A Mossbauer Spectroscopy and Magnetometry Study of Magnetic Multilayers ... · A M ossbauer...

A Mossbauer Spectroscopy and MagnetometryStudy of Magnetic Multilayers and Oxides

John Bland, M.Phys. (Hons)

Submitted in partial fulfilment of the requirements of the degree ofDoctor of Philosophy

Oliver Lodge Laboratory,Department of Physics, University of Liverpool

September 2002

Abstract

A study of the magnetic properties of thin films, multilayers and oxides has beenperformed using Mossbauer spectroscopy and SQUID magnetometry. The systemsstudied are DyFe2, HoFe2 and YFe2 cubic Laves Phase thin films, DyFe2/Dy andDyFe2/YFe2 multilayers; Ce/Fe and U/Fe multilayers; and iron oxide powders andthin films.

CEMS results at room temperature show a low symmetry magnetic easy axisfor all of the Laves Phase samples studied. Analysis of the dipolar and contacthyperfine fields show that this axis is close to the [241] and [351] directions butcannot be fully determined. The spin moments lie out of plane in all samplesby approximately 22◦, indicating a significant magneto-elastic anisotropy. 2.5 kGinplane applied field measurements indicate a much larger magnitude of magne-tocrystalline anisotropy in the DyFe2 system than in the YFe2 system. In theDyFe2/YFe2 multilayer samples the anisotropy is dominated by the dysprosiumsingle-ion anisotropy, propagated through the antiferromagnetic coupling with theiron moments and then through the YFe2 layers by the strong iron-iron exchangecoupling. The DyFe2(50 A)/YFe2(50 A) sample shows average hyperfine fields con-sistent with the DyFe2 and YFe2 thin film results, whilst samples with thinnerlayers show an enhanced hyperfine field of up to 17%. The DyFe2/Dy multilayershave identical zero field properties to the DyFe2 thin film system down to a DyFe2

thickness of 50 A. In all samples studied under applied field the hyperfine fieldswere reduced from their zero field values.

SQUID magnetometry results from the Ce/Fe multilayers show that most of thesamples exhibit antiferromagnetic coupling, with a TN ranging between 125 K and190 K, dependent upon both cerium and iron layer thicknesses. The exchange cou-pling constant, J(z), has been calculated for antiferromagnetically coupled samplesand shows an oscillatory z dependence. CEMS results from the U/Fe multilayersshows that each iron layer is composed of BCC iron, a poorly-crystalline iron layerwith a reduced hyperfine field of up to 3%, and a doublet from a paramagneticUFe2 layer. The relative thicknesses of these layers scale nonlinearly with the thick-ness of the deposited iron layer below 60 A. Above this thickness the disorderediron and UFe2 layers reach maximum thicknesses of 20 A and 18 A respectively.Where the uranium layer has poor crystalline growth this is propagated into theiron layer and increases these thicknesses.

Room temperature Mossbauer spectroscopy results from a selection of printertoner powders were used to produce the ratio of magnetite to maghemite in thepowders. CEMS results on magnetite thin films showed good crystal growth ona Pt(111) substrate, with some iron forming a non-magnetic layer diffused in theplatinum. Magnetite deposited on Al2O3(0001) substrates showed good crystalgrowth when using an oxygen plasma source, but that from a normal sputteringsource showed a distribution of hyperfine fields and a paramagnetic contributionfrom iron substituting for aluminium in the substrate.

Acknowledgements

First and foremost I offer my sincerest gratitude to my supervisor, Dr MikeThomas, who has supported me thoughout my thesis with his patience andknowledge whilst allowing me the room to work in my own way. I attributethe level of my Masters degree to his encouragement and effort and withouthim this thesis, too, would not have been completed or written. One simplycould not wish for a better or friendlier supervisor.

In the various laboratories and workshops I have been aided for manyyears in running the equipment by Keith Williams, a fine technician who keptme in sample holders and liquid helium against all odds. The smooth runningof the Mossbauer laboratory is much more a testament to his efforts than myown. Simon Case and Gaby Milford helped tutor me in the more esotericmethods necessary to run Mossbauer spectrometers and how to analyse thedata from them. Dr Jon Goff gave useful guidance in the use of the SQUIDmagnetometer along with Pascale Deen, and her ingenious sample holderconstruction. As well as keeping me stocked with general supplies, PeterDavenport has also inadvertently, and without fail, provided something muchgreater in all the years I’ve known him: a friendly smile and a hello everytime we met.

Drs Ward and Wells have provided me with all of the Laves Phase MBEsamples covered in this thesis as well as many others, with consistent quality.Professor Bowden has offered much advice and insight throughout my workon Laves Phase systems. Drs F. Schedin, P. Morrel and G. Thornton providedme with the magnetite thin films I studied.

In my daily work I have been blessed with a friendly and cheerful group offellow students. Pascale Deen, as well as SQUID information, has providedgood arguments about Physics theory and helped me regain some sort offitness: healthy body, healthy mind. Adina Toader often made sure noneof us starved and Simon Lee made sure none of us went thirsty (or sober).Tarek (Taz) Nouar kept us entertained with his huge repertoire of anecdotesand stories. Mark Gallagher amused us with his dry wit and a great no-nonsense Christmas shindig (and did a good job of trying to kill me withsnakebite and black). Stuart Medway was a good companion on an otherwiseexhausting and disappointing experiment in Grenoble and although he didonce explain the difference between League and Union rugby I must confessto have forgotten every word since. Matt Ball has had the good grace topester me much less than average with computer questions and pulls a goodpint in the Cambridge. Jonathan Pearce helped me get on the road to LATEXand provided an experienced ear for my doubts about writing a thesis. PeterNormile has fascinated me with his ability to break computer systems but has

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also given me detailed discussions on physics theory and some good laughs.In many ways I have learnt much from and because of him! Angela Beeselyhas impressed me with her willingness to learn how to use both the computersystems I set up and the finer points of running the Mossbauer lab, which Inow consider to be in her capable hands. She also kept me on my theoreticaltoes with her Mossbauer questions.

Beyond Physics (which sometimes seemed to be nothing more than adistant dream) Andrew Herring has been a companiable housemate for manyyears as well as a colleague and possesses the greatest quality in a housemate:not driving me up the wall too often! Simon Lee has been an invaluable helpin taking over the computer systems from me and sometimes managed tocounter my introversion with the occasional sneaky one up the Cambridge(this being an approximation that only holds for large values of ‘one’). Hiswillingness to help people and make sure everyone has a good time is onlymatched by his willingness to bare his behind at all and sundry. Thanks alsogo to the other (million or so) residents at 8, Church Road, for living withouttheir front room for a month. Gillian Howden has brightened many a dulllunchtime.

Kira Brown, as well as essentially teaching me everything I know aboutunix, has often had to bear the brunt of my frustration and rages against theworld and recalcitrant spectrometers with equanimity and friendship. Shealso (eventually!) sourced me a quality workstation which much of the workhas been done on. I am also indebted to the many countless contributorsto the “Open Source” programming community for providing the numeroustools and systems I have used to produce both my results and this thesis.The entirety of my thesis has been completed using such technologies and Iconsider it to have been an enormous benefit. Thanks chaps, keep up thegood work.

The Department of Physics has provided the support and equipment Ihave needed to produce and complete my thesis and the EPSRC has fundedmy studies.

Finally, I thank my parents for supporting me throughout all my studiesat University, moving my vast collections of “stuff” across most of Liverpooland for providing a home in which to complete my writing up.

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Contents

1 Introduction 11.1 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2 Mossbauer Spectroscopy 42.1 The Mossbauer Effect . . . . . . . . . . . . . . . . . . . . . . . 4

2.1.1 Recoil and Line Broadening . . . . . . . . . . . . . . . 42.1.2 Recoil-Free Events . . . . . . . . . . . . . . . . . . . . 62.1.3 Resolution . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2 Mossbauer Spectroscopy . . . . . . . . . . . . . . . . . . . . . 72.3 Hyperfine Interactions . . . . . . . . . . . . . . . . . . . . . . 8

2.3.1 Center Shift . . . . . . . . . . . . . . . . . . . . . . . . 92.3.2 Electric Quadrupole Splitting . . . . . . . . . . . . . . 102.3.3 Magnetic Hyperfine Splitting . . . . . . . . . . . . . . 112.3.4 Combined Magnetic and Quadrupole Interactions . . . 142.3.5 Spectrum Line Intensities . . . . . . . . . . . . . . . . 15

2.4 Relaxation Phenomena . . . . . . . . . . . . . . . . . . . . . . 172.5 Conversion Electron Mossbauer Spectroscopy . . . . . . . . . . 19

2.5.1 CEMS Decay Scheme . . . . . . . . . . . . . . . . . . . 192.5.2 Depth Dependence . . . . . . . . . . . . . . . . . . . . 19

3 Magnetometry 223.1 Magnetic Measurements . . . . . . . . . . . . . . . . . . . . . 22

3.1.1 Magnetic Moments . . . . . . . . . . . . . . . . . . . . 233.1.2 Magnetisation . . . . . . . . . . . . . . . . . . . . . . . 243.1.3 Magnetic Response . . . . . . . . . . . . . . . . . . . . 253.1.4 Background Contributions . . . . . . . . . . . . . . . . 25

3.2 Hysteresis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263.2.1 Diamagnetism and Paramagnetism . . . . . . . . . . . 263.2.2 Ferromagnetism . . . . . . . . . . . . . . . . . . . . . . 273.2.3 Remanence . . . . . . . . . . . . . . . . . . . . . . . . 283.2.4 Coercivity . . . . . . . . . . . . . . . . . . . . . . . . . 30

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3.3 Antiferromagnetism . . . . . . . . . . . . . . . . . . . . . . . . 313.4 Temperature Dependence . . . . . . . . . . . . . . . . . . . . 313.5 SQUID Magnetometry . . . . . . . . . . . . . . . . . . . . . . 35

3.5.1 Electron-pair Waves . . . . . . . . . . . . . . . . . . . 353.5.2 Josephson Tunnelling . . . . . . . . . . . . . . . . . . . 383.5.3 Superconducting Quantum Interference Device (SQUID) 393.5.4 SQUID Magnetometer . . . . . . . . . . . . . . . . . . 41

4 Experimental Techniques 434.1 Mossbauer Spectrometers . . . . . . . . . . . . . . . . . . . . 43

4.1.1 Gamma-ray Source . . . . . . . . . . . . . . . . . . . . 434.1.2 Basic Mossbauer Spectrometer . . . . . . . . . . . . . . 444.1.3 CEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

4.2 Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 484.2.1 χ2 Minimisation . . . . . . . . . . . . . . . . . . . . . . 484.2.2 Fitting Routines . . . . . . . . . . . . . . . . . . . . . 484.2.3 Calibration . . . . . . . . . . . . . . . . . . . . . . . . 49

4.3 SQUID Magnetometer . . . . . . . . . . . . . . . . . . . . . . 494.3.1 Magnetometer Overview . . . . . . . . . . . . . . . . . 494.3.2 RSO Measurements . . . . . . . . . . . . . . . . . . . . 50

5 Magnetic Interactions 525.1 Magnetic Anisotropy . . . . . . . . . . . . . . . . . . . . . . . 525.2 Magnetocrystalline Anisotropy . . . . . . . . . . . . . . . . . . 53

5.2.1 Uniaxial Anisotropy . . . . . . . . . . . . . . . . . . . 535.2.2 Interface and Volume Anisotropy . . . . . . . . . . . . 535.2.3 Single-ion Anisotropy . . . . . . . . . . . . . . . . . . . 535.2.4 Shape Anisotropy . . . . . . . . . . . . . . . . . . . . . 545.2.5 Exchange Interaction and Exchange Anisotropy . . . . 55

5.3 Magnetostriction . . . . . . . . . . . . . . . . . . . . . . . . . 555.3.1 Magneto-elastic Anisotropy . . . . . . . . . . . . . . . 56

5.4 The RKKY Interaction . . . . . . . . . . . . . . . . . . . . . . 56

6 RFe2 Laves Phase Thin Films 586.1 Introduction to Rare Earth/Iron Laves Phase Systems . . . . 58

6.1.1 Bulk Properties . . . . . . . . . . . . . . . . . . . . . . 606.1.2 Thin Films and Multilayers . . . . . . . . . . . . . . . 626.1.3 Sample Construction . . . . . . . . . . . . . . . . . . . 63

6.2 RFe2 Thin Films . . . . . . . . . . . . . . . . . . . . . . . . . 636.2.1 Determining the Magnetic Easy Axis . . . . . . . . . . 636.2.2 DyFe2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

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6.2.3 YFe2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 716.2.4 HoFe2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

6.3 DyFe2/Dy Multilayers . . . . . . . . . . . . . . . . . . . . . . 746.4 DyFe2/YFe2 Multilayers . . . . . . . . . . . . . . . . . . . . . 77

6.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 776.4.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

7 RE/Fe & A/Fe Magnetic Multilayers 837.1 Ce/Fe Multilayers . . . . . . . . . . . . . . . . . . . . . . . . . 84

7.1.1 Temperature vs Magnetisation Scans . . . . . . . . . . 857.1.2 Estimation of Coupling Constant, J(z) . . . . . . . . . 937.1.3 Hysteresis Loops . . . . . . . . . . . . . . . . . . . . . 95

7.2 U/Fe Multilayers . . . . . . . . . . . . . . . . . . . . . . . . . 977.2.1 CEMS Results . . . . . . . . . . . . . . . . . . . . . . . 98

8 Magnetic Iron Oxides 1078.1 Introduction to Magnetite . . . . . . . . . . . . . . . . . . . . 1078.2 Printer Toner Powders . . . . . . . . . . . . . . . . . . . . . . 108

8.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 1088.2.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

8.3 Single Crystal Fe3O4 Thin Films . . . . . . . . . . . . . . . . . 1118.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 1118.3.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

9 Concluding Remarks 119

A Publications 122

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List of Figures

2.1 Recoil in a free nucleus during gamma ray emission. . . . . . . 52.2 Gamma ray energy distributions for emission and absorption

in free atoms. The overlap is shown shaded and not to scaleas it is extremely small. . . . . . . . . . . . . . . . . . . . . . 6

2.3 Example Mossbauer spectrum showing the simplest case ofemitter and absorber nuclei in the same environment. Theuncertainty in the energy of the excited state, Γ, is shownexaggerated. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.4 The effect on the nuclear energy levels for a 3/2 → 1/2 transi-tion, such as in 57Fe or 119Sn, for an asymmetric charge distri-bution. The magnitude of quadrupole splitting, ∆ is shown. . 12

2.5 The effect of magnetic splitting on nuclear energy levels in theabsence of quadrupole splitting. The magnitude of splitting isproportional to the total magnetic field at the nucleus. . . . . 13

2.6 The effect of a first-order quadrupole perturbation on a mag-netic hyperfine spectrum for a 3/2 → 1/2 transition. Lines2,3,4,5 are shifted relative to lines 1,6. . . . . . . . . . . . . . 15

2.7 Decay scheme of 57Fe following excitation of the 14.41 keV state. 202.8 Probability of a 7.3keV K-conversion electron reaching the ab-

sorber surface in metallic iron. . . . . . . . . . . . . . . . . . . 21

3.1 Effect of moment alignment on magnetisation: (a) Single mag-netic moment, m, (b) two identical moments aligned paralleland (c) antiparallel to each other. . . . . . . . . . . . . . . . . 24

3.2 Typical effect on the magnetisation, M , of an applied magneticfield, H, on (a) a paramagnetic system and (b) a diamagneticsystem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.3 Schematic of a magnetisation hysteresis loop in a ferromag-netic material showing the saturation magnetisation, Ms, coer-cive field, Hc, and remanent magnetisation, Mr. Virgin curvesare shown dashed for nucleation (1) and pinning (2) type mag-nets. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

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3.4 The process of magnetisation in a demagnetised ferromagnet. . 293.5 Shape of hysteresis loop as a function of θH , the angle between

anisotropy axis and applied field H, for: (a) θH = 0◦, (b) 45◦

and (c) 90◦. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.6 Rotation of sublattice magnetisation under an applied field,

H, perpendicular to the spin axis. . . . . . . . . . . . . . . . . 323.7 Variation of reciprocal susceptibility with temperature for: (a)

antiferromagnetic, (b) paramagnetic and (c) diamagnetic or-dering. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.8 Variation of saturation magnetisation below, and reciprocalsusceptibility above Tc for: (a) ferromagnetic and (b) ferri-magnetic ordering. . . . . . . . . . . . . . . . . . . . . . . . . 34

3.9 Superconductor enclosing a non-superconducting region. . . . 373.10 Superconducting quantum interference device (SQUID) as a

simple magnetometer. . . . . . . . . . . . . . . . . . . . . . . 403.11 Critical measuring current, Ic, as a function of applied mag-

netic field. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.1 Decay scheme for a 57Co source leading to gamma-ray emis-sion. Internal conversion accounts for the remaining 91% of14.41 keV events. . . . . . . . . . . . . . . . . . . . . . . . . . 44

4.2 Mossbauer spectrometer schematic. . . . . . . . . . . . . . . . 454.3 CEMS detector used at Liverpool University. . . . . . . . . . . 474.4 Illustration of an RSO measurement with a small amplitude.

(a) shows the ideal SQUID response for a dipole and (b) showsthe movement of the sample within the SQUID pickup coils. . 51

5.1 Variation of the indirect exchange coupling constant, j, of afree electron gas in the neighbourhood of a point magneticmoment at the origin r = 0. . . . . . . . . . . . . . . . . . . . 57

6.1 The atomic positions in the C15 MgCu2 Cubic Laves Phaseunit cell. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

6.2 Schematic of the Laves Phase sample construction. . . . . . . 646.3 Comparison of spectra of DyFe2, YFe2 and HoFe2 thin films

at room temperature under zero applied field. . . . . . . . . . 686.4 750 A DyFe2 thin film under 0 kOe and 2.5 kOe in plane ap-

plied magnetic fields. . . . . . . . . . . . . . . . . . . . . . . . 696.5 Spectra for 1000A YFe2 thin film under 0 kOe and 2.5 kOe in

plane applied fields. . . . . . . . . . . . . . . . . . . . . . . . . 736.6 Spectra for

[DyFe2(xA)/Dy(yA)

]z, multilayers. . . . . . . . . 76

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6.7 Exchange coupling between iron sublattices in DyFe2/YFe2

multilayers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 786.8 Spectra for

[DyFe2(x A)/YFe2(y A)

]z, multilayers. . . . . . . . 79

7.1 Normalised magnetisation vs temperature scans for Ce(20 A)/Fe(x A)multilayers. Cerium layer thickness is constant. . . . . . . . . 86

7.2 Normalised magnetisation vs temperature curves for Ce(27 A)/Fe(x A)multilayers. Cerium layer thickness is constant. . . . . . . . . 88

7.3 Normalised magnetisation vs temperature scans for Ce(x A)/Fe(10 A)multilayers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89



7.6 Percentage change in resistance under an applied field for the[Ce(20 A)/Fe(17 A)

]60

sample. . . . . . . . . . . . . . . . . . . 927.7 Exploded view of a Ce/Fe multilayer showing the antiferro-

magnetic coupling between the iron layers. . . . . . . . . . . . 937.8 Variation of antiferromagnetic coupling constant, J(z), with

cerium layer thickness, z. The dashed line, representing atheoretical picture of oscillatory coupling, is added to guidethe eye. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

7.9 Hysteresis loops taken at room temperature for all measuredCe/Fe samples. The magnetisation is normalised relative tothe iron layers volume only. The hysteresis loop for the 20/10sample is shown truncated in the main plot for clarity, but iscompared to the other loops in the inset. . . . . . . . . . . . . 96

7.10 CEMS spectra for U/Fe multilayers: [U(40)/Fe(60)]10, [U(80)/Fe(60)]20,[U(101)/Fe(60)]20 and [U(42)/Fe(113)]21. The spectra are un-affected by the uranium layer thicknesses. . . . . . . . . . . . 100

7.11 CEMS spectra for U/Fe multilayers: [U(28)/Fe(30)]31, [U(28)/Fe(43)]31

and [U(22)/Fe(180)]5. Increasing crystallinity is observed withinthe iron layers as the thickness increases. . . . . . . . . . . . . 102

7.12 DCEMS spectra recorded from the [U(28)/Fe(43)]31 sample.Spectrum (a) is obtained from the top ∼ 5 bilayers in thesample, whilst spectrum (b) was recorded from the remaininglayers underneath. . . . . . . . . . . . . . . . . . . . . . . . . 104

7.13 X-ray reflectivity scans for a) [U(42)/Fe(113)]21 and b) [U(22)/Fe(180)]5samples. Sharp peaks indicate well defined interfaces. . . . . . 106

8.1 Room temperature Mossbauer spectra for all toner samples. . 115

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8.2 77K Mossbauer spectra for all toner samples. . . . . . . . . . . 1168.3 Fe3O4 thin films on (a) platinum and (b) sapphire substrates.

Sample (b) was grown using an oxygen plasma source. . . . . 1178.4 Fe3O4 thin film on a sapphire substrate, grown with a standard

sputtering source. (a) shows the fitted spectrum and (b) showsthe hyperfine field distribution. . . . . . . . . . . . . . . . . . 118

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List of Tables

2.1 Relative probabilities for a dipole 3/2→ 1/2 transition. C2 andΘ are the angular independent and dependent terms arbitrar-ily normalised. Relative intensities for θ = 90◦ and θ = 0◦ areshown with arbitrary normalisation. . . . . . . . . . . . . . . . 16

3.1 Variation of susceptibility, χ, and permeability, µ, with mate-rial and magnetic ordering. . . . . . . . . . . . . . . . . . . . . 25

6.1 Final fit parameters for 750 A DyFe2 sample assuming [241] or[351] easy axis in zero applied field. . . . . . . . . . . . . . . . 67

6.2 Final fit parameters for the 750 A DyFe2 sample in 0 kOe or2.5 kOe in plane applied field. No particular easy axis is ap-plied to the fitting parameters. The average angle is relativeto the sample plane. . . . . . . . . . . . . . . . . . . . . . . . 70

6.3 Final fit parameters for 1000 A YFe2 sample assuming [241] or[351] easy axis in zero applied field. . . . . . . . . . . . . . . . 72

6.4 Final fit parameters for the 1000 A YFe2 sample in 0 kOe or2.5 kOe in plane applied field. No particular easy axis is ap-plied to the fitting parameters. The average angle is relativeto the sample plane. . . . . . . . . . . . . . . . . . . . . . . . 72

6.5 Final fit parameters for the[DyFe2(x A)/Dy(y A)

]z

samples

and a 750 A DyFe2 thin film sample. The average angle isrelative to the sample plane. . . . . . . . . . . . . . . . . . . . 75

6.6 Fit parameters for[DyFe2(x A)/YFe2(y A)

]z

multilayers. Theaverage angle is relative to the sample plane. . . . . . . . . . . 80

7.1 Sample thicknesses, areas and volumes. “−” denotes a samplefrom which magnetometry data has been taken but whose areawas not measured. . . . . . . . . . . . . . . . . . . . . . . . . 84

7.2 Hyperfine values for all U/Fe multilayers studied. . . . . . . . 99

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7.3 Calculated thickness of iron layers in a fully crystalline (FE),paramagnetic (PM) or reduced crystallinity (RC) state for allU/Fe samples studied. . . . . . . . . . . . . . . . . . . . . . . 103

8.1 Final room temperature fit parameters for all toner powdersamples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

8.2 Calculated Fe2+:Fe3+ and N1:N2 ratios for the room temper-ature spectra. . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

8.3 Best fit parameters for magnetite thin film samples. The mag-netic hyperfine field for the Fe3O4/Al2O3B sample is a distri-bution, shown in Figure 8.4(b). . . . . . . . . . . . . . . . . . 112

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Only in silence the word,only in dark the light,only in dying life :bright the hawk’s flighton the empty sky.

Ursula Le Guin

xii

or

Only in recoil-free the event,only in resonance the line,only in decay emission :bright the peak’s heighton the empty channel.

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Chapter 1

Introduction

A fleck, a flight in feather ’til,In hanging air to drift and fall,Alight in spot of light and gentle

Rests a time to states unveil.

Magnetic materials have been an important part of the technological ad-vances of the past century. Most notable in recording media such as tapesand discs they also have crucial roles in many other areas; motors, actuators,sensors and a variety of industrial processes.

The key to the rapid enhancement of magnetic devices is the ability to tai-lor materials with specific magnetic properties. Of particular current interestare magnetic multilayers, on which much research has already been done.1,2

These can display many novel properties compared to bulk systems due totheir construction. Interfacial and geometrical elements combine to producethese novel properties and can be adjusted by varying layer thicknesses andthe composition of the layers. Fully understanding the mechanisms involvedin the interactions between the layers and the effects of layer construction isvital to engineering new technologies from these materials.

1.1 Thesis Outline

The aims of this thesis are to investigate the structure and magnetic interact-ions in multilayer systems and how these affect their magnetic properties, tounderstand the mechanisms at work in nanoscale structures such as thin filmsand how these affect bulk properties, and to contrast the different propertiesof iron as a magnetic constituent in intermetallics, multilayers and oxides.

The main investigatory technique used in this thesis is 57Fe Mossbauerspectroscopy. Mossbauer spectroscopy is an isotope specific technique which

1

CHAPTER 1. INTRODUCTION 2

can provide information about magnetic ordering via the hyperfine field, mo-ment orientation, charge states and the local environment of the Mossbauerisotope. Atoms in sites which differ in their electronic or magnetic environ-ment can be distinguished.

Chapter 2 covers the theory of the Mossbauer effect, its physical basis andhow it can be utilised as a spectroscopic technique. The various hyperfineinteractions which affect the shape of the resultant spectrum are explainedand illustrated. Most Mossbauer data in this thesis have been obtained usingConversion Electron Mossbauer Spectroscopy, a surface sensitive technique.The differences between this and the more common Transmission MossbauerSpectroscopy technique and CEMS’ depth dependence are explained.

