 178 MeGuire, T.R., s e e Gambino, R.J. 180

McGuire, T.R., s e e Hartmann, M. 180 McGuire, T.R., s e e Pickart, S.J. 178 McGuire, T.R., s e e von Molnar, S. 178, 180 Mclntyre, GJ., s e e Jehan, D.A. 379 McMasters, O.D., s e e Gschneidner Jr, K.A. 6, 52 McMasters, O.D., s e e Ikeda, K. 305 McMasters, O.D., s e e Johanson, W.R. 52, 53 McMirm, R. 134 McMorrow, D.E, s e e Jehan, D.A. 379 McWhan, D.B., s e e Lowe, W.P. 125 Medveded, V.K., s e e Gonchar, EM. 118 Medveded, V.K., s e e Lozovyi, Ya.B. 119 Meeson, P., s e e Chapman, S.B. 92, 94, 95 Meeson, P., s e e Hunt, M. 81, 82 Meeson, P., s e e Satoh, K. 42, 44, 48, 51 Megtert, S., s e e Mathevet, J.R 180 Mehrhoff, T.K. 144 Mekata, M., s e e Wada, H. 303, 304 Mekata, M., s e e Yoshimura, K. 301 Melczer, M.E., s e e Croft, M. 181 M~linon, D., s e e Rayane, D. 114 Melmed, A.J. 118, 119 Melmed, A.J., s e e Ciszewski, A. 118 Melnikov, V.I., s e e Kuzmenko, V.M. 118, 121,

122 Melton, K.N. 174 Mendes, P.J., s e e Ferreira, R 260 Mendia-Monterroso, R., s e e Ballou, R. 310 Mendia-Monterroso, R., s e e Gignoux, D. 309,

310 Menovsky, A.A., s e e Franse, J.J.M. 325, 336 Menovsky, A.A., s e e Sinnema, S. 336, 337 Menth, A., s e e Klein, H.P. 311 Meschede, D., s e e Steglich, E 6 Messer, C.E. 240 Methfessel, S., s e e Gu, B.X. 145 Methfessel, S., s e e Homburg, H. 145 Metzger, T.H. 236 Meyer, A., s e e Besnus, M.J. 74 Meyer, E., s e e Grtitter, P. 148 Meyer, E., s e e Heirlzelmann, H. 148 Meyer, R.T.W. 51 Mibu, K. 158 Mibu, K., s e e Hosoito, N. 158 Mibu, K., s e e Shinjo, T. 158 Mibu, K., s e e Yoden, K. 158 Mieeli, RE, s e e Palmstrom, C.J. 186, 187 Michelutti, B., s e e Aubert, G. 339 Miedema, A.B., s e e Buschow, K.H.J. 108 Migliori, A., s e e Leisure, R.G. 232, 236 Mihalisin, T., s e e Parks, R.D. 181 Mikhailova, N.R, s e e Savrin, V.D. 109 Miles, M.H., s e e Chen, D.Y. 132 Miller, A.E., s e e Allen, C.W. 174

AUTHOR INDEX 443

Miller, R.E 118, 126, 127 Miller, R.E, s e e Rahman Khan, M.S. 127, 135 Miller, S.A. 132 Min, B.I. 36 Minakata, R. 303 Minc, K., s e e Sakamoto, Y. 182 Ming Lei, s e e Leisure, R.G. 236 Minier, M., s e e Le Corre, A. 187 Mintz, M.H. 213, 240 Mintz, M.H., s e e Jacob, I. 241 Mintz, M.H., s e e Kumar, R. 136, 137 Mirabal-Garcia, M., s e e Salas, EH. 123 Miroshnichenko, I.S., s e e Tkach, V.I. 110 Misawa, S. 305 Mitchell, DJ. 141, 142 Mitsuda, S. 389 Mittsev, M.A. 119 Mittsev, M.A., s e e Burmistrova, O.R 119 Miura, T., s e e Sakamoto, I. 70, 72-74 Miura, T., s e e Takahashi, M. 70, 392 Miyahara, S., s e e Harima, H. 89 Miyahara, T. 129, 130 Miyahara, T., s e e Ishii, T. 3 Miyarna, T., s e e Inoue, A. 166 Miyamoto, K. 157 Miyamoto, T., s e e Sakamoto, I. 73, 74 Miyatake, H., s e e Tsunashima, S. 168 Miyazaki, T. 162 Miyoshi, K., s e e Sakamoto, I. 70, 72-74 Mizoguchi, T., s e e Sahashi, M. 156, 174 Mizuno, H., s e e Ishida, A. 188, 189 Mizushima, T., s e e Isikawa, Y. 85 Mizutani, S., s e e Suzuki, A. t66, 168 Moch, Th. 178 Mokeda, M., s e e Yamashita, S. 155 Moldovan, A . G . , s e e Smith, H.K. 137 Molho, R, s e e Ballou, R. 308 Molho, P., s e e Gignoux, D. 303, 308, 309 Moncton, D.E., s e e Bohr, L 417 Moncton, D.E., s e e Gibbs, D. 268, 378, 417 Mondal, S. 320 Montenegro, J.ED., s e e del Moral, A. 355 Morfin-L6pez, J.L., s e e Aguilera-Granja, E 122 Moreau, J.M. 182 Moreau, J.M., s e e Gignoux, D. 309, 310 Moreau, LM., s e e Parth~, E. 174 Moreira, J.M., s e e Freitas, P.P. 185 Moreu, M.A., s e e Martinez, B. 146 Morgen, E, s e e Onsgaard, J. 111, 126, 128-131 Moil, K., s e e Isikaw~, Y. 85 Moil, K., s e e Sato, K. 362, 363 Mori, T., s e e Ishii, T. 3 Morin, R 338, 353, 355-360, 394, 396-399, 408,

414, 417

Morin, P., s e e Al~onard, R. 355, 357, 394, 395, 397

Mofin, P., s e e Amara, M. 398 Morin, P., s e e Galera, R.M. 33 Morin, E, s e e Gignoux, D. 366, 389, 406 Morin, P., s e e Jaussaud, C. 355, 356 Morin, E, s e e Ltithi, B. 357, 358 Morishita, T. 157, 159 Morishita, T., s e e Kajiura, M. 157 Morishita, T., s e e Sato, R. 166 Moriya, T. 305 Moriya, T., s e e Ueda, K. 324 Morozov, Yu.G. 134 Morozov, Yu.G., s e e Kostygov, A.N. 134 Morozova, L.V, s e e Varkanova, R.G. 136, !42 Morrison, G.R., s e e Chapman, J.W. 126 Moser, H.R. 130--132 Moser, E, s e e Vajda, E 219, 232, 233 Moshchalkov, V.V., s e e Brandt, N.B. 5 M6ssbauer, R.L., s e e Petrich, G. 301 Motokawa, M. 380 Motokawa, M., s e e Nojiri, H. 381 Motoya, K. 323 Motoya, K., s e e Freltoft, T. 323 Motoya, K., s e e Shigeoka, T. 383 Mounier, S., s e e Palmstram, C.J. 186, 187 Mounier, S., s e e Zhu, J.G. 186 Mowry, G.S., s e e Thome, D.K. 236, 241, 246,

247, 252 Mrachkov, J. 352 Miieller, EM., s e e Arko, A.J. 31, 33 Mueller, M.H., s e e Shaked, H. 27t, 275, 281-284 Mtihle, E., s e e Goremychkin, E.A. 339, 342 Mukhuchev, A.M., s e e Burmistrova, O.R 119 Mukhuchev, A.M., s e e Mittsev, M.A. 119 Mulford, R.N.R., s e e Sturdy, G.E. 231 Muller, EA., s e e Franse, J.J.M. 336 Mfiller, H. 225 Mtiller, H., s e e Greis, O. 221,225, 231 M/iller, H., s e e Knappe, R 225 Mtiller, J. 140 Muller, J., s e e Kuboth, M. 185 M~iller, J.E., s e e Materlik, G. 112 M~ller, T. 35, 36 Murakami, M., s e e Uchida, K. 178 Murani, A.P., s e e Ball, A.R. 403-405 Murao, T., s e e Tsuneto, T. 353 Muraoka, Y. 303 Murata, K., s e e Goto, T. 300, 301,306 Murata, K.K. 327 Murgai, V. 129, 130 Murgai, V, s e e Huang, Y.S. 179 Murgai, V., s e e Parks, R.D. 181 Murgai, V, s e e den Boer, M.L. 115, 130

444 AUTHOR1NDEX

Mustaehi, A. 279 Mutka, H., s e e Arons, R.R. 273 Myers, H.P., s e e Fgldt, ,~,. 115, 116

Naberhuis, S., s e e Anthony, T.C. 168 Nabli, H,, s e e Pieeueh, M. 159, 161 Naris, S., s e e Shan, Z.S. 158 Nagahama, K., s e e lwamura, E. 150 Nagai, H., s e e Adachi, G. 170-172 Nagai, H., s e e Sakaguchi, H. 169-172 Nagai, N., s e e Adaehi, G. 170, 172 Nagai, N., s e e Kurosawa, Y. 42, 44, 51 Nagai, N., s e e Satoh, K. 42, 44, 48, 51 Nagai, N., s e e Umehara, I. 29, 30, 41, 42, 47-58,

70-73 Nagai, N., s e e Onuki, Y. 91-93 Nagano, H., s e e Sttmiyama, A. 4 Nagao, K., s e e Adaehi, G. 140 Nagaoka, Y., s e e Sakamoto, Y. 182 Nagasawa, S., s e e Shimizu, M. 297 Nagata, H., s e e Yamamoto, H. 151, 152 Nagel, H., s e e MeGuiness, RJ. 148 Nagel, H., s e e Melton, K.N. 174 Nagel, H., s e e Perkins, R.S. 311, 312 Naidyuk, Y.G., s e e Reiffers, M. 339-341,351 Nait-Saada, A., s e e Aubert, G. 339 Nait-Saada, A., s e e Barthem, V.M.T.S. 339-341,

343, 344 Nait-Saada, A., s e e Gignoux, D. 339, 342 Naito, K., s e e Ishii, T. 3 Nakagawa, Y., s e e Abe, S. 388 Nakagawa, Y., s e e Kaneko, T. 388, 397 Nakagawa, Y., s e e Kitai, T. 388 Nakahara, J., s e e Goltros, W. 188 Nakahara, N., s e e Ishida, A. 188, 189 Nakahara, S., s e e Kwo, J. 119 Nakajima, K. 178 Nakajima, T., s e e Ishizawa, Y. 31, 33, 35 Nakamura, H. 319 Nakamura, H., s e e Kamimura, H. 324 Nakamura, H., s e e Shiga, M. 323, 324 Nakamura, H., s e e Wada, H. 317-319, 323-325 Nakamura, O. 118, 125 Nakamura, O., s e e Baba, K. 188 Nakamura, O., s e e Takeda, K. 133 Nakamura, T. 162 Nakamura, Y. 304, 320 Nakamura, Y., s e e Ballou, R. 319, 320, 322 Nakamura, Y., s e e Hirosawa, S. 313 Nakamura, Y., s e e Kamimura, H. 324 Nakamura, Y., s e e Minakata, R. 303 Nakamura, Y., s e e Mttraoka, Y. 303 Nakamura, Y., s e e Nakamura, H. 319 Nakamura, Y., s e e Oomi, G. 321

Nakamura, Y., s e e Sakakibara, T. 300, 301 Nakamura, Y., s e e Shiga, M. 323, 324 Nakamura, Y., s e e Tanaka, Y. 303 Nakamura, Y., s e e Wada, H. 303, 304, 317-319,

323-325 Nakamura, Y., s e e Yoshie, H. 311 Nakamura, Y., s e e Yoshimura, K. 306, 321,323 Nakao, T., s e e GondS, Y. 167 Nakao, T., s e e Suezawa, Y. 167 Namoradze, N.Z., s e e Ratishvili, I.G. 227 Naoe, M. 168 Naoe, M., s e e Hoshi, Y. 168 Narayanamurti, V., s e e Jayaraman, A. 7 Nasu, S. 40 Natkaniec, I., s e e Goremyehkin, E.A. 339 Natsui, H., s e e Settai, R. 87-89 Nawate, M., s e e Tsunashima, S. 163 Nawate, N., s e e Honda, S. 164 Nazareth, A., s e e Strzeszewski, J. 151 Nazarov, A.S., s e e Varkanova, R.G. 142 Ndjaka, J.M.B., s e e Dieny, B. 165 Needham, D., s e e Eley, D.D. 136, 140 Neifield, R., s e e Croft, M. 181 Netzer, EP. 108, 111, 143, 144 Netzer, ER, s e e Matthew, J.A.D. 132 Neumann, H.H., s e e Nasu, S. 40 N6vot, L., s e e Gasgnier, M. 109 Newns, D.M., s e e Strange, D. 14, 55 Nieki, K., s e e Adachi, G. 170, 172 Nieklow, R.M., s e e Arons, R.R. 273, 277 Niemann, W. 114 Niemann, W., s e e LiJbcke, M. 114 Niihara, T. 168 Niki, K., s e e Adaehi, G. 170, 172 Niki, K., s e e Sakaguehi, H. 169, 170 Nikseh, M. 38, 39 Nilsson, A. 116 Nilsson, A., s e e Andersen, J.N. 116 Nilsson, A., s e e Stenborg, A. 117 Nilsson, P.O., s e e Kanski, J. 131 Nimori, S. 350 Ninomiya, N., s e e Kawahata, T. 136 Nishi, M, s e e Shigeoka, T. 383 Nishiguehi, I., s e e Hosoda, N. 136 Nishihara, M., s e e 0nuki, Y. 33-37, 90-93, 390 Nishihara, Y., s e e Katayama, T. 166 Nishikawa, M., s e e Iwata, N. 401 Nix, R.M. 179 Nix, R.M., s e e Bryan, S.I. 179 Nix, R.M., s e e Hay, C.M. 179 Nix, R.M., s e e Jennings, J.R. 179 Nix, R.M., s e e Owen, G. 179 Noce, C., s e e Maneini, E 184 Nogami, J., s e e Rossi, G. 130