SQUID magnetometry has been used as the primary technique for exam-ining the Ce/Fe multilayers. The physics of SQUIDs is given in Chapter 3.This is combined with an overview of magnetometry in general. Althoughmagnetometry data were only used for a small part of the data presented inthis thesis they are included to provide a resource for the basic principles ofmagnetism which are used in the explanation of much of the Mossbauer dataas well.

Chapter 4 gives information about the actual equipment used to facili-tate the theoretical techniques outlined in the above chapters, along with anoverview of the analysis routines used for analysing the Mossbauer results.

As magnetic interactions, such as magnetic anisotropy, play an importantrole in the behaviour of many of the systems studied, Chapter 5 comprises abrief account of these topics.

Chapter 6 is the first chapter of experimental results. The crystal struc-ture of Rare Earth/Iron cubic Laves Phase systems is discussed with respectto bulk systems. The effects, such as strain, of growing these systems as thinfilms with Molecular Beam Epitaxy, are then applied to the bulk system.Results and analysis of the CEMS data obtained from thin film samples arepresented first. These are then extended to multilayer samples of DyFe2 anda non-magnetic Dy spacer layer, or DyFe2/YFe2 multilayers of varying layerthicknesses. Applied field measurements were made on all samples apartfrom the DyFe2/Dy system, to give information on the magnetic anisotropy.

Chapter 7 presents results from two contrasting multilayer systems; Lan-thanide/Iron and Actinide/Iron. SQUID magnetometry results from Ce/Femultilayers are presented complementary to Mossbauer Spectroscopy resultsobtained by S. Case.3 The variation in the coupling type, and strength, ofthe iron layers across the cerium layers is examined. CEMS data and analysisfrom a series of U/Fe multilayers with different uranium and iron thicknessesare then presented. The moment orientations and crystalline nature of theiron layers is discussed. The data are compared to x-ray reflectivity data

CHAPTER 1. INTRODUCTION 3

taken by A. Herring of the Liverpool University Condensed Matter Physicsgroup.

Chapter 8 is an investigation of iron oxide systems, with particular ref-erence to magnetite. The crystalline and magnetic structure of magnetite isoutlined. A commercial study for Laporte is given, where the ratios of ironoxides was determined in printer toner powders. The behaviour of magnetitein bulk systems is then compared to thin film systems, with a Mossbauerstudy of magnetite thin films on different substrates. The crystalline growthand composition of the layers is discussed.

Finally, Chapter 9 presents the conclusions produced from the analysisand suggestions for future work on the samples studied.

Chapter 2

Mossbauer Spectroscopy

Alone, to give and lose,Far partner, never seen.Others, to join and help,Give all, take everything.

Nuclei in atoms undergo a variety of energy level transitions, often associatedwith the emission or absorption of a gamma ray. In a free atom the nucleusrecoils, due to conservation of momentum, resulting in the emitted gammaray being of lower energy than the nuclear transition energy. The sameis observed in absorption where the absorbing nucleus recoils, meaning theenergy of the resonantly absorbed photon has to be greater than that of thetransition.

Thus, in these circumstances, resonant emission or absorption doesn’t oc-cur.∗ In 1957 Rudolph Mossbauer discovered the phenomenon of Recoil-FreeNuclear Resonance Fluorescence;4 a phenomenon later to become commonlyknown as the “Mossbauer effect”.

2.1 The Mossbauer Effect

2.1.1 Recoil and Line Broadening

The two main obstacles in the path of achieving nuclear resonant emissionand absorption are the recoil energy shift and the thermal Doppler shift.Figure 2.1 shows an isolated atom in the gas phase undergoing a nucleartransition from an excited state, Ee, to the ground state, Eg.

∗Heisenberg Natural Linewidth and random thermal motion leads to line broadeningand thus an overlap of the two energies in this simple regime but the effect is extremelysmall.

4

CHAPTER 2. MOSSBAUER SPECTROSCOPY 5

M

Vx

ER

Vx v

Eγ

γRecoilM

Figure 2.1: Recoil in a free nucleus during gamma ray emission.

The recoil kinetic energy of the free nucleus, ER, is proportional to themass of the nucleus, M , and the energy of the emitted gamma ray, Eγ, andis given by

ER =E2γ

2Mc2(2.1)

The gamma ray energy will also be broadened into a distribution by theDoppler-effect energy, ED = Mv · Vx, which is proportional to the initialvelocity, Vx, from the random thermal motion of the atom, and v from therecoil of the nucleus. This can be expressed as

ED = Eγ

√2Ek

Mc2(2.2)

where Ek is the mean kinetic energy per translational degree of freedom ofa free atom.5

Heisenberg Natural Linewidth also broadens the lineshape. The uncer-tainty in the mean lifetime of the excited state, ∆t, is related to the uncer-tainty in the energy of the excited state, ∆E, by the Heisenberg uncertaintyprinciple

∆E∆t ≥ ~ (2.3)

Typical values of the linewidth broadening due to this are of the order of106 times less than that due to ER and ED for isolated atoms and can beneglected in this case.

The same equations apply for absorption. This leads to a distributionof emitted and absorbed gamma ray energies as shown in Figure 2.2. Theresonance overlap is extremely small and so practically useless as the basisof a technique.


P�Eγ �

2ED 2ED

� ER EREγ

Figure 2.2: Gamma ray energy distributions for emission and absorption infree atoms. The overlap is shown shaded and not to scale as it is extremelysmall.

2.1.2 Recoil-Free Events

The Mossbauer effect occurs when atoms are in a solid lattice or matrix.The chemical binding energies in solids (1-10 eV) are much greater than freeatom recoil energies, ER. The mass, M , recoiling then becomes effectivelythat of the entire crystal, which can be of the order of 1015 greater than asingle atom. It can be seen from equations 2.1 and 2.2 that ER and ED willnow be negligible in this case.

However, although the nucleus is bound within the lattice it is still freeto vibrate. The recoil energy can still be transferred to the lattice as aquantised lattice vibration, or phonon. If the recoil energy is less than thelowest quantised vibrational mode then a recoil-free event will occur. Theprobability of such an event is governed by the recoil-free factor, f , which isgiven as

f = exp

(−E2γ〈x2〉~c2

)(2.4)

where 〈x2〉 is the mean square vibrational amplitude of the emitting or ab-sorbing nucleus.5 It can be seen that f decreases exponentially with thesquare of the gamma ray energy; this is why the Mossbauer effect is onlydetected in isotopes with a very low lying excited state. The other depen-dent factor, 〈x2〉, is a function of both the binding strength and temperature.


The optimum f factor, and hence the best signal/noise ratio, is obtained forisotopes with very low lying excited states at temperatures well below theirDebye Temperature, θD. A good example is 57Fe, with a Mossbauer gammaray energy of 14.41 keV and a θD of 470 K, allowing strong signals to berecorded at room temperature.

2.1.3 Resolution

Earlier the Heisenberg Natural Linewidth (HNL) was ignored as being to-tally negligible compared to ER. However, in recoil-free events ER is 0 andhence the HNL becomes the major limit on the resolution of the gamma rayenergies.

This spread in energies of width Γs is 4.67× 10−9 eV in 57Fe. Comparedto the Mossbauer gamma ray energy of 14.41 keV for this isotope this gives aresolution of ∼1 in 1012. This is an incredibly high level of energy resolutionand is of the order of nuclear hyperfine interactions. Hence, the Mossbauereffect can be used to probe the electronic environment of a sample via thehyperfine interactions.

2.2 Mossbauer Spectroscopy

The technique of Mossbauer spectroscopy involves using the gamma raysemitted from the nuclei of a radioactive source to probe those in the sampleto be studied.∗ The source contains the parent nucleus of the Mossbauerisotope, embedded in a rigid matrix to ensure a high f factor. The gammarays emitted from this are passed through the material being investigatedand those transmitted through the absorber are detected and counted.

If the nuclei in the source and absorber are in the exact same environment(ie the energy of the nuclear transition is equal in both nuclei) the gammarays will be resonantly absorbed and an absorption peak will be observed.

In order to probe the energy levels in nuclei in different environmentswe must scan the energy of the Mossbauer gamma ray. This is achievedby moving the source relative to the absorber. The Doppler effect producesan energy shift in the gamma ray energy allowing us to match the resonantenergy level(s) in the absorber.

The simplest case is shown in Fig 2.3. The spectrum recorded is a plot oftransmission intensity versus source velocity in mm/s. The x-axis, through the

∗The radioactive source can be replaced by a synchrotron x-ray radiation source, whichhas certain advantages, particularly in time-dependent effects, but this is beyond the scopeof the subject of this thesis.


γ γ

detector

velocity

coun

ts

Absorber NucleusEmitter NucleusΓ

Figure 2.3: Example Mossbauer spectrum showing the simplest case of emit-ter and absorber nuclei in the same environment. The uncertainty in theenergy of the excited state, Γ, is shown exaggerated.

Doppler effect on the gamma ray energy, is effectively an energy scale. Thelineshape of the recorded peak in a thin sample is theoretically a Lorentzian,with a FWHM of twice the uncertainty in the energy of the excited state, Γ.

2.3 Hyperfine Interactions

The interaction between a nucleus and its surrounding environment is knownas a hyperfine interaction. These interactions are very small compared to theenergy levels of the nucleus itself but the extreme energy resolution of theMossbauer effect enables these interactions to be observed. The hyperfineinteractions may shift energy levels or lift their degeneracy. Both of thesevariations will affect the shape of a Mossbauer spectrum.

The nuclear Hamiltonian can be expressed as

H = H0 + E0 +M1 + E2 + . . . (2.5)

where H0 represents all of the terms of the Hamiltonian other than thehyperfine interactions. E0 refers to the electric monopole interactions, M1

the magnetic dipole interactions and E2 the electric quadrupole interactions.These effects will be discussed in turn with reference to their physical

causes and their effects on the Mossbauer spectrum lineshapes and positions.


2.3.1 Center Shift

The Center Shift (CS) of a Mossbauer spectrum, which sets the centroid ofthe spectrum, is composed of two factors: the Chemical Isomer Shift, δ, andthe Second Order Doppler Effect (SODS), meaning that

CS = δ + SODS

Chemical Isomer Shift (δ)

The Isomer Shift arises due to the non-zero volume of the nucleus and theelectron charge density due to s-electrons within it leading to an electricmonopole (Coulomb) interaction which alters the nuclear energy levels. Thevolume of the nucleus in its ground and excited states are different and the s-electron densities are affected by the chemical environment. This relationshipbetween s-electron density and nuclear radius is given by

δ =2

3πZe2{|ψs(0)E|2 − |ψs(0)A|2}{〈R2

e〉 − 〈R2g〉} (2.6)

where 〈R2g〉 and 〈R2

e〉 are the mean square radii of the ground and excited nu-clear states, |ψs(0)E|2 and |ψs(0)A|2 are the electron densities at the emittingand absorbing nuclei and Z is the atomic number.5

Any difference in the s-electron environment between emitter and ab-sorber thus produces a shift in the resonance energy of the transition. Thisshift cannot be measured directly and so a suitable reference is necessary,such as a specific source or an absorber. In all of the results presented inthis thesis isomer shifts are quoted relative to α-Fe at room temperature(any isomer shifts quoted from other work which use a different calibrationmaterial are quoted relative to α-Fe in this thesis for consistency).

The Isomer Shift is good for probing the valency state of the Mossbaueratom. As the wavefunctions of the s-electrons penetrate into outer shellschanges in these shells will directly alter the s-electron charge density at thenucleus. For example, Fe2+ and Fe3+ have electron configurations of (3d)6

and (3d)5 respectively. The ferrous ions have less s-electron density at thenucleus due to the greater screening of the d-electrons. This produces apositive Isomer Shift greater in ferrous iron than in ferric.

Second Order Doppler Shift (SODS)

The Second Order Doppler Shift (SODS) is a temperature-dependent effecton the center shift of a Mossbauer spectrum. Above 0 K atoms in a latticeoscillate about their mean position. The frequency of this oscillation is of the


order of 1012 Hz meaning that the average displacement during the lifetimeof a Mossbauer event is zero. However, the second term in the Doppler shiftdepends on v2 leading to the mean square displacement being non-zero. Thisenergy shift is given by

δEγEγ

= −〈v2〉

2c2(2.7)

For 57Fe in the high temperature limit this gives a change of +0.07 mms−1

for a decrease of 100 K.5

2.3.2 Electric Quadrupole Splitting

A nucleus that has a spin quantum number I > 1/2 has a non-spherical chargedistribution. The magnitude of the charge deformation, Q, is given by

eQ =

∫ρr2(3 cos2 θ − 1

)dτ (2.8)

where e is the charge on the proton, ρ is the charge density in a volumeelement dτ at a distance r from the center of the nucleus and making anangle θ to the nuclear spin quantisation axis. The sign of Q indicates theshape of the deformation. Negative Q is due to the nucleus being flattenedalong the spin axis, an elongated nucleus giving positive Q.5

An asymmetric charge distribution around the nucleus causes an asym-metric electric field at the nucleus, characterised by a tensor quantity calledthe Electric Field Gradient (EFG) ∇E. The electric quadrupole interactionbetween these two quantities gives rise to a splitting in the nuclear energylevels. The interaction between nuclear moment and EFG is expressed bythe Hamiltonian

HEq = −1

6eQ∇E (2.9)

where ∇E may be written as

∇Eij = − ∂2V

∂xi∂xj= −Vij, (2.10)

{xi, xj} = {x, y, z}

where V is the electrostatic potential.There are two contributions to the EFG i) lattice contributions from

charges on distant ions and ii) valence contributions due to incompletelyfilled electron shells. If a suitable coordinate system is chosen the EFG canbe represented by three principal axes, Vxx, Vyy and Vzz. If an asymmetry


parameter is defined using these axes as

η =

(Vxx − Vyy

Vzz

)(2.11)

where |Vzz| ≥ |Vyy| ≥ |Vxx| so that 0 ≤ η ≤ 1, the EFG can be specified bytwo parameters: Vzz and η.

The Hamiltonian for the quadrupole interaction can be rewritten as

HEq =e2qQ

4I(2I − 1)

[3I2z − I(I + 1) +

η

2

(I2

+ + I2−)]

(2.12)

where I+ and I− are shift operators and Iz is a spin operator.5

The excited state of 57Fe has a spin I = 3/2. The EFG has no effect onthe I = 1/2 ground state but does remove degeneracy in the excited state,splitting it into two sub-states mI = ±1/2 andmI = ±3/2 where themI = ±3/2

states are higher in energy for positive Vzz. The energy eigenvalues for I = 3/2

have exact solutions given by

EEq =e2qQ

4I(2I − 1)

[3m2

I − I(I + 1)](

1 +η2

3

) 12

(2.13)

whilst the energies for higher spin states require analytical methods to cal-culate the energies.

The now non-degenerate excited states give rise to a doublet in theMossbauer spectrum as illustrated in Figure 2.4. The separation betweenthe lines, ∆, is known as the quadrupole splitting and is given by

∆ =e2qQ

2

(1 +

η2

3

) 12

(2.14)

with the line intensities being equal for polycrystalline samples. Texture ororientation effects can lead to asymmetric doublets.

As the nuclear quadrupole moment is fixed the magnitude and sign of ∆gives information about the sign of the EFG and magnitude of η.

2.3.3 Magnetic Hyperfine Splitting

Magnetic hyperfine splitting is caused by the dipole interaction between thenuclear spin moment and a magnetic field ie Zeeman splitting. The effectivemagnetic field experienced by the nucleus is a combination of fields from theatom itself, from the lattice through crystal field effects and from external


mI

� 32

� 12

� 12

∆

∆I32

12

Figure 2.4: The effect on the nuclear energy levels for a 3/2 → 1/2 transi-tion, such as in 57Fe or 119Sn, for an asymmetric charge distribution. Themagnitude of quadrupole splitting, ∆ is shown.

applied fields. This can be considered for now as a single field, H , whosedirection specifies the principal z axis.

The Hamiltonian for the magnetic hyperfine dipole interaction is given as

H = −µ.H = −gµNI.H (2.15)

where µN is the nuclear Bohr magneton, µ is the nuclear magnetic moment,I is the nuclear spin and g is the nuclear g-factor.5

This Hamiltonian yields eigenvalues of

EM = −gµNHmI (2.16)

where mI is the magnetic quantum number representing the z componentof I (ie mI = I, I − 1, . . . ,−I). The magnetic field splits the nuclear levelof spin I into (2I + 1) equispaced non-degenerate substates. This and theselection rule of ∆mI = 0,±1 produces splitting and a resultant spectrum asshown in Figure 2.5 for a 3/2→ 1/2 transition.

This splitting is a combination of a constant nuclear term and a variablemagnetic term, influenced by the electronic structure. The magnetic field at


mI

� 32

� 12

�12

�32

�12

� 12

12

32

I

Figure 2.5: The effect of magnetic splitting on nuclear energy levels in theabsence of quadrupole splitting. The magnitude of splitting is proportionalto the total magnetic field at the nucleus.

the nucleus has several terms associated with it. A general expression is

H = H0 −DM +4

3πM +HS +HL +HD (2.17)

where H0 is the value of magnetic field at the nucleus due to an externalmagnetic field, −DM is the demagnetising field, 4/3πM is the Lorentz field,HS is the Fermi contact term, HL is the orbital magnetic term and HD is thedipolar term. The demagnetising field and Lorentz field are usually negligiblecompared to the other terms.

HS is produced by the polarisation of electrons whose wavefunctions over-lap the nucleus, ie s-electrons. This polarisation is due to unpaired electronsin the d or f orbitals and gives an imbalance in spin density at the nu-cleus from the difference in interaction between the unpaired electron withs-electrons of parallel or antiparallel spin to its own. This can be expressedformally as

HS = −8π

3µ0µB

∑{|ψs↑(0)|2 − |ψs↓(0)|2} (2.18)


HL arises from the net orbital moment at the nucleus caused by the orbitalmotion of electrons in unfilled shells and given by

HL =2µ0µB

4π〈r−3〉〈L〉 (2.19)

In transition metals L is usually quenched by interactions with the crystalfield, but it can be substantial in Rare Earth ions.

HD arises from the dipolar interaction between the nucleus and the spinmoment of 3d or 4f electrons and can be expressed as

HD = −2µB〈S〉〈r−3〉〈3 cos2 θ − 1〉 (2.20)

In transition metal compounds with cubic symmetry this has zero magnitudebut can be substantial in Rare Earths.

2.3.4 Combined Magnetic and Quadrupole Interact-ions

When dealing with quadrupole or magnetic splitting separately with chemicalisomer shifts the recorded spectrum has uniform shifts of resonance lines withno change in their relative separations. However, both the quadrupolar andmagnetic interactions depend upon angle and so when they are both presentthe interpretation of the spectrum can be complex.

The situation can be simplified a great deal if two assumptions are made

1. the electric field gradient is axially symmetric with its principal axis,Vzz, at an angle θ to the magnetic axis

2. the strength of the quadrupole interaction is much less than the mag-netic interaction, ie e2qQ� µH.

The solution to the Hamiltonian can then be solved by treating the quad-rupole interaction as a perturbation so that the resultant energy levels aregiven by

E = −qµNHmI + (−1)|mI |+12e2qQ

4

(3 cos2 θ − 1

2

)(2.21)

giving a spectrum as in Figure 2.6.5

For most 57Fe spectra the result is a shift in the relative position of lines1,6 with lines 2,3,4,5. For a positive quadrupole splitting lines 1,6 are shiftedpositively relative to lines 2,3,4,5 and vice versa. The line separations areequal when there is no quadrupole effect or when cos θ = 1/

√3.


mI

� 32

� 12

�12

�32

�12

� 12

12

32

I

Magnetic Magnetic+

Quadrupole

1 2 3 4 5 6

Figure 2.6: The effect of a first-order quadrupole perturbation on a magnetichyperfine spectrum for a 3/2→ 1/2 transition. Lines 2,3,4,5 are shifted relativeto lines 1,6.

2.3.5 Spectrum Line Intensities

The hyperfine interactions thus far have given the relative energies of thevarious transitions taking place but have not given information on the rela-tive intensities of these transitions in the recorded spectrum. The intensitiesarise from the coupling of two angular momentum states, which can be ex-pressed as the product of both an angular dependent term and an angularindependent term by

A(L, θ) = C2(J)Θ(J, θ) (2.22)

where C2(J) is the transition probability of the γ-ray transition between twonuclear sub-levels, and Θ(J, θ) is the angular dependence of the radiationprobability at an angle θ to the quantisation axis.

The angular independent term is given by the square of the appropriate


m2 −m1 m C C2 Θ θ = 90◦ θ = 0◦

+3/2 +1/2 +1 1 3 1 + cos2 θ 3 6

+1/2 +1/2 0√

2/3 2 2 sin2 θ 4 0

−1/2 +1/2 −1√

1/3 1 1 + cos2 θ 1 2−3/2 +1/2 −2 0 0 0 0 0+3/2 −1/2 +2 0 0 0 0 0

+1/2 −1/2 +1√

1/3 1 1 + cos2 θ 1 2

−1/2 −1/2 0√

2/3 2 2 sin2 θ 4 0−3/2 −1/2 −1 1 3 1 + cos2 θ 3 6

Table 2.1: Relative probabilities for a dipole 3/2 → 1/2 transition. C2 andΘ are the angular independent and dependent terms arbitrarily normalised.Relative intensities for θ = 90◦ and θ = 0◦ are shown with arbitrary normal-isation.

Clebsch-Gordan coefficient

C2(J) = 〈I1J −m1m|I2m2〉2 (2.23)

where J is the vector sum J = I1+I2 and m is the vector sum m = m1−m2.5

J is the multipolarity of the radiation, J = 1 being dipolar and J = 2 beingquadrupolar. As the multipolarity of the radiation increases the transitionprobability decreases.

In 57Fe the 14.41 keV transition is primarily dipolar and values for thistransition are given in Table 2.1.

In a magnetic spectrum the intensities of the outer, middle and innerlines are in a ratio derived from the product C2(J)Θ(J, θ). Using the valuesfrom Table 2.1 gives

3(1 + cos2 θ

): 4 sin2 θ : 1 + cos2 θ (2.24)

from which it can be seen that the outer and inner lines are always in theratio of 3:1 whilst the middle line varies between 0 → 4 with angle. Inpolycrystalline samples there is no angular dependence and thus the intensitydepends only on C2(J), giving a sextet of 3:2:1:1:2:3.

Non-magnetic spectra with quadrupole splitting have several degenerate


transitions and the intensity of the two lines are in the ratio

3(1 + cos2 θ

): 2 + 3 sin2 θ (2.25)

2.4 Relaxation Phenomena

There are many contributions to the hyperfine field at the nucleus as seen inEquation 2.17 but the major contributor for transition metals such as 57Fe,when in zero applied field, is HS. This arises from the polarising effect ofunpaired electron spins with the direction of the field being related to that ofthe electron spins. However, this direction is not invariant and can flip aftera period of time. This is the relaxation phenomenon. The effects upon theMossbauer lineshape depend upon the relative time scales of measurementand the relaxation mechanism, there being three time scales to consider:the lifetime of the Mossbauer event, the Larmor precession time and therelaxation time.

The lifetime of the Mossbauer event, τm, which is also the limiting timescale of the measurement technique, is determined by the Heisenberg uncer-tainty relationship as shown in Equation 2.3. For 57Fe this is of the order of10−7 s.

The second time scale to consider is the minimum time required for thenucleus to detect the hyperfine field. This is usually assumed to be equal tothe Larmor precession time, τl, which can be considered as the time takenfor a nuclear spin state, I, to split into (2I+ 1) substates under the influenceof a hyperfine field. τl is proportional to the magnitude of the hyperfine field(and hence related to the nuclear energy levels as in Equation 2.16) with thefollowing relation

τl =2π~

gµnB(2.26)

where g is the gyromagnetic constant and µn is the nuclear Bohr magneton.In iron oxides the hyperfine field is ∼ 400→ 500 kG giving τl of the order of10−8 s. This means that τm � τl and hence the hyperfine fields are detectableby the technique.

The final time scale is the relaxation time, τr, associated with the timedependent fluctuations of the electron spin. For the hyperfine field to beobserved it must remain constant at the nucleus for at least one Larmorprecession period.

There are three regimes which are important when considering the effectof relaxation on the Mossbauer lineshape:

1. If τr � τl then the hyperfine field is static during a single Larmor


precession period. The spectral lines are narrow and Lorentzian inshape.

2. If τr � τl then the nucleus experiences a time averaged hyperfine field.The magnitude is less than the value obtained for a static field as theinteraction will have changed many times during a single precessionperiod and tends to zero as τr decreases. Narrow Lorentzian lines arestill observed.

3. If τr ≈ τl then resonance between the relaxation and the precessionoccurs leading to complex spectra and broadened lineshapes. As τl isproportional to the energy difference between the spectral lines τl forthe outer lines will be less than for the inner lines, causing the innerlines of a sextet to broaden and disappear before the outer ones.6

The two main mechanisms involved in the spin relaxation are Spin-Spinand Spin-Lattice relaxation.

Spin-Spin Relaxation

This involves energy transfer between interacting spins via dipole and ex-change interactions. The relaxation rate depends heavily on the concentra-tion of paramagnetic ions in the sample. This mechanism is largely temper-ature independent. The relaxation rate can be expressed as

R ∝ |〈i|H|f〉|2φ (2.27)

where i and f are the initial and final spin states, H is the Hamiltonian ofthe mechanism and φ is a phase factor.

Spin-Lattice Relaxation

This mechanism involves energy transfer between the electron spin and latticephonons mostly via the spin-orbit interaction but also weakly through dipolarinteractions. The relaxation rate is of the same form as Equation 2.27 butwith φ now involving the population of phonon modes. This leads to the spin-lattice contribution to relaxation being strongly temperature dependent.


2.5 Conversion Electron Mossbauer Spectro-

scopy

Standard Transmission Mossbauer Spectroscopy (TMS) records the absorp-tion of gamma rays in the beam transmitted through the absorber. If theabsorber is too thick or on an opaque substrate so that the beam cannot passthrough or the signal is too small, then a reflective technique must be used,such as Conversion Electron Mossbauer Spectroscopy (CEMS).

2.5.1 CEMS Decay Scheme

A nucleus that is promoted to an excited state by gamma ray absorption cande-excite by a number of mechanisms. These fall into two categories

1. Radiative: by the emission of a gamma ray with a probability of N(γ)

2. Non-Radiative: by internal conversion and the ejection of an atomicelectron with a probability of N(e)

The ratio of these two process is given by the internal conversion coefficient,α, given by

α =N(e)

N(γ)(2.28)

which for 57Fe is 8.21, ie internal conversion is 8.21 times more probable thanphoton emission.7

The conversion electron is ejected from the atom with an energy Ec =Eγ−Eb where Eγ is the energy of the transition and Eb is the binding energyof the electron. In 57Fe the internal conversion can occur from K, L and Mshells, in order of probability. This ejection leaves a hole which can be filledby an electron from an outer shell. This releases energy in the form of anX-ray or an Auger electron, with the process continuing in this manner untilall of the energy has been dissipated. The principal decay scheme is shownin Figure 2.7.

To exploit the decay of the resonantly excited nucleus the conversion andAuger electrons need to be detected. This is achieved by placing the sampleinside a gas-flow proportional counter as shown in Section 4.1.3.

2.5.2 Depth Dependence

The conversion and Auger electrons produced by the resonant event have afinite range in the material of the absorber due to interactions with other


Figure 2.7: Decay scheme of 57Fe following excitation of the 14.41 keV state.

charged particles. The range is dependent on both the mean free path ofthe electron in the absorber and the initial kinetic energy of the electron.This is illustrated in Figure 2.8. The dependence is essentially an inverseexponential one with the majority of the signal coming from the uppermost1000 A.

This depth dependency is a double-edged sword in that the quite shal-low detection depth may prevent the probing of deeper structures and thatsurfaces have to be kept relatively clean but it also prevents such things asbuffer and seed layers in multilayer samples contaminating the signal. Inthe samples studied in this thesis using CEMS the whole of the thin filmor multilayer is 2000 A or less and deposited onto thick, opaque substrates


Figure 2.8: Probability of a 7.3keV K-conversion electron reaching the ab-sorber surface in metallic iron.

making this technique a practical solution.The depth dependency can also be combined with the selection of electron

energies to obtain separate spectra for different depths into the sample. Thisis known as Differential CEMS or DCEMS.

Chapter 3

Magnetometry

Random grains to clasp,Regimented lines to wear,Snare in serpent’s grasp,Shake their secrets bare.

Mossbauer Spectroscopy, as outlined in Chapter 2, is an effective probe ofmagnetic ordering in materials. In particular it can distinguish differentcontributions to magnetic structure arising from different ions and differentsites as in the Fe2+ and Fe3+ ions on A and B sites in Fe3O4 (see Chapter 8).It cannot, however, provide a complete description of the magnetism alone.For example, Mossbauer Spectroscopy in zero applied field cannot distinguishbetween ferromagnetic and antiferromagnetic ordering. It is sensitive onlyto the particular Mossbauer isotope being probed and the spectra take arelatively long time to accumulate. Magnetometry can produce results onthe total moment of the system and its variation with applied field andtemperature relatively quickly and easily, providing complementary data tothe Mossbauer spectrum as well as other techniques.

3.1 Magnetic Measurements

The principle aim of magnetometry is to measure the magnetisation (eitherintrinsic or induced by an applied field) of a material. This can be achieved ina number of ways utilising various magnetic phenomena. The various typesof magnetometer fall within two categories:

1. Measuring the force acting on a sample in an inhomogeneous magneticfield

22

CHAPTER 3. MAGNETOMETRY 23

• Magnetic balance

• Magnetic pendulum

2. Measuring the magnetic field produced by a sample.

• Vibrating Sample Magnetometer (VSM)

• Superconducting Quantum Interference Device (SQUID)

Magnetometry data in this thesis has been recorded using a SQUID, thetheoretical principles of which are outlined in Section 3.5 and the physicaldetails in Section 4.3.

3.1.1 Magnetic Moments

A magnet in a field has a potential energy, Ep, relative to the parallel positiongiven by

Ep = −m ·H (3.1)

where H is the applied field and m is the magnetic moment.8 From thisthe units of magnetic moment can be seen to be J/T (emu in cgs notation,where emu is an acronym for ElectroMagnetic Unit).

The origin of atomic magnetic moments is the incomplete cancellation ofelectronic magnetic moments. Electron spin and orbital motion both havemagnetic moments associated with them but in most atoms the electronicmoments are oriented so that they cancel giving no net atomic magneticmoment, leading to diamagnetism. If the cancellation of electronic momentsis incomplete then the atom has a net magnetic moment. These “mag-netic atoms” can display para-, ferro-, antiferro- or ferrimagnetic orderingdepending upon the strength and type of magnetic interactions and externalparameters such as temperature.

The magnetic moments of atoms, molecules or formula units are oftenquoted in terms of the Bohr magneton∗, which is equal to the magneticmoment due to electron spin

µB =eh

4πm= 9.27× 10−24 J/T

eg the atomic moment is 2.22 µB/atom for metallic iron and 10.34 µB/atom formetallic holmium.

∗Derived from three fundamental constants; electronic charge e, electronic mass m andPlanck’s constant h, the Bohr magneton is a natural unit of magnetic moment in the sameway that e is a natural unit of electric charge.


Figure 3.1: Effect of moment alignment on magnetisation: (a) Single mag-netic moment, m, (b) two identical moments aligned parallel and (c) antipar-allel to each other.

3.1.2 Magnetisation

The output from a magnetometer, a single value of magnetic moment for thesample, is a combination of the magnetic moments on the atoms within thesample, the type and level of magnetic ordering and the physical dimensionsof the sample itself. The moment is also affected by external parameters suchas temperature and applied magnetic field.

The “Intensity of Magnetisation∗”, M , is a measure of the magnetisationof a body. It is defined as the magnetic moment per unit volume or

M =m

V(3.2)

with units of A/m (emu/cm3 in cgs notation).8

A sample contains many atoms and their arrangement affects the mag-netisation. In Figure 3.1(a) a magnetic moment m is contained in unitvolume. This has a magnetisation of m A/m. Figure 3.1(b) shows two suchunits, with the moments aligned parallel. The vector sum of moments is 2min this case, but as the both the moment and volume are doubled M remainsthe same. In Figure 3.1(c) the moments are aligned antiparallel. The vectorsum of moments is now 0 and hence the magnetisation is 0 A/m.

Scenarios (b) and (c) are a simple representation of ferro- and antifer-romagnetic ordering. Hence we would expect a large magnetisation in aferromagnetic material such as pure iron and a small magnetisation in anantiferromagnet such as γ-Fe2O3.

∗This is often shortened to simply “Magnetisation”.


Material/Ordering χ µ

Vacuum 0 = 1

Diamagnetic Small and negative . 1

Paramagnetic Small and positive & 1

Antiferromagnetic Small and positive & 1

Ferromagnetic Large and positive � 1

Ferrimagnetic Large and positive � 1

Table 3.1: Variation of susceptibility, χ, and permeability, µ, with materialand magnetic ordering.

3.1.3 Magnetic Response

The response of a material to a magnetic field is quantified by two quantities:the susceptibility, χ, which is the variation of magnetisation, M , with appliedfield, H,

χ =M

H(3.3)

and the permeability, µ, the variation of magnetic induction, B = µ0(H+M),with applied field,

µ =B

H(3.4)

Permeability is often quoted relative to µ0 = 4π× 10−7 H/m, the permeabilityof a vacuum or (within a high degree of accuracy) air.

The susceptibility and permeability of a material depends upon its mag-netic characteristics. Table 3.1 gives an indication of how they vary with thetype of material and magnetic ordering (if any) it displays.

3.1.4 Background Contributions

A single measurement of a sample’s magnetisation is relatively easy to obtain,especially with modern technology. Often it is simply a case of loading thesample into the magnetometer in the correct manner and performing a singlemeasurement.

This value is, however, the sum total of the sample, any substrate orbacking and the sample mount. A sample substrate can produce a substantialcontribution to the sample total. The samples studied in this thesis using


magnetometry have a single type of substrate, silicon, substantially greaterin volume and mass than the sample itself.

Fortunately the substrate is diamagnetic (see Section 3.2.1). Under zeroapplied field this means it has no effect on the measurement of magnetisation.Under applied fields its contribution is linear and temperature independent.The diamagnetic contribution can be calculated from a knowledge of thevolume and properties of the substrate and substracted as a constant linearterm to produce the signal from the sample alone.

The diamagnetic background can also be seen clearly at high fields wherethe sample has reached saturation: the sample saturates but the linear back-ground from the substrate continues to increase with field. The gradient ofthis background can be recorded and subtracted from the readings if thesubstrate properties are not known accurately.

3.2 Hysteresis

The response of a material to an applied field and its magnetic hysteresis isan essential tool of magnetometry. Paramagnetic and diamagnetic materialscan easily be recognised, soft and hard ferromagnetic materials give differenttypes of hysteresis curves and from these curves values such as saturationmagnetisation, remanent magnetisation and coercivity are readily observed.More detailed curves can give indications of the type of magnetic interactionswithin the sample.

Hysteresis is a subject which covers a wide range of behaviour in materials,both in magnetism and other disciplines. The aim of this section is to coverthe basic principles of the use of hysteresis as a probe of magnetism.

3.2.1 Diamagnetism and Paramagnetism

As explained in Section 3.1.2 the intensity of magnetisation depends uponboth the magnetic moments in the sample and the way that they are orientedwith respect to each other, known as the magnetic ordering.

Diamagnetic materials, which have no atomic magnetic moments, haveno magnetisation in zero field. When a field is applied a small, negativemoment is induced on the diamagnetic atoms proportional to the appliedfield strength. See Figure 3.2(b). As the field is reduced the induced momentis reduced.

In a paramagnet the atoms have a net magnetic moment but are orientedrandomly throughout the sample due to thermal agitation, giving zero mag-netisation. As a field is applied the moments tend towards alignment along


Figure 3.2: Typical effect on the magnetisation, M , of an applied magneticfield, H, on (a) a paramagnetic system and (b) a diamagnetic system.

the field, giving a net magnetisation which increases with applied field as themoments become more ordered. See Figure 3.2(a). As the field is reducedthe moments become disordered again by their thermal agitation. The figureshows the linear response of M vs H where µH � kT .

3.2.2 Ferromagnetism

The hysteresis curves for a ferromagnetic material are more complex thanthose for diamagnets or paramagnets. Figure 3.3 shows the main features ofsuch a curve for a simple ferromagnet.

In the virgin material (point 0) there is no magnetisation. The process ofmagnetisation, leading from point 0 to saturation at M = Ms, is outlined inFigure 3.4.8 Although the material is ordered ferromagnetically it consists ofa number of ordered domains arranged randomly giving no net magnetisation.This is shown in Figure 3.4(a) with two domains whose individual saturationmoments, Ms, lie antiparallel to each other.

As the magnetic field, H, is applied, (b), those domains which are moreenergetically favourable increase in size at the expense of those whose momentlies more antiparallel to H. There is now a net magnetisation, M . Eventuallya field is reached where all of the material is a single domain with a momentaligned parallel, or close to parallel, with H. The magnetisation is nowM = Ms cos θ where θ is the angle between Ms along the easy magnetic axis


Figure 3.3: Schematic of a magnetisation hysteresis loop in a ferromagneticmaterial showing the saturation magnetisation, Ms, coercive field, Hc, andremanent magnetisation, Mr. Virgin curves are shown dashed for nucleation(1) and pinning (2) type magnets.

and H. Finally Ms is rotated parallel to H and the ferromagnet is saturatedwith a magnetisation M = Ms.

The process of domain wall motion affects the shape of the virgin curve.There are two qualitatively different modes of behaviour known as nucleationand pinning,9 shown in Figure 3.3 as curves 1 and 2 respectively.

In a nucleation-type magnet saturation is reached quickly at a field muchlower than the coercive field. This shows that the domain walls are easilymoved and are not pinned significantly. Once the domain structure hasbeen removed the formation of reversed domains becomes difficult, givinghigh coercivity. In a pinning-type magnet fields close to the coercive fieldare necessary to reach saturation magnetisation. Here the domain walls aresubstantally pinned and this mechanism also gives high coercivity.

3.2.3 Remanence

As the applied field is reduced to 0 after the sample has reached saturationthe sample can still possess a remanent magnetisation, Mr. The magnitudeof this remanent magnetisation is a product of the saturation magnetisation,


Figure 3.4: The process of magnetisation in a demagnetised ferromagnet.

the number and orientation of easy axes and the type of anisotropy symmetry.If the axis of anisotropy or magnetic easy axis is perfectly aligned with thefield then Mr

∼= Ms, and if perpendicular Mr∼= 0.

At saturation the angular distribution of domain magnetisations is closelyaligned to H. As the field is removed they turn to the nearest easy magneticaxis. In a cubic crystal with a positive anisotropy constant, K1, the easydirections are 〈100〉. At remanence the domain magnetisations will lie alongone of the three 〈100〉 directions. The maximum deviation from H occurswhen H is along the 〈111〉 axis, giving a cone of distribution of 55◦ aroundthe axis.10 Averaging the saturation magnetisation over this angle gives aremanent magnetisation of 0.832Ms

In a system with uniaxial anisotropy with positive K1 at remanence themagnetisation vectors cover a hemicircle in a two-dimensional system anda hemisphere in a three-dimensional system. These give Mr

∼= 0.637 andMr = 0.5 respectively.9

These situations are for ideal cases and can be modified greatly by furtherinteractions and sample characteristics.


Figure 3.5: Shape of hysteresis loop as a function of θH , the angle betweenanisotropy axis and applied field H, for: (a) θH = 0◦, (b) 45◦ and (c) 90◦.

3.2.4 Coercivity

The coercive field, Hc, is the field at which the remanent magnetisation isreduced to zero. This can vary from a few A/m for soft magnets to 107 A/m

for hard magnets. It is the point of magnetisation reversal in the sample,where the barrier between the two states of magnetisation is reduced to zeroby the applied field allowing the system to make a Barkhausen jump∗ to alower energy. It is a general indicator of the energy gradients in the samplewhich oppose large changes of magnetisation.

The reversal of magnetisation can come about as a rotation of the mag-netisation in a large volume or through the movement of domain walls underthe pressure of the applied field. In general materials with few or no domainshave a high coercivity whilst those with many domains have a low coerciv-ity. However, domain wall pinning by physical defects such as vacancies,dislocations and grain boundaries can increase the coercivity.

∗Named after H. Barkhausen who, in 1919, gave experimental evidence of spontaneousreconfiguration of domains as an applied field continuously alters the system’s energybalance. These jumps can be small, resulting from localised domain wall movement, orlarge when associated with the nucleation of domains with reverse magnetisation, forexample. The Berkhausen effect gives fine structure to magnetisation curves.


The loop illustrated in Figure 3.3 is indicative of a simple bistable sys-tem. There are two energy minima: one with magnetisation in the positivedirection, and another in the negative direction. The depth of these minimais influenced by the material and its geometry and is a further parameterin the strength of the coercive field. Another is the angle, θH , between theanisotropy axis and the applied field. Figure 3.5 shows how the shape of thehysteresis loop and the magnitude of Hc varies with θH . This effect showsthe importance of how samples with strong anisotropy are mounted in amagnetometer when comparing loops.

3.3 Antiferromagnetism

Below TN the two sublattices of an antiferromagnet spontaneously magnetisein the same way as a ferromagnet but the net magnetisation is zero due tothe opposing orientation of the sublattice’s magnetisation. If an externalfield, H, is applied a small net magnetisation can be detected. The resultantmagnetisation depends upon the orientation of the field with respect to themagnetisation or spin axis.

If the field is applied parallel to the spin axis the zero-field value of mag-netisation of one sublattice, A, is increased by ∆MA whilst the other, B, isdecreased by ∆MB. The net magnetisation in the direction of the field isthen

M = |∆MA|+ |∆MB| (3.5)

If the field is applied perpendicular to the spin axis each sublattice mag-netisation is turned from the spin axis by a small angle, α, as shown inFigure 3.6. The spins reorient by angle α given by

2 (HmA sinα) = H (3.6)

where HmA is the molecular field given by HmA = 2AM where A is theexchange energy and the resultant magnetisation is then equal to

M = 2MA sinα (3.7)

This magnetisation is linear with applied field with no hysteresis.

3.4 Temperature Dependence

A hysteresis curve gives information about a magnetic system by varying theapplied field but important information can also be gleaned by varying the


Figure 3.6: Rotation of sublattice magnetisation under an applied field, H,perpendicular to the spin axis.

temperature. As well as indicating transition temperatures, all of the maingroups of magnetic ordering have characteristic temperature/magnetisationcurves. These are summarised in Figures 3.7 and 3.8. At all temperatures adiamagnet displays only any magnetisation induced by the applied field anda small, negative susceptibility.

The curve shown for a paramagnet is for one obeying the Curie law,

χ =C

T(3.8)

and so intercepts the axis at T = 0. This is a subset of the Curie-Weiss law,

χ =C

T − θ(3.9)

where θ is a specific temperature for a particular substance (equal to 0 for


Figure 3.7: Variation of reciprocal susceptibility with temperature for: (a)antiferromagnetic, (b) paramagnetic and (c) diamagnetic ordering.

paramagnets).Above TN and Tc both antiferromagnets and ferromagnets behave as para-

magnets with 1/χ linearly proportional to temperature.∗ They can be distin-guished by their intercept on the temperature axis, T = θ. Ferromagneticshave a large, positive θ, indicative of their strong interactions. For paramag-netics θ ∼= 0 and antiferromagnetics have a negative θ.

The net magnetic moment per atom can be calculated from the gradientof the straight line graph of 1/χ versus temperature for a paramagnetic ion,rearranging Curie’s law to give

µ =

√3Ak

Nx(3.10)

where A is the atomic mass, k is Boltzmann’s constant, N is the number ofatoms per unit volume and x is the gradient.

Ferromagnets below Tc display spontaneous magnetisation. Their suscep-tibility above Tc in the paramagnetic region is given by the Curie-Weiss law10

χ =J(J + 1)Ng2m2

3k(T − θ)(3.11)

∗The slight curvature for the ferrimagnet is due to the differing Curie temperaturesand interactions for the two types of magnetic atom.


Figure 3.8: Variation of saturation magnetisation below, and reciprocal sus-ceptibility above Tc for: (a) ferromagnetic and (b) ferrimagnetic ordering.

where g is the gyromagnetic constant. In the ferromagnetic phase withT . Tc the magnetisation M(T ) can be simplified to a power law, for ex-ample the magnetisation as a function of temperature can be given by

M(T ) ≈ (Tc − T )β (3.12)

where the term β is typically in the region of 0.33 for magnetic ordering inthree dimensions.

The susceptibility of an antiferromagnet increases to a maximum at TNas temperature is reduced, then decreases again below TN . In the presenceof crystal anisotropy in the system this change in susceptility depends onthe orientation of the spin axes: χ‖ decreases with temperature whilst χ⊥ isconstant. These can be expressed as

χ⊥ =C

2θ(3.13)

where C is the Curie constant and θ is the total change in angle of the twosublattice magnetisations away from the spin axis, and

χ‖ =2ngµ

2HB

′(J, a′0)

2kT + ngµ2HγρB

′(J, a′0)(3.14)


where ng is the number of magnetic atoms per gramme, B′ is the derivativeof the Brillouin function with respect to its argument a′, evaluated at a′0, µHis the magnetic moment per atom and γ is the molecular field coefficient.

3.5 SQUID Magnetometry

One of the most sensitive forms of magnetometry is SQUID magnetome-try. This uses a combination of superconducting materials and Josephsonjunctions to measure magnetic fields with resolutions up to ∼ 10−14 kG orgreater.11

3.5.1 Electron-pair Waves

In superconductors the resistanceless current is carried by pairs of electrons,known as Cooper Pairs. Each pair can be treated as a single particle with amass and charge twice that of a single electron, whose velocity is that of thecenter of mass of the pair.

In a normal conductor the coherence length of the conduction electronwave is quite short due to scattering. Cooper pairs, however, are not scatteredhence their wavefunctions are coherent over very long distances.

Each pair can be represented by a wavefunction of the form12

ΦP = Φei(P .r)/~ (3.15)

where P is the net momentum of the pair whose center of mass is at r. Ina uniform current density all the electron wavelengths will be equal with thesuperposition of these coherent waves producing a single wave of the samewavelength, meaning all of the electron-pairs in a superconductor can bedescribed by a single wavefunction

ΨP = Ψei(P �r)/~ (3.16)

This electron-pair wave retains its phase coherence over long distancesand it is this characteristic which leads to interference and diffraction phe-nomena. As they are macroscopic manifestations of quantum interactionsthe phenomena are collectively termed “Quantum Interference”.

Phase and Coherence

An implication of this long range coherence is the ability to calculate phaseand amplitude at any point on the wave’s path from the knowledge of its


phase and amplitude at any single point, combined with its wavelength andfrequency. The wavefunction of the electron-pair wave in Equation 3.16 canbe rewritten in the form of a one-dimensional wave as

ΨP = Ψ sin 2π(xλ− vt

)(3.17)

If we take the wave frequency, ν, as being related to the kinetic energy of theCooper pair with a wavelength, λ, being related to the momentum of the pairby the relation λ = h/P then it is possible to evaluate the phase differencebetween two points in a current carrying superconductor.

If a resistanceless current flows between points X and Y on a supercon-ductor there will be a phase difference between these points that is constantin time. The phase difference for such a plane wave is given by

(∆φ)XY = φX − φY = 2π

∫ Y

X

x

λ� dl (3.18)

where x is a unit vector in the direction of the wave propagation, and dl isan element of a line joining X to Y.12

The relation of v to the supercurrent density, Js, is Js = 1/2ns.2e.v, wherens is the superelectron density, and 1/2ns is the electron-pair density. Thewavelength can therefore be written as

λ =hnse

2mJs(3.19)

and hence the phase difference between points X and Y can be written as

(∆φ)XY =2πm

hnse

∫ Y

X

J s � dl (3.20)

Effect of a Magnetic Field

The phase of the electron-pairs can be affected not only by the current densitybut also quite strongly by an applied magnetic field. In the presence of amagnetic field the momentum, p, of a particle with charge q in the presence ofa magnetic field becomes mv+qA where A is the magnetic vector potential.For electron-pairs in an applied field their moment P is now equal to 2mv+2eA.12

In an applied field the phase difference between points X and Y is nowa combination of that due to the supercurrent and that due to the applied


field, ie(∆φ)XY = [(∆φ)XY ]i + [(∆φ)XY ]B (3.21)

where

[(∆φ)XY ]i =4πm

hnse

∫ Y

X

J s � dl (3.22)

and

[(∆φ)XY ]B =4πe

h

∫ Y

X

A � dl (3.23)

The Fluxoid

One effect of the long range phase coherence is the quantisation of magneticflux in a superconducting ring. This can either be a ring, or a supercon-ductor surrounding a nonsuperconducting region. Such an arrangement canbe seen in Figure 3.9 where region N has a flux density B within it due tosupercurrents flowing around it in the superconducting region S.

Figure 3.9: Superconductor enclosing a non-superconducting region.

In the closed path XYZ encircling the nonsuperconducting region therewill be a phase difference of the electron-pair wave between any two points,such as X and Y, on the curve due to the field and the circulating current asgiven by Equation 3.21.

The total phase change around the path XYZX can be written as

∆φ =4πm

hnse

∮J s � dl +

4πm

h

∫∫S

B � dS (3.24)


where S is the area enclosed by XYZX.12

If the superelectrons are represented by a single wave then at any pointon XYZX it can only have one value of phase and amplitude. Due to thelong range coherence the phase is single valued meaning around the circum-ference of the ring ∆φ must equal 2πn where n is any integer.13 RewritingEquation 3.24 using this condition we have a definition for Φ′

Φ′ =m

nse2

∮J s � dl +

m

2e

∫∫S

B � dS = nh

2e(3.25)

with the central part of this equation named the fluxoid by F. and H. London.Due to the wave only having a single value the fluxoid can only exist inquantised units. This quantum is termed the fluxon, Φ0, given by

Φ0 =h

2e= 2.07× 10−15 Wb (3.26)

3.5.2 Josephson Tunnelling

If two superconducting regions are kept totally isolated from each other thephases of the electron-pairs in the two regions will be unrelated. If the tworegions are brought together then as they come close electron-pairs will beable to tunnel across the gap and the two electron-pair waves will becomecoupled. As the separation decreases the strength of the coupling increases.The tunnelling of the electron-pairs across the gap carries with it a super-conducting current as predicted by B.D. Josephson14 and is called “Joseph-son Tunnelling” with the junction between the two superconductors called a“Josephson Junction”.

Like a superconductor this gap has a critical current. If a supercurrent, is,flows across a gap between regions with a phase difference, ∆φ, it is relatedto the critical current, ic, by

is = ic sin ∆φ (3.27)

so that the maximum current flows across the gap when there is a phasedifference of π/2, where is = ic.

The Josephson Tunnelling Junction is a special case of a more generaltype of weak link between two superconductors. Other forms include con-strictions and point contacts but the general form is of a region between twosuperconductors which has a much lower critical current and through whicha magnetic field can penetrate.


3.5.3 Superconducting Quantum Interference Device(SQUID)

A Superconducting Quantum Interference Device (SQUID) uses the proper-ties of electron-pair wave coherence and Josephson Junctions to detect verysmall magnetic fields. The central element of a SQUID is a ring of super-conducting material with one or more weak links. An example is shown inFigure 3.10, with weak-links at points W and X whose critical current, ic, ismuch less than the critical current of the main ring. This produces a verylow current density making the momentum of the electron-pairs small. Thewavelength of the electron-pairs is thus very long leading to little differencein phase between any parts of the ring.