AUTHOR INDEX 445

Nogami, J., s e e Yeh, J.J. 130 Nojiri, H. 381 Nojiri, H., s e e Motokawa, M. 380 Nordstr6m, L. 313, 314 Norman, M., s e e Chapman, S.B. 92, 95 Norman, M.R. 7, 55, 64 Notarys, H., s e e Marinero, E.E. 166 Nozaki, H. 365 Nozaki, H., s e e Ishizawa, Y. 31, 33, 35 Nozi6res, E, s e e Pines, D. 327 Numata, T. 156 Numata, T., s e e Lii, Z.Y. 156 Nunez-Regueiro, M.D. 325 Ntmez-Regueiro, M.D., s e e Ballou, R. 325-327 Nurmiko, A.V, s e e Goltros, W. 188 Nuttall, R.H.D., s e e Shin, S.C. 160 Nyholm, R. 116 Nyholm, R., s e e Chorkendorff, I. 116

Obradors, X., s e e Martinez, B. 146 Ochiai, Y., s e e Hashimoto, S. 168 Oda, Y., s e e Sumiyama, A. 4 Oddou, J.L. 321 Oesterreicher, H. 137 Oestreieh, V., s e e Czjzek, G. 366 Ogawa, S., s e e Shinjo, T. 158 Oguro, I., s e e Kitazawa, H. 60, 63 Oguro, I., s e e Komatsubara, T. 31 O g u r o , I . , s e e Sakamoto, I. 73, 74 Oguro, I., s e e Shigeoka, T. 383 O g u r o , I., s e e Yamashita, M. 388 O'Handley, R.C., s e e Li, H. 185 Ohashi, M., s e e Abe, S. 388 Ohashi, M., s e e Kaneko, T. 388 Ohe, Y., s e e Goto, T. 33, 34 Ohe, Y., s e e Settai, R. 87-89 Ohe, Y., s e e Suzuki, T. 31, 33 Ohkawa, EJ. 308 Ohki, C. 239, 240 Ohkoshi, M. 311 Ohkoshi, M., s e e Honda, S. 164 Ohkuma, H., s e e Miyahara, T. 129, 130 Ohmaki, M., s e e Sakamoto, Y. 182, 184 Ohtani, Y., s e e Hosoda, N. 136 Ohtani, Y., s e e Kawahata, T. 136 Ohyama, R., s e e Koyama, M. 165 Okamoto, T. 360, 361 Okamoto, T., s e e Hashimoto, Y. 387 Okamoto, T., s e e Shigeoka, T. 380, 401 Okamura, T., s e e Ishida, A. 188, 189 Okazaki, M., s e e Onodera, Y. 12 O l d , K . , s e e Kuwano, N. 182, 184 Okuda, H., s e e Muraoka, Y. 303 Okuno, H. 163

Okuno, H., s e e Lii, Z.Y. 156 Olsen, C.E., s e e Huang, C.Y. 185 Olsen, J.A., s e e Amato, A. 94, 95 Olson, C.G., s e e Weaver, J.H. 126-129 Olson, C.G., s e e Wieliczka, D.M. 115, 116 Omi, T., s e e 0nuki, Y. 33-37, 87-89, 91-93, 95 Onaya, T., s e e Sato, N. !60, 164 Onellion, M., s e e Dowben, P.A. 124 Onellion, M., s e e LaGraffe, D. 124 Onellion, M., s e e Li, D. 123 Ono, M., s e e Tomiyama, E 336 Onodera, Y. 12 Onsgaard, J. 111, 116, 117, 126-131 Onsgaard, J., s e e Andersen, J.N. 115, 116 Onsgaard, J., s e e Chorkendorff, I. 114, 116 Onsgaard, J., s e e Nilsson, A. 116 0nuki, Y. 7, 33-37, 74-78, 80, 83, 84, 86-93,

95, 390 0nuki, Y., s e e Aoki, H. 76-78 O n u k i , Y . , s e e Asano, H. 91 0nuki, Y., s e e Ebihara, T. 42, 44-46, 48, 49, 51 Onuki, Y., s e e Endoh, D. 92, 93 Onuki, Y., s e e Ishii, T. 3 Onuki, Y., s e e Komatsubara, T. 31 0nuki, Y., s e e Kurosawa, Y. 42, 44, 51 0nuki, Y., s e e Maezawa, K. 83, 84, 86, 90 0nuki, Y., s e e Mitsuda, S. 389 0nuki, Y., s e e Satoh, K. 5, 42, 44, 48, 51, 89, 90,

94 0nuki, Y., s e e Settai, R. 52, 53, 87-89 0nuki, Y., s e e Sumiyama, A. 4 0nuki, Y., s e e Suzuki, T. 91 0nuki, Y., s e e Takayanagi, S. 90, 94, 363, 364,

389, 390 0nuki, Y., s e e Umehara, I. 29, 30, 41, 42, 47-58,

70-73 Oomi, G. 321 Opyrchal, J. 278 Opyrchal, J., s e e Bieganski, Z. 282 Opyrchal, J., s e e Drulis, M. 282 Ormerod, J., s e e McGuiness, RJ. 148 Osborn, R., s e e Bennington, S.M. 234, 269 Oskotski, V.S., s e e Smirnov, I.A. 251,264 Osterwalder, J., s e e Schefer, J. 225, 273, 277 Otaki, K., s e e Sakai, O. 60, 61, 63, 64 Ott, H.R., s e e Andres, K. 339, 341 Ott, H.R., s e e Schlapbach, L. 252, 257 Ouladdiaf, B. 317, 318 Ouladdiaf, B., s e e Ballou, R. 317, 319, 320, 322,

325, 327 Ouladdiaf, B., s e e Brown, P.J. 321 Ouladdiaf, B., s e e D6portes, J. 321-323 Ouladdiaf, B., s e e Oddou, J.L. 321 Ousset, J.C., s e e Ballou, R. 336

446 AUTHOR INDEX

Owen, G. 179 Owen, G., s e e Bryan, S.I. 179 Owen, G., s e e Hay, C.M. 179 Owen, G., s e e Jennings, J.R. 179 Owen, G., s e e Nix, R.M. 179 Oyamada, A., s e e Kitazawa, H. 65 Oyamada, A . , s e e Takeda, N. 67 Ozeki, S. 65, 66

Paccard, D., s e e B~cle, C. 367 Pack, J.G., s e e Libowitz, G.G. 251,256 Pa'idassi, S., s e e Cochet-Muchy, D. 151 Palenzona, A. 182 Palmer, P., s e e L/isser, R. 265 Palmstrom, C.J., s e e Allen Jr, S.J. 186, 187 Palmstrom, C.J. 186, 187 Palmstrom, C.J., s e e Zhu, J.G. 186 Palyukh, B.M., s e e Lozovyi, Ya.B. 119 Pan, S.M. 175 Pan, S.M., s e e Zhao, Z.B. 152 Pan6i~in, R.S., s e e Kosak, M.M. 118, 120 Parfen'eva, L.S., s e e Smirnov, I.A. 251,264 Park, M.K., s e e Messer, C.E. 240 Parker, D.G., s e e Jennings, J.R. 179 Parker, S.EH. 153 Parks, R.D. 4, 181 Parks, R.D., s e e Croft, M. 181 Parmigiani, E 134 Parshin, P.P. 243 Parth~, E. 174 Parth~, E., s e e Moreau, J.M. 182 Partin, D.L. 188-190 Partin, D.L., s e e Goltros, W. 188 Partin, D.L., s e e Salamanca-Young, L. 189 Parvin, K., s e e Webb, D.J. 162 Pasechnik, M.V., s e e Goremychkin, E.A. 339,

342 Patrick, R.C., s e e Mitchell, D.J. 141, 142 Pebler, A. 225, 231 Pecharsky, V.K. 379 Peuncey, T., s e e Kaindl, G. 117 Perenboom, J.A.A.J., s e e van der Meulen, H.P. 81 Perkins, R.S. 311,312 Perkins, R.S., s e e Klein, H.P. 311 Perkins, R.S., s e e Melton, K.N. 174 Perrier de la Bathie, R., s e e Gignoux, D. 339, 342 Peshkov, A.V, s e e Zhavoronkova, K.N. 136 Peterman, D.J., s e e Franciosi, A. 132 Peterman, D.J., s e e Raisanen, A. 132 Peterman, D.J., s e e Wall, A. 132 Peterson, D.T., s e e Kai, K. 229, 241,252, 256 Peterson, D.T., s e e Phua, T.T. 237 Peterson, D.T., s e e Shinar, J. 251,255 Peterson, D.T., s e e Weaver, J.H. 265

Peterson, D.T., s e e Zamir, D. 256 Petinov, V.I., s e e Chizhov, RE. 134 Pefinov, VI., s e e Kostygov, A.N. 134 Petinov, VI., s e e Morozov, Yu.G. 134 P&rakian, J.P., s e e Ahmed-Mokhtar, N. 127 Petdch, G. 301 Petroff, Y., s e e Schlapbach, L. 252, 257, 265, 266 Petrov, A.E., s e e Morozov, Yu.G. 134 Petzow, G., s e e Grieb, B. 152 Petzow, G., s e e Knoch, K.G. 152, 153 Philip, P., s e e Franciosi, A. 132 Philip, P., s e e Raisanen, A. 132 Philip, E, s e e Wall, A. 132 Philip, R., s e e Ahmed-Mokhtar, N. 127 Phillips, N.E., s e e Amato, A. 94, 95 Phillips, N.E., s e e Fisher, R.A. 324 Phua, T.T. 237 Phua, T.T., s e e Zamir, D. 256 Piacentini, M., s e e Sigrist, M. 126, 128 Pickart, S.J. 178 Piecuch, M. 159, 161 Piecuch, M., s e e Baczewski, L.T. 159, 161 Piecueh, M., s e e Brouder, C. 159, 165 Pientka, Z., s e e CereS,, S. 143 Pierre, J., s e e Lethuillier, P. 48 Pierre, J., s e e Morin, E 397 Pillmayr, N., s e e Daou, J.N. 248, 251,269 Pillmayr, N., s e e Vajda, P. 245, 269, 270 Pines, D. 327 Pinettes, C. 313-315, 326 Pinettes, C., s e e Due, N.H. 307, 308 Ping, J., s e e Zhao, Z.B. 152 Pintschovius, L., s e e Blaschko, O. 234 Plaskett, T.S., s e e Freitas, ER 185 Plaskett, T.S., s e e Kaindl, G. 117 Pleschiutschnig, J. 234 Pleschiutschnig, J., s e e Blaschko, O. 219, 220,

234 Poate, J.M. 167 Poldy, C.A., s e e Klrchmayr, H.R. 295, 296, 328,

369 Pollack, R.A., s e e Kaindl, G. 117 Pollard, R.J., s e e Parker, S.EH. 153 Pols, R.E., s e e van Deursen, A.J.R 33, 34, 36 Ponyatovskii, E.G., s e e Bashkin, I.O. 225, 231 Ponyatovskii, E.G., s e e Fedotov, VK. 225 Popeseu, M., s e e Goremychkin, E.A. 339 P6rschke, E., s e e Bracconi, R 137 Porte, M., s e e Krishnan, R. 166 Port, R., s e e Czopnik, A. 398 Potzel, W., s e e Waibel, E 285 Pourarian, E, s e e Lee, E.W. 303 Pradal, E, s e e Frandon, J. 128-130 Prietsch, M., s e e Domke, M. 114, 115

AUTHOR INDEX 447

Probst, P.-A., s e e Hunt, M. 81, 82 Probst, P.-A., s e e Satoh, K. 42, 44, 48, 51 Protsenko, I.E. 120 Protsenko, I.E., s e e Loboda, V.B. 120, 134, 137 Provo, J.L. 141 Provo, J.L., s e e Harris, J.M. 177 Provo, J.L., s e e Mitchell, D.J. 142 Pszczola, J. 329 Pulham, R.J., s e e Hubberstey, R 140 Purwins, H.G. 360

Qian, X.R., s e e Kamprath, N. 155 Qiu, M., s e e Li, H. 185 Quang, RH., s e e Radwanski, R.J. 334, 335 Quang, EH., s e e Verhoef, R. 333 Quemerais, A. 127, 129 Quezel, S., s e e Rossat-Mignod, J. 401