If a magnetic field, Ba, is applied perpendicular to the plane of the ring,a phase difference is produced in the electron-pair wave along the path XYWand WZX. A small current, i, is also induced to flow around the ring, produc-ing a phase difference across the weak links. Normally the induced currentwould be of sufficient magnitude to cancel the flux in the hole of the ring butthe critical current of the weak-links prevents this.

The quantum condition that the phase change around the closed pathmust equal n2π can still be met by large phase differences across the weak-links produced by even a small current. An applied magnetic field producesa phase change around a ring, as shown in Equation 3.23, which in this caseis equal to

∆φ(B) = 2πΦa

Φ0

(3.28)

where Φa is the flux produced in the ring by the applied magnetic field.12

Φa may not necessarily equal an integral number of fluxons so to ensure thetotal phase change is a multiple of 2π a small current flows around the ring,producing a phase difference of 2∆φ(i) across the two weak-links, giving atotal phase change of

∆φ(B) + 2∆φ(i) = n2π (3.29)

The phase difference due to the circulating current can either add to orsubtract from that produced by the applied magnetic field but it is more en-ergetically favourable to subtract: in this case a small anti-clockwise current,i−.12

Substituting values from Equations 3.27 and 3.28, the magnitude of the


Figure 3.10: Superconducting quantum interference device (SQUID) as asimple magnetometer.

circulating current, i−, can be obtained

|i−| = ic sin πΦa

Φ0

(3.30)

As the flux in the ring is increased from 0 to 1/2Φ0 the magnitude of i−

increases to a maximum. As the flux is increased greater than 1/2Φ0 it is nowenergetically favourable for a current, i+, to flow in a clockwise direction,


decreasing in magnitude to 0 as the flux reaches Φ0. The circulating currenthas a periodic dependence on the magnitude of the applied field, with aperiod of variation of Φ0, a very small amount of magnetic flux. Detectingthis circulating current enables the use of a SQUID as a magnetometer.

3.5.4 SQUID Magnetometer

The circulating current produced by a flux change in the SQUID can bedetected by the use of a measuring current, I, as shown in Figure 3.10. Thiscurrent divides equally between both weak-links if the ring is symmetrical.Whilst the current through the weak-links is small there will be no voltagedetected across the ring. As I is increased it reaches a critical measuringcurrent, Ic, at which voltages begin to be detected.

The magnitude of the critical measuring current is dependent upon thecritical current of the weak-links and the limit of the phase change aroundthe ring being an integral multiple of 2π. For the whole ring to be supercon-ducting the following condition must be met

α + β + 2πΦa

Φ0

= n � 2π (3.31)

where α and β are the phase changes produced by currents across the weak-links and 2πΦa/Φ0 is the phase change due to the applied magnetic field.

When the measuring current is applied α and β are no longer equal,although their sum must remain constant. The phase changes can be writtenas

α = π

[n−

(Φa

Φ0

)]− δ (3.32)

β = π

[n−

(Φa

Φ0

)]+ δ (3.33)

where δ is related to the measuring current I. Using the relation betweencurrent and phase in Equation 3.27 and rearranging to eliminate i we obtainan expression for I,

I = 2ic

∣∣∣∣cos πΦa

Φ0

· sin δ∣∣∣∣ (3.34)

As sin δ cannot be greater than unity we can obtain the critical measuring


Figure 3.11: Critical measuring current, Ic, as a function of applied magneticfield.

current, Ic from Equation 3.34 as

Ic = 2ic

∣∣∣∣cos πΦa

Φ0

∣∣∣∣ (3.35)

which gives a periodic dependence on the magnitude of the magnetic field,with a maximum when this field is an integer number of fluxons and a min-imum at half integer values as shown in Figure 3.11.

Chapter 4

Experimental Techniques

Hunt with eyes of falling light,A single jewel on the shore,

Reveals itself with rising light,Hidden in its shell no more.

Cupped the shell to ears so tight,Now to hear these secrets roar.

This chapter outlines the equipment used to obtain the data for this thesisusing the phenomena covered in Chapters 2 and 3.

4.1 Mossbauer Spectrometers

This section covers a generic Mossbauer spectrometer and the specific equip-ment used in the Mossbauer laboratory in the University of Liverpool for theroom temperature spectrometer and an electromagnet CEMS spectrometer.

4.1.1 Gamma-ray Source57Fe Mossbauer spectroscopy uses a 57Co source. The decay scheme of thisisotope is shown in Figure 4.1. The half-life of 57Co is 271.7 days and decaysby electron capture to the I = 5/2 excited state of 57Fe. This excited statedecays to the I = 3/2 excited state (14.41 keV) or to the I = 1/2 ground stateby gamma-ray emission. The 14.41 keV state decays in turn to the groundstate by gamma-ray emmission or internal conversion. The ratio of thesetwo decay rates are given by Equation 2.28, where α = 8.21 for 57Fe. Thehalf-life of the 14.41 keV excited state is 97.8 ns, giving a Mossbauer gamma-ray with a linewidth of 0.097mm/s. The linewidth of a resonant emission andabsorption event is thus 0.194mm/s in perfect conditions.7

43

CHAPTER 4. EXPERIMENTAL TECHNIQUES 44

Figure 4.1: Decay scheme for a 57Co source leading to gamma-ray emission.Internal conversion accounts for the remaining 91% of 14.41 keV events.

The sources used in this thesis are fabricated by diffusing 57Co atoms ina rhodium foil matrix: the rhodium matrix provides a solid environment forthe 57Co atoms with a high recoil-free fraction and a cubic, non-magneticsite environment to produce mono-energetic gamma-rays. The initial sourceactivities are ∼ 100 mCi with a linewidth of 0.22mm/s measured with a thinabsorber.

4.1.2 Basic Mossbauer Spectrometer

Figure 4.2 shows a schematic diagram of a simple Mossbauer spectrometer.The source velocity is controlled by a transducer which is oscillated withconstant acceleration. A waveform generator sends a reference waveform(triangular in the spectrometers at Liverpool) to the drive amplifier, via aDigital to Analogue Converter. This signal is sent to the vibrator where it isconverted to a mechanical oscillation of the drive shaft and source. A small


Figure 4.2: Mossbauer spectrometer schematic.

coil within the vibrator provides a feedback signal to correct any deviationsfrom the reference waveform.

The detector is a proportional counter containing a 90% argon and 10%methane gas mixture. It uses an applied bias voltage of −2.0 to −2.5 keV andhas a 65% detection efficiency for 14.41 keV gamma-rays. The pulse mag-nitude from the detector is directly proportional to the gamma-ray energyand is sorted by a single channel analyser after amplification. This allowsthe selection of the Mossbauer gamma-ray from any other radiation emittedfrom the source.

The detector counts and source velocity are synchronised by a micropro-cessor system. The counts accumulate in 576 channels for one complete cycle,which contain two complete spectra: one for positive acceleration and onefor negative acceleration of the source. As the acceleration is constant thetime interval is equal for all velocity intervals, hence each channel records forthe same amount of time. During analysis the full spectrum is folded arounda center point to produce a single spectrum. This increases the number ofcounts (and hence gives better statistics) and flattens the background profileproduced by the difference in intensity of the source radiation as the source


moves relative to the absorber and detector.

4.1.3 CEMS

Conversion Electron Mossbauer Spectroscopy utilises the emission of conver-sion electrons from the decay of the 14.41 keV state in the absorber to recordthe spectrum. This is useful for samples with thick substrates which wouldblock transmission of gamma-rays or for studies of the surfaces of samplesrather than the bulk. As the ratio of conversion electrons to gamma-raysemitted by the 14.41 keV Mossbauer event in 57Fe is 8.21 the counting effi-ciency of CEMS is much greater than the transmission method.

A schematic diagram of the CEMS spectrometer as used in this thesis isshown in Figure 4.3.15 As the emitted electrons are of a low energy they wouldbe attenuated by a detector window hence the sample is inserted directly intothe detector.

The source irradiates the sample through the window. An anode wire ismaintained at a high voltage (∼ 800 V) directly in front of the sample. Elec-trons emitted from the sample are accelerated towards the anode, ionisingatoms in the counting gas, producing an avalanche effect which amplifies thesignal from the original emitted electron. This electronic pulse is detectedand recorded as for Transmisson Mossbauer Spectroscopy.

The counting gas, a 90% helium and 10% methane mix, is constantly re-plenished by a small flow from a cannister. This flushes out any contaminantsfrom the atmosphere, such as oxygen, which would reduce the counting effi-ciency. The methane acts as a quenching gas, preventing helium ions reach-ing the cathode whilst maintaining a high gain. The counting gas mixture ofhelium/methane has negligible reaction with the incident 14.41 keV gamma-rays - making it transparent to the incident radiation - but when electronsare emitted from the sample the normal proportional counter effect describedabove takes place. The perspex window attenuates the 6.3 keV x-rays fromthe source which would otherwise produce a large background signal fromnon-resonantly emitted electrons, but only attenuates the 14.41 keV gamma-ray by a small amount.

Measurements with this system are restricted to room temperature dueto the bulk of the detector itself and the condensation of the methane gasat low temperatures. A magnetic field of up to 2.5 kOe can be applied inthe plane of the sample. This is supplied by placing the CEMS detectorbetween the soft iron poles of an electromagnet. Fields greater than 2.5 kOeare prohibited due to the curved trajectory of the emitted electrons in amagnetic field producing a reduced counting efficiency.

Samples are mounted upon the aluminium faceplate of the sample mount


Figure 4.3: CEMS detector used at Liverpool University.

using a thin layer of vacuum grease. The samples are then covered with asample shroud constructed from aluminium foil to present a smooth, contin-uous face to the anode wire. This surface is cleaner than the sample mountwhich can become coated with contaminants stuck to the vacuum grease andprevents electric fields building at sharp corners or edges on the sample whichmay produce electron discharges towards the anode and hence increase thebackground noise.


4.2 Data Analysis

Although simple analysis can be performed by eye on Mossbauer spectra (egseeing whether a sample is magnetised or not) to determine the hyperfineparameters computer analysis is necessary. The raw data is collected by adata acquisition computer system and transferred to a Sun Solaris systemfor analysis. The spectrum is folded and a theoretical spectrum is calculatedaccording to specified hyperfine parameters and compared to the data. Theparameters can then be varied to obtain the lowest χ2 value and give thebest fit.

As there are a number of minima of χ2 that can be obtained from var-ious points in parameter space the resulting fits must then be checked forconsistent parameters to ensure a fit that is physically valid.

4.2.1 χ2 Minimisation

χ2 is a measure of the deviation of the theoretical spectrum and the exper-imental spectrum, giving a best fit when it is at a minimum. The analysisprograms vary the parameters of the theoretical spectrum to find a minimumin χ2 according to the following formula:

χ2 =1

N − n

N∑i=1

[Ei − Ti√

Ei

]2

(4.1)

where N is the number of channels (576 in this case) and n is the number ofparameters that are free to vary. Ei and Ti are the number of counts in theith channel of the experimental and theoretical spectra respectively.

4.2.2 Fitting Routines

The core program of the main fitting routines as used at Liverpool is called“fcfcore” which contains code to read and write the data files, vary the pa-rameters and perform χ2 minimisation (using NAG routine E04FCF). Thephysics which determines the line positions and intensities is contained inseparate subroutines, making it easy to alter and add new types of fittingroutines.

For most spectra a general purpose subroutine called “FFitA” is used.This can produce multiple singlets, doublets or sextets using Lorentzian line-shapes. To reduce the computing time necessary for fitting it uses the ap-proximations described in Section 2.3.4.


For spectra with distributions of hyperfine field or quadrupole splittingvalues a program called NORMOS/DIST is used. This is an extension to theNORMOS/SITE fitting package. This uses the VA02A routine for χ2 min-imisation. The routines can fit with multiple hyperfine field or quadrupolesplitting distribution blocks as well as multiple crystalline sites.

4.2.3 Calibration

To analyse the recorded spectra the spectrometer needs to be calibrated. Thethree main calibration parameters are the velocity scale, the center point ofthe spectrum and the alinearity of the velocity/time profile of the oscillationcompared to a standard reference. The calibration is performed using aspectrum recorded from an α-iron foil at room temperature and fitted withthe “FCal” subroutine.

The velocity scale is calibrated using the well defined line positions of thesextet from α-iron, which occur at±5.312mm/s, ±3.076mm/s and±0.840mm/s.16

The center of this α-iron spectrum at room temperature is taken as the ref-erence point (0.0mm/s) for isomer shift values of sample spectra.

4.3 SQUID Magnetometer

The magnetometry data for this thesis have been taken using a QuantumDesign Magnetic Property Measurement System (MPMS) XL SQUID mag-netometer.

4.3.1 Magnetometer Overview

The MPMS system comprises of two main sections: the dewar, probe andSQUID assembly, and the electronic control system. The probe system ismodular allowing the addition of extra component options (such as the RSOoption, see Section 4.3.2).

The probe contains a high precision temperature control system, allowingmeasurements between 1.9 K and 400 K with an accuracy of 0.01 K, andsuperconducting electromagnet, giving a field of up to 50 kG with an accuracyof up to 0.1 G.

The dewar consists of an inner liquid helium reservoir and outer liquidnitrogen jacket, to reduce excessive liquid helium boil off. The liquid heliumis used both for maintaining the electromagnet in a superconducting stateand for cooling the sample space.


Samples are mounted within a plastic straw and connected to one endof a sample rod which is inserted into the dewar/probe. The other end isattached to a stepper motor which is used to position the sample within thecenter of the SQUID pickup coils.

The pickup coils are configured as highly balanced second-derivative coils,approximately 3 cm long. The coils reject the applied field from the super-conducting magnet to a resolution of 0.1%.

4.3.2 RSO Measurements

The data were taken using the Reciprocating Sample Option (RSO). Un-like DC measurements where the sample is moved through the coils in dis-crete steps the RSO measurements are performed using a servo motor whichrapidly oscillates the sample, see Figure 4.4. These measurements have asensitivity of 5× 10−9 EMU.17

A shaft encoder on the servo motor records the position of the samplesynchronous with the SQUID signal. The data received is fitted to an idealdipole moment response. To ensure this assumption is applicable samplesneed to be small: the calibration sample is a cylinder of 3 mm diameter and3 mm height. Samples of this size or smaller match an ideal point dipole toan accuracy of approximately 0.1%.17

RSO measurements can be made in one of two configurations: Center orMaximum slope. Center scans use large oscillations (2 to 3 cm) around thecenter point of the pickup coils. These scans take a long time but the samplealways remains properly located and a large number of measurements arerecorded. These give the most accurate readings.

The Maximum Slope method oscillates the sample over a small region(2 mm) at the most linear part of the SQUID response (as shown in Fig-ure 4.4). The smaller amplitude makes measurements quicker and preventsthe sample being subjected to significant magnetic field variation, howeverit also makes the measurement less accurate and susceptible to drift in thesample position.

All measurements taken in this thesis using the MPMS XL SQUID wereperformed in Center mode with an amplitude of 3 cm.


Figure 4.4: Illustration of an RSO measurement with a small amplitude. (a)shows the ideal SQUID response for a dipole and (b) shows the movementof the sample within the SQUID pickup coils.

Chapter 5

Magnetic Interactions

Hawk alone in wait, hunkered down tograsp with talons bare, talons barbed,

tight within its perch, in branch embedand feeling naught from wind andsquall, none to break its steadfast

gaze upon its prey; a sparkling shoal.Scale and movement mirrored, facing all

towards the stream, its flow and whirlportrayed in their gently twisting dance.

This chapter gives an overview of some of the more important magneticinteractions that occur within the thin film systems studied in this thesis.Of particular importance is the magnetic anisotropy of a system, as thiscan change considerably when going from bulk to thin film and multilayersystems. The RKKY interaction can also greatly influence the magneticordering in some systems as distances between magnetic entities are varied.

5.1 Magnetic Anisotropy

Magnetic anisotropy is the dependence of the internal energy of a systemon the direction of the spontaneous magnetisation. An energy term of thiskind is called magnetic anisotropy energy. In general most kinds of mag-netic anisotropy are related to the crystal symmetry of a material and thisis known as magnetocrystalline anisotropy. Anisotropy can also be relatedto mechanical stress in the system and this is known as magnetostrictiveanisotropy.

52

CHAPTER 5. MAGNETIC INTERACTIONS 53

5.2 Magnetocrystalline Anisotropy

5.2.1 Uniaxial Anisotropy

The simplest form of crystal anistropy is uniaxial anisotropy. For cubiccrystals the anisotropy energy can be expressed in terms of the directioncosines (α1, α2, α3) of the internal magnetisation with respect to the threecube edges. Due to the high symmetry of the cubic crystal this can beexpressed in a simple manner as a polynomial series in the direction cosines.This can be simplified further10 to

Ea = K1

(α2

1α22 + α2

2α23 + α2

3α21

)+K2

(α2

1α22α

23

)+ · · · (5.1)

When K1 > 0 the first term of Equation 5.1 becomes a minimum for〈100〉 directions, whilst for K1 < 0 it is a minimum for 〈111〉 directions.

5.2.2 Interface and Volume Anisotropy

It has been shown18 that in multilayers the effective magnetic anisotropyenergy, Kef , can be phenomenologically split into two components: a volumecontribution, KV , and an interface contribution, KS, which are related toKef by

Kef = KV +2KS

t(5.2)

where t is the thickness of the magnetic layer. The relation is a weightedaverage of the magnetic anisotropy energy of the interface atoms and theinner “volume” atoms in the layer. The factor of 2 arises from the layerbeing bounded by two interfaces.

In bulk systems the magnetocrystalline anisotropy of a system is domi-nated by the volume term. In thin films and multilayers, however, the surfaceterm can become more significant as t becomes small (∼ 2KS/KV ). In mostcases the anisotropy in thin magnetic layers is dominated by the dipolarshape anisotropy, favouring inplane moment alignment.

5.2.3 Single-ion Anisotropy

Single-ion anisotropy (often referred to simply as “magnetocrystalline anisotropy”)is determined by the interaction between the orbital state of a magnetic ionand the surrounding crystalline field which is very strong. The anisotropyis a product of the quenching of the orbital moment by the crystalline field.


This field has the symmetry of the crystal lattice. Hence the orbital momentscan be strongly coupled to the lattice.

This interaction is transferred to the spin moments via the spin-orbit cou-pling, giving a weaker d-electron coupling of the spins to the crystal lattice.When an external field is applied the orbital moments may remain coupledto the lattice whilst the spins are more free to turn. The magnetic energydepends upon the orientation of the magnetisation relative to the crystalaxes.

In a magnetic layer, the single-ion anisotropy is present throughout thelayer volume, and so contributes to KV . Whether this is in addition to orsubtraction from KV depends upon the crystal orientation of the layer. Intransition metals this contribution is generally much smaller than the shapeanisotropy but can be comparable in magnitude in rare earth metals, hencethe large interest in rare earth materials in thin film systems to tailor momentorientation such as Perpendicular magnetic Anisotropy.

The single-ion anisotropy can also contribute to the surface anisotropyvia Neel interface anisotropy,19 where the reduced symmetry at the interfacestrongly modifies the anisotropy at the interface compared to the rest of thelayer. This can be in addition to or subtraction from the interface anisotropydepending upon the crystal properties of the layer and the sample construc-tion.

5.2.4 Shape Anisotropy

The magnetic dipolar anisotropy, or shape anisotropy, is mediated by thedipolar interaction. This interaction is long range and so its contribution isdependent upon the shape of the sample. Hence shape anisotropy becomesimportant in thin films and often produces inplane alignment of moments.

In a thin film considered as a magnetic continuum the dipolar anisotropyenergy per unit volume is given by20

E =1

2µ0M

2s cos2 θ (5.3)

where Ms is the saturation magnetisation, assumed to be uniform throughoutthe layer. The magnetisation subtends an angle, θ, to the plane normal. Thedipolar anisotropy energy is thus minimised for an angle of 90◦ ie momentslying in the plane of the layer.


5.2.5 Exchange Interaction and Exchange Anisotropy

The origin of the interaction which lines up the spins in a magnetic system isthe exchange interaction. When spin magnetic moments of adjacent atoms iand j make an angle φij, the exchange energy, wij, between the two momentscan be expressed as10

wij = −2JS2 cosφij (5.4)

where J is the exchange integral and S is the total spin quantum number ofeach atom. For positive values of J this gives a minimum when φij = 0 iethe spins are aligned parallel to each other.

Although the exchange interaction produces strong interactions betweenneighbouring magnetic atoms it can also be mediated by various mechanisms,producing long range effects. As the exchange energy for neighbouring atomsis dependent only upon the angle between them it does not give rise toanisotropy.

In multilayers where magnetic layers are separated by a non-magneticlayer, there can be an exchange coupling between the two magnetic layersmediated by, for example, the RKKY interaction (see Section 5.4). Theexchange coupling is composed of two terms: an isotropic exchange couplingand an anisotropic Dzialoshinski-Moriya exchange coupling.

The total exchange interaction energy is given by21

EEX = −2J(z)M 1 �M 2 (5.5)

where J(z) is the exchange coupling constant, M 1 and M 2 are the mag-netisation of the adjacent magnetic layers and z is the non-magnetic layerthickness. This product is a maximum for ferromagnetically aligned layers.

The anisotropic exchange energy is given by21

EDM = JDM(z) � (M 1 ×M 2) (5.6)

where JDM is the Dzialoshinski-Moriya exchange constant. The cross prod-uct gives a resultant that is perpendicular to the direction of the layer mag-netisation. This is at a maximum when the two layer magnetisations are atright angles to each other. This can favour inplane moment alignment forpositive JDM and out of plane alignment for negative JDM .

5.3 Magnetostriction

Magnetostriction is the change in length in a given direction of a magneticmaterial when it is magnetised along that direction. Similarly strain in a


ferromagnet can alter the direction of the magnetisation.

5.3.1 Magneto-elastic Anisotropy

The magneto-elastic effect arises from the spin-orbit interaction. The spinmoments are coupled to the lattice via the orbital electrons. If the lattice ischanged by strain the distances between the magnetic atoms is altered andhence the interaction energies are changed. This produces magneto-elasticanisotropy.

Magnetostriction constants, λhkl, are defined for various crystal direc-tions. For an elastically isotropic medium, with isotropic magnetostriction,the magneto-elastic energy per unit volume is given by8

E = −3

2λσ cos2 θ (5.7)

where σ is the stress and θ is the angle between the magnetisation and stressdirections. For positive λ, as in metallic iron, the easy magnetic directionwill be along a direction of tensile stress, or perpendicular to a compressivestress.

Strain in thin films and multilayers can be produced by the growth con-ditions, such as lattice mismatch between layers or thermal stress caused bydifferences in thermal expansion coefficients of adjacent layers.

5.4 The RKKY Interaction

Indirect exchange couples moments over relatively large distances. It is thedominant exchange interaction in metals where there is little or no directoverlap between neighbouring magnetic electrons. It therefore acts throughan intermediary which in metals are the conduction electrons (itinerant elec-trons). This type of exchange was first proposed by Ruderman and Kittel22

and later extended by Kasuya and Yosida to give the theory now generallyknow as the RKKY interaction.

The interaction is characterised by a coupling coefficient, j, given by23

j (Rl −Rl′) = 9π

(j2

εF

)F (2kF |Rl −Rl′|) (5.8)

where kF is the radius of the conduction electron Fermi surface, Rl is the


Figure 5.1: Variation of the indirect exchange coupling constant, j, of a freeelectron gas in the neighbourhood of a point magnetic moment at the originr = 0.

lattice position of the point moment, εF is the Fermi energy and

F (x) =x cosx− sin x

x4(5.9)

The RKKY exchange coefficient, j, oscillates from positive to negativeas the separation of the ions changes and has the damped oscillatory natureshown in Figure 5.1. Therefore, depending upon the separation between apair of ions their magnetic coupling can be ferromagnetic or antiferromag-netic. A magnetic ion induces a spin polarisation in the conduction electronsin its neighbourhood. This spin polarisation in the itinerant electrons is feltby the moments of other magnetic ions within range, leading to an indirectcoupling.

In rare-earth metals, whose magnetic electrons in the 4f shell are shieldedby the 5s and 5p electrons, direct exchange is rather weak and insignificantand indirect exchange via the conduction electrons gives rise to magneticorder in these materials.

Chapter 6

Binary Laves Phase Multilayersand Thin Films

Strong and closed,Locking selfish and within,

Weak and opened,Reaching shared and calling,

Face out and unite,Free yet in nature chained,

Let loose in flight,Power set on wings claimed.

This chapter presents CEMS measurements of Rare Earth/Iron Laves Phasethin films and multilayers. The first section gives an outline of the character-istics of these systems and their potential uses. Then the results are displayedand discussed from the viewpoint of a Mossbauer spectroscopy study of themagnetic anisotropy in thin film samples. We are attempting to determinethe magnetic easy axis through analysis of accurate line positions which aresensitive to the dipolar magnetic hyperfine field. The latter sections observethe effects of multilayers of different Laves Phase materials on the anisotropyand hyperfine fields.

6.1 Introduction to Rare Earth/Iron Laves

Phase Systems

The Lanthanides are the group of elements with atomic numbers between 57and 71. They are often accompanied by yttrium as it has similar chemicalcharacteristics and are termed Rare Earths due to the difficulty with which

58

CHAPTER 6. RFE2 LAVES PHASE THIN FILMS 59

they are chemically isolated. This difficulty arises from the typical atomicconfiguration of a rare earth,13 [Xe]4fn5d(1 or 0)6s2. The 4f shell is partiallyfilled whilst the outer valence electrons are much the same in nature through-out the series, giving similar chemical characteristics to all fifteen elements.The partially filled 4f shells in rare earths lead to magnetic properties in asimilar manner to the partially filled 3d shell in transition elements.