Raaen, S. 180 Raaen, S., s e e Braaten, N.A. 178 Raaen, S., s e e Croft, M. 181 Raaen, S., s e e Parks, R.D. 181 Rabalais, J.W., s e e Kumar, R. 136, 137 Rabe, R, s e e Lfibcke, M. 114 Rabe, E, s e e Niemann, W. 114 Radhakrishna, R, s e e Daou, J.N. 216, 268, 269 Radhakrishna, R, s e e Vajda, E 268, 269 Radwanski, R.J. 331,334-336, 339, 342 Radwanski, R.J., s e e Franse, J.J.M. 328, 336, 350,

417 Radwanski, R.J., s e e Sinnema, S. 329, 336, 337 Radwanski, R.J., s e e Szytuta, A. 384 Radwanski, RJ., s e e Verhoef, R. 331-333 Radwanski, R.J., s e e Zhang, EY. 339, 340, 342,

343, 361 Raffius, G. 355 Rahman Khan, M.S. 127, 135, 137 Raigorodskii, R.M., s e e Linetski, Ya.L. 153 Rainford, B.D., s e e Mondal, S. 320 Raisanen, A. 132 Raisanen, A., s e e Franciosi, A. 132 Raisanen, A., s e e Wall, A. 132 Rajora, O.S. 133 Rakhubovskii, V.A., s e e Kuzmenko, V.M. 118,

122 Rakoto, H., s e e Ballou, R. 336 Rama Ran, K.MS., s e e Annapoorni, S. 168 Ramakrisna, K. 171 Ramesh, R. 150, 151 Ramesh, R., s e e Koestler, C. 150, 151 Ran, X.L., s e e Fang, R.Y. 157 Ratajczak, H. 157

Ratajczak, H., s e e Dud~s, J. 120 Rath, J. 22 Ratishvili, I.G. 227 Rather, E.R., s e e Johnson, R.W. 178 Rau, C. 123, 124 Raub, E., s e e Loebich Jr, O. 182 Rauchschwalbe, U., s e e Franse, J.J.M. 325 Ravot, D., s e e Rossat-Mignod, J. 62, 401 Rayane, D. 114 Rayment, T., s e e Hay, CM. 179 Rayment, T., s e e Nix, R.M. 179 Reehuis, M., s e e Ball, A.R. 375, 386 Regnault, L.P., s e e Rossat-Mignod, J. 62, 81 Reichelt, J. 67, 68 Reichl, R. 111,131 Reiffers, M. 339-341,351 Reihl, B., s e e Kaindl, G. 1 t 5, 117 Reihl, B., s e e Schneider, W.D. 118 Reihl, R. 122 Reikhrudel, E.M., s e e Kozlovskii, L.V i34 Reimer, V.A., s e e Borombaev, M.K. 364 Reinders, EH.P. 30, 69, 70 Reinders, P.H.R, s e e Chapman, S.B. 92, 95 Reinders, P.H.E, s e e Hunt, M. 81, 82 Reinders, PH.P., s e e Springford, M. 92 Reinders, P.H.R, s e e ()unki, Y. 33-36 Remy, E, s e e Vajda, R 219, 232, 233 Ren, Y.G., s e e Jaswal, S.S. 151 Reshentnikova, L.V. 118 Ressouche, E., s e e Fillion, G. 393 Rez, P., s e e Manoubi, T. 132 Rhodes, E, s e e Wohlfarth, E.R 298, 306 Rhyne, J.J., s e e Gignoux, D. 342 Ribas, R., s e e Ferrater, C. 158 Richter, HJ. 187 Riedel, A.A., s e e Bacon, EM. 141 Ritter, C. 321 Ritter, C., s e e Arons, R.R. 271,273 Ritter, C., s e e Mondal, S. 320 Rivory, J., s e e Frigerio, J.M. 177 Rivory, J., s e e Martin, M. 177 Roberts, M. de V., s e e Longuet-Higgins, H.C. Rochow, R., s e e Carbone, C. 124, 158 Rodewald, W. 152, 153, 155 Rodriguez Fernandez, J., s e e Ball, A.R. 392 Rodriguez Fernandez, J., s e e Barandiaran, J.M.

366 Roeland, L.W., s e e McEwen, K.A. 350, 351 Roeland, L.W., s e e Meyer, R.T.W. 51 Rojek, A., s e e Cendtewska, B. 184 Ronay, M. 185 Ropars, G., s e e Caulet, J. 187 Ropars, G., s e e Le Corre, A. 187 Rosei, R., s e e Weaver, J.H. 265

32

448 AUTHOR INDEX

Rosenberg, M., s e e Homburg, H. 145 Rosengren, A. 111 Rosenthaler, L., s e e Griitter, P. 148 Rosenthaler, L., s e e Heinzelmann, H. 148 Ross, D.K., s e e Anderson, I.S. 216, 233 Ross, D.K., s e e Beunington, S.M. 234, 269 Ross, D.K., s e e Fairclough, J.P.A. 219 Ross, D.K., s e e Hunt, D.G. 243 Rossat-Mignod, J. 62, 81,401,413 Rossat-Mignod, J., s e e Chattopadhyay, T. 401 Rossat-Mignod, J., s e e Effantin, J.M. 31,359,

397 Rossat-Mignod, J., s e e Jerjini, M. 70, 392 Rossi, D. 184 Rossi, G. 130 Rossi, G., s e e Yeh, J.J. 130 Rossignol, M., s e e Barbara, B. 360 Rossignol, M., s e e Purwins, H.G. 360 Rossignol, M.E, s e e Barbara, B. 67 Rostoker, R., s e e Kohn, W. 12 Rouault, R, s e e Ballou, R. 324 Rouault, P., s e e Berthier, Y. 313 Rouchon, C., s e e Gignoux, D. 371,385, 387 Rouchy, J., s e e Al6onard, R. 394, 395 Rouehy, J., s e e Morin, R 353, 355-357, 394, 396,

397 Roudaut, E., s e e D~portes, J. 321, 322 Roudaut, E., s e e Gignoux, D. 371,385, 387 Roux, J.-Ph., s e e Br~chignac, C. 114 Rowe, J.M., s e e Anderson, I.S. 234 Rowe, J.M., s e e Glinka, C.J. 243 Rowell, J.M., s e e Lowe, W.E 125 Rozendaal, E., s e e McGuiness, P.J. 148 Ruderman, M.A. 3, 415 Rudigier, H., s e e Schlapbach, L. 252, 257 Ruiz, A., s e e Martinez, B. 146 Rumyantsev, A.Yu., s e e Parshin, P.R 243 Runge, E., s e e Zwicknagl, G. 14, 77, 78 Rush, J.J. 243 Rush, J.J., s e e Anderson, I.S. 234 Rush, J.J., s e e Berk, N.E 232 Rush, J.J., s e e Cannelli, G. 232 Rush, J.J., s e e Glinka, C.J. 243 Rush, J.J., s e e Gygax, EN. 232 Rush, J.L, s e e Udovic, T.J. 234, 235, 243 Rustamov, P.G., s e e Efendiev, E.G. 187 Rustamov, R.G., s e e Efendiev, E.G. 187 Ryborg, E, s e e Onsgaard, J. 126, 128-131

Saad, EM., s e e Comer, W.D. 126 Sadikov, I.P., s e e Alekseev, P.A. 339, 341 Saeki, M., s e e Shigeoka, T. 384, 385 Sagasaki, M. 166 Sagawa, M., s e e Yamamoto, H. 151, 152

Sahashi, M. 156, 174 Sahni, VC. 18 Saito, N., s e e Sato, R. 166 Sakaguchi, H. 169-172 Sakaguchi, H., s e e Adachi, G. 140, 170-172 Sakaguchi, H., s e e Shirai, H. 172 Sakai, O. 60, 61, 63, 64 Sakai, O., s e e Harima, H. 32, 33 Sakai, O., s e e Kasuya, T. 13, 59, 60, 6345 Sakaki, Y., s e e Okuno, H. 163 Sakakibara, T. 300, 301 Sakakibara, T., s e e Goto, T. 300, 301,306 Sakakibara, T. , s e e Takayanagi, S. 363, 364 Sakakibara, T., s e e Yoshimura, K. 301 Sakamoto, I. 70, 72-74 Sakamoto, I., s e e Satoh, K. 42, 44, 48, 51 Sakamoto, Y. 182, 184 Sakamoto, Y., s e e Takao, K. 182 Sakatsume, S., s e e Goto, T. 33, 34, 65, 66 Sakatsume, S., s e e Kitazawa, H. 65 Sakatsume, S., s e e Settai, R. 60, 61, 65 Sakatsume, S., s e e Suzuki, T. 33, 34 Sakatsume, S., s e e Takeda, N. 67 Sakurada, S., s e e Kaneko, T. 397 Sakurai, J., s e e Benoit, A. 52 Sakurai, J., s e e Fukuhara, T. 74-76 Sakurai, J., s e e Kamimura, H. 324 Sakurai, J., s e e Nakamura, H. 319 Sakurai, Y., s e e Lii, Z.Y. 156 Sakurai, Y., s e e Okuno, H. 163 Salamanca-Young, L. 189 Salas, EH. 123 Salas, F.H., s e e Alameda, J.M. 145 Salibi, N., s e e Zamir, D. 256 Salo, I.P., s e e Linetski, Ya.L. 174 Sanadze, V.V., s e e Dadiani, T.O. 188 Sanadze, V.V., s e e Dzhabua, Z.U. 188 Sanchez, J.P., s e e Shinjo, T. 158 Sandratskii, L., s e e Uhl, M. 326 Sands, T., s e e Allen Jr, S.J. 186, 187 Sands, T., s e e Palmstrom, C.J. 186 Sankar, S.G., s e e Cheng, S.E 155 Sankar, S.G., s e e Smith, H.K. 137 Sarma, D.D., s e e Hillebrecht, EU. 63 Sarma, D.D., s e e Weller, D. 122 Sarpal, B.K. 112 Sarpal, B.K., s e e Blancard, C. 112, 114 Sase, Y., s e e Ishida, A. 188, 189 Sato, H., s e e Sakamoto, I. 70, 72-74 Sato, K. 362, 363 Sato, K., s e e Isikawa, Y. 85 Sato, K., s e e Maezawa, K. 83, 84, 86, 90 Sato, K., s e e 0nuki, Y. 83, 84, 86 Sato, K . , s e e Umehara, I. 53-58

AUTHOR INDEX 449

Sato, M., s e e 0nuki, Y. 33, 34 Sato, N. 160, 164 Sato, N., s e e Komatsubara, T. 31 Sato, N., s e e Takeda, N. 65, 67 Sato, N., s e e Tanaka, K. 65, 66 Sato, N., s e e Yarnauchi, K. 160 Sato, R. 166 Sato, S., s e e Ishii, T. 3 Sato, T., s e e Nakajima, K. 178 Satoh, H., s e e Sakamoto, I. 73, 74 Satoh, K. 5, 42, 44, 48, 51, 89, 90, 94 Satoh, K., s e e Ebihara, T. 42, 44-46, 48, 49, 51 Satoh, K., s e e Kurosawa, Y. 42, 44, 51 Satoh, K . , s e e Umehara, I. 47-51, 70-72 Satoh, K., s e e Onuki, Y. 74-78, 80, 87-89, 91-93 Satoh, T., s e e Kitazawa, H. 65 Satoh, T., s e e Takahashi, M. 70, 392 Savitskii, E.M., s e e Alekseev, P.A. 339, 341 Savitskii, E.M., s e e Goremychldn, E.A. 339, 342 Savrin, V.D. 109 Saw, C.K. 216, 219 Sawatsky, G.A., s e e Thole, B.T. 114 Sawatzky, G.A., s e e Esteva, J.M. 131, 132 Sayetat, E, s e e D~portes, J. 321,322 Schaefer, W . , s e e Arons, R.R. 281 Schafer, H., s e e Steglich, E 6 Schaudy, G., s e e Gignoux, D. 375, 377, 415 Schefer, J. 225, 273, 277 Schellenberg, L., s e e Kuboth, M. 185 Schelleng, J.H. 167 Schelleng, J.H., s e e Forester, D.W. 168 Schelleng, J.H., s e e Vittoria, C. 168 Schenk, A., s e e Gygax, F.N. 232 Schiffmacher, G. 177 Schiffmacher, G., s e e Gasgnier, M. 132 Sehinkel, C. 300 Schlapbach, L. 210, 252, 257, 265, 266 Schlapbach, L., s e e Fujimori, A. 265 Schlapbach, L., s e e Schefer, J. 225, 273, 277 SchlegeI, H., s e e Krost, A. 188, 189 Schmidt, H., s e e Czjzek, G. 366 Schmidt-May, J., s e e Chorkendorff, I. 116 Schmidt-May, J., s e e Nyholm, R. 116 Schmitt, D. 414 Schmitt, D., s e e Al6onard, R. 355 Schmitt, D., s e e Ball, A.R. 342, 351-353, 375,

377, 378, 380, 386, 391,392, 402-406, 417 Schmitt, D., s e e Barandiaran, J.M. 366 Schmitt, D., s e e Barthem, V.M.T.S. 339-341,

343, 344 Schmitt, D., s e e Blanco, J.A. 365, 370-373, 382,

383, 401-406 Schmitt, D., s e e Bouvier, M. 365, 405 Schmitt, D., s e e Fr6my, M.A. 392

Schmitt, D., s e e Gignoux, D. 297, 300, 345, 366, 369, 371,373, 375-377, 385, 387, 392, 393, 409, 415

Schmitt, D., s e e Jaussaud, C. 355, 356 Schmitt, D., s e e Morin, P. 338, 353, 355-357,

359, 360, 394, 396, 397, 408, 414, 417 Schmitt, D., s e e Radwanski, R.J. 339, 342 Schmitt, D., s e e Reiffers, M. 339-341,351 Schmitt, D., s e e Shigeoka, T. 368 Schrnitt, D., s e e Zhang, EY. 339, 340, 342, 343,

361 Schmitzer, C. 236, 248, 268 Schmitzer, C., s e e Vajda, P. 245, 246, 268 Schnabel, B., s e e Zogal, O.J. 237 Schneider, G. 152 Schneider, G., s e e Fidler, L 152, 153 Schneider, G., s e e Knoch, K.G. 152 Schneider, W.D. 118 Schneider, W.D., s e e Domke, M. 114, 115 Schneider, W.D., s e e Kaindl, G. 115, 117 Schneider, W.D., s e e Moser, H.R. 130-132 Schoenberger, R.J., s e e Belhoul, M. 277 Schoenberger, R.J., s e e Lichty, L.R. 233 Schokawa, J., s e e Sakaguchi, H. 172 Scholz, U.D., s e e McGuiness, P.J. 148 Schotte, K.D., s e e Bred1, C.D. 70 Schreiber, D.S. 236, 237 Schrey, E, s e e Rodewald, W. 155 Schrieffer, J.R., s e e Berk, N. 304 Schr6der, K., s e e W e l l e r , D. 122, 124 Schuller, I.K., s e e Homma, H. 119 Schuller, I.K, s e e Yang, K.A. 119 Schuurmans, M.EH., s e e Daalderop, G.H.O.

313-315 Schwartz, C.L., s e e Palmstrom, C.J. 186 Schwarz, R.B. 180 Schwarz, R.B., s e e Leisure, R.G. 232, 236 Schwarz, W., s e e Andr6, G. 227, 230, 281 Schwarz, W., s e e Pleschiutschnig, J. 234 Schweizer, J. 311 Schweizer, J., s e e Arons, R.R. 271,278, 279,

281 Schweizer, J., s e e Ballou, R. 310 Schweizer, J, s e e Barandiaran, LM. 366 Schweizer, J., s e e Barbara, B. 67 Schweizer, J., s e e Benoit, A. 52 Schweizer, J., s e e Fillion, G. 393 Schweizer, J., s e e Gignottx, D. 309, 310 Scott, C.A., s e e Chowdhury, M.R. 229, 237 Seehman-Eggebert, M., s e e Richter, H.J. 187 Segre, C.U., s e e Croft, M. 181 Seitz, E. 67-69 Selke, W. 399 Sellmyer, D.J. 40, 151, 158, 159, 164

450 AUTHOR INDEX

Sellmyer, D.J., s e e Aylesworth, K.D. 146, 150, 151

Sellmyer, D.J., s e e Jaswal, S.S. 151, 152 Sellmyer, D.J., s e e Shan, Z.S. 158-161, 164, 165 Sellmyer, D.J., s e e Strzeszewski, J. 151 Sellmyer, D.J., s e e Tiwald, T.E. 158 Senoussi, S. 271,273, 277, 279 Sera, M., s e e Kitazawa, H. 60, 63 Serano, C.M., s e e Ronay, M. 185 Seri, H., s e e Sakaguchi, H. 169, 170 Settai, R. 52, 53, 60, 61, 65, 87-89 Settai, R., s e e Goto, T. 65, 66 Seymour, E.EW., s e e Barnes, R.G. 216 Seymour, E.EW., s e e Bamfather, K.J. 237 Seymour, E.EW., s e e Chowdhury, M.R. 229, 237 Seymour, E.EW., s e e Hart, J.W. 233 Seymour, E.EW., s e e Lichty, L.R. 232, 244 Seymour, E.EW., s e e Phua, T.T. 237 Seymour, E.EW., s e e Torgeson, D.R. 233 Shaburov, V.A., s e e Smimov, I.A. 251,264 Shah, J.S., s e e Givord, E 301 Shaked, H. 271,275, 281-284 Shaltiel, D. 285 Shaltiel, D., s e e Daou, J.N. 213, 217, 251,264,

271 Sham, L.J., s e e Kohn, W. 14 Shamir, N., s e e Venkert, A. 179 Shah, Z.S. 158-161, 164, 165 Shah, Z.S., s e e Sellmyer, D.J. 158, 159, 164 Shah, Z.S., s e e Tiwald, T.E. 158 Shapiro, S.M., s e e Lawrence, J.M. 40 Sharnonja, V.G., s e e Loboda, V.B. 120, 134 Shelton, R.N., s e e Klavins, P. 215, 221,225, 226,

229 Shelton, R.N., s e e Xu, Y. 185 Shen, J.X., s e e Shah, Z.S. 164 Shen, 3(. 175 Shenoy, G.K., s e e Carlin, R.L. 275, 281 Shenoy, G.K., s e e Friedt, J.M. 282 Shevlyakov, S.A., s e e Gorodetskii, D.A. 118 Shi, S.Y., s e e Huang, G.X. 150 Shibata, T., s e e Suzuki, Y. 162 Shibutani, K., s e e Sumiyama, A. 4 Shida, H., s e e Kitazawa, H. 41-43 Shiga, M. 323, 324 Shiga, M., s e e Kamimura, H. 324 Shiga, M., s e e Minakata, R. 303 Shiga, M., s e e Muraoka, Y. 303 Shiga, M., s e e Nakamura, H. 319 Shiga, M., s e e Nakamura, Y. 320 Shiga, M., s e e Oomi, G. 321 Shiga, M., s e e Sakakibara, T. 300, 301 Shiga, M., s e e Wada, H. 303, 304, 317-319,

323-325

Shiga, M., s e e Yoshie, H. 311 Shiga, M., s e e Yoshimura, K. 321,323 Shigeoka, T. 368, 380, 382-385, 401 Shigeoka, T., s e e Fujii, H. 380, 381,384 Shigeoka, T., s e e Iwata, N. 368, 374, 375, 401 Shigeoka, T., s e e Nojiri, H. 381 Shigeoka, T., s e e Sugiyama, K. 371 Shijo, T., s e e Hosoito, N. 158 Shikhmanter, L. 179, 181 Shimamori, T., s e e Miyazaki, T. 162 Shimizu, K. 317 Shimizu, M. 297 Shimizu, M., s e e Bloch, D. 300, 301 Shimizu, M., s e e Yamada, H. 301,306, 325 Shimizu, T., s e e Yoshimura, K. 306 Shimizu, Y., s e e ()nuki, Y. 87 Shimoghori, T., s e e Adachi, G. 171 Shimohara, K., s e e Ishida, A. 188 Shin, S.C. 160 Shinar, J. 251,253, 255, 257 Shinjo, T. 158 Shinjo, T. , s e e Hosoito, N. 158 Shinjo, T., s e e Mibu, K. 158 Shinjo, T., s e e Yoden, K. 158 Shinoda, T., s e e Tsunashima, S. 168 Shiokawa, J., s e e Adachi, G. 170-172 Shiokawa, J., s e e Arakawa, T. 144 Shiokawa, J., s e e Sakaguchi, H. 169-172 Shiozaki, I., s e e Sakamoto, I. 73, 74 Shirai, H. 172 Shirane, G., s e e Freltoft, T. 323 Shirane, G., s e e Motoya, K. 323 Shirley, D.A., s e e Mason, M.G. 114 Shivaprasad, S.M., s e e Ashrit, P.V. 133 Shiwaku, T., s e e Kuwano, N. 182 Shoenberg, D. 11, 27 Shohata, N. 361,362 Sholl, C.A., s e e Lichty, L.R. 232, 244 Shopov, V.S., s e e Apostolov, A.V. 127 Shubina, T.S., s e e Volkenshtein, N.V. 271 Shuler, K., s e e Oesterreicher, H. 137 Siari, A., s e e Malterre, D. 182 Siconolfi, D.J., s e e Frankenthal, R.P. 168 Siconolfi, D.J., s e e van Dover, R.B. 168 Siegel, R.W., s e e Li, Z. 110 Sigrist, M. 126, 128 Sima, V., s e e Lebech, B. 373 Singh, A.K. 177 Singh, A.K., s e e Singh, S.K. 169-172 Singh, O. 134 Singh, O., s e e Curzon, A.E. 120, 135, 137 Singh, S.K. 169-172 Singleton, J.H. 141 Sinha, V.L., s e e Cheng, S.E 155

AUTHOR INDEX 451

Sinitsyn, E.V., s e e Borombaev, M.K. 364 Sinnema, S. 329, 336, 337 Sinnema, S., s e e Franse, J.J.M. 336 Sinnema, S., s e e Radwanski, R.J. 336 Sinnema, S., s e e Verhoef, R. 333 Sinnemann, Th., s e e Homburg, H. 145 Skalicky, R, s e e Fidler, J. 174 Skillman, S., s e e Herman, E 9 Skriver, H.L., s e e Boulet, R.M. 52 Slater, J.C. 12 Slisenko, V.V., s e e Goremychkin, E.A. 339, 342 Smereka, T.P., s e e Gonchar, EM. 118 Smereka, T.P., s e e Lozovyi, Ya.B. 119 Smetana, Z . , s e e Borombaev, M.K. 364 Smetana, Z., s e e Lebech, B. 373 Smirnitskaya, G.V., s e e Kozlovskii, L.V. 134 Smimov, I.A. 25 I, 264 Smith, D.A. 182 Smith, H.K. 137 Smith, J.E, s e e Subramanian, RR. 217 Smith, J.E, s e e Thome, D.K. 236, 241,246, 247,

252 Smith, M.E., s e e Barnes, R.G. 216 Smith, R.L. 126 Smith, R.L., s e e Comer, W.D. 126 Smith, R.S., s e e Richter, H.J. 187 Smutek, M. 136 Smutek, M., s e e Boeva, O.A. 136, 143, 240 Smutek, M., s e e CereS,, S. 143 Soda, K., s e e Ishii, T. 3 Sommer, R., s e e Lfithi, B. 357, 358 Sonntag, B., s e e Ltibcke, M. 114 Sonntag, B., s e e Materlik, G. 112 Sorensen, O., s e e Onsgaard, J. 116, 127, 129, 131 Soubeyroux, J.L, s e e BaIlou, R. 324 Southall, J., s e e Jones, P.M.S. 217 Sov~k, P., s e e Ratajczak, H. 157 Spain, G., s e e Franse, J.J.M. 325 Spedding, EH., s e e Beaudry, B.J. 217, 219, 234,

245 Spencer, E.G., s e e Croft, M. 181 Spencer, E.G., s e e Lu, E 181 Springford, M. 81, 92 Springford, M., s e e Chapman, S.B. 92, 94, 95 Springford, M., s e e Hunt, M. 81, 82 Springford, M., s e e Reinders, P.H.R 30, 69, 70 Springford, M., s e e Satoh, K. 42, 44, 48, 51 Springford, M., s e e Wasserman, A. 35 Springfurd, M., s e e 0nuki, Y. 33-36 Sprokel, G.S., s e e Marinero, E.E. 166 Spruijt, A.M.J., s e e Heitmann, H. 168 Srivastava, O.N., s e e Ramak.risna, K. 171 Srivastava, O.N., s e e Singh, A.K. 177 Srivastava, O.N., s e e Singh, S.K. 169-172

Stadelmaier, H.H. 155 Stalinski, B., s e e Bieganski, Z. 283, 284 Stalinski, B., s e e Czopnik, A. 398 Stalinski, B., s e e Drulis, M. 241, 252, 258, 263,

273, 275, 278, 279, 285 Stalinski, B., s e e Kletowski, Z. 52 Stamateli, M.Yu., s e e Glurdzhidze, L.N. 188 Stassis, C., s e e Khatamian, D. 216, 219 Stassis, C., s e e Saw, C.K. 216, 219 Stasfik, Z . V . , s e e Kosak, M.M. l 18, 120 Steglich, E 6 Steglich, E, s e e Bredl, C.D. 70 Steglich, E, s e e Franse, J.J.M. 325 Steglich, E, s e e Gratz, E. 87 Steinbinder, D., s e e Stuhr, U. 237 Stenborg, A. 116, 117 Sticht, J. 81 Stierman, R.J. 246, 271 Stierman, R.J., s e e Gschneidner Jr, K.A. 6, 52 Stierman, R.J., s e e Ikeda, K. 305 Strange, D. 14, 55 Strange, P., s e e Taillefer, L. 26 Strasser, G. 115 Strasser, G., s e e Matthew, J.A.D. 132 StrSssler, S., s e e Perkins, R.S. 312 Strauss, A., s e e Waibel, E 285 Streit, P., s e e Everett, G.E. 394, 411 Strnat, K.J. 328 Stryjewski, E. 345-347 Strzeszewski, J. 144, 151 Stuhr, U. 237 Stunault, A., s e e Fillion, G. 393 Sturdy, G.E. 231 Styles, G.A., s e e Bamfather, K.J. 237 Styles, G.A., s e e Chowdhury, M.R. 229, 237 Styles, G.A., s e e Phua, T.T. 237 Subia Jr, S.R., s e e Bacon, FM. 141 Subramanian, RR. 217 Sudovtsov, A.I., s e e Kuzmenko, V.M. 118, 121,