In an intermetallic of a rare earth and a transition element the spatial ex-tent of the 4f wavefunction is highly localised giving very weak interactionsbetween rare earth atoms. In such compounds where the transition elementcarries no magnetic moment this gives rise to low ordering temperatures,24 egTc = 26.5 K for DyNi2. Any interactions must take place indirectly throughsuch mechanisms as spin polarization of the s-conduction electrons.24 Thelocalised 4f moments are affected by the polarisation produced by 4f mo-ments elsewhere in the lattice and can orient themselves accordingly. Thispolarization is not uniform in space and has an oscillitatory form as given bythe RKKY interaction (see Section 5.4).

The transition element, however, has much stronger and more long rangeinteratomic interactions due the large spatial extent of the 3d electron wave-functions. The wavefunctions of neighbouring atoms overlap producing 3d-electron energy bands rather than levels. The strong exchange interactionsbetween the 3d electrons can produce unequal numbers of spin-up and spin-down electrons. Relative differences in the density of states of 3d electronsproduces a net moment given by

m =∑E

(N(E) ↑ −N(E) ↓) (6.1)

where N(E)↑ and N(E)↓ are the density of states of the spin-up and spin-down electrons respectively. Chemical substitution can alter the number of3d electrons producing changes in the 3d magnetic moment.24

The magnetic interaction between the rare earth and transition elementhas a strength intermediate between that of the two cases discussed above.The rare earth and transition element sublattices couple antiparallel in thecase of a heavy rare earth (eg Holmium) and parallel in the case of a light rareearth (eg Praseodymium). The 3d moments align antiferromagnetically withthe spin-moment of the rare earth and the difference in coupling between thelight and heavy rare earth cases is attributed to the total angular momentumof a rare earth being J = L−S for light rare earths and J = L+S for heavyrare earths.24

Another way in which the rare earth and transition element differ is in thestrength and types of magnetic anisotropy they display. Dipolar interactions


are proportional to the square of the moment, the pair energy of a magneticdipole interaction given by10

l = − 3M2

4πµ0r3(6.2)

where M is the magnetic moment and r the distance between the atoms.As the magnetic moment of a rare earth is typically an order of magnitudegreater than a transition element a large anisotropy could be expected dueto dipolar interactions. However, there is only appreciable ordering of rareearth magnetic moments at low temperatures and so at room temperatureor above the dipolar interactions are small and of comparable magnitude tothose for a transition element.24

The dominant contribution to anisotropy in these intermetallics is due tothe effects of the crystal field on the rare earth’s 4f wavefunction. Rare earthshave very strong single-ion magnetocrystalline anisotropy (see Section 5.2),essentially the interaction between orbital state and the crystal field. Inbulk materials rare earth metals require applied fields of hundreds of kOeto overcome the anisotropic forces, compared to a few kOe for a transitionelement such as metallic Iron.

Intermetallics of rare earths and transition elements can combine thequite different natures of the two types of material via the antiferromagneticcoupling between the 3d moment and 4f spin-moment. The rare earth canprovide strong magnetocrystalline anisotropy, a large magnetic moment peratom and a large degree of magnetostriction (see Section 5.3), and this iscombined with the strong magnetic exchange coupling of the 3d moments.Using particular elements and compositions we can engineer magnetic sys-tems with specific properties for applications such as permanent magnetsand recording media and readheads. The similar chemical properties butvarying magnetic properties of the rare earths across the entire series alsooffers benefits for research as often the same compositions of intermetalliccan be produced with all the rare earths but with widely varying physicalproperties allowing the investigation of fundamental properties such as spinand angular momentum under different conditions.

6.1.1 Bulk Properties

The bulk properties of RFe2 systems have been studied extensively for manyyears.25,26,27,28 They show ferro- or ferrimagnetic structures in binary com-pounds. Their crystal structure is the cubic Laves Phase MgCu2 type, shownin Figure 6.1, and the iron atoms occupy corner-sharing tetrahedral networks


RFe

Figure 6.1: The atomic positions in the C15 MgCu2 Cubic Laves Phase unitcell.

with a (3m) point symmetry and a threefold axis lying along one of the 〈111〉directions. This direction is the principal axis of the electric field gradient,Vzz. The rare earth atoms have a cubic (43m) site symmetry.

In the high temperature paramagnetic state the four iron sites are equiv-alent, giving a single Mossbauer spectrum. In the magnetically ordered statethe number of sites which are magnetically equivalent or inequivalent dependsupon the angle between the magnetisation and the axes of local symmetryalong the 4 〈111〉 directions. If the magnetisation is parallel to the [100]direction (as in DyFe2 or HoFe2) this makes an equivalent angle to all ironsites of 54.7◦. Again a single Mossbauer spectrum is observed.27

If the magnetisation is parallel to the [111] direction (as in YFe2) there aretwo inequivalent types of iron site; one at an angle of 0◦ to the magnetisationand the remaining three at an angle of 70.5◦. The hyperfine interactions aredifferent at the two sites due to the total hyperfine splitting at the nucleusbeing a function of the angle between the hyperfine field and the principalaxis of the quadrupole interaction, Vzz, (Equation 2.21) and the angulardependence of dipolar fields on this same angle (Equation 2.20). Hence in aMossbauer spectrum we would expect two components in a ratio of 3:1 andthis is observed.27

If the magnetisation is along an arbitrary direction then all the iron sitesmay be inequivalent, giving a Mossbauer spectrum with four components ofequal intensity.


6.1.2 Thin Films and Multilayers

The RFe2 family of intermetallics have shown potential uses in a number ofnano-scale applications such as magnetic media readheads and nanosensorsand so their behaviour in thin films and other low-dimensional systems hasbecome of great interest to fundamental and applied research. Going frombulk to a thin film increases the effect of otherwise negligible effects such asshape anisotropy, strain and interface effects.

Previous work29 on expitaxial Laves Phase DyFe2 thin film samples high-lighted the importance of expitaxial strain in perturbing the magnetic be-haviour seen in bulk samples. In pure rare earths the anisotropy energy isroughly an order of magnitude greater than the magnetoelastic energy. RFe2

systems, however, show giant magnetostriction at room temperature. Themagnetoelastic energies in these samples can be large enough to stronglyinfluence the overall anisotropy energy and hence the magnetic easy axis.

In an unstressed sample the dominant influence on the direction of theeasy axis is the magnetocrystalline anisotropy energy, Emc, given by30

Emc = K1

(α2xα

2y + α2

xα2z + α2

yα2z

)+K2

(α2xα

2yα

2z

)(6.3)

where αi are the cosines of the magnetisation direction and K1 and K2 arethe anisotropy constants. The direction of magnetisation is mainly relatedto the magnitude and sign of the anisotropy constants (eg in DyFe2 K1 ispositive and K2 is negative, and |K2|/K1 < 9 leading to a magnetisationalong the [100] direction, see Section 5.2.1).

In the samples studied in this chapter there are strains caused by a differ-ence in thermal contraction between film and substrate as the sample coolsfrom the deposition temperature.30 It is now necessary to take into accountthe magnetoelastic energy, Eme, given by

Eme = b0 (εxx + εyy + εzz) + b1

(α2xεxx + α2

yεyy + α2zεzz

)+b2 (αxαyεxy + αxαzεxz + αyαzεyz) (6.4)

where εij is the strain tensor and b0, b1 and b2 are the magnetoelastic coeffi-cients, and the elastic energy, Eel, given by

Eel =1

2C11

(ε2xx + ε2

yy + ε2zz

)+ C12 (εxxεyy + εyyεzz + εxxεzz)

+1

2C44

(ε2xy + ε2

yz + ε2xz

)(6.5)

where C11, C12 and C44 are the cubic elastic constants.30


The main strain in the samples is a negative shear30 of εxy = −0.55%.This simplifies Equation 6.4 to Eme = b2εxyαxαy. The total energy, Etot, isthus

Etot = Emc + b2εxyαxαy + πM2 (αx + αy)2 (6.6)

where πM2 (αx + αy)2 is the shape anisotropy as a function of the magnetisa-

tion, M .30 The magnetic easy axis will orient so as to minimise the energies ofthe competing magnetocrystalline and magnetoelastic energies and the shapeanisotropy. The shape anisotropy favours an in plane alignment. DyFe2 inbulk has an easy axis along the [001] direction, which lies in plane for thinfilm samples so we would expect these samples to show the same easy axis inthe absence of significant magnetoelastic anisotropy. However, results fromother studies do not show an in plane magnetisation.29,30

6.1.3 Sample Construction

All of the samples studied in this chapter have been prepared using MolecularBeam Epitaxy (MBE) by Dr R.C.C. Ward and Dr M.R. Wells, ClarendonLaboratory, Oxford University. An outgassed (1120) sapphire substrate isplaced into an MBE chamber at 4 × 10−11 Torr and 500 A of Niobium isdeposited as a buffer. A thin Fe seed layer of 15 A is then deposited followedby an 800 A YFe2 seed layer. This provides basis for growth of good qualityfilms and multilayers.

The sample growth direction is (110), perpendicular to the plane of thesample. A generic schematic of the samples is shown in Figure 6.2.

6.2 RFe2 Thin Films

This section presents analysis of data from a CEMS study of the easy axis di-rection in thin films (500 A–1000 A) of rare earth/iron intermetallics. CEMSwas used as all samples have a thick Sapphire substrate which is opaque tothe 14.41 keV Mossbauer gamma ray. All measurements are taken at roomtemperature in either 0 kOe or 2.5 kOe in plane applied magnetic field. Thesamples are not 57Fe enriched.

6.2.1 Determining the Magnetic Easy Axis

A particularly important parameter to extract from the spectra is the di-rection of the magnetic easy axis. This is well known in bulk RFe2 inter-metallics24 but has been shown to not be along any expected high-symmetry


Al2O3 Substrate

500A Nb Buffer

Film orMultilayer

800A YFe2 Seed

(110)

15A Fe Seed

Figure 6.2: Schematic of the Laves Phase sample construction.

axis in thin films at room temperature.29,30 Mossbauer spectroscopy is par-ticularly sensitive to the orientation of magnetic moments at a particular site,either through the angular dependency of the dipolar hyperfine field (Equa-tion 2.20) or from the relative line intensities (Equation 2.24). The latteris often much more pronounced and so easy to obtain reliable informationfrom.

Previous work on single-crystal RFe2 thin films by V. Oderno et al29

showed that the easy direction was 〈100〉 at 4.2 K but was a direction of lowsymmetry at room temperature. Their best fits were for those assuming aneasy magnetic axis of 〈241〉, with [142], [241], [124] and [124] being the mostlikely as they were closest to the angle displayed by their Mossbauer spectra.Subsequent experiments by Mougin et al30 again showed the difference ineasy axis at 4.2 K and room temperature. Their analysis indicated an easyaxis along 〈351〉 directions, with the most likely being [351]. Consequently


our analysis starts with the assumption of a 〈241〉 or 〈351〉 easy axis at roomtemperature.

However, the proposed easy axes of 〈241〉 or 〈351〉 both have a high levelof degeneracy in a cubic system, corresponding to 24 different directions.These samples are conceived as single-crystal, thus a given axis such as [351]denotes a unique axis in the sample. However, there will be magnetic do-mains in which the magnetisation direction, while linked to an equivalentdirection of 〈351〉, does not define a unique direction in the sample. Thusthe Mossbauer spectrum will display the relative directions of Vzz and Hthrough line positions but will not give reliable information through relativeline intensities as these can be affected by different magnetic domain pat-terns which can be affected by sample history. In the absence of a trainingfield there are still physical characteristics which favour particular directions.The shape anisotropy of the sample will favour moments that are more inplane and this is corroborated by the average angle obtained from the lineintensities of 21◦ to the sample plane (for DyFe2). This does, however, stillleave at least four non-equivalent directions and with no direct evidence oftheir relative populations.29

In interpreting the line positions of the Mossbauer spectra with highaccuracy it is necessary to consider the dipole contribution to the total fieldat the iron nuclei. The dipolar hyperfine field is determined by the localenvironment of the nucleus: the interaction between the hyperfine field andEFG vectors at that site. As a localised interaction it is invarient with respectto the domain or sample orientation and so it is not subject to any averagingeffects across the sample volume. The dipolar field influences the relative linepositions both by its contribution to the magnitude of the total hyperfine fielddetected at the nucleus and also to its direction. This affects the quadrupolarhyperfine interaction (explained in Section 2.3.4) as the dipolar field tips thespins away from the primary EFG axis, Vzz, which for RFe2 Laves Phasesamples is one of the 〈111〉 directions.

The dipolar hyperfine field can be calculated using a matrix form devisedby G.J. Bowden et al31 of

HD = D〈111〉µ (6.7)

where µ is the direction of the magnetic easy axis and D〈111〉 is a set ofmatrices for each inequivalent iron site. These are shown in Equation 6.9.This can be used to evaluate the direction of the dipolar field at each site.For example to calculate HD for the [111] Fe site assuming an easy axis of


[351] we would use

HD = Dzz

0 1/2 1/2

1/2 0 1/2

1/2 1/2 0

−351

= Dzz

3−1

1

(6.8)

where Dzz is the magnitude of the dipolar field, estimated as 16 kG in DyFe2

and 5 kG in YFe2.27

D[111] =

0 1/2 1/2

1/2 0 1/2

1/2 1/2 0

D[111] =

0 1/2 −1/2

1/2 0 −1/2

−1/2 −1/2 0

D[111] =

0 −1/2 −1/2

−1/2 0 1/2

−1/2 1/2 0

D[111] =

0 −1/2 −1/2

−1/2 0 −1/2

1/2 −1/2 0

(6.9)

The Fermi contact field, HS (Equation 2.18), is much larger (≈ 215 kGin DyFe2) and lies along the magnetic easy axis, [351] in this case. Vectoradding HD and HS gives the total hyperfine field at the site, H .∗ Therelative magnitude of the quadrupolar interaction can then be calculatedusing the angle, φ, between the resultant total hyperfine field, H , and thedirection of Vzz for that site using

∆ =

(eqQ

2

)· 1

2

(3 cos2 φ− 1

)(6.10)

where 1/2 (3 cos2 φ− 1) can be evaluated and the value of (eqQ/2) is determinedthrough least squares analysis of the spectrum.

The initial magnitudes of HS and HD are estimates taken from bulksystems. After the spectrum is fitted according to the values obtained as inthe above method and the best fit is obtained, the fitting parameters can beanalysed. Taking a pair of total hyperfine field values and the known anglebetweenHS andHD a simultaneous equation can be used to extract HS andHD. These derived values can then be used to calculate a new set of initial fitparameters and the whole process is repeated in an interative fashion untilstable values are obtained.

∗Any other terms are taken as having negligible effect on the total field and its direc-tion.


[241] [351]

HS = 205± 2 kG HS = 205± 5 kGHD = 15± 4 kG HD = 17± 7 kG

χ2 = 2.05 χ2 = 2.06Site IS QS Field IS QS Field

(mm/s) (mm/s) (kG) (mm/s) (mm/s) (kG)[111] −0.1 −0.0604 198.8 −0.1 −0.0935 199.7[111] −0.1 −0.1387 182.5 −0.1 −0.1432 182.5[111] −0.1 +0.2191 209.1 −0.1 +0.2167 208.8[111] −0.1 +0.0644 205.7 −0.1 +0.0949 204.8

Table 6.1: Final fit parameters for 750 A DyFe2 sample assuming [241] or[351] easy axis in zero applied field.

6.2.2 DyFe2

In common with all the samples studied in this chapter at room temperaturethe 750 A DyFe2 sample needs a minimum of four components to be fittedproperly. Figure 6.3 shows the spectra for all of the thin film samples studiedin zero applied field. Four inequivalent iron sites confirm the easy axis is notalong any of the high symmetry directions expected in bulk systems.

The best fit parameters for the DyFe2 samples in zero applied field areshown in Table 6.1 for fits assuming [241] or [351] easy axis directions withvalues calculated according to the dipole hyperfine field analysis in Sec-tion 6.2.1.

The isomer shift values (IS) are fixed to be equal for all components butfree to vary as a whole. The IS value of −0.1mm/s is consistent with thosereported for bulk samples.32 The quadrupole splitting is fixed and its valueis calculated using the analysis outlined in Section 6.2.1.

The hyperfine fields are initially fixed according to the values calculatedfrom HS and HD and then allowed to vary. The theoretical values do notgive satisfactory fits and are allowed to freely vary (with the quadrupolesplitting remaining constant). Iteratively varying HS and HD to accountfor the difference is prohibitively time consuming as it is not an automatedprocess: there is no way to automatically transfer the parameters from thedipolar field analysis into the Mossbauer fitting routines. The spread invalues is from the different angle that the axis of symmetry at each iron sitemakes with the magnetic easy axis, and hence the dipolar field contributionis different.


0.0

0.5

1.0

1.5

Per

cent

Em

issi

on

0.0

0.5

1.0

1.5

Velocity (mm/s)−8 −6 −4 −2 0 2 4 6 8

0.0

0.2

0.4

0.6

DyFe2(750A)

YFe2(1000A)

HoFe2(500A)

Figure 6.3: Comparison of spectra of DyFe2, YFe2 and HoFe2 thin films atroom temperature under zero applied field.


Figure 6.4: 750 A DyFe2 thin film under 0 kOe and 2.5 kOe in plane appliedmagnetic fields.

The values of HS and HD (Table 6.1) obtained are consistent with thosefound for bulk samples.27 There is no significant difference between the fitsfor [241] and [351] easy axes either in the quality of the fitting of theory tothe spectrum or in the comparison of the derived hyperfine field values withthose from other studies.

A spectrum was recorded under an in plane applied field, (H0 in Equa-tion 2.17) of 2.5 kOe. This spectrum is compared to the zero applied fieldspectrum in Figure 6.4 and the fit parameters compared in Table 6.2. Thefitting parameters do not have any particular easy axis applied. The IsomerShifts and relative line intensities are fixed to be equal for all sites but freeto vary.

The change in average angle of the spin moments under applied field is0.2◦. The two spectra were not recorded sequentially and thus this change inangle is well within the experimental error of the relative angular positioningof the source and sample, taken to be 2◦.


0 kOe 2.5 kOe

χ2 = 2.53 χ2 = 1.91Site IS QS Field Angle IS QS Field Angle

(mm/s) (mm/s) (kG) (◦) (mm/s) (mm/s) (kG) (◦)1 −0.10 −0.24 186.6 23.3 −0.09 −0.32 185.2 23.12 −0.10 +0.12 200.6 23.3 −0.09 +0.19 197.0 23.13 −0.10 +0.22 209.2 23.3 −0.09 +0.16 208.6 23.14 −0.10 −0.01 200.2 23.3 −0.09 −0.01 197.1 23.1

Table 6.2: Final fit parameters for the 750 A DyFe2 sample in 0 kOe or 2.5 kOein plane applied field. No particular easy axis is applied to the fitting pa-rameters. The average angle is relative to the sample plane.

The change in the average hyperfine field∗ due to the applied field is−2.35 kG. The negative change in the hyperfine field indicates the iron mo-ments being parallel toH0: the hyperfine field lies antiparallel to the magneticmoment. It was expected that the hyperfine fields would increase as the dys-prosium moments, being significantly larger than the iron moments, wouldtend to align parallel with an applied field. Through the antiferromagneticcoupling the iron moments would then be lying antiparallel to the appliedfield.

To explain this there are competing effects in the sample under an appliedfield from the sample and the seed layer. Although the signal from the seedlayer underneath the 750 A sample layer produces at most a 15% backgroundcontribution to the spectrum (using the theory outlined in Section 2.5.2), theseed layer can influence the moment orientation of the sample layer. In thisbilayer arrangement a magnetic exchange-spring can be produced, where themoments in the soft magnetic seed layer twist at their free end whilst beingpinned by the hard magnetic sample layer.

The onset of this exchange spring under an applied field is governed by acritical bending field BB. For a bilayer this is related to the exchange field,BEX , by the relation

BB = BEX

( π

2N

)2

(6.11)

where N is the number of monolayers in the soft magnetic layer.33 Theexchange spring also penetrates into the hard magnetic layer, with the extentdetermined by the strength of the applied field and the axial anisotropy of

∗Individual components cannot be compared due to the amount of overlap betweenall four components.


the hard magnetic layer. Using the conditions cited in Reference 33 forDyFe2/YFe2, an iron-iron exchange field BEX = 6000 kOe and N = 114gives a bending field BB = 0.7 kOe. Our applied field of 2.5 kOe is thussufficient to produce an exchange spring.

The applied field should, however, be far too small to overcome the singleion anisotropy of the DyFe2 thin film (fields an order of magnitude greaterthan used in these measurements were used in Reference 33 without over-coming the anisotropy of the hard magnetic pinning layer). Whilst a smallportion at the interface with the YFe2 seed layer would be rotated somewhatalong the applied field direction it is expected that the majority of the uppersample layer (also from which the majority of the CEMS signal is obtained)would be unperturbed. A sample oriented with the Dy moments antipar-allel to the applied field would give the observed results. The arrangementof the sample within the spectrometer was not recorded, however, so this iscurrently conjecture.

DyFe2, in bulk, has an easy axis that lies along one of the 〈100〉 directions.As the sample geometry includes the [001] direction in the plane of the sam-ple, also favoured by the shape anisotropy of a thin film, the magneto-elasticenergy must be substantial to produce an easy axis so far out of plane. Thisdirection is seemingly unperturbed by the application of a 2.5 kOe field, alsotrying to force the moments into the plane of the sample. Without higherfield or temperature measurements (both of which are impossible with theCEMS equipment) an absolute value of Eme cannot be calculated but thedata point to it being of at least the same order as the magnetocrystallineand shape anisotropy energies combined.

6.2.3 YFe2

A 1000 A YFe2 sample was also studied in the the same way as that outlinedfor the DyFe2 sample. The zero applied field spectrum is compared to otherthin film samples in Figure 6.3.

The Isomer Shifts of each site are fixed to be equal but free to vary asa whole, as are the relative line intensities. The Isomer Shift values arethe same as for DyFe2 which is expected as rare earths are chemically verysimilar.

The results from applying a 2.5 kOe in plane magnetic field are shown incomparison to zero field in Table 6.4 and Figure 6.5. The most noticeabledifference is in the angle of the iron moments to the incident gamma ray(from the relative line intensities), the moments have been forced more inplane by 10.8◦ to lie at an angle of 14◦ to the sample plane. There is no erroron the change in angle as the spectra were recorded sequentially.


[241] [351]

HS = 187± 2 kG HS = 189± 4 kGHD = 9± 4 kG HD = 8± 6 kG

χ2 = χ2 =Site IS QS Field IS QS Field

(mm/s) (mm/s) (kG) (mm/s) (mm/s) (kG)[111] −0.10 −0.48 184.8 −0.10 −0.66 185.4[111] −0.10 −0.93 172.3 −0.10 −0.96 173.2[111] −0.10 +0.73 187.0 −0.10 +0.72 185.1[111] −0.10 +0.13 188.5 −0.10 +0.26 189.0

Table 6.3: Final fit parameters for 1000 A YFe2 sample assuming [241] or[351] easy axis in zero applied field.

0 kOe 2.5 kOe

χ2 = 1.14 χ2 = 1.19Site IS QS Field Angle IS QS Field Angle

(mm/s) (mm/s) (kG) (◦) (mm/s) (mm/s) (kG) (◦)1 −0.10 −0.31 178.8 24.8 −0.09 +0.02 182.5 14.02 −0.10 −0.03 179.4 24.8 −0.09 −0.02 171.3 14.03 −0.10 +0.09 187.7 24.8 −0.09 +0.13 184.4 14.04 −0.10 +0.22 183.5 24.8 −0.09 −0.08 180.2 14.0

Table 6.4: Final fit parameters for the 1000 A YFe2 sample in 0 kOe or 2.5 kOein plane applied field. No particular easy axis is applied to the fitting pa-rameters. The average angle is relative to the sample plane.

As yttrium does not carry a magnetic moment in this system there is nosingle ion magnetocrystalline anisotropy, as in the DyFe2 sample, stronglylocking the iron moments to a particular crystalline direction. The appliedfield of 2.5 kOe is of the order necessary to overcome the exchange anisotropybetween iron atoms, displacing the domain walls in the untrained sampleproducing a single domain sample. In this case the relative line intensitiesgive a unique angle for the direction of the iron moments, recorded as 14◦

to the sample plane. This lies in between either the [241] or [351] directions,which make angles of 18◦ and 13.8◦ respectively to the sample plane fora sample normal direction of (110). Although the observed angle is muchcloser to the [351] direction it is also closer to the sample plane. With no


Figure 6.5: Spectra for 1000A YFe2 thin film under 0 kOe and 2.5 kOe inplane applied fields.

magnetocrystalline anisotropy to overcome through coupling with the rareearth it would be expected that the iron moments would be more free torotate in the direction of the applied field, which is into the plane of thesample. The angle observed is one that balances the magneto-elastic andexternal field energies in this sample and so is unlikely to be truly indicativeof the magnetic easy axis in zero field. Thus this result cannot be taken asabsolute evidence of a [351] direction without other corroborating data.

The iron moments would be expected to lie in plane, even under zeroapplied field; the shape anisotropy favours in plane alignment, as does theapplied field. As this isn’t the case the strain in the sample plane must becausing a magnetostrictive effect through the iron atom’s dipolar interactionsbut of a much smaller magnitude than for the DyFe2 system as evidenced bythe much larger change in moment alignment under applied field. Magneticrare earths display much stronger magnetostriction than transition elements.


The change in the average magnetic hyperfine field is −2.75 kG. This isslightly larger than the applied field and significantly larger than the changerecorded in the DyFe2 sample. This is explained by the iron moments lyingmore parallel to the applied field and the increased magnetisation of thesample as the separate domains rotate with the field, increasing the magneticfield within the sample. In the DyFe2 sample the domains were still pinnedby the magnetic anisotropy of the dysprosium atoms and thus the change inmagnetisation was negligible.