122 Suezawa, N., s e e Arakawa, T. 144 Suezawa, Y. 167 Suezawa, Y., s e e Gond6, Y. 167 Sugita, Y., s e e Niihara, T. 168 Sugiura, E. 401 Sugiyama, K. 7, 365, 371 Sugiyama, K., s e e Shigeoka, T. 401 Sugiyama, K., s e e Sugiura, E. 401 Sumiyama, A. 4 Sun, W., s e e Hunt, M. 81, 82 Sun, Z., s e e Webb, D.J. 163 Surplice, N.A. 135, 137, 139, 143 Surplice, N.A., s e e Kandasamy, K. 137, 140 Surplice, N.A., s e e Mfiller, J. 140

452 AUTHOR INDEX

Sttryanarayanan, R. 189 Suryanarayanan, R., s e e Das, S.K. 190 Suzuki, A. 166, 168 Suzuki, H., s e e Kitazawa, H. 65 Suzuki, T. 31, 33, 34, 67, 91 Suzuki, T., s e e Endoh, D. 92, 93 S u z u k i , T . , s e e Fukuma, H. 394 Suzuki, T., s e e Goto, T. 33, 34 S u z u k i , T . , s e e Iwamura, E. 150 S u z u k i , T . , s e e Kasuya, T. 13, 59, 60, 63~i5 Suzuki, T., s e e Kitazawa, H. 41-43, 60, 63, 65 Suzuki, T., s e e Kwon, Y.S. 65, 67 Suzuki, T., s e e Nirnori, S. 350 Suzuki, T., s e e Ozeki, S. 65, 66 S u z u k i , T . , s e e Settai, R. 60, 61, 65 Suzuki, T., s e e Takeda, N. 65, 67 S u z u k i , T . , s e e Tanaka, K. 65, 66 Suzuki, Y. 162 Svare, I., s e e Leisure, R.G. 232 Svoboda, P. 387 Swartz Jr, W.E., s e e Holloway, D.M. 142 Switendick, A.C. 243 Switendick, A.C., s e e Mattheiss, L.E 22 Syms, M., s e e Miller, R.E 118, 126, 127 Szofran, ER., s e e Sellmyer, D.J. 40 Szymazek, J., s e e Bohdziewicz, A. 184 Szytula, A. 384 Szytuta, A., s e e Ivanov, V. 384, 385 Szytuta, A . , s e e Vinokurova, L. 382

Tabatabaie, N., s e e Allen Jr, S.J. 186, 187 Tabatabaie, N., s e e Palmstrom, C.J. 186 Taborelli, M. 124 Taborelli, M., s e e LandoR, M. 124 Tada, M., s e e Ohki, C. 240 Tada, M., s e e Toguchi, K. 240 Taillefer, L. 26 Tajika, H., s e e Umemura, S. 159 Takabatake, T., s e e Shigeoka, T. 383-385 Takabatake, T., s e e Sugiura, E. 401 Takada, S. 12 Takahashi, H. 62 Takahashi, M. 70, 162, 392 Takahashi, T., s e e Hosoda, N. 136 Takahashi, T., s e e Kawahata, T. 136 Takahashi, Y., s e e Moriya, T. 305 Takao, K. 182 Takao, K., s e e Sakamoto, Y. 182, 184 Takayama, S., s e e Niihara, T. 168 Takayanagi, S. 90, 94, 363, 364, 389, 390 Takayanagi, S., s e e 0nuki, Y. 90-93, 390 Takeda, H., s e e Isikawa, Y. 85 Takeda, K. 133 Takeda, N. 65, 67

Takeda, N., s e e Kitazawa, H. 65 Takeda, N., s e e Tanaka, K. 65, 66 Takeda, S. 173, 174 Takeda, S., s e e Horikoshi, H. 173 Takeda, S., s e e Komura, Y. 174 Takeda, T., s e e Baba, K. 188 Takeda, T., s e e Nakamura, O. 118, 125 Takeda, T., s e e Takahashi, M. 162 Takei, H., s e e Takahashi, M. 70, 392 Takeshige, M., s e e Sakai, O. 60, 61, 63, 64 Takeshita, T., s e e Ito, T. 229 Takeuchi, A., s e e Barthem, V.M.T.S. 339, 343,

344 Takeuchi, A., s e e Fr6my, M.A. 392 Takeuchi, A., s e e Gignoux, D. 392, 393 Takeuchi, T., s e e Gignoux, D. 371,385, 387 T a l d , K . , s e e Suzuki, A. 166, 168 Takigawa, M., s e e Yoshimura, K. 306, 323 Talianker, M., s e e Shikhmanter, L. 179, 181 Talianker, M., s e e Venkert, A. 179 T a m a k i , A . , s e e Suzuki, T. 33, 34, 91 Tanaka, H., s e e Takahashi, M. 70, 392 Tanaka, J., s e e Kasuya, T. 13, 59, 60, 63-65 Tanaka, K. 65, 66 Tanaka, K., s e e Takeda, N. 67 Tanaka, M. 160, 161 Tanaka, T., s e e Ishizawa, Y. 31-33, 35 Tanaka, T., s e e Nozaki, H. 365 Tanaka, Y. 303 Tang, J. 70, 72 Tang, J., s e e Gschneidner Jr, K.A. 264 Tang, W. 150 Taniguehi, M., s e e Ishii, T. 3 Taniguchi, N., s e e Sakaguchi, H. 169, 170, 172 Tanner, B.K., s e e Smith, R.L. 126 Tanoue, H., s e e Tsukahara, S. 167 Tarascon, J.M., s e e Kasaya, M. 6 Tasaki, A., s e e Umemura, S. 159 Tasset, F., s e e Gignoux, D. 83, 85, 299, 300, 302,

308, 309 Tasset, F., s e e Schweizer, J. 311 Tauner, B.K., s e e Corner, W.D. 126 Taush, M., s e e Materlik, G. 112 Tawara, Y., s e e Fidler, J. 150 Taylor, K.N.R., s e e Krizek, J. 126, 127 Tazaki, A., s e e Miyamoto, K. 157 Teisseron, G., s e e Ferreira, P. 260 Tejada, J., s e e Badia, F. 157 Tejada, J., s e e Ferrater, C. 158 Tejada, J., s e e Martinez, B. 146 Tellefsen, M., s e e Bischof, R. 214, 217 Tellefsen, M., s e e Kaldis, E. 225 Temmerman, W.M., s e e Langford, H.D. 33 Terada, T., s e e Oomi, G. 321

AUTHOR INDEX 453

Terao, K., s e e Uchida, H. t69 Terao, K., s e e Yamada, H. 306 Tessier, M., s e e Krishnan, R. 166 Thaper, C.L., s e e Rush, J.J. 243 Thiry, E, s e e Schlapbach, L. 252, 257, 265, 266 Thole, B.T. 114 Tholence, J.L., s e e Amato, A. 94, 95 Tholence, J.L., s e e Joss, W. 33, 34, 36 Thomas, G., s e e Koestler, C. 150, 151 Thomas, G., s e e Ramesh, R. 150, 151 Thomas, J., s e e Quemerais, A. 127, 129 Thome, D.K. 236, 241,246, 247, 252 Thrush, C.M., s e e Partin, D.L. 188 Thuy, N.R 311,312 Thuy, N.R, s e e Franse, JJ.M. 336 Tian, E, s e e Pan, S.M. 175 Tian, J., s e e Li, L. 152 Tibbetts, G.G. 116 Tibbetts, G.G., s e e Egelhoff Jr, W.E 116, 131 Tilley, D.R., s e e Camley, R.E. 159 Tillman, D., s e e Carbone, C. 124, 158 Tissier, B., s e e Coey, J.M.D. 178 Titcomb, C.G. 225 Tiwald, T.E. 158 Tkach, VI. 110 Tlianker, M., s e e Shikhmanter, L. 179 Togami, Y., s e e Kajiura, M. 157 Togami, Y., s e e Morishita, T. 157, 159 Toguchi, K. 240 Tohyama, T., s e e Yamada, H. 301,306 Toki, K. 178 Tokita, T., s e e Tanaka, M. 160, 161 Tokuhara, K., s e e Yamamoto, H. 151, 152 Toktmaga, M., s e e Fidler, J. 153 Tokunaga, M., s e e Gr6ssinger, R. 153 Tomala, K., s e e Czjzek, G. 366 Tomiyama, R 336 Tomiyoshi, S., s e e Kitai, T. 388 Tomokiyo, Y., s e e Kuwano, N. 182 Torgeson, D.R. 233 Torgeson, D.R., s e e Barnes, R.G. 216 Torgeson, D.R., s e e Bamfather, K.J. 237 Torgeson, D.R., s e e Belhoul, M. 277 Torgeson, D.R., s e e Borsa, F. 237 Torgeson, D.R., s e e Han, J.W. 233 Torgeson, D.R., s e e Leisure, R.G. 232 Torgeson, D.R., s e e Lichty, L.R. 232, 233, 244 Torgeson, D.R., s e e Phua, T.T. 237 Torgeson, D.R., s e e Zamir, D. 256 Torikaehvili, M.S., s e e Huang, C.Y. 185 Tougaard, S. 111, 126, 128 Tougaard, S., s e e Onsgaard, J. 111, 126, 128-131 Tourillon, G., s e e Brouder, C. 159, 165 Tourillon, G., s e e Guilmin, R 165

Toxen, A.M. 163 Toxen, A.M., s e e Webb, D.J. 163 Tran Minh Duc, s e e Frigerio, LM. 177 Tran Mirth Duc, s e e Martin, M. 177 Traverse, A., s e e Mathevet, J.R 180 Trebbia, R, s e e Bmusseau-Lahaye, B. 128, 129 Trebbia, R, s e e Colliex, C. 117, 128-130, 137 Trequattrini, F., s e e Cannelli, G. 232 Tribollet, H., s e e Rayane, D. 114 Trouiller, N., s e e Franciosi, A. 132 Trouiller, N., s e e Raisanen, A. 132 Trouiller, N., s e e Wall, A. 132 Truong, V.V., s e e Ashrit, RV. 133 Truong, V . V . , s e e Chee, K.T. 128, 129 Tsang, T.-W.E., s e e Gschneidner Jr, K.A. 6, 52 Tsang, T.-W.E., s e e Ikeda, K. 305 Tsoukatos, T., s e e Strzeszewski, J. 144 Tsuchida, T., s e e Tanaka, Y. 303 Tsuchiya, R., s e e Gond6, Y. 167 Tsuchiya, R., s e e Suezawa, Y. 167 Tsukahara, S. 167 Tsunashima~ S. 163, 168 Tsunashima, S., s e e Sagasaki, M. 166 Tsuneto, T. 353 Tsushima, K., s e e Kajiura, M. 157 Tsushima, K., s e e Morishita, T. 157, 159 Tsushima, T., s e e Ohkoshi, M. 311 Tsuzuki, S., s e e Uchida, H. 169, 170 Tsvetkov, V.Yu., s e e Linetski, Ya.L. 153 Tukahashi, M., s e e Miyazaki, T. 162 Tur , R . , s e e Daou, J.N. 269 Turek, K., s e e Kakol, Z. 311

Uchi, M., s e e Nojiri, H. 381 Uchida, H. 169, 170 Uchida, H., s e e Hosoda, N. 136 Uchida, H., s e e Kawahata, T. 136 Uchida, H., s e e Kojima, T. 169 Uchida, H., s e e Ohki, C. 239, 240 Uehida, H., s e e Uchida, H. 169 Uchida, H.H., s e e Ohki, C. 240 Uehida, K. 178 Uchiyama, S., s e e Sagasaki, M. 166 Uchiyama, S., s e e Tsun~shima, S. 163, 168 Udovic, T.J. 234, 235, 243 Udovic, T.J., s e e Anderson, I.S. 234 Udovic, T.J., s e e Berk, N.E 232 Ueda, K. 324 Uhl, M. 326 Uji, S., s e e Aoki, H. 76-78 Ukon, I., s e e 0nuki, Y. 87 Umeda, T., s e e Iwamura, E. 150 Umehara, I. 29, 30, 41, 42, 47-58, 70-73

454 AUTHOR INDEX

Umehara, I., s e e Ebihara, T. 42, 44-46, 48, 49, 51

Umehara, I., s e e Kurosawa, Y. 42, 44, 51 Umehara, I., s e e Maezawa, K. 83, 84, 86 Umehara, I., s e e Satoh, K. 42, 44, 48, 51, 89, 90 Umehara, I., s e e ()nuki, ¥. 74-78, 80, 83, 84, 86,