6.2.4 HoFe2

As can be seen in Figure 6.3 the HoFe2 film has a markedly different Mossbauerspectrum compared to YFe2 and DyFe2. Unfortunately this may not be apure HoFe2 spectrum as, due to the thinness of the sample layer, part of thespectrum will be recorded from the YFe2 seed layer.

Using the CEMS theory outlined in Section 2.5.2 an upper limit can beplaced on the relative spectral contributions from the two layers. For a 500 Asample layer the ratio of sample to seed layer is 55%:45%. Thus the spectrumis more akin to that from a HoFe2/YFe2 bilayer. Hence we cannot analysethe spectrum to give any accurate information about a HoFe2 thin film dueto the overlap of the two sub-spectra and any possible interface effects.

In the 750 A DyFe2 thin film this ratio is 85%:15% giving a more repre-sentative spectrum of the sample layer. In the YFe2 thin film this effect doesnot apply as the sample and seed layer are the same material and continuous.

6.3 DyFe2/Dy Multilayers

A series of spectra from DyFe2/Dy multilayers were obtained to investigatethe effect of reduced thickness on DyFe2 thin films between 50 A and 200 A.A limiting factor on examining such thin films using Mossbauer spectroscopyis that the signal to noise ratio will be far too large when there is so littleiron to obtain a signal from, especially if the iron is non-enriched with the57Fe isotope.

To counter this the signal from a number of such films needs to be accu-mulated. To achieve this we used a number of DyFe2 films in a multilayer,spaced by layers of dysprosium. Dysprosium is not magnetically ordered atroom temperature, with a TN = 180 K, and provides good epitaxial growthconditions for the DyFe2 layers. The substrate, buffer and seed are the sameas for the previous thin film samples.


Sample Site IS QS Field Angle(mm/s) (mm/s) (kG) (◦)[

DyFe2(200 A)/Dy(100 A)]

51 −0.12 −0.04 200.0 22.62 −0.11 −0.21 186.0 22.63 −0.10 +0.21 210.0 22.64 −0.10 +0.09 205.0 22.6[

DyFe2(200 A)/Dy(50 A)]

51 −0.11 −0.07 200.1 21.42 −0.08 −0.19 186.5 21.43 −0.11 +0.21 210.5 21.44 −0.10 +0.10 206.0 21.4[

DyFe2(100 A)/Dy(50 A)]

81 −0.12 −0.05 197.5 20.62 −0.07 −0.16 186.4 20.63 −0.10 +0.19 209.0 20.64 −0.10 +0.10 205.0 20.6[

DyFe2(50 A)/Dy(50 A)]

121 −0.12 −0.06 198.0 21.12 −0.09 −0.15 186.0 21.13 −0.09 +0.19 209.0 21.14 −0.09 +0.07 205.0 21.1

DyFe2(750 A) 1 −0.12 −0.02 200.0 23.32 −0.10 −0.23 187.4 23.33 −0.11 +0.20 209.0 23.34 −0.08 +0.15 202.2 23.3

Table 6.5: Final fit parameters for the[DyFe2(x A)/Dy(y A)

]z

samples and

a 750 A DyFe2 thin film sample. The average angle is relative to the sampleplane.

The spectra are shown in Figure 6.6 and the fitting parameters are givenin Table 6.5. The spectra have been fitted with four sextets of equal inten-sity, adopting a model of a low symmetry magnetic easy axis giving fourinequivalent iron sites. No particular easy axis direction is assumed in thefits. The relative intensity of lines 2 and 5 to lines 1,3,4 and 6 has been fixedto be equal for all four components but free to vary. All other parameterswere free to vary individually.

Comparison between the four dysprosium spaced samples shows little sig-nificant variation in hyperfine parameters. The isomer shift and quadrupolesplitting values for all sites are identical for the four samples within a fit-ting error of 0.05mm/s. The average angle which the spin moments make


Figure 6.6: Spectra for[DyFe2(xA)/Dy(yA)

]z, multilayers.


to the sample plane show no trend with thickness and at most vary by 2◦,comparable to the nominal error on the source and sample positioning of±2◦.

There are small variations in the hyperfine fields for particular sites butwhether these are physical or artifacts of the overlapping nature of four com-ponents in a small area is hard to determine. The average hyperfine field isconstant across all samples within 1 kG.

The 750 A DyFe2 sample was also fitted with the same parameter restric-tions as the dysprosium spaced samples as a comparison with a “thick” film.The results are also shown in Table 6.5. This spectrum was recorded on adifferent spectrometer to the dysprosium spaced samples so the margins oferror when comparing the hyperfine parameters and average moment angleare larger. Again there is no significant variation to be seen.

From these results we can conclude that the mechanisms which werepresent in the 750 A sample are unaffected by reducing the thickness of thelayer to at least 50 A.

6.4 DyFe2/YFe2 Multilayers

This section presents analysis of data from a CEMS study of DyFe2/YFe2

multilayers. All spectra were recorded at room temperature under an inplane applied field of 0 kOe or 0.25 kOe. The results are compared to thethin film samples presented in Sections 6.2.2 and 6.2.3.

6.4.1 Introduction

There has been much interest recently in layered magnets34,35 particularlythose composed of a two-phase distribution of hard and soft magnetic ma-terials. One potential application of such systems is in permanent magnetswhere the hard magnetic layers provide high anisotropy and coercive fields,whilst the soft magnetic layers can enhance the magnetic field and reducethe rare earth content. These systems also have potential as GMR readheadswith a reported ∆R/R of 12% in an applied field of 230 kOe.36

A series of DyFe2(x A)/YFe2(y A) multilayers were investigated with vary-ing DyFe2 and YFe2 layer thicknesses of 50 A/50 A, 40 A/20 A, 20 A/40 A and20 A/20 A. They have the same sample structure as for all the previous sam-ples, shown in Figure 6.2.

In these multilayers the soft magnetic YFe2 layers will be exchange-coupled to the DyFe2 layers through the strong (∼ 6000 kOe) iron-iron ex-change coupling. This is illustrated in Figure 6.7. The strong single-ion


Figure 6.7: Exchange coupling between iron sublattices in DyFe2/YFe2 mul-tilayers.

anisotropy coupled antiferromagnetically through the dysprosium momentsto the iron moments, as seen in the DyFe2 thin film results in Section 6.2.2,will be transferred to the YFe2 layers by the strong iron-iron exchange cou-pling. Hence we expect the system as a whole to be dominated by thedysprosium moments.

CEMS spectra were recorded at room temperature under in plane appliedmagnetic fields of 0 kOe and 2.5 kOe. The applied field of 2.5 kOe will not besufficient to induce exchange springs in the YFe2 layers where the bendingfield, BB, is of the order of 70 kOe,36 but there will be an exchange springinduced in the 800 A YFe2 seed layer as discussed in Section 6.2.2.

6.4.2 Results

The spectra are shown in Figure 6.8 and the fitting parameters are shown inTable 6.6.

The spectra have been fitted with four components. Although the spec-trum will be composed of subspectra from both the DyFe2 and YFe2 layerswith four components each, eight components would be too many to realis-


Figure 6.8: Spectra for[DyFe2(x A)/YFe2(y A)

]z, multilayers.


0 kOe 2.5 kOeSite IS QS Field Angle IS QS Field Angle

(mm/s) (mm/s) (kG) (◦) (mm/s) (mm/s) (kG) (◦)[DyFe2(50 A)/YFe2(50 A)

]20

1 −0.10 +0.15 206.1 23.0 −0.10 +0.17 203.0 21.72 −0.18 −0.16 186.6 23.0 −0.18 −0.19 185.1 21.73 +0.02 −0.03 184.5 23.0 +0.01 −0.03 183.6 21.74 −0.10 +0.22 193.2 23.0 −0.09 +0.09 190.2 21.7[

DyFe2(40 A)/YFe2(20 A)]

16

1 −0.14 +0.23 240.0 22.3 −0.14 +0.25 236.8 19.62 −0.23 −0.21 218.6 22.3 −0.27 −0.13 216.6 19.63 +0.01 −0.06 216.1 22.3 −0.00 −0.06 211.6 19.64 −0.12 +0.09 226.5 22.3 −0.06 +0.00 223.0 19.6[

DyFe2(20 A)/YFe2(40 A)]

16

1 −0.11 −0.21 227.0 20.9 −0.15 +0.11 227.5 17.62 −0.22 −0.19 214.0 20.9 −0.14 −0.27 205.0 17.63 +0.02 −0.05 214.1 20.9 −0.07 −0.11 210.0 17.64 −0.15 +0.06 222.0 20.9 −0.14 +0.04 216.0 17.6[

DyFe2(20 A)/YFe2(20 A)]

25

1 −0.13 +0.13 235.3 27.2 −0.15 +0.20 233.0 24.32 −0.14 −0.25 214.7 27.2 −0.15 −0.14 211.9 24.33 −0.07 +0.15 218.6 27.2 −0.06 +0.07 213.0 24.34 −0.16 +0.02 225.0 27.2 −0.14 −0.02 226.0 24.3

Table 6.6: Fit parameters for[DyFe2(x A)/YFe2(y A)

]z

multilayers. Theaverage angle is relative to the sample plane.

tically fit the spectrum. To maintain consistency with the previous resultsfour components are used to fit the spectra.

The results for the DyFe2(50 A)/YFe2(50 A) sample are consistent withthe thin film results in Sections 6.2.2 and 6.2.3. The average hyperfine field of192.6 kG for the zero field results match closely that of averaging the hyper-fine fields of the thin film DyFe2 and YFe2 results, giving 190.8 kG. The smallenhancement of 1.8 kG may be the onset of the hyperfine field enhancementseen in the other multilayer samples with thinner layers although slight dif-ferences in calibration and fitting error could also account for this. The ironmoments are 23.0◦ out of plane, again consistent with the values obtained


for all the other samples studied, where iron moments lie in the region of 20to 25◦ out of plane.

Under an applied field the iron moments are forced only slightly in planeby 1.3◦. This is greater than that seen in the DyFe2 thin film where thischange was 0.2◦ but also much less than that seen in YFe2 where the changewas 10.8◦. As the other results in this sample and the DyFe2/Dy samplesstudied in Section 6.3 point to 50 A DyFe2 layers having the same propertiesas the 750 A thin film the small increase in the average angle can be attributedto the YFe2 layers possessing an induced anisotropy through the variouscoupling mechanisms less than that of the dysprosium moments.

Under the applied field the average hyperfine field is reduced by 2.13 kG,consistent with that observed in the DyFe2 thin film. Although the exactmechanism by which the hyperfine fields are reduced rather than increasedas expected is not currently explained (see the discussion in Section 6.2.2), wecan expect that this effect would be seen in this sample as this layer thicknessof 50 A appears to not affect the DyFe2 layer properties. The YFe2 layer willbe strongly coupled to the DyFe2 layer and so will orient itself to the field inthe same manner, producing the same vector addition of hyperfine field andapplied field.

The results for the DyFe2(40 A)/YFe2(20 A) sample show a variation fromthe thin film results. The hyperfine fields have been enhanced by an averageof 17% compared to the DyFe2(50 A)/YFe2(50 A) sample, and 18% comparedto the DyFe2 thin film. The hyperfine fields are reduced by an average of3.30 kG under an applied field of 2.5 kOe. The iron moments lie 22.3◦ out ofplane, within the range seen for all of the Laves Phase samples studied, andare rotated by an average of 2.7◦ under the applied field.

The hyperfine field enhancement for the DyFe2(20 A)/YFe2(40 A) sampleis 14% compared to the DyFe2(50 A)/YFe2(50 A) sample. The hyperfinefields are reduced by an average of 4.65 kG under an applied field of 2.5 kOe.The iron moments lie 20.9◦ out of plane and are rotated by an average of3.3◦ under the applied field.

The DyFe2(20 A)/YFe2(20 A) sample has a hyperfine field enhancementof 16% compared to the DyFe2(50 A)/YFe2(50 A) sample. The hyperfinefields are reduced by an average of 2.43 kG under an applied field of 2.5 kOe.The iron moments lie 27.2◦ out of plane, greater than that seen for any othersample, and are rotated by an average of 2.9◦ under the applied field.

The biggest change in parameters with the applied field occurs in theDyFe2(20 A)/YFe2(40 A) sample, which has the largest proportion of softmagnetic material. All samples show a reduction in anisotropy compared tothe DyFe2 thin film sample, with iron moments being rotated in plane by anangle an order of magnitude greater than that for the thin film sample.


A change in behaviour is occurring as the layer thicknesses are reducedbelow 50 A. There is expected to be an interface roughness of ∼ 5 A. Thisroughness becomes significant in the thinner layers, particularly the 20 Alayers where the roughness is 25% of the layer thickness. An increased out ofplane moment alignment is also seen in the sample with the thinnest layers.There appears to be some form of interfacial effect occurring in the system,which becomes significant as the layer thicknesses are reduced below 50 A,although the hyperfine field enhancement doesn’t seem significantly affectedby the relative thicknesses of the DyFe2 or YFe2 layers.

Chapter 7

4f/3d and 5f/3d MagneticMultilayers: Ce/Fe and U/Fe

Brothers stay in jealous guardGifts to loose and render freedHidden skill and talent barred,Save the younger of their creed.Easy finds what kin fears hard,Profit comes in more than greed.

In crowd and mob of heavy menAll fight stuck in seething mess,

Weapons pressed too close againAll actions met with no success.Lone and free to might unchain,Gains the more from giving less.

This chapter presents results on multilayers combining the effects of elementswith delocalised f -shell electrons (4f in cerium, 5f in uranium) with the3d electrons of iron. SQUID magnetometry results have been taken as acontinuation of the Mossbauer spectroscopy work on Ce/Fe multilayers byG.S. Case.3 The magnetometry data can indicate the presence and typeof magnetic ordering across the layers (ferromagnetic, antiferromagnetic oruncoupled) and can then be compared with a study of GMR in these samplesby A. Mohamed and M.F. Thomas.37 The data can also provide informationon the magnetic moments of the samples, particularly to ascertain whetherthe cerium atoms possess a magnetic moment or not.

CEMS spectra have been recorded at room temperature of U/Fe multilay-ers with various thicknesses of uranium and iron. These samples have beenproduced by UHV magnetron sputtering by A. Herring, Liverpool, work-ing at the Clarendon Laboratory, Oxford University with Dr. R.C.C. Wardand Dr. M.R. Wells. The results are interpreted to provide information onthe state of the iron layers: level of crystallinity, direction of the iron mag-netic moments with respect to the sample plane, whether or not the iron ismagnetically ordered and to detect any alloys/intermetallics or changes in

83

CHAPTER 7. RE/FE & A/FE MAGNETIC MULTILAYERS 84

Sample Label Area Ce volume Fe volume Total(mm2) (mm3) (mm3) (mm3)

(10−4) (10−4) (10−4)[Ce(12 A)/Fe(10 A)

]60

12/10 − − − −[Ce(16 A)/Fe(10 A)

]60

16/10 4.07 3.91 2.44 6.35[Ce(20 A)/Fe(10 A)

]60

20/10 4.40 5.28 2.64 7.92[Ce(20 A)/Fe(15 A)

]60

20/15 8.80 10.56 7.92 18.48[Ce(20 A)/Fe(17 A)

]60

20/17 − − − −[Ce(20 A)/Fe(20 A)

]60

20/20 − − − −[Ce(27 A)/Fe(15 A)

]60

27/15 2.86 4.64 2.58 7.21[Ce(27 A)/Fe(20 A)

]60

27/20 8.02 12.99 9.46 22.45[Ce(40 A)/Fe(20 A)

]60

40/20 8.96 21.50 10.75 32.26

Table 7.1: Sample thicknesses, areas and volumes. “−” denotes a samplefrom which magnetometry data has been taken but whose area was not mea-sured.

magnetism formed at the layer interfaces. These data are complementary tox-ray reflectivity data obtained by A. Herring on the same samples.

7.1 Ce/Fe Multilayers

Multilayers containing cerium display many interesting properties,38 partic-ularly as a result of its delocalised 4f electrons and their interactions withthe 3d electrons of the transition metals. The hybridisation of the two shellsis seen to induce a small magnetic moment on interface cerium atoms.39

The Ce/Fe multilayers studied in this section were fabricated by P. Boniand S. Tixier at the Laboratory for Neutron Scattering, Switzerland, usingDC sputtering using a Leybold Z600 high vacuum system onto silicon sub-strates. These were characterised and studied using CEMS by G.S. Case,3

the results of which will be compared to the data acquired in this thesis.All of the samples studied are listed in Table 7.1, with the sample compo-

sition, label, and, where available, the sample area allowing the calculationof volumes for normalising the magnetisation to the sample size. All ap-plied field measurements were performed with the applied field parallel tothe plane of the sample.


7.1.1 Temperature vs Magnetisation Scans

The variation with temperature of a sample’s magnetisation can give infor-mation upon the type and strength of magnetic ordering in the sample. Allsamples were field cooled from room temperature to 1.8 K under an appliedfield of 1000 Oe. The sample magnetisation was then measured under thesame applied field from 1.8 K to 400 K.

As the sample size is not known for all of the samples the magnetisationcannot be compared quantitatively for these scans. As information can beobtained from the shape of the scans rather than the actual magnetisationthe magnetisation vs temperature data has been normalised for each sampleto its own magnetisation at 1.8 K. This allows groups of samples to becompared visually.

Most of the datasets were obtained whilst the SQUID unit was experi-encing considerable electronic noise problems. This has been reduced signifi-cantly by smoothing the resultant data with a Gaussian convolution. Whilstthe main shape of the scan becomes more visible the smoothing cannot to-tally remove large noise artifacts when they are over a large number of datapoints and so any fine structure in the scans obtained from the sample cannotbe distinguished from that produced by the noise.

The room temperature CEMS results obtained by G.S. Case3 show theiron to be composed of ordered bcc iron and an amount of paramagneticamorphous iron which increases in proportion as the iron layer thickness de-creases. In samples with iron layer thicknesses < 20 A the amorphous/bcciron ratio increases and Perpendicular Magnetic Anisotropy increases, tippingthe spins out of the plane of the sample. For the discussion of the magne-tometry results the iron layers are taken to be ferromagnetically ordered inthe iron layers, whilst the interlayer coupling can be antiferromagnetic, fer-romagnetic or uncoupled depending upon the cerium layer thickness and themagnetisation of the iron layers. The results are plotted in sets for compari-son, where either the cerium or iron layer thickness has been kept constant.The data is plotted as magnetisation, but as the field, H, is constant they-axis also corresponds to χ = M/H.

Ce(20 A)/Fe(x A)

Figure 7.1 shows the scans for Ce(20 A)/Fe(x A) multilayers. The samplewith the thinnest iron layer, 20/10, shows either ferromagnetic or no inter-layer coupling. There is a small reduction in magnetisation as the temper-ature increases, as expected in the ferromagnetic layers below Tc. This isillustrated in Figure 3.8(a). Although coupling will be seen in other sam-


Figure 7.1: Normalised magnetisation vs temperature scans forCe(20 A)/Fe(x A) multilayers. Cerium layer thickness is constant.

ples with iron layers of this thickness, Mossbauer results3 show this to bean anomalous sample, most probably because of the thinness of both thecerium and iron layers. The Mossbauer data for this sample shows iron mo-ments lying 51◦ out of plane and with a hyperfine field 12% less than that ofother samples with 10 A iron layers. Hysteresis measurements also show thisanomalous behaviour (see Section 7.1.3).

As the iron layer thickness is increased to 15 A in the 20/15 sample wesee coupling between the iron layers. The data for this sample shows anantiferromagnetic temperature dependence around TN , as illustrated in Fig-ure 3.7(a) (note the y-axis is 1/χ), with a TN = 152 ± 10 K. The Mossbauerdata for this sample shows a 12% reduction in magnetic hyperfine field andspin moments lying 31◦ out of plane. This is one possible explanation for thesmall effect compared to the samples with thicker iron layers.

The flat value of M up to TN = 152 ± 10 K corresponds to a system of


layers antiferromagnetically coupled and, due to small in plane anisotropy,spin flopped with the antiferromagnetic axis normal to the applied field.The M response is then due to the canting of the layer moments until theircoupling to the applied field overcomes the antiferromagnetic coupling atTN . The increase in M with temperature up to TN for the 20/17 and 20/20samples is likely to arise from incomplete spin flop of the antiferromagneticsystem which allows some χ‖ combination to the χtot = χ‖ + χ⊥.

At an iron layer thickness of 17 A the characteristic change in χtot foran antiferromagnet is much more pronounced. The Mossbauer data showthis sample to have only a 9% reduction in hyperfine field and spin momentsfully in plane. The increased in plane magnetisation in the iron layers may begiving an increased variation in χtot compared to the 20/15 sample, assumingthe same moment orientation. This sample has a TN = 160± 5 K.

As the iron layer thickness is increased further to 20 A the effect becomesstronger still. For this sample TN = 96± 5 K. A larger change in χ between1.8 K and TN is tending to give a lower TN , consistent with a less uniformalignment of spin moments to the field producing a weaker coupling acrossthe cerium layers (the 20/15 sample cannot be included in this comparisondue to its undetermined moment orientation).

From this set of results it can be seen that at this cerium layer thicknesswhere the iron moments are not significantly out of plane the coupling isantiferromagnetic.

Ce(27 A)/Fe(x A)

Figure 7.2 shows the scans for Ce(27 A)/Fe(x A) multilayers. This is anotherset of scans with a fixed cerium layer thickness. Here, too, the coupling canbe seen to be antiferromagnetic. The 27/15 sample shows a strong increasein χtot with increasing temperature approaching TN , indicative of antifer-romagnetic coupling with a mixture of parallel and perpendicular momentalignment. This sample has a TN = 125 ± 5 K. Mossbauer data show thissample to have a 20% reduction in hyperfine field and has moments lying 38◦

out of plane.The 27/20 also shows an antiferromagnetic coupling. The data shows a

much flatter curve below TN , indicating the sample has fully spin-floppedmoments. This sample has a TN = 145 ± 5 K, 20 K higher than that of the27/15 sample.

At this cerium layer thickness of 27 A the iron layers are coupled antifer-romagnetically.


Figure 7.2: Normalised magnetisation vs temperature curves forCe(27 A)/Fe(x A) multilayers. Cerium layer thickness is constant.

Ce(x A)/Fe(10 A)

Figure 7.3 shows the scans for Ce(x A)/Fe(10 A) multilayers. This set ofscans has a fixed iron layer thickness of 10 A.

The 12/10 sample shows a ferromagnetic coupling between iron layers.The magnetisation slowly decreases before dropping off more sharply at aTc = 240±5 K. The magnetisation then drops linearly as for the samples withantiferromagnetically coupled iron layers in their “paramagnetic” region.

The 16/10 sample shows an antiferromagnetic temperature dependence.The data for this sample was particularly poor so it is difficult to tell if thereis an increase in χ approaching TN = 185± 5 K or if it is merely an artifact.The data does, however, favour at least a flat χ⊥ below TN as expected forsuch an antiferromagnet.

The 20/10 sample, as discussed in Section 7.1.1, shows anomalous be-haviour and will not be compared to the rest of the set.

This set of data shows the type of interlayer coupling changing from


Figure 7.3: Normalised magnetisation vs temperature scans forCe(x A)/Fe(10 A) multilayers.

ferromagnetic at a cerium layer thickness of 12 A to antiferromagnetic at16 A.

Ce(x A)/Fe(15 A)


The 20/15 sample shows an antiferromagnetic coupling, with a TN =157 ± 5 K. The region below TN is relatively flat (within equipment error),indicating moments perpendicular to the applied field.

The 27/15 sample also shows antiferromagnetic coupling, with a TN =125± 5 K, but with the temperature dependence of a mixed state of perpen-dicular and parallel moments. The TN for this sample is lower than that ofthe 20/15 sample with the more perpendicularly aligned moments.

Mossbauer measurements show both samples have moments lying 32◦ out



of plane, but the 27/15 sample has a lower hyperfine field compared to bcciron than the 20/15 sample. The hyperfine fields are reduced by 20% and 12%for the 27/15 and 20/15 samples respectively. This difference in hyperfinefields and perpendicular or parallel moment alignment does not coincide forall samples, however.

It cannot be determined from these data alone whether the variation inmoment alignment is due to the cerium layer thickness or merely a coin-cidence of the sample construction. Indeed the following Ce(x A)/Fe(20 A)measurements show the opposite arrangement for cerium layer thicknesses of20 A and 27 A.

Ce(x A)/Fe(20 A)


The 20/20 and 27/20 samples have already been discussed. Both samples



show antiferromagnetic coupling across the cerium layers. The 20/20 sampleshows a mix of parallel and perpendicular moment alignment whilst the 27/20sample shows perpendicular alignment.

The 40/20 sample shows either weak ferromagnetic or no coupling of theiron layers. It shows a similar temperature dependence to the 20/10 layer,with a small decrease in magnetisation with temperature of the ferromag-netically ordered iron layers far below their TC point. The iron layers in thissample have spins at most 10◦ out of plane and only a 4% reduction in hyper-fine field compared to bcc iron, according to the Mossbauer measurements.

This set of data shows antiferromagnetic coupling for 20 A and 27 Acerium layers, and no or weak ferromagnetic coupling for 40 A layers.


Figure 7.6: Percentage change in resistance under an applied field for the[Ce(20 A)/Fe(17 A)

]60

sample.

GMR Results

GMR data was taken on some of the Ce/Fe samples studied in this thesisby A. Mohamed.37 All samples studied at room temperature showed nosignificant change in resistance under an applied magnetic field.

One sample,[Ce(20 A)/Fe(17 A)

]60

, was studied at 77 K and this data isplotted in Figure 7.6. A reduction in resistance from the zero field state isseen as the field is applied in the positive or negative direction. A quadraticfit is included as a guide for the eye.

This result is typical of the GMR effect in antiferromagnetically coupledmultilayers.40 This correlates with the typical antiferromagnetic temperaturedependence seen for this sample in Figure 7.1. The SQUID data shows thesample has a TN = 160 ± 5 K, placing the 77 K GMR measurement withinthe antiferromagnetic region.