87, 91-93 Umemura, S. 159 Umezawa, A., s e e Onuki, Y. 33-37, 91-93, 95 Umezawa, H., s e e Huang, C.Y. 185 Umino, M., s e e Asano, H. 91 Urbaniak-Kucharczyk, A. 125 Uwatoko, Y., s e e Shigeoka, T. 383

Vajda, E 210, 213, 219, 220, 227, 229, 230, 232, 233, 236-238, 243-246, 251,253-260, 262, 263, 265, 267-271,273, 275, 277-285

Vajda, R, s e e Andr6, G. 227, 230, 281 Vajda, R, s e e Blaschko, O. 215, 219, 220, 234 Vajda, E, s e e Boukraa, A. 275, 282-285 Vajda, R, s e e Burger, J.E 229, 238, 243, 251,

252, 257-261,268, 271,273, 275-277, 283, 285 Vajda, E, s e e Chiheb, M. 221,225, 227 Vajda, P., s e e Danielou, R. 216 Vajda, P., s e e Daou, J.N. 213, 216, 217, 219-221,

225, 229, 233, 238, 239, 241,243-246, 248, 251-253, 255, 258, 261,262, 264, 267-269, 271,273, 275, 277-279, 283, 284

Vajda, R, s e e Lucasson, A. 241,243, 251,252 Vajda, R, s e e Metzger, T.H. 236 Vajda, R, s e e Plesehiutschnig, J. 234 Vajda, R, s e e Ratishvili, I.G. 227 Vajda, R, s e e Schmitzer, C. 236, 248, 268 Vajda, R, s e e Senoussi, S. 271,273, 277, 279 Vajda, R, s e e Shaltiel, D. 285 Vajda, R, s e e Udovic, T.J. 234, 235 van Aken, EB., s e e Buschow, K.H.J. 4 van Alphen, EM., s e e de Haas, WJ. 27 van Daal, H.J., s e e Buschow, K.HJ. 4 Van der Goot, A.S. 301 Van der Kraan, A.M., s e e Gubbens, EC.M. 339 van der Laan, G., s e e Thole, B.T. 114 van der Meulen, H.E 81 van Deursen, A.J.R 33, 34, 36 van Deursen, A.J.E, s e e Joss, W. 33, 34, 36 Van Diepen, A.M., s e e Nasu, S. 40 van Dover, R.B. 168 van Dover, R.B., s e e Frankenthal, R.E 168 van Dover, R.B., s e e Hellman, E 165 van Kempen, H., s e e van der Meulen, H.E 81 van Ruitenbeek, J.M., s e e Joss, W. 33, 34, 36 van Ruitenbeek, J.M., s e e Mtiller, T. 35, 36 van Stapele, R.R, s e e Busehow, K.H.J. 329 van Vucht, J.H.N., s e e Busehow, K.HJ. 177

Varkanova, R.G. 136, 142 Vasilkevich, A.A., s e e Goremychkin, E.A. 339,

342 Velichkov, I.V., s e e Apostolov, A.V. 126, 127 Venkataraman, G.,see Sahni, V.C. 18 Venkert, A. 179 Veres, T., s e e Amara, M. 398 Verhoef, R. 331-333 Verhoef, R., s e e Franse, J.J.M. 350 Verhoef, R., s e e Radwanski, RJ. 331 Verhoef, R., s e e Tomiyama, E 336 Verma, A.R. 172 Vettier, C., s e e Barbara, B. 299 Vettier, C., s e e Blanco, J.A. 370, 371,382, 383 Vettier, C., s e e Rossat-Mignod, J. 62, 81 Vettier, C., s e e Voiron, J. 303 Viallard, R. 240 Viallard, R., s e e Daou, J.N. 212 Victor, Y., s e e Bosca, G. 132 Viescas, A.J., s e e Heeht, M.H. 131 Vinokurova, L. 382 Vinokurova, L., s e e Ivanov, V 384, 385 Vitton, J.P., s e e Krishnan, R. 166 Vittoria, C. 168 Vittoria, C., s e e Forester, D.W. 168 Vittoria, C., s e e Sehelleng, J.H. 167 Vladychkin, A.N., s e e Kuzmenko, V.M. 118, 121,

122 Vogt, O., s e e Rossat-Mignod, J. 62, 401 Voiron, J. 303, 321 Voiron, J., s e e Bloch, D. 300, 301,303 Voiron, J., s e e Gignoux, D. 375, 377, 389, 406,

415 Volkenshtein, N.V 271 V61kl, J. 233 von Boehm, J., s e e Bak, P. 399 yon Molnar, S. 178, 180 Vorderwisch, R 243 Vorderwisch, E, s e e Wegener, W. 234 Vuillet, E, s e e Ferreira, E 260

Waber, J.T., s e e Liberman, D. 9, 21 Wachter, R, s e e Bischof, R. 271,273, 279 Wada, H. 303, 304, 317-319, 323-325 Wada, H., s e e Nakamura, H. 319 Wada, H., s e e Shiga, M. 323,324 Wada, N., s e e Mitsuda, S. 389 Wada, N., s e e 0nuki, Y. 90-93, 390 Wada, N., s e e Takayanagi, S. 90, 94, 363,364,

389, 390 Wadas, A., s e e Griitter, P. 148 Wagner, EE., s e e Waibel, E 285 Waibel, E 285 Waind, P.R. 338

AUTHOR INDEX 455

Wakabayashi, S., s e e Maezawa, K. 90 Westlake, D.G., s e e Carlin, R.L. 275, 281 Wakabayashi, S., s e e ()nuki, Y. 91-93, 95 Westlake, D.G., s e e Friedt, J.M. 282 Waldyama, T., s e e Miyazaki, T. 162 Westlake, D.G., s e e Shaked, H. 271, 275, Wakiyama, T., s e e Takahashi, M. 162 281-284 Walco, R.J., s e e Bacon, EM. 141 Weymouth, J.W., s e e Sellmyer, D.J. 40 Waldrop, J.R. 186 White, R.L. 158, 159 Walker, E., s e e Purwins, H.G. 360 White, R.M., s e e Toxen, A.M. 163 Walker, E., s e e Rossat-Mignod, J. 81 White, R.M., s e e Webb, D.J. 162, 163 Wall, A. 132 Whitehead, J.R, s e e Huang, C.Y. 185 Wall, A., s e e Franciosi, A. 132 Wickersham, C.E., s e e Frausto, RR. 168 Wall, A., s e e Raisanen, A. 132 Wickramasekara, L., s e e Kamprath, N. 155 Wallace, WE., s e e Cheng, S.E 155 Wickramasekara, L., s e e Liu, N.C. 155 Wallace, W.E., s e e Ganapathy, E.V. 301 Wieliczka, D.M. 115, 116 Wallace, W.E., s e e Mansmann, W. 231 Wiesinger, G. 210 Wallace, WE., s e e Pebler, A. 225, 231 Wilkins, J.W., s e e Materlik, G. 112 Wallace, W.E., s e e Smith, H.K. 137 Williams, A.R., s e e Janak, J.E 303 Walmsley, R.G., s e e Webb, D.J. 162 Williams, G.E, s e e Parks, R.D. 181 Walser, R.M., s e e Choe, G. 163 Williams, W.E., s e e Cheng, S.E 155 Wan, H., s e e Fang, R.Y. 157 Willich, E, s e e Heitmann, H. 168 Wang, C.R., s e e Zhao, Z.B. 152 Wilson, K.G. 4 Wang, E E . , s e e Huang, C.Y. 185 Wilting, H., s e e Heitmann, H. 168 Wang, G.A., s e e Huang, G.X. 150 Windmiller, L.R. 30 Wang, R., s e e Tang, W. 150 Windmiller, L.R., s e e Arko, A.J. 31, 33 Wang, Y.J., s e e Shah, Z.S. 164 Winter, H., s e e Shaltiel, D. 285 Wang, Y.Z., s e e Jaswal, S.S. 152 Winzer, K., s e e Reichelt, J. 67, 68 Ward, M., s e e McGuiness, P.J. I48 Wipf, H., s e e Stuhr, U. 237 Wasserman, A. 35 Wipf, H., s e e V61kl, J. 233 Watamura, S., s e e Nojiri, H. 381 Wise, M.L.H., s e e Hirst, J.R. 182 Watanabe, H., s e e Takahashi, M. 162 Wnuk, J.J., s e e Bohdziewicz, A. 184 Watanabe, K., s e e Hashimoto, S. 168 Wohlfarth, E.P. 298, 306, 308 Watanabe, N., s e e Asano, H. 91 Wolf, A . , s e e Jacob, I. 241 Watanabe, T., s e e Takayanagi, S. 90, 94, 363, 364 Wolf, WP., s e e Lea, K.R. 273 Watanabe, Y., s e e Koyama, M. 165 Wood, J.H., s e e Mattheiss, L.E 22 Watanabe, Y., s e e Suzuki, A. 166, 168 Woods, S.B., s e e Kadowaki, K. 5 Waters, K., s e e Rau, C. 123 Woollam, J.A., s e e Tiwald, T.E. 158 Watson, L.M., s e e Gimzewski, J.K. 137 Wortmann, G., s e e Waibel, E 285 Weaver, J.H. 126-129, 265 Wu, L.H., s e e Huang, G.X. 150 Weaver, J.H., s e e Mason, M.G. 114 Wu, R. 122 Webb, DJ. 162, 163 Wu, R.T., s e e Li, D. 123 Weber, K. 369 Wulz, H.G. 136, 169 Wecker, J., s e e Koestler, C. 150, 151 Wyder, R, s e e Mtiller, T. 35, 36 Wegener, W. 234 Wyder, R, s e e Reiffers, M. 339-341,351 Wegener, W., s e e Vorderwisch, R 243

Xia, S.K., s e e Zhao, Z.B. 152 Wehenkel, C., s e e Cukier, M. 128, 129, 131 Wei, W., s e e Lin, H. 379 Xu, Y. 185 Weinert, M. 309, 314 Xu, Y., s e e Cheng, S.E 155

Weller, D. 122-124 Yagi, Y., s e e Sakaguchi, H. 171, 172 Welp, U., s e e Mtiller, T. 35, 36 Yamada, H. 301,306, 325 Wendin, G., s e e Kanski, J. 131 Yamada, K. 5 Wennekers, E, s e e Richter, H.J. 187 Yamagami, H. 13, 75, 77-79, 84-86 Wemick, J.H., s e e Fawcett, E. 26 Yamagami, H., s e e Hasegawa, A. 22, 52-58 Wertheim, G.K. 115 Yamagishi, A., s e e Morin, E 396, 397 West, G.W., s e e Barnes, R.G. 216 Yamagishi, A., s e e Tomiyama, E 336 West, G.W., s e e Torgeson, D.R. 233 Yamaguchi, I., s e e Baba, K. 188

456 AUTHOR INDEX

Yamaguchi, S. 133 Yamaguchi, S., s e e Miyahara, T. 129, 130 Yamamoto, H. 151, 152 Yamamoto, H., s e e Nakamura, T. 162 Yamamoto, K . , s e e Kuwano, N. 182, 184 Yamanaka, S., s e e Hoshi, Y. 168 Yamanaka, S., s e e Naoe, M. 168 Yamashita, M. 388 Yamashita, S. 155 Yamashita, S., s e e Harada, T. 157 Yamauchi, K. 160 Yamazaki, T., s e e 0nuki, Y. 33-37, 91-93 Yanase, A . , s e e Harima, H. 14, 32, 33, 72, 73,

81, 82, 89, 92, 94 Yanase, A., s e e Hasegawa, A. 32, 39, 40, 67-69 Yanase, A., s e e Kitazawa, H. 60, 63 Yanase, A., s e e Kubo, ¥. 14, 36, 37 Yang, D., s e e Li, L. 152 Yang, K.A. 119 Yang, K.Y., s e e Homma, H. 119 Yannopoulos, L.N., s e e Singleton, J.H. 141 Yanson, I.K., s e e Reiffers, M. 339-341,351 Yaremenko, A.V., s e e Loboda, V.B. 120, 134, 137 Yashiyama, M., s e e Honda, S. 164 Yasuoka, H., s e e Yoshimura, K. 323 Yeh, J.J. 130 Yeh, J.L, s e e Rossi, G. 130 Yelon, W.B., s e e Herbst, J.H. 312 Yelon, W.B., s e e Jaswal, S.S. 152 Yin, X.J., s e e McGuiness, P.J. 148 Yoden, K. 158 Yoden, K., s e e Hosoito, N. 158 Yoden, K., s e e Shinjo, T. 158 Yonenobu, K., s e e Morin, P. 396, 397 Yonenobu, K., s e e Shigeoka, T. 401 ¥onenobu, K., s e e Sugiyama, K. 371 Yoshida, H., s e e Kaneko, T. 397 Yoshida, M., s e e Sakamoto, ¥. 182 ¥oshida, M., s e e Takao, K. 182 Yoshie, H. 311 Yoshimoto, Y., s e e Yoshimura, K. 301 Yoshimura, K. 301,306, 321,323 Yoshimura, K., s e e Nakamura, H. 319 Yoshimura, K., s e e Sakakibara, T. 300, 301 Yoshimura, K., s e e Shiga, M. 323, 324 Yoshimura, K., s e e Wada, H. 303, 304, 317-319,