Figure 7.7: Exploded view of a Ce/Fe multilayer showing the antiferromag-netic coupling between the iron layers.

7.1.2 Estimation of Coupling Constant, J(z)

The magnetisation vs temperature scans can be used to estimate the strengthof the exchange coupling between the iron layers when they are antiferromag-netically coupled. Figure 7.7 shows an exploded view of an Fe/Ce/Fe sectionof a multilayer in an applied field.

In this system there is an energy, WAFM , associated with the antiferro-magnetic exchange coupling and an energy, WH , from the applied field, H.These are related to the magnetisation of the iron layers by the following

WAFM = −2J(z)M 1 �M 2

WH = −M 1 �H −M 2 �H

W = WAFM +WH (7.1)

where M1 and M2 are the respective magnetisations of the two layers. In oursystems we take the layer magnetisations to be equal, hence M1 = M2 = M .We can find the minimum in energy with respect to the angle φ between the


Figure 7.8: Variation of antiferromagnetic coupling constant, J(z), withcerium layer thickness, z. The dashed line, representing a theoretical pic-ture of oscillatory coupling, is added to guide the eye.

applied field and the magnetisation, where ∂W/∂φ = 0. This yields the result

J(z) = − H

4M cosφ(7.2)

When the system is at TN the spins will be fully aligned with the appliedfield and φ = 0, hence

J(z) = − H

4M(7.3)

The magnetisation, M , can be read from the magnetisation vs tempera-ture scans at the TN of each sample. As J(z) is a function of the distance, z,between the two iron layers we would expect the values obtained to vary withthe cerium layer thickness. This is likely to be an oscillatory dependence onseparation distance between the magnetic layers similar to the RKKY inter-


action between magnetic atoms that has been observed in many transitionmetal systems.41 The calculated J(z) values are plotted in Figure 7.8.

The plot does show a variation with z although with so few points the ac-tual dependence upon z cannot be calculated. The scans for the 40/20 sampleappear to show either weak ferromagnetic or no coupling between the ironlayers, hence it can be assumed that J(40 A) ≈ 0, showing a rapid reductionin coupling strength with z consistent with the 1/z3 dependence of the oscil-latory interaction. The ferromagnetically coupled 12/10 sample shows thatJ(12 A) is positive, although the magnitude cannot be determined. This toois consistent with an oscillatory z dependence, as illustrated in Figure 5.1.This oscillatory dependence in coupling has been discussed theoretically asarising from RKKY or quantum well mechanisms. The reader is referred toReferences 41,42,43 for more detailed information.

There is some verification of the results as both the 27/15 and 27/20samples give consistent values of J within experimental error, as is expectedfor samples with the same non-magnetic layer thickness.

7.1.3 Hysteresis Loops

A series of hysteresis loops were taken from the Ce/Fe samples at roomtemperature. Only the data for those samples with known sample sizes arepresented. All magnetisation results have been normalised to the total vol-ume of the iron layers. These data are shown in Figure 7.9. The errors forthe data points in each loop are shown only once for clarity.

Saturation Magnetistion

The room temperature hysteresis loops show the distinction between ferro-magnetic, antiferromagnetic and weak ferromagnetic/uncoupled samples.

The samples with a 15 A iron layer thickness have the lowest volumemagnetisation. Both the 20/15 and 27/15 samples have saturation magneti-sations which are consistent within experimental error, of 230 ± 50 EMU/cm3

and 300± 60 EMU/cm3 respectively This is as expected as both samples showantiferromagnetic iron layer coupling in the magnetisation vs temperaturescans and have the same iron layer thickness.

The 27/20 sample has a larger volume magnetisation than the sampleswith a 15 A iron layer thickness, of 500 ± 60 EMU/cm3. As the layer couplingis also antiferromagnetic in this case this is expected for a thicker magneticlayer. The 40/20 has the same iron layer thickness but has a much largervolume magnetisation than the 27/20 sample. The 40/20 sample has weakly


Figure 7.9: Hysteresis loops taken at room temperature for all measuredCe/Fe samples. The magnetisation is normalised relative to the iron layersvolume only. The hysteresis loop for the 20/10 sample is shown truncated inthe main plot for clarity, but is compared to the other loops in the inset.

ferromagnetic or uncoupled iron layers rather than the antiferromagneticallycoupled layers in the 27/20 sample.

The 16/10 and 20/10 samples show larger than expected magnetisationsat room temperature, of 700±160 EMU/cm3 and 2100±500 EMU/cm3 respectively.These samples have the thinnest iron layers and so would be expected to havea lower TC than the thicker layers and hence have a lower magnetisation atroom temperature.

The saturation magnetisation values at room temperature reflect stronglythe rapidity of the decrease in M with temperature seen in Figures 7.1 to7.5. Samples that show a relatively slow decrease in M with T , such asthe 20/10 and 40/20 samples, show the greatest saturation magnetisation atroom temperature.


The antiferromagnetically coupled samples 16/10, 20/15, 27/15 and 27/20show much smaller saturation magnetisations at room temperature. Thisseparation in behaviour is likely to arise from the fact that at room tempera-ture the aligning influence on the layers are either ferromagnetic in additionto the applied field for ferromagnetic layers, solely from the applied field foruncoupled layers and applied field against antiferromagnetic alignment forthe layers coupled antiferromagnetically below TN .

Coercivity

The temperature scans showed the 20/10 and 40/20 samples to be ferromag-netically coupled or uncoupled. Both of these samples have different loopshapes compared to all of the other, antiferromagnetically coupled layers.

The hysteresis loops for both the 20/10 and 40/20 samples have a highercoercive field than the coupled samples, of 154 ± 10 Oe. The coercive fieldgives the typical field necessary to produce magnetisation reversal in thesample. Assuming a bistable system the uncoupled layers have to overcomea much larger energy gradient to change their magnetisation direction thanthe coupled layers. The more magnetically continuous coupled layers have asmaller gradient to overcome.

The coercivity of the antiferromagnetically coupled samples seen in Fig-ure 7.9 is exaggerated by the lack of resolution. The coercive field for thesesamples is of the order of 100 Oe yet the step size in the loop is also 100 Oe.Whilst this is still less than the uncoupled layers it is most probably muchsmaller still.

7.2 U/Fe Multilayers

Some of the properties exhibited by Ce in multilayers can be expected insamples incorportating the Actinides, by using uranium. Uranium has somevery interesting and potentially useful magnetic properties. Uranium canpossess very large orbital magnetic moments which, through their couplingto the lattice, produce substantial magnetic anisotropy. This may allowperpendicular magnetic anisotropy, an important goal in magneto-opticaldevices. Also of interest for magneto-optical applications is the Kerr-effect,also of a large magnitude in some uranium compounds.

Similar to the 4f electrons in cerium, uranium 5f electrons have a largespatial extent and can potentially hybridise with 3d electrons. These canproduce polarisation effects across the multilayer interfaces, potentially ofgreater magnitude than in Ce/Fe multilayers.


In its elemental form uranium is not magnetic. When in close proximitythe itinerant 5f electrons form wide bands through f -d hybridisation, pro-ducing no localised magnetic moment.44 To attain a magnetically orderedstate the uranium atoms must be forced sufficiently apart to reduce the for-mation of 5f bands. Although unlikely to occur within the uranium layersof the U/Fe multilayer, interface effects such as strain or interdiffusion of ele-ments may produce magnetic uranium atoms within the immediate presenceof the U/Fe interface.

7.2.1 CEMS Results

All of the 57Fe Mossbauer results for the U/Fe multilayers were recorded usingCEMS at room temperature. Transmission mode Mossbauer spectroscopy isprohibited by the attenuation of the Mossbauer gamma ray by the glasssubstrates. The spectra were recorded with the sample plane normal tothe incident gamma ray direction. The hyperfine parameters from the leastsquares fits are given in Table 7.2.

The parameters for the sextets are consistent with magnetically orderedbcc iron. In all iron layers there are two magnetic components: one having thevalues of crystalline bcc iron with a linewidth close to that of the calibration(indicating good crystalline growth) and hyperfine fields close to those forbulk bcc iron and a second, broader component with a reduced hyperfinefield.

The hyperfine parameters are unaffected by the thickness of the uraniumlayer. Figure 7.10 shows four spectra, three with the same iron layer thick-ness but varying thicknesses of uranium. These three spectra are essentiallyidentical in both hyperfine parameters and the relative areas of each compo-nent. The fourth spectrum shows a sample with a much thicker iron layerand the relative amount of each component can be seen to have changedconsiderably.

The first component is attributed to a layer of crystalline bcc iron inthe center of the iron layer. The linewidth is the same as a pure iron foilused for calibrating the spectrometer. The slightly reduced hyperfine fieldin the samples with iron layers < 60 A arises from a reduction in Tc asthe strength of interactions between the iron layers is diminished by theinterspacing of uranium layers and reduced coordination with neighbouringiron atoms. This effect is at its greatest in the sample with the thinnestiron layer, [U(28)/Fe(30)]31, where there is a 3% reduction in hyperfine field.The effect decreases as the iron layer thickness is increased and the hyperfinefield reaches a maximum for samples with an iron layer thickness > 60 A of≈ 329 kG, identical to that of pure bulk iron.


Sample IS QS Γ Field Area(mm/s) (mm/s) (mm/s) (kG) (%)[

U(28 A)/Fe(30 A)]

31+0.02 −0.05 0.31 320.7 14+0.05 −0.02 0.94 288.0 38−0.15 −0.71 0.78 0 48[

U(28 A)/Fe(43 A)]

31+0.02 +0.02 0.26 325.3 30−0.10 −0.13 0.90 288.0 34−0.20 −0.76 0.73 0 36[

U(40 A)/Fe(60 A)]

10+0.01 +0.00 0.28 328.9 38+0.00 −0.07 0.72 304.6 34−0.18 −0.73 0.73 0 28[

U(80 A)/Fe(60 A)]

20+0.01 +0.00 0.27 327.8 35+0.00 −0.07 0.73 304.0 34−0.19 −0.69 0.70 0 31[

U(101 A)/Fe(60 A)]

20+0.02 −0.02 0.27 328.3 34+0.00 −0.02 0.76 300.0 34−0.20 −0.69 0.64 0 32[

U(42 A)/Fe(113 A)]

21+0.01 −0.01 0.28 329.0 69−0.01 −0.09 0.67 302.0 15−0.19 −0.70 0.69 0 16[

U(22 A)/Fe(180 A)]

5+0.02 +0.00 0.29 328.8 53−0.06 −0.12 1.10 299.0 31−0.24 −0.89 0.72 0 16

Table 7.2: Hyperfine values for all U/Fe multilayers studied.

The second magnetic component has a much reduced hyperfine field of upto 13% and a very broad linewidth. This is a region of iron at the interfaceswith much reduced crystallinity and subject to interface effects. Interdiffu-sion of iron and uranium atoms, and assuming only the iron atoms carry amoment, gives fewer magnetic neighbours for each iron atom and hence areduction in hyperfine field. The large linewidth is due to a distribution ofiron sites with increasing hyperfine field as the concentration of iron atomsincreases further into the iron layer. Thicker iron layers will have more pureiron sites and so the hyperfine field of the second component increases. Theproportion of this region to the crystalline iron is very large in the samplewith the thinnest layer (the iron layers are only just thick enough to begin


�U � 40 �� Fe � 60 �� 10

�U � 80 � Fe � 60 �� 20

�U 101 �� Fe 60 �� 20

�U � 42 �� Fe � 113 �� 21

0.0

0.5

1.0

Per

cent

Em

issi

on

0.0

0.2

0.4

0.6

0.8

0.0

0.2

0.4

0.6

Velocity (mm/s)−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7

0

1

2

3

Figure 7.10: CEMS spectra for U/Fe multilayers: [U(40)/Fe(60)]10,[U(80)/Fe(60)]20, [U(101)/Fe(60)]20 and [U(42)/Fe(113)]21. The spectra areunaffected by the uranium layer thicknesses.


fully crystalline growth) but this proportion decreases with increasing ironlayer thickness.

This change in the proportion of crystalline iron to the distribution ofmagnetic iron sites is illustrated in Figure 7.11. The first spectrum fromthe [U(28)/Fe(30)]31 sample shows the majority of the iron is the poorly-crystalline state or as part of the UFe2 intermetallic. As the iron thicknessis increased to 43 A the crystalline component can be seen to increase inintensity. At 180 A the iron layer is predominantly crystalline.

The paramagnetic doublet matches well the bulk hyperfine parameters ofthe Laves Phase intermetallic UFe2, with the same crystal structure as theRe/Fe2 samples studied in this thesis (Figure 6.1). The values reported inReferences 45 and 46 for room temperature measurements show that UFe2

is in a paramagnetic phase (Tc = 167 K) with an isomer shift of −0.21 mm/s

and a quadrupole splitting of −0.45 mm/s (the sign of the quadrupole split-ting is obtained from low temperature magnetically ordered spectra). Thedoublet has a much broader linewidth of 0.50 mm/s than that of magneticallysplit spectra. The broader linewidth and slightly larger quadrupole splittingobserved in the UFe2 component within the U/Fe layers studied in this thesiscan be explained by the decreased crystallinity compared to the bulk samplesstudied in Reference 45.

The magnetron sputtering process may be forming UFe2 by co-evaporationat room temperature producing the formation of the intermetallic as theatoms of either element are driven into the surface of the newly formed thinfilm. Other possible materials which could form such as UFe, U6Fe and amor-phous iron do not match all of the hyperfine parameters consistently recordedfor the doublet in all of the multilayer spectra. The current samples can onlybe recorded using CEMS and this restricts the readings to room temperature.Future work with samples on kapton backings will allow confirmation of thecomposition of the doublet as these will allow low temperature (below Tc)measurements.

Analysis of the intensity of each component can give an indication of theamount (roughly corresponding to layer thickness) of the total iron depositedwhich is in a particular state: crystalline iron, iron with reduced crystallinityor UFe2 intermetallic. These values are shown in Table 7.3.

In the sample with the thinnest iron layer, [U(28)/Fe(30)]31, the crys-talline iron layer is very thin, only amounting to 3–4 monolayers (using aniron atom spacing of 2.5 A. The amount of crystalline iron does not increaselinearly with the increase of iron layer thickness at first. An increase of 13 Ain the iron layer only gives an increase of 4 A of crystalline iron. Similarlythe next increase of 17 A in the total iron layer only gives a further 10 A atmost. Once the total iron layer is above 60 A, however, the increase is more


�U � 28 �� Fe � 30 �� 31

�U � 28 � Fe � 43 �� 31

�U 22 �� Fe 180 �� 5

0.0

0.2

0.4

0.6

0.8P

erce

nt E

mis

sion

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Velocity (mm/s)−10 −8 −6 −4 −2 0 2 4 6 8 10

0.0

0.2

0.4

0.6

0.8

Figure 7.11: CEMS spectra for U/Fe multilayers: [U(28)/Fe(30)]31,[U(28)/Fe(43)]31 and [U(22)/Fe(180)]5. Increasing crystallinity is observedwithin the iron layers as the thickness increases.


Sample Fe Fe PM PM RC RCArea Layer Area Layer Area Layer(%) (A) (%) (A) (%) (A)

[U(28)/Fe(30)]31 14 9 48 14 38 11

[U(28)/Fe(43)]31 30 13 36 15 34 15

[U(40)/Fe(60)]10 38 23 28 17 34 20

[U(80)/Fe(60)]20 35 21 31 18 34 20

[U(101)/Fe(60)]20 34 21 32 19 34 20

[U(42)/Fe(113)]21 69 78 16 18 15 17

[U(22)/Fe(180)]5 53 95 16 29 31 56

Table 7.3: Calculated thickness of iron layers in a fully crystalline (FE),paramagnetic (PM) or reduced crystallinity (RC) state for all U/Fe samplesstudied.

linear. At low thicknesses the different iron layers appear to not be formingin a set ratio but in an equilibrium between each type of iron site.

Apart from the sample with the very thickest iron layers ([U(22)/Fe(180)]5,which will be discussed later) the amount of UFe2 and non-crystalline ironis relatively constant once there is sufficient iron. Although smaller in thethinner iron layers, as there is less room for their growth, there appears tobe a maximum of ≈ 18 A of UFe2 and ≈ 20 A for the diffuse iron sites. It isnot possible to determine from these spectra whether the UFe2 and diffuseiron form one on top of the other or whether there is interdiffusion of ironwith both uranium and UFe2.

Normal CEMS spectra cannot give any information about the relativedepths of particular iron sites and so the spectra presented so far cannot de-termine whether the paramagnetic doublet is from a thin layer on the surfaceof the sample or whether it is distributed throughout the sample thicknessas in the proposed model of UFe2 forming at U/Fe interfaces. To test themodel a DCEMS experiment was run on one sample, [U(28)/Fe(43)]31, withone spectrum recorded from approximately 5 bilayers at the top of the sam-ple, and one spectrum recorded from the remaining layers underneath. Thesespectra are shown in Figure 7.12.

The first conclusion to be drawn is that the paramagnetic doublet ispresent in both spectra with a substantial intensity. This iron site is thusdistributed throughout the sample thickness and supports the model of UFe2

forming at the U/Fe interfaces. The relative intensity of the ordered iron


Figure 7.12: DCEMS spectra recorded from the [U(28)/Fe(43)]31 sample.Spectrum (a) is obtained from the top ∼ 5 bilayers in the sample, whilstspectrum (b) was recorded from the remaining layers underneath.

sites and the paramagnetic sites are slightly different in the two spectra.The ratio of UFe2/Fe is 3:2 in the top layers and 2:3 in the lower layers. Thismay be due to slight differences in growth conditions during sample growthor the central doublet in the top layers may have a small contribution from asurface iron oxide contaminant, such as FeO which is paramagnetic at roomtemperature.


The relative areas of the components in the spectrum from the samplewith the thickest iron layer, [U(22)/Fe(180)]5, give disproportionately largeamounts of UFe2 and non-crystalline iron compared to the trends seen in therest of the series. As the iron layer thickness is increased the relative areas ofthese two components should decrease compared to the crystalline iron. Al-though the iron layer is very thick the uranium layer is the thinnest of all thesamples. At 22 A the uranium layer is at the lower limit necessary to deposithomogenous uranium films and hence produce well defined layers. If thelayer is not well defined this will be propagated into the iron layers depositedupon it, increasing the thickness of iron necessary to reach a state where fullycrystalline growth can start. This explains the larger than expected thicknessof the non-crystalline component. This badly defined uranium layer couldalso make it easier for iron atoms to penetrate during the sputtering process,increasing the probability of forming UFe2. The multilayer thus consists ofthick layers of crystalline iron between disproportionately large amounts ofnon-crystalline iron and UFe2 and inhomogenous layers of uranium.

The lack of well defined interfaces is supported by specular x-ray reflec-tivity measurements taken by A.Herring. In Figure 7.13 a reflectivity scan ofthe [U(22)/Fe(180)]5 sample is compared with one from [U(42)/Fe(113)]21, asample which Mossbauer shows to have less interdiffusion at the interfaces.

It can be seen that the reflectivity scan from [U(42)/Fe(113)]21 has manysharp peaks. This is indicative of well defined interfaces.47 The scan from the[U(22)/Fe(180)]5 sample shows no sharp peaks, indicating either very diffuseor very rough interfaces∗.

All recorded spectra show that the iron spins are entirely within the planeof the sample, as expected from the shape anisotropy of a thin film. Thereappears to be no appreciable perpendicular magnetic anisotropy of any formin the system as might be expected from the coupling of the uranium orbitalmoment to the lattice if it possessed a magnetic moment. It should be notedhowever that in the analogous Ce/Fe multilayers perpendicular magneticanisotropy was only observed for iron layer thicknesses less than 15 A.3 Thisresult gives no indication of there being any significant magnetic moment onthe uranium atoms at the U/Fe interfaces in the studied samples.†

∗Specular reflectivity alone cannot distinguish between roughness or diffusion.47

†Actinides in Laves Phase AFe2 intermetallics possess no, or very small, magneticmoments.


Figure 7.13: X-ray reflectivity scans for a) [U(42)/Fe(113)]21 and b)[U(22)/Fe(180)]5 samples. Sharp peaks indicate well defined interfaces.

Chapter 8

Magnetic Iron Oxides

Over breathed, ever stirring,life from tired metal pry,

roles juggled, never dropping,faster than the watching eye.

The magnetic properties of iron oxides have had wide-ranging technologi-cal applications for many years, ranging from navigation with magnetite (orLodestone) to modern high-density magnetic recording media and readheaddevices. The two systems studied in this chapter concentrate on magnetiteand maghemite (Fe3O4 and γ-Fe2O3). Mossbauer spectroscopy is particularlyadept at investigating these materials and obtaining information on oxida-tion states and sample compositions and has been used extensively for bothtechnological and fundamental research.48

The first section is a commercial study of the magnetite content in printertoner materials. The emphasis is on determining the ratio of magnetite tomaghemite in the materials. The following section concerns the growth ofthin films of magnetite upon various substrates, using Mossbauer spectro-scopy to determine the growth quality and to confirm the growth of magne-tite.

8.1 Introduction to Magnetite

Magnetite, Fe3O4 is a member of the Spinel family of minerals, all of whosecrystal structures are similar. Crystallographically magnetite takes a cubicinverse spinel form.49 The oxygen ions form a close-packed cubic lattice withthe iron ions located at interstices between the oxygen ions. There are twodifferent interstices that the metal ions can take, tetrahedral (A) sites andoctohedral (B) sites.

107

CHAPTER 8. MAGNETIC IRON OXIDES 108

Chemically magnetite/maghemite can be represented by the formula

Fe3+[Fe2+

1−y Fe3+1−y Fe3+

1.67y�0.33y

]O4

where y = 0 for pure magnetite and y = 1 for pure maghemite, and vacanciesare represented by �.50

Magnetite exhibits a variety of characteristics, dependent on its tem-perature. There are three regions of temperature where magnetite behavesdifferently:

1. between 0 K and 119 K (the Verwey transition temperature, Tv),

2. between 120 K and 840 K (the Curie temperature, Tc),

3. above 840 K.

In region 3 magnetite is paramagnetic with metallic-like conductivity. Inregion 2 the A sites are populated by Fe3+ ions and the B sites by Fe3+

and Fe2+ ions, with twice as many B sites populated as A sites. At thesetemperatures electron-hopping occurs between the B sites. This electronhopping occurs over a timescale of approximately 10−9 s. As the timescaleof the Mossbauer event is 10−7 s the nuclei at each site display an averagecharge state of 2.5+ during this time interval. Thus a Mossbauer spectrumdisplays two distinct components: one from the Fe3+ ions on the A sites andone from the Fe2.5+ average on the B sites.

Below Tv the electron hopping process stops and the ions on the B siteshave a fixed charge. A Mossbauer spectrum now has three components: onefrom Fe3+ ions on the A sites, one from Fe3+ ions on the B sites and onefrom the Fe2+ ions on the B sites.

8.2 Printer Toner Powders

8.2.1 Introduction

As part of a commercial collaboration with Laporte Pigments, TechnicalCenter UK, we have investigated the magnetite content of printer and pho-tocopier toners of both Laporte’s own materials and that of competing com-panies.

Magnetite forms a pivotal role in laser printing technologies. The maincomponent of toner is a resin which when heated (or forced under pressureinto the paper) binds the toner to the paper. Approximately 10% of toner isthe actual colourant, usually carbon. These colourants must be able to hold


an electronic charge which allows them to be attracted to photoreceptorswhich then electrostatically transfer the toner to the charged paper.

If the colourant is of a low charge it may not stick to the developer rolland so a small amount of magnetic material is added and the developer rollcontains a small permanent magnet. The magnetic field then helps hold thetoner particles to the developer roll. Magnetite is the most common magneticfield creating material used.

The ability of the magnetite additive to increase the acceptance of toneronto the roll improves the reliability of the printer, reduces toner usage andthe build up of machine dirt (which can have damaging effects on the printer’sinternal mechanisms). Toners containing magnetic materials are also impor-tant components of Magnetic Ink Character Recognition (MICR) systemswhere characters are read directly from documents with magnetic sensors.

Laporte asked us to evaluate the ratio of Fe3O4 to Fe2O3 in the tonersamples, using spectra recorded at room temperature and 77 K.

8.2.2 Results

All of the room temperature spectra showed that the iron oxide contentwas not pure Fe3O4. In pure Fe3O4 there is a distinctive ratio between theintensity of the two spectral components. This ratio, R, should equal 1:1.88(A:B).∗ In all cases for the toner samples R was greater than this. Thisindicated another iron oxide being present and comparison with the examplespectra in Reference 50 shows this to be γ-Fe2O3 (maghemite). In this casewe can use the areas of the two components to calculate the Fe2+/Fe3+ ratioand the Fe3O4/Fe2O3 ratio.

Taking y as the the proportion of Fe2O3 to the whole (between 0, pureFe3O4, and 1, pure Fe2O3)

y =N2

N1 +N2

(8.1)

where N1 is the number of Fe atoms in the Fe3O4 compound and N2 is thenumber of Fe atoms in the Fe2O3 compound. The ratio of the areas of thetwo components, R, can be used to calculate y from the following relation:50

R =1 + 0.94

(5y3

)0.94(2− 2y)

(8.2)

where the factor of 0.94 arises from the Fe ions on the B sites having a slightly

∗This is not 1:2 as the recoil-free fraction of the B sites is a factor of 0.94 smaller thanthat of the A site.51


A-site B-siteSample IS QS Field Area IS QS Field Area

(mm/s) (mm/s) (kG) % (mm/s) (mm/s) (kG) %L1 +0.35 −0.02 494.2 60 +0.72 +0.02 459.4 40L2 +0.28 −0.02 489.7 46 +0.66 +0.02 457.5 54C1 +0.29 −0.01 489.0 50 +0.65 −0.01 456.6 50C2 +0.31 −0.02 491.3 66 +0.64 +0.01 454.1 34C3 +0.30 −0.02 492.7 63 +0.67 +0.01 456.6 37

Table 8.1: Final room temperature fit parameters for all toner powder sam-ples.

smaller recoil-free fraction.51 Once y is obtained the ratio of Fe2+/Fe3+ isgiven by:

Fe2+

Fe3+=

1− y2 + 0.67y

(8.3)

Laporte supplied five samples for study: two of their own (L1 and L2)and three competiting brands (C1, C2 and C3). No information was givenconcerning the composition of any of the samples. The room temperatureMossbauer spectra obtained from these samples are shown in Figure 8.1 andthe fitting parameters in Table 8.1.