323-325 Yoshizaki, R., s e e 0nuki, Y. 95 Yoshizawa, H., s e e Mitsuda, S. 389 Yoshizawa, M., s e e Ikeda, K. 305

Yosida, K. 3, 415 Yosida, K., s e e Yamada, K. 5 Yosida, Y., s e e Sato, K. 362, 363 Yosuoka, H., s e e Yoshimura, K. 306 Yu, S.E, s e e Huang, G.X. 150 Yuldasheva, M.Kh., s e e Reshentnikova, L.V. 118 Yurasova, V.E., s e e Bachurin, V.I. 125 Yuzurihara, H., s e e Tanaka, M. 160, 161

Zachariasen, W.H., s e e Ellinger, EH. 110 Zajac, S. 125 Zalesky, M.P., s e e Jensen, C.L. 245 Zamir, D. 256 Zdansky, E., s e e Andersen, J.N. 116 Zema, N., s e e Sigrist, M. 126, 128 Zemirli, S., s e e Gratz, E. 87 Zemlyanov, M.G., s e e Parshin, P.R 243 Zerguine, M., s e e Gignoux, D. 369, 375, 376 Zhai, H.R., s e e Gu, B.X. 145 Zhang, EY. 339, 340, 342, 343, 361,403, 404 Zhang, EY., s e e Ball, A.R. 375, 377, 378, 380,

386, 404, 417 Zhang, EY., s e e Gignoux, D. 371,375, 377, 385,

387, 392, 393, 415 Zhang, EY., s e e Radwanski, R.J. 339, 342 Zhang, EY., s e e Shigeoka, T. 368 Zhang, X.J., s e e McGuiness, P.J. 148 Zhao, K.L., s e e Takao, K. 182 Zhao, Z.B. 152 Zhao, Z.B., s e e Pan, S.M. 175 Zhao, Z.R., s e e Aylesworth, K.D. 146, 150, 151 Zhao, Z.R., s e e Strzeszewski, J. 151 Zhavoronkova, K.N. 136 Zhavoronkova, K.N., s e e Boeva, O.A. 136, 143,

240 Zheng, C.H., s e e Huang, G.X. 150 Zhong, X.P., s e e Tomiyama, E 336 Zhou, S., s e e Tang, W. 150 Zhu, J.G. 186 Zhukova, T.B., s e e Smimov, I.A. 251,264 Zhuravski, V.E., s e e Bachurin, V.I. 125 Ziebeck, K.R.A., s e e D6portes, J. 323 Zochowski, S.W., s e e MeEwen, K.A. 391 Zogal, O.J. 221,225, 231,237 Zolandz, A., s e e Croft, M. 181 Zomack, M., s e e Baberschke, K. 122 Zomaek, M., s e e Farle, M. 123 Zukowska, K., s e e Idczak, E. 128 Zwicknagl, G. 14, 77, 78 Zygmunt, A., s e e Ivanov, V. 384, 385

SUBJECT INDEX

acoustic lattice vibrations 239 • zoustic phonons 248 activation energy 232 - for diffusion 232, 233 c~-ErHx 248 c~*-ErH x 268 «-ErH(D)x 236 «*-ErH(D)x 219 c~*-HOHx 267 ~-LuD x 216 c~*-LuD x 219 c~*-LuH x 219, 246, 271 c~-LuH(D)x 235 c~*-LuH(D, T)x 244 c~-phase 208 c~*-phase 211 c~-RHx 215, 244 cd-RH(D)x 219, 232 «*-RH(D, T)x 220 c~-ScDx 216 cd-ScD x 219 c~-ScHx 232 c~*-SCHx 271 e~*-ScH(D)x 219 c~-TmD x 216 cx-TmH x 248 c~-YD x 216 (x*-YD x 219 ~x-YH x 215 (x*-YH(D)x 244 « --+ ~ transformation 212, 214 anionic model 243 ANNNI model 399 anomaly temperature 219 anticrossing 351,360 antiferromagnetic (AF) interactions 257 antiferroquadrupolar ordering 359, 394, 408 antiphase structure 373, 385, 409

band structure calculations, s e e energy band calculations

B-phase 208 ~3-RH2_ 6 213

-RH2 244 ~-RH2+x 212, 244

457

B-TbH(D)2+x 227 B/(13 +'~) phase boundary 263 B ---+ -~ transformation 214

Ce-H 214 CeAI2 68-70 CeAs 60, 65, 67 CeB 6 31, 34-36 CeBi 60 CeCu 2 88, 90 CeCu6 91, 92, 95 CeCu2Si2 82 CeD2+x 225 CeGa2 71-73 CeH2+x 209, 212, 221,256 CeH3_x 209 CeH(D)2+x 229 CeIn3 41, 44-46, 48 CeNi 83-86 CeRu2Ge2 75, 76, 78 CeRu2Si2 75, 76, 78-80 CeSb 60, 62, 64, 65 CeSn3 52, 54, 56, 58 (Co/(Pr, Nd))n films 162 (Co/Dy)n films 164 (Co/Gd)n films 162 (Co/R)n films 162 Co-Er quasicrystals 185 colleetive electron metamagnetism 298-308 commensurate structure 409 compensated metal 26 critical field 300, 332, 349 critical point 346 critical temperature 212 cross-sectional area of Fermi surfaee 28 crossing 350, 351,353, 360 crystalline electric field (CEF) 209, 267, 338,

350, 367, 373 crystalline state of R films on substrates 122 crystallographic parameters 218 crystallographic properties of R-Pd alloys 182 cyclotron mass 28

de Haas-van Alphen (dHvA) effect 27 - CeA12 8, 67-70

458 SUBJECT INDEX

de Haas-van Alphen (dHvA) effect (cont 'd)

- CeAs 8, 60, 65, 67 - CeB 6 8, 31, 33-35 - Ceßi 8, 60, 62, 65

- CeCu2 8, 87-90 - CeCu6 8, 90-95

- CeCu2Si2 8, 81, 82 - CeGa 2 8, 70-73 - Celn 3 8, 40-46, 48 - CeNi 8, 82-87

- CeRu2Ge2 8, 75, 76 - CeRu2Si2 8, 75-81 - CeSb 8, 60, 62-65 - CeSn 3 8, 52-59 - frequency 28

- Gdln 3 8, 41, 48, 50, 51 - GdSb 8, 60, 65, 66 - LaAg 8, 38, 39 - LaA12 8, 67-69

- Laß6 8, 30-35 - LaBi 8, 60, 61 - LaCu 6 8, 91-95 - LaCu2Si 2 82 - LaGa2 8, 70-73 - Laln3 8, 41-43, 48 - LaNi 8, 82-87 - LaRu2Ge2 8, 74-76 - LaRu2Si 2 8, 74-76, 81 - LaSb 8, 60, 61, 65 - LaSn3 8, 29, 52-54, 56-59

- NdB6 8 , 3 1 , 3 5 - 3 7 - NdCu6 8, 90-93, 95 - Ndln 3 8, 41, 47-49

- PrB 6 8, 31, 33-35 - PrCu 6 8, 90-92, 95 - Prln 3 8, 41, 47, 48 - PrNi 8, 82, 83, 86 - PrSb 8, 60, 65, 66 - SmCu2 8, 87, 88, 90 - SmCu6 8, 90-93, 95 - SmGa2 8, 71, 73, 74 - Smln 3 8, 41, 48-50 - SmSb 8, 60, 65, 66 - YA12 8, 68, 69 - YCu2 8, 87-89 - YZn 8, 38-40 - YbAs 8, 60, 65, 67 demagnetizing field 347 deuterides 140, 141,216-265, 272, 274-277,

280-283 devil's staircase 62, 400 dHvA, see de Haas-van Alphen effect Dingle temperature 28 DyH2+x 230, 260

easy-axis anisotropy 367, 401 easy-plane anisotropy 335, 390 eleetric resistivity in LaNi 5 170 electrical properties of RH 2 137-139 electrieal properties of R metal films 120 electronic configurations

- gaseous atom (vapor) 112 - metallic 112 - neutral atom 10 - trivalent ion 10 electronic specific-heat coefficient 6, 31, 38, 41,

52, 60, 68, 71, 75, 83, 88, 91,236, 244 endpoint 346, 376 energy band calculations

- CeA12 8, 67-70 - CeAs 8, 60, 65, 67 - Ceß6 8, 31, 33-35

- CeBi 8, 60, 62, 65 - CeCu 2 8, 87-90 - CeCu6 8, 90-95 - CeCu2Si2 8, 81, 82 - CeGa z 8, 70-73 - CeIn 3 8, 40-46, 48 - CeNi 8, 82-87 - CeRu2Ge2 8, 75, 76 - CeRu2Si2 8, 75-81 - CeSb 8, 60, 62-65 - CeSn 3 8, 52-59 - Gdln 3 8, 41, 48, 50, 51 - GdSb 8, 60, 65, 66 - LaAg 8, 38, 39 - LaA12 8, 67-69

- LaB 6 8, 30-35 - LaBi 8, 60, 61 - LaCu 6 8, 91-95 - LaCu2Si2 82 - LaGa2 8, 70-73 - LaIn3 8, 41-43, 48

- LaNi 8, 82-87 - LaRu2Ge2 8, 74-76 - LaRu2Si 2 8, 74-76, 81 - LaSb 8, 60, 61, 65 - LaSn 3 8, 29, 52-54, 56-59 - NdB6 8, 31, 35-37 - NdCu6 8, 90-93, 95 - Ndln 3 8, 41, 47-49 - PrB6 8, 31, 33-35 - PrCu6 8, 90-92, 95

- PrIn 3 8, 41, 47, 48 - PrNi 8, 82, 83, 86 - PrSb 8, 60, 65, 66

- SmCu2 8, 87, 88, 90 - SmCu 6 8, 90-93, 95 - SmGa2 8, 71, 73, 74

SUBJECT INDEX 459

energy band calculations (cont'd)

- SmIn 3 8, 41, 48-50 - SmSb 8, 60, 65, 66 - YA12 8, 68, 69 - YCuz 8, 87-89 - YZn 8, 38~40

YbAs 8, 60, 65, 67 energy gap 251 epitaxial crystal growth 118 ErHz+x 239, 251 ,261,263 Er0.sHo0.5 Rb.4B 4 184 ErRh4B4 184 exchange interaction 330, 334, 414 external field 347

fan structure 410 fcc phase of R metals 133 (Fe/Gd)n films 159 (Fe/R)n films 157 (Fe/Tb)ù films 160 (FeFFm)n films 161 Fermi surface

- intermetallie compounds 1-98 - metals with dissolved H 243 ferromagnetic films 125 ferromagnetism 338, 359 ferroquadrupolar ordering 356, 357, 408 first-order magnetie transition 356 first-order transition 345, 347 flopside strueture 394, 411 frustration 310, 316, 411

gadolinium compounds 363 GdH2+x 221,230, 251,259 GdH(D)2+x 230, 237 GdIn 3 41, 48, 51 GdSb 60, 65, 66

heat capacity, see also electronic specific-heat eoefficient 282

helical structure 364, 412 HoA1Ga 385, 403 HoD x 246 HoD 3 231 Hort x 246 HoH2+x 239, 251,261 hydrides 135-140, 208-215, 221-231,236-243,

248-265, 271-286 see also ~3-XX and the specific rare-earth

hydride - atomic configuration 248 - atomic volume 235

CF-excitations 273

- carrier hopping 264 - characteristic magnetic temperatures 272, 274,

275 - charge transfer 265 - eoherent-incoherent transformation 275 - eommensurate components 284 - commensurate phase 268, 281 - complex antiferromagnetic (AF) structures

277, 284 - Compton profiles 265 - critical concentrations 211 - crystal field (CF) 209, 267 - - splitting 277 - cubic-to-tetragonal deformation 214 - de Germes faetor 273, 286 - "defect" migration 236 - "defect"-recovery 237 - deloealized band 251 - density of stares 248 - differential thermal analysis (DTA) 227

dihydrides (f3-phase) 208-214, 221-232, 236-244, 248-267, 271-285

- EPR 256 - effective gap 263 - electrical properties of RH2 137-139 - electron-phonon coupling 239 - electronic properties 243-265 - enthalpy for dihydride formation 239 - f-electmn spins 273 - ferromagnetie (FM) interactions 257

fluctuating valence 263 - formation enthalpy 241 - 5-phase 208, 214, 231 - gap 251 - Gorsky effect 232 - ground state 277 - grormd-state magnetic moments 273 - ground-state resistivities 273

Gffmeisen law 239 - Grüneisen temperamre 239 - heat capaeity 282 - heavy fermions 209 - hydrogen sublattice 209 - hydrogen trapping 227 - hydroxides 213 - incommensuracy 273, 279 - incommensurate - - components 284 - - magnetic structure 277

- - phase 281 - intermediate structure 282

ionicity 236 - isothermal plateau 213 - kinetie properties 232-243

460 SUBJECT INDEX

hydrides (cont'd)

- Kondo

- - effect 210, 273, 276

- - lattice 209

- - max ima 276

- - min ima 276

- - transition 275

- X-type peaks 278

- lattice expansions 221

- lattice parameters

- - 13-RH2 222-225

- - "/-RH2+x 231 - l iquid phase 213

- local ized states 251

- local ized vibrational modes 241

- magnet ic anomalies 276

- magnet ie configuration 273

- magnet ic fluctuations 283

- magnet ic ground stare 277

- magnetie ordering 260 - magnet ic phase diagram 257, 273

- magnet ie properties 271-285

- magnet ic transformation 273

- metal - insula tor (M-I ) transition 209, 239

- metal -semiconductor (M-S) transition 244,

251

- mixed valence 264

- modulat ion 275

- l~+-diffusion 236

- muons 232 - neutron scattering 273

- nonmagnet ic first excited stare 277

- O sites 214

- octahedral H atoms 209

- octahedral site 208

- optical phonons 248

- optieal spectroscopy 265

- optical vibrations 243

- order--disorder transformation 209

- ordering temperatures 227

- orthorhombic CF distortion 277

- orthorhombie dihydrides 231

- orthorhombic structure 208

- overlap region 284

- paramagnet ism 209

- percolation 264

- perturbed angular correlation 261 - phase diagram 209, 214, 215

- phonon scattering 277

- photoelectron spectroseopy 265 - potential barrier 237

- preparation 210-214 - propagation vector 275

- proton NMR 277

- quench-induced disorder 261 - quenching effects 281

- RKKY exchartge interaction 209, 277

- resistivity isothermals 247

- semiconduetor-metal (S-M) transition 254

- short-range ordered spin fluctuations 273

- single erystals 212

- sinusoidal incommensurate magnetic structure

281

- solubili ty l imit 213

- solution enthalpy 239

- solution entropy 239

- spin axis 283

- spin disorder 248

- spin-disorder resistivity 271 - spin glass 264, 277

- spin wave 257 - stoichiometric composit ion 227

- stoichiometrie defieit 212

- structural disorder 278 - structural transformations 239

- structure 216-231

- sublatfice ordering 214

- superconductivity 256

- superstoichiometric dihydrides RH2 +x 209

- T sites 214

- tetragonal distortion 221

- tetrahedral H atoms 209

- tetrahedral site 208

- thermal conduetivity 264

- thermodynamie properties 236-243

- thermoelectric power 264 - trihydride (',(-phase) 208, 214, 231

- uniaxial anisotropy energy 277

- Van Vleck compound 285

- Van Vleck paramagnet 285

- variable-range hopping 251

- weak localization 254

- x-atoms 214 - x-sublattice 221

hydrogen absorption in LaNi5 169

hydrogen dissolved in R (a-phase) 208-221,

232-236, 244-248, 2 6 7 - 2 7 1 , 2 8 6 see also (x-XX and the speeific rare-earth metal

(e.g. La-H)

- b-axis 219

- basal plane 219 - binding energy 219, 221

- blocking effects 232

- c-axis 219 - c-axis modulated (CAM) structure 268

- c/a-ratio 217 - earrier density 243 - chain ordering 235

SUBJECT INDEX 461

hydrogen dissolved in R (a-phase) (cont'd) - chains 219 - conduetion-electron density 243 - eritieal temperature for phase transitions 211 - erystallographic parameters 218 - D - D pairs 219 - Debye temperature 232 - deuterium 221 - diffuslon process 234

- effective magnetie moments 267 - Einstein temperature 232 - eleetron density 266 - electron irradiation 232 - electron-phonon coupling 244 - electronie density 244

- electronic properties 244-248 - electronie speeifie-heat coeffieient 236, 244

- electronic structure 265 - energy for "defect" formation 234 - expansivity 216 - Fermi surface 243 - ferrimagnetie ordering 270 - ferrimagnetic-ferromagnetie transition 269 - ferrimagnetism 269

- ferromagnetic eone 268 Gorsky effect 232

- H - H pairs 215 - H-eonfigurations 220 - H-"defeet" reeovery 232 - heat ofsolu t ion 235

- helieoidal strueture 268 - "hydridie" model 243 - hydrogen "defects" 232 - hydrogen isotope 244 - hydrogen loeal mode energies 242 - hydrogen ordering 209 - hydrogen solubility 211 - hydrogen ttmneling 271 - hydrogenation 211,213 - inelastie energy loss 235

- inelastic relaxation 232 - interatomie potential 219

- intermediate phase 268 - internal frietion 210

isothermals 244 isotope effect 219

- kinetic properties 232-236 - lanthanide contraction 211 - local mode energy 235 - Iocalized motion 232 - lock-in transitions 268 - long-range-ordered (LRO) struetures 219 Kondo - magnetic anomaly 267, 268 - effect - magnetic properties 267-271 - lattice

- magnetic structures 267 - magnetic superzone 270 - magnetic susceptibility 247, 267

- magnetic transitions 267 - magnetization 268

- magnetoelastic interactions 267, 268 - magnon 268

magnon excitation 271 - migration energy 233 - Néel temperature 246 - nesting 243

neutron seattering 209 order~tisorder process 234

- pair-binding energy 232 - paramagnetic Curie temperature 267 - paramagnetism 269, 271 - peak temperature 232

- phase diagram 209, 214, 215 - photoelectron spectra 266 - preparation 210-212 - protonic model 243 - quenehing 232 - RKKY exchange interaction 209, 266 - recovery stage 232

- relaxation times 232 - residual resistivity 245 - resistivity anomaly 219 - short-range order (SRO) 219 - solid solution 208 - solubility limit 211 - spectroseopy 244

- spin fluctuations 271 - spin-slip structure 268 - spin-wave exeitation gap 271 - structure 216-22t - superconductivity 244 - superstructure 219 - thermodynamic properties 232-236 - tritium 221 - tunneling 232 hydrogen gaseous contarninants in R-TM films

167

hydrogen separation and permeation in LaNi 5 171 hysteresis 349, 389, 406

incommensurate magnetic structure 370, 399-406, 409

internal field 347 ion implantation 167 itinerant ferromagnetism 308

277, 365,

4 ~ , 210, 273, 275, 276, 285 6, 209, 285

462 SUBJECT INDEX

Kondo (contä) - maxima 276

- minima 276 - regime 4-6

- transition 275 Kondo lattice compounds - CeA12 6, 69, 70 - Ceß6 6, 30, 31, 33-35 - CeCu2 6, 34, 87, 89, 90 - CeCu6 6, 90-95 - CeCu2Si 2 6, 81

- Celn3 6, 40-46, 48 - CeNi 6, 83-86

- CeRu2Si 2 6, 75-81 - CeSb 6, 59-65 - CeSn 3 6, 52-59

La-H 214 LaAg 38, 39 LaAlz 68, 69 Laß 6 31, 32, 34, 35 Laßi 60 LaCo 1 _ ~ 309 LaCu 6 91, 94, 95 LaCu2 Si2 82 LAD2+ x 255 LaGa2 71-73 LaH2_x 256 LaH 2 256 LaH2+ x 221 ,251 ,256 LaH3 -x 209 LaH(D)2+x 229 Laln3 41-43, 48 LaNi 83-86 LaNi5 169 - electric resistivity 170 - hydrogen absorption 169 - hydrogen separation and permeation 171 LaRu2Ge2 75, 76 LaRu2Si2 75-77 LaSb 60, 61, 65, 67 LaSn 3 29, 52, 53, 56, 58 lead-europium films 188 lead-ytterbium films 190 long-period commensurate structure 370 Lu-H 214 Lu2Fe 3 Si 5 185 LuH2+x 264 LuRhl.2Sm4 184

magnetic anisotropy 310-316, 322, 331-337 magnetic domain structure 126, 147 magnetic instability 297, 317, 318 magnetic phase diagram 257, 273, 345-398, 401

magnetic properties see also specific topic

- of H in R 267-271 - of HoA1Ga 385, 403 - of incommensurate magnetic systems 277,

399-406 - ofintermetallic compounds 6, 31, 38, 41, 52,

60, 68, 71, 75, 83, 88, 91,293-417 - of LaCol_e 309 - ofmetamagnets 298-308, 336, 345-398 - of PrCo2Si2 380, 401 - of PrGa2 377, 380, 391 - ofPrNi 5 351 - of PrNi2Si 2 373, 403 - o f R alloys 145 - o fRCo 2 299, 303, 304 - of RCo5 311 - o f R H 2 140, 271-285

- of RMn2 316 - ofRNi 5 338 - of TbNi2Si 2 403 - of ThCo5 301

- of thin films - - alloys 144-167 - - metals 122-126 - of TmGa3 397 - of TmSb 350 - o fYNi 3 308 magnetic state 298, 319, 325 magnetic structures 267, 345-398 - amplitude-modulated 370, 373, 386, 408

- - specific heat 405 - anisotropy 269 magnetlc transitions, see also metamagnetic

transition and metamagnetism 267 magnetocrystalline anisotropy 310-316, 322-337 magnetoelastic effects 303, 317 magnetostriction 303 mass enhancement factors 24 metallic R alloys 144 metalloid R-compounds 186 metamagnetic transitlon 298, 300, 306, 336 metamagnetism 345-398

- collective electron 298-308 - multistep 380, 392, 401,413 mixed structure 320, 326 modulated and multilayered films 157 multi-Q structure 413 multiaxial structure 394, 413 multilayer (Er, Tm/Lu)n films 125 multilayer systems, other 165

NdB6 31, 35-37 NdCu6 91-93, 95

SUBJECT INDEX 463

NdFeB - crystallographic properties 150 - hydrogen treatment 148 NdklFe4B4 150 Nd2Fe14B 145 NdI-I2+x 229, 239, 258 NdIn3 41, 48-50 nesting conditions 279 neutron diffraction 273 (Ni/Ce)n layers 165 (Ni/Dy)n layers 165 (Ni/R), films 165 Ni3Mo-type structure 209, 227 noncollinear structure 336, 362, 365, 391,395,

409 noncompensated antiphase structure 375, 377 nonmagnetic state 298, 317, 319, 325

optical properties of R metal films 126 optieal spectra (0-t200eV) 126

periodic field model 402 permanent magnets 144 phase diagram 208, 210 - magnetic 346 piezoresistance of foils 132 polytypic structures 172 Pr-H 214 PrB 6 31, 34, 35 PrCo2Si 2 380, 401 PrCu6 91, 92, 95 PrGa2 377, 380, 391 PrH2+x 239, 258 PrIn3 41, 47, 48 PrNi 83, 86 PrNi 5 351 PrNi2Si 2 373, 403 PrSb 60, 65, 66

quadrupolar interactions 355 quadrupolar moment 413 quasicrystal Co Er 185

R-H 207-286 R-hoble metal alloys (Cu, Au) 177 R-Pd alloys 181 - crystallographic properties 182

valence change in 181 RA12 68 RAs films 186 RBi films 188 R clusters 114 RCo2 299, 303, 304 RCo5 144,311 - hydrogen storage films 169

R2Co17 333 RCo(B) amorphous films 156 R crystallographic properties 118 RH(D)0.2 235 RKKY exchange interaction 209, 266, 277 R layers on crystals 115 RMn2 316 RNi5 144, 338 - hydrogen storage films 169 RsOs4Si15 185 R/Re systems 119 RSb films 188 RTiFe(Co) alloys 155 R/V systems 119 R/W systems 118 rare earth metal films 111 - reactivity with CO, CO2 and CnHn 143 rare earth nitrides 142 rare earth trialuminides 177

samarium-cobalt polytypes 174 samarium-nickel polytypes 173 ScH(DL 245 scattering lifetime 28 second-order transition 346 singlet ground stare 350, 373 Sm2(Co, Fe, Zr)17 145 SmCu 2 88 SmCu6 91-93, 95 SmGa2 71, 73 SmH2+x 221,258 SmIn3 41, 48, 51 SmSb 60, 65, 66 spin-flip transition 367, 373, 380, 415 spin-flop transition 363, 416 spin fluctuations 304, 323 spin-slip transition 379, 380, 417 Stoner factor 298 structural properties 210 superconducting materials 184

TbD2 213 TbD2+x 230 TbH2 +x 259 TbNi2Si2 403 ThCo5 301 thin films 105-190 - addition effects of elements 152-155 - amorphous 121, 122, 125, I26, 156, 157 - hydrides 135-140, 169-172 - metallic alloys

- n o b l e metal 177-181 ù palladium 181-184 - - permanent magnet 144-157

464 SUBJECT INDEX

thin films (cont'd) - metalloid 143, 144, 186-190 - metals - - crystallography 118, 119 - - electrical properties 120-122 - - magnetic properties 122-126 - - optical properties 126-132 - - reactivity 133, 134 third-order magnetic suseeptibility 353, 355

TmGa3 397 TmSb 350 transverse magnetoresistance 26 triangular structure 309 tritides 140, 141,221

U-R films 185 uncompensated metal 26

valence change in R-Pd alloys 181 valence-fluctuation regime 6 valence in vapor and solid stare 111 very weak itinerant ferromagnetism 308

Y, La-Pb multilayers 185 Y-H 214 YA12 68 YCu2 88, 89 YH2+ x 209, 221,251 YH(D)x 246 YNi 3 308

Y4Os4SiI3 185 YZn 38, 40 YbAs 60, 65, 67 YbH2+x 263

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Handbook on the Physics and Chemistry of Rare Earths

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