Using Equations 8.2 and 8.3 the ratio of Fe2+ to Fe3+ can be calculated.These values are shown in Table 8.2. Rearranging Equation 8.1 to obtain theratio of atoms, N1:N2, gives the relation

N1

N2

=1− yy

(8.4)

the results of which are also shown in Table 8.2. The molecular ratio ofFe3O4 to γ-Fe2O3 can be obtained by multiplying the N1:N2 ratio by a factorof 0.67, to take account of the fact that a molecule of γ-Fe2O3 contains 2Fe atoms while a molecule of Fe3O4 contains 3. The ratio of magnetite tomaghemite was thus calculated to an accuracy between 1% and 17% fromthese results, where higher concentrations of magnetite have a larger error.

Mossbauer spectra were recorded from the same samples at 77 K. Thesespectra are shown in Figure 8.2.

At 77 K the samples are below the Verwey transition temperature, Tv, of119 K. The single B site component has now become two separate compo-nents for 2+ and 3+ ions. The hyperfine fields for Fe3+ A sites and Fe3+ Bsites in magnetite and the Fe3+ A and B sites all lie close to each other, mean-


Sample R y Fe2+:Fe3+ N1:N2

L1 1.56± .05 0.43± .01 0.25± .01 1.33± .03L2 0.84± .05 0.18± .03 0.39± .03 4.56± .75C1 1.01± .05 0.26± .02 0.34± .01 2.85± .20C2 1.92± .05 0.50± .01 0.21± .01 1.00± .02C3 1.71± .05 0.46± .01 0.23± .01 1.17± .02

Fe3O4 0.53 0 0.50 NA

Table 8.2: Calculated Fe2+:Fe3+ and N1:N2 ratios for the room temperaturespectra.

ing they overlap in the spectrum. This, combined with the broad linewidthof the Fe2+ B site makes these data much less reliable for accurate assessmentof area ratios than the room temperature spectra. Thus the final results werebased on the room temperature fits only.

8.3 Single Crystal Fe3O4 Thin Films

In collaboration with F. Schedin, P. Morrel and G. Thornton of the Depart-ment of Chemistry in the University of Manchester, we have investigated thegrowth of [111] oriented magnetite thin films using Mossbauer spectroscopy.

8.3.1 Introduction

In recent years, high values of magnetoresistance (MR) have been obtained inferromagnetic tunnel junctions and spin valve structures involving exchange-biasing antiferromagnetic metal oxide layers.52 In particular magnetite hasbeen suggested as a promising material for magnetoresistive sensors becauseof its significant spin polarisation at the Fermi level at room temperature.Magnetite’s half-metallic nature could, in principle, lead to MR tending to-wards infinity.53

Fe2O3, Fe3O4 and FeO share a common oxygen close packed plane leadingto good epitaxial growth of one phase upon another along the [111] direc-tion.54 Fe3O4(111) has been shown to have a sizeable magnetoresistance(∼ 7%) at room temperature whilst [100] orientated layers show none at thistemperature.55 The study thus focusses on [111] oriented oxide layers as baselayers for further epitaxial growth (eg α-Fe2O3).

The Fe stacking sequence of Fe3O4 in the (111) direction is comprisedof alternating antiferromagnetically coupled octahedrally and tetrahedrally


Sample IS QS Field Area(mm/s) (mm/s) (kG) (%)

Fe3O4/Pt 0.24 −0.06 479.8 280.65 +0.00 450.6 620.35 +0.00 0 10

Fe3O4/Al2O3A 0.32 +0.00 490.2 210.66 +0.04 451.2 79

Fe3O4/Al2O3B 0.45 −0.08 (Fig. 8.4) 800.33 +0.89 0 20

Table 8.3: Best fit parameters for magnetite thin film samples. The mag-netic hyperfine field for the Fe3O4/Al2O3B sample is a distribution, shownin Figure 8.4(b).

coordinated sites. Hence each layer along the (111) direction has a welldefined magnetisation direction in the plane of the sample.

Heteroepitaxial Fe3O4(111) thin films were grown on two subtrates, Pt(111)and Al2O3(0001). Two different processes were used for deposition on Al2O3:A) standard sputtering source and B) using an oxygen plasma source. Theoxygen plasma source gives higher quality epitaxial films on alumina sub-strates.56 The three samples produced are named Fe3O4/Pt, Fe3O4/Al2O3Aand Fe3O4/Al2O3B for samples grown on Pt(111), Al2O3(0001) with the oxy-gen plasma source and Al2O3(0001) with a normal source, respectively.

The sample Fe3O4/Pt was grown, using iron enriched with the 57Fe iso-tope, to a thickness of 54 A. Samples Fe3O4/Al2O3A and Fe3O4/Al2O3Bwere grown each with non-enriched iron to a nominal thickness of 100 A.

CEMS was used to determine the magnetic hyperfine interactions, mo-ment orientation, and the growth quality of the film.

8.3.2 Results

The CEMS fit results are shown in Table 8.3 and the spectra are shown inFigures 8.3 and 8.4.

The spectrum for Fe3O4/Pt shows good crystalline growth of magnetite.The spectrum can be fitted well with three components: two magnetic sextetsand one non-magnetic singlet. The two sextets show an exact match withthe bulk hyperfine parameters for Fe3O4 A and B sites.57,58

The non-magnetic singlet, with an isomer shift of 0.35mm/s, matches ex-actly that for iron in a platinum matrix.7 Thus we conclude that this com-


ponent is obtained from iron diffused into the platinum substrate.The ratio of A sites to B sites for this spectrum is 0.45:1 which is slightly

less than that of bulk samples where this ratio is 0.53:1. In this systemthere are a limited number of layers. With A and B layers stacking one onthe other it is possible that there is an uneven number of A sites, giving asmaller fraction of A sites than in an infinite lattice. If B sites were formedon the upper and lower extent of the thin film this would give a ratio of A:Bof 0.45:1 for a 54 A film assuming the bulk lattice constant of 8.39 A.59

The spectrum for the Fe3O4/Al2O3A sample also shows good crystallinegrowth. This spectrum requires only two components to give a good fit: twomagnetic sextets. The hyperfine parameters for the two sextet componentsagain are consistent with those for bulk samples.

The statistics of the Fe3O4/Al2O3A spectrum are too poor to give accu-rate information about the relative intensity of the A and B sites: the A sitelinewidth needs to be fixed to give a sensible result.

The spectrum for the Fe3O4/Al2O3B sample is shown in Figure 8.4(a).This has been fitted with two components: a distribution of magnetic sextetsand a doublet. The population of hyperfine fields in the distribution is shownin Figure 8.4(b).

The distribution has an average isomer shift of 0.45mm/s. This is inbe-tween the values for A and B site isomer shifts in magnetite and is due to thesingle distribution component combining both the A and B site componentsas would be expected in a spectrum from a more crystalline sample. Thedistribution population reaches a peak and then ends at ∼ 470 kG, consis-tent with an iron oxide, most probably magnetite as evidenced by the isomershift value.

The hyperfine field depends sensitively upon the local environment of theMossbauer atom. A distribution of hyperfine fields indicates a distributionof inequivalent iron sites. The distribution shows that the most likely en-vironment is that of normal, crystalline magnetite. There is also, however,a substantial area of iron at a reduced hyperfine field, showing a reducednumber of magnetic neighbours or an increased spacing between them. Themajority of the reduced hyperfine field component occurs between ∼ 280 kGand ∼ 380 kG. A small peak at 330 kG may indicate the presence of somemetallic bcc iron. Both effects point to substantial defects in the thin filmand that the normal sputtering source is not capable of producing films onAl2O3 substrates of the quality necessary for MR applications.

The doublet has an isomer of shift of 0.33mm/s, indicative of an Fe3+

charge state. A possible cause is a small amount of iron pentrating intothe substrate and substituting for aluminium in the Al2O3 compound. Atlow concentrations in the Al2O3 substrate the Fe3+ ions would not be mag-


netically ordered and at room temperature the spin-lattice relaxation timeswould be much shorter than the Mossbauer sensing time (see Section 2.4)resulting in a doublet component.


0

2

4

6

Per

cent

Abs

orpt

ion

0

5

10

0

2

4

6

0

1

2

3

4

Velocity (mm/s)−15 −10 −5 0 5 10 15 20

0

2

L1

L2

C1

C2

C3

300 K

Figure 8.1: Room temperature Mossbauer spectra for all toner samples.


0

5

Per

cent

Abs

orpt

ion

0

5

10

0

5

0

2

4

Velocity (mm/s)−10 −5 0 5 10

0

1

2

3

L1

L2

C1

C2

C3

77 K

Figure 8.2: 77K Mossbauer spectra for all toner samples.


Figure 8.3: Fe3O4 thin films on (a) platinum and (b) sapphire substrates.Sample (b) was grown using an oxygen plasma source.


Figure 8.4: Fe3O4 thin film on a sapphire substrate, grown with a standardsputtering source. (a) shows the fitted spectrum and (b) shows the hyperfinefield distribution.

Chapter 9

Concluding Remarks

Winding breeze, through paths willAirs contain from course and journey,

Which stir the secret, resting still,Picked anew by restless air to carry,

As fleck, a flight in feather ’til...

We have investigated some of the mechanisms working in nanoscale systems,particularly multilayers. The effects of strain and layer thicknesses have beenobserved in a number of multilayer and thin film samples. The compositionand growth quality of thin film structures has been investigated.

The room temperature CEMS results for all of the REFe2 Laves Phasesamples show a low symmetry magnetic easy axis as expected from earlierstudies on similar systems. The analysis of dipolar and contact hyperfinefields showed the magnetic easy axis to be close to the [241] and [351] di-rections. Mossbauer spectroscopy on these samples appears to lack the res-olution necessary to determine the easy axis with great accuracy using thismethod. Persistent problems in determining angular data from these spec-tra have been the overlap of the components and the multidomain natureof the untrained samples. The analysis of the hyperfine field contributionsis sensitive to small differences in hyperfine field and quadrupole splitting,differences which are smeared by the close proximity of the four components.There is ample room in the spectra for reducing the velocity range of theattenuator and thus increasing the energy resolution of the spectra. A fieldtrained sample, where one of the equivalent easy axis directions is prefer-entially populated, would allow the use of peak intensities to be used forangular information as well as peak positions.

The spin moments in all REFe2 Laves Phase samples have been seen tolie out of plane in all samples by approximately 22◦, indicating a significant

119

CHAPTER 9. CONCLUDING REMARKS 120

magneto-elastic anisotropy. The use of 2.5 kOe in plane applied field measure-ments indicated a much larger magnitude of magnetocrystalline anisotropyin the DyFe2 system than in the YFe2 system as expected from the largesingle ion anisotropy of the dysprosium moments.

In the DyFe2/YFe2 multilayer samples the anisotropy is seen to be domi-nated by the dysprosium single-ion anisotropy. The DyFe2(50 A)/YFe2(50 A)sample shows average hyperfine fields consistent with the DyFe2 and YFe2

thin film results, whilst samples with thinner layers show an enhanced hy-perfine field of up to 17%. The current data do not provide any informationon the basis of this effect. Although the calibration of these spectra has beenchecked, sequential runs of at least some of these samples would validate thefindings of the data. More samples with thinner layers still, if possible, wouldinvestigate further this effect.

The DyFe2/Dy multilayers have shown identical zero field properties tothe DyFe2 thin film system down to a DyFe2 thickness of 50 A. Although theresults are rather uninteresting they do provide complementary informationfor the multilayers of two magnetic layers, helping to isolate the sources ofstructural effects in other samples.

In all samples studied under applied field the hyperfine fields were re-duced. This is expected in YFe2 where only the iron atoms possess a mo-ment. It would be expected in all other systems containing dysprosium forthe hyperfine fields to increase. Sample alignment with respect to appliedfields is very important in systems with significant magnetic anisotropy andthis alignment is not known and cannot be easily measured. In any futurework care must be taken to record the positioning of the samples withinequipment where possible.

Preliminary SQUID magnetometry data were taken from these samplesbut the rather large YFe2 seed layer producing exchange springs and difficul-ties in sample alignment to the applied field precluded any further magne-tometry work. Other groups have countered these problems by using sampleswith only a thin Fe seed layer to remove the unwanted exchange springs andVector VSM equipment to allow precise angular positioning of the samples.Any further samples studied should therefore follow the same example, al-lowing magnetometry data to be taken to complement the Mossbauer data.

SQUID magnetometry results from the Ce/Fe multilayers show that mostof the samples exhibit antiferromagnetic coupling, with a TN ranging between125 K and 190 K, dependent upon both cerium and iron layer thicknesses.The poor signal to noise ratio of much of the data has made some of theinterpretation difficult and prevented definite conclusions to be drawn onbehaviour trends with layer thickness. A lack of sample area measurementshas also prevented a full comparison of some of the data recorded. Retaking

CHAPTER 9. CONCLUDING REMARKS 121

some of the data with known sample sizes would enhance the analysis greatly.The exchange coupling constant, J(z), has been calculated for the anti-

ferromagnetically coupled samples and shows an oscillatory z dependence.The number of data points does not allow a real comparison with theoreticalpredictions for exchange coupling across nonmagnetic layers, although thedata so far suggest an RKKY-like z dependence.

CEMS results from the U/Fe multilayers shows that each iron layer iscomposed of BCC iron, a poorly-crystalline iron layer with a reduced hyper-fine field of up to 3% and a doublet from a paramagnetic UFe2 layer. Thehyperfine parameters for the paramagnetic doublet match best UFe2 butother intermetallics cannot be totally discounted. Low temperature workbelow TC = 167 K for UFe2 on these samples would help corroborate thisfinding.

The relative thicknesses of the constituent layers within the U/Fe ironlayer scale nonlinearly with the thickness of the deposited iron layer below60 A. Above this thickness the disordered iron and UFe2 layers reach maxi-mum thicknesses of 20 A and 18 A respectively. Where the uranium layer haspoor crystalline growth this is propagated into the iron layer and increasesthese thicknesses. This sets a layer thickness limit on the growth of gooduranium layers of 22 A.

Room temperature Mossbauer spectroscopy results from a selection ofprinter toner powders were used to produce the ratio of magnetite to mag-hemite in the powders.

CEMS results on magnetite thin films showed good crystal growth on aPt(111) substrate, with some iron forming a non-magnetic layer diffused inthe platinum. The amount of iron in such sites may have been exaggeratedby the substrate preparation history. Magnetite deposited on Al2O3(0001)substrates showed good crystal growth when using an oxygen plasma source.The statistics on the spectrum obtained from this sample are very poor,preventing any quantitative analysis of site occupancy. A longer run on thissample would be beneficial, particularly as this sample is the most favourabletype for technological applications. A sample produced from a normal sput-tering source showed a distribution of hyperfine fields and a paramagneticcontribution from iron substituting for aluminium in the substrate. Thisshows the benefits of the oxygen plasma source for producing quality thinfilms on the Al2O3 substrate.

Appendix A

Publications

• Magnetic Anisotropy in Multilayers.M F Thomas, J Bland, G S Case, J A Hutchings and O Nikolov, Hy-perfine Interactions, 126:377–86 (2000)

• Off-Center Sn Atoms in PbSnTeSe Studied by the Mossbauer Effect.J Bland, M F Thomas and T M Tkachenka, Hyperfine Interactions,131:61–65 (2000)

• Temperature Dependent Mossbauer Study at Sn Sites in Some IV-VISemiconductors Containing Off-Center Atoms.J Bland, M F Thomas and T M Tkachenka, Physica Status Solidi,221:617–24 (2000)

• Tin Germanate Glasses.D Holland, M E Smith, I J F Poplett, J A Johnson, M F Thomas andJ Bland, Journal of Non-Crystalline Solids, 293-295:175–181 (2001)

• Mossbauer effect study of off-centre atoms in IV-VI semiconductors.J Bland, M F Thomas, V A Virchenko, V S Kuzmin and T M Tkachenko,Semiconductors, 35:15–20 (2001)

• Redox processes in Sb-containing mixed oxides used in oxidation catal-ysis. I. Tin dioxide assisted antimony oxidation in solid state.M Calderaru, M F Thomas, J Bland and D Spranceana, Applied Catal-ysis A: General., 209:383–90 (2001)

• Mossbauer study of the superspin glass transition in nanogranular Al49Fe30Cu21.J A de Toro, M A lopez de la Torre, J M Riveiro, J Bland, J P Goffand M F Thomas, Physical Review B, 64:224421–6 (2001)

122

APPENDIX A. PUBLICATIONS 123

• Magnetic anisotropy studies in Ce/Fe and U/Fe multilayersM F Thomas, G S Case, J Bland, C A Lucas, A Herring, W G Stirling,P Boni, S Tixier, R C C Ward, M R Wells and S Langridge, PhysicaStatus Solidi, 189:537–43 (2002)

• A Mossbauer study of DyFe2, YFe2 and HoFe2 thin films and multilay-ers.J Bland, M F Thomas, M R Wells and R C C Ward, Physica StatusSolidi, 189:919–21 (2002)

• Magnetic nano granularity and spin glass behaviour in mechanicallyalloyed Fe35Al50B15.J A de Toro, M A Lolez de la Torre, J M Riveiro, J Bland, J P Goff andM F Thomas, Accepted for publication in Journal of Applied Physics

• Studies of Rare-Earth/Iron and Actinide/Iron multilayers.M F Thomas, G S Case, J Bland, A Herring, W G Stirling, S Tix-ier, P Boni, R C C Ward, M R Wells and S Langridge, Accepted forpublication in Hyperfine Interactions

• Cation Coordination in Oxychloride Glasses.J A Johnson, D Holland, J Bland, C E Johnson and M F Thomas,Submitted to Journal of Non-Crystalline Solids

Bibliography

[1] U. Gradmann. Handbook of Magnetic Materials, volume 7.

[2] J.A.C. Bland and B. Heinrich, editors. Ultrathin Magnetic Structures,volume 1&2. Springer, Berlin.

[3] G.S. Case. Mossbauer Spectroscopic and Structural Studies of MagneticMultilayers. PhD thesis, Oliver Lodge Laboratory, University of Liver-pool, 2000.

[4] R.L. Mossbauer. Z. Physik, 151:124, 1958.

[5] N.N. Greenwood and T.C. Gibb. Mossbauer Spectroscopy. Chapmanand Hall Ltd, London, 1971.

[6] H.H. Wickman and I.J. Gruverman. Mossbauer Effect Methodology.Plenum Press, New York, 1966.

[7] J.G. Stevens and V.E. Stevens, editors. Mossbauer Effect Data Index.IFI/Plenum, New York, 1975.

[8] B.D. Cullity. Introduction to Magnetic Materials. Addison-Wesley, Mas-sachusetts, 1972.

[9] G. Bertotti. Hysteresis in Magnetism. Academic Press, San Diego,1998.

[10] S. Chikazumi and S.H. Charap. Physics of Magnetism. Krieger Pub-lishing Company, Malabar, Florida, 1978.

[11] J. Clarke. Scientific American, 271 #2:46, 1994.

[12] A.C. Rose-Innes and E.H. Rhoderick. Introduction to Superconductivity,Second Edition. Pergamon Press, Oxford, 1978.

[13] N.W. Ashcroft and N.D. Mermin. Solid State Physics. Holt Saunders,Japan, 1981.

124

BIBLIOGRAPHY 125

[14] B.D. Josephson. Phys. Lett., 1:251, 1962.

[15] O. Nikolov. Private Communication.

[16] J.G. Stevens, V.E. Stevens, and W.L. Gettys. Mossbauer Effect Refer-ence and Data Journal, 3:99, 1980.

[17] Quantum Design. MPMS XL Options Manual, 1999.

[18] H.J.G Draaisma et al. J. Magn. Magn. Mat., 66:351, 1987.

[19] L. Neel. J. Physique Radium, 15:225, 1954.

[20] M.T. Johnson et al. Rep. Prog. Phys., 59:1409, 1997.

[21] K. Xia, W. Zhang, M. Lu, and H. Zhai. Phys. Rev. B, 55:12561–5,1997.

[22] M.A. Ruderman and C. Kittel. Phys. Rev., 96:99–102, 1954.

[23] A.J. Freeman. Magnetic Properties of Rare Earth Metals.

[24] K.H.J Buschow. Rep. Prog. Phys., 40:1179–1256, 1977.

[25] J.H Wernick and S Geller. Trans. Am. Inst. Min. Metall. Petrol. Engrs,218:866–8, 1960.

[26] R.L. Cohen. Phys. Rev., 134:A94–8, 1964.

[27] G.J. Bowden, D.ST.P. Bunbury, A.P. Guimaraes, and R.E. Snyder. J.Phys. C, 1:1376–87, 1968.

[28] E. Burzo. Solid State Communications, 14:1295–98, 1974.

[29] V. Oderno, C. Dufour, K. Dumesnil, Ph. Bauer, Ph. Mangin, andG. Marchal. Phys. Rev. B, 54:375–8, 1996.

[30] A. Mougin, C. Doufour, K. Dumesnil, and Ph. Mangin. Phys. Rev. B,52:9517–31, 2000.

[31] G.J. Bowden et al. Physica B, 86-88:179, 1977.

[32] G.J. Bowden. J. Phys. F: Metal Phys., 3:2206–2217, 1973.

[33] G.J. Bowden, J.M.L. Beaujour, S. Gordeev, P.A.J. de Groot, B.D. Rain-ford, and M. Sawicki. J. Phys.: Condes. Matt., 12:9335–46, 2000.

BIBLIOGRAPHY 126

[34] E.E. Fullerton, J.S. Jiang, and S.D. Bader. J. Magn. Magn. Mater.,200:392, 1999.

[35] J.M.D. Coey and R. Skomski. Phys. Scr., 49:315, 1993.

[36] S.N. Gordeev, J.-M.L. Beaujour, G.J. Bowden, B.D. Rainford, P.A.J.de Groot, R.C.C. Ward, M.R. Wells, and A.G.M Jansen. Phys. Rev.Lett., 87:186808–1–4, 2001.

[37] A. Mohamed. M.Phys. Project. Oliver Lodge Laboratory, University ofLiverpool, 2002.

[38] M. Arend. Phys. Rev. B, 57:2174–87, 1998.

[39] W. Felsch, M. Arend, M. Finazzi, O. Schutti, M. Munzenberg, A.-M.Dias, F. Baudlet, Ch. Giorgetti, E. Dartyge, P. Schaaf, J.-P. Kappler,and G. Krill. Phys. Rev. B, 57:2174–87, 1998.

[40] J. Barnas and Y. Brugnesaed. Phys. Rev. B, 53:5449, 1996.

[41] S.S.P. Parkin. Phys. Rev. Lett., 67:3598–601, 1991.

[42] M. van Schilfgaarde and W.A. Harrison. Phys. Rev. Lett., 71:3870–3,1993.

[43] P. Bruno and C. Chappert. Phys. Rev. Lett., 67:1602–5, 1991.

[44] A.J. Freeman and G.H. Lander, editors. Handbook on the Physics andChemistry of the Actinides, volume 1. North Holland, Amsterdam.

[45] S. Blow. J. Phys. C, 3:835–44, 1970.

[46] S. Tsutsui, M. Nakada, Y. Kobayashi, S. Nasu, Y. Haga, and Y. Onuki.Hyperfine Interactions, 133:17–21, 2001.

[47] D.Mannix. X-ray and neutron scattering studies of f-electron multilayersand single crystals. PhD thesis, Oliver Lodge Laboratory, University ofLiverpool, 1998.

[48] R.E. Vandenberghe and E de Grave. Mossbauer Spectroscopy Applied toInorganic Chemistry, 3:59–182, 1989.

[49] R.S. Hargrove and W. Kundig. Solid State Communications, 8:303–8,1970.

[50] G.N. da Costa, E. de Grave, P.M.A de Bakker, and R.E. Vandenberghe.Clays and Clay Minerals, 43 #6:656–68, 1995.

[51] G.A. Sawatzky, F. Van der Woude, and A.H. Morrish. Phys. Rev.,183:383–6, 1969.

[52] C.H. Shang, G.P. Berera, and J.S. Moodera. Appl. Phys. Lett., 72:605,1998.

[53] A.M. Bratkovsky. Appl. Phys. Lett., 72:2334, 1998.

[54] N.G. Condon, F.M. Leibsle, T. Parker, A.R. Lennie, D.J. Vaughan, andG. Thornton. Phys. Rev. B, 55:15885, 1997.

[55] S.B. Ogale, K. Ghosh, R.P. Sharma, R.L. Greene, R. Ramesh, andT. Venkatesan. Phys. Rev. B, 57:7823, 1998.

[56] Gota et al. Proceedings of the 2nd International Workshop on OxideSurfaces, 2001.

[57] E. de Grave, R.M. Persoons, R.E. Vandenberghe, and P.M.A de Bakker.Phys. Rev. B, 47:5881, 1993.

[58] L. Haggstrom, H. Annersten, T. Ericsson, R Wappling, W. Karner, andS. Bjarman. Hyperfine Interactions, 5:201–14, 1978.

[59] R.W.G. Wyckoff. Crystal Structure, volume 3. John Wiley and Sons,New York.

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I do not know what I may appear to the world; but tomyself I seem to have been only like a boy, playing on thesea-shore, and diverting myself, in now and then finding asmoother pebble, or a prettier shell than ordinary, whilstthe great ocean of truth lay all undiscovered before me.Sir Isaac Newton

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