PHYSICAL REVIEW B 15 MAY 2000-IVOLUME 61, NUMBER 19
Electronic structure of plutonium monochalcogenides
P. M. Oppeneer* and T. KraftInstitute of Theoretical Physics, University of Technology, D-01062 Dresden, Germany
M. S. S. BrooksEuropean Commission, Joint Research Center, Institute for Transuranium Elements, D-76125 Karlsruhe, Germany
~Received 21 April 1999; revised manuscript received 2 September 1999!
The anomalous properties of the Pu monochalcogenides are investigated on the basis of electronic structurecalculations. The Pu monochalcogenides are calculated to be semimetallic because, first the large spin-orbitinteraction of the Pu 5f states splits the 5f 5/2 and 5f 7/2 subbands away from the Fermi energy, and second thehybridization between Pu 6d and chalcogenidep and 5f bands leads to a hybridization gap. The anomalouslattice constants, which correspond neither to Pu21 nor to Pu31 are consistent with the energy band approach,as is the lattice constant where the transition to Pu21 is expected. Our calculations suggest that Pu has a5 f 62x6dx configuration, wherex depends on the lattice parameter, but the sum of 5f and 6d occupancy isconstant. Calculations of the optical conductivity spectra show that there are two optical pseudogaps, one ofabout 20 meV and one of 0.2 eV. A magnetic phase transition is predicted to occur in the NaCl structure underpressure. When this phase transition is enforced in a magnetic field and takes place before the martensitictransition to the CsCl structure occurs, it is predicted to lead to a giant magnetoresistance of about285%.
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I. INTRODUCTION
The plutonium monochalcogenides display a varietyanomalous physical properties.1–3 Exceptionally, for actinidechalcogenides, they do not order magnetically buttemperature-independent paramagnets.1 The temperature dependence of the resistivity suggests a complex semicontor. There is evidence for energy gaps of 0.2 eV, 20 meV1,4
and 3 meV.1,2 The precise low-temperature electronspecific-heat coefficientg is not known, but an extrapolatioto zero temperature yieldedg530 mJ mol21 K22 for PuTe,a very high value for a semiconductor.5 On the other handx-ray photoemission spectroscopy on PuSe reveale5 f -related intensity directly at the Fermi energy, someththat cannot be simply reconciled with a semiconductor.6 Theinduced magnetic form factor is incompatible with Pu21 orPu31 ions.7
The lattice constants of the Pu monochalcogenidesalso anomalous. Figure 1 shows the lattice constants ofactinide pnictides and chalcogenides with, for comparisthose of the corresponding rare earths.8 They are far toosmall for divalent ions. There is a 5f bonding contribution inthe light actinide pnictides and chalcogenides and the mmum bonding occurs for the uranium pnictides. Actinide-fanion-p bonding is larger early in the series when therefewer 5f -electron states occupied.9 The lattice constant oPuTe is consistent with a trivalent Pu ion but the lattconstants of PuSe and PuS are anomalously small.
Two theoretical explanations of the unusual propertiesthe Pu chalcogenides have been proposed. Brooks10 carriedout self-consistent electronic structure calculations usingDirac equation in the atomic sphere approximation~ASA!for the Pu monochalcogenides. One of the essential resulthat study was that the large spin-orbit~SO! interaction of Pusplits the 5f states by approximately 1 eV, so that the Ferenergy (EF) falls in the gap between the SO-split 5f sub-
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bands. The Pu chalcogenides were therefore proposed trelativistic semiconductors.10 Subsequently Hasegawa anYamagami11 made self-consistent linearized augmenteplane-wave~LAPW! calculations for PuTe and found it to bsemimetallic. The essential difference between the twoof self-consistent calculations was that the former did notthe combined correction terms to ASA, resulting in ancreased energy gap. Wachteret al.2 suggested that PuTe ian intermediate valence~IV ! compound, and that the propeties of PuTe should be comparable to those of SmS incollapsed phase. NaCl-type rare earth and actinide cpounds normally make the transition to CsCl structure unpressure. Wachteret al.argued that if thef n2d separation isless than about 1 eV, corresponding to an applied pressuabout 100 kbar, a transition to intermediate valence occ
FIG. 1. Lattice constants of the NaCl-type rare-earth andtinide pnictides and monochalcogenides. The lines denote the laconstants of the rare earths, and the symbols those of the actinThe lattice constant of ThTe is anomalously small since it foronly in the CsCl structure and shown is the NaCl lattice constantthe same volume.
12 826 PRB 61P. M. OPPENEER, T. KRAFT, AND M. S. S. BROOKS
before the end of a NaCl-CsCl structural transition. WhWachteret al.2 consider Pu and Sm chalcogenides to be alogs, the latter are semiconducting at ambient pressurebecome IV and then trivalent under pressure, whereasformer are proposed to be intermediate valent at ambpressure. The argument is based upon the high specific-g value and the optical plasma resonance of free carriwhich appear to rule them out as true semiconductors atbient pressure. The argument is supported by the low bmodulus, a feature of IV.
Since the theory of IV in rare earths is based uponlocalized 4f configuration the energy of the 4f states is dis-persionless in the absence of 4f -5d hybridization. If 4f -5dhybridization is local at the atom, it must, on parity groundbe due to nonspherical components of the potential whichsmall in the region where the 4f density is large. If 4f -5dhybridization arises from a 4f -5d hopping integral, which ismore realistic, it is also small as it relies upon 4f -electrontunneling. In the former case 4f -5d hybridization is constanacross the zone, there are no hybridized solutions atoriginal unhybridized 4f energy, and there is always a gaIn the latter case it is possible but unlikely that 4f -5d hy-bridization vanishes somewhere in the zone therefore thshould also be a small energy gap. The presence of a senergy gap of the order of meV is therefore evidence sporting IV. In rare earths, since 4f -4 f electron interactionleads to Russell-Saunders coupling, the SO interaction isfinal perturbation to be applied when it forms the total anglar momentum and it does not affect the energy gap.
A reasonable starting point for the discussion of tanomalous properties of the Pu monochalcogenides is atailed knowledge of the electronic structure obtained frself-consistent calculations. In the present paper we rethe results of such electronic structure calculations. As pticular models have been proposed previously for the etronic structure of PuTe, for which also most experimewere carried out,2–5,12 we shall give this compound speciattention. We find for the Pu monochalcogenides thatcombination of intra-atomic 5f -5 f and 5f -chalcogenidephybridization is not negligible. The 5f bands are dispersiveven in the absence of 5f -6d hybridization; therefore 5f -6dhybridization alone cannot be responsible for the gap atFermi energy as in rare earths. We find, in contrast, thatSO interaction is large in the actinides and that it affects thproperties to first order, leading to the formation of 5f 5/2 and5 f 7/2 bands. When these bands hybridize with other condtion bands the SO splitting produces a quasigap of justthan 1 eV between the SO-split bands. The 5f 5/2-derivedbands hold just six electrons and are filled in the Pu monoalcogenides. The Pu valence is noninteger and, since5 f 5/2-derived bands are almost filled, the electrons contaiin them are almost localized.
The results of the band-structure calculations are psented in Sec. II. We find the Pu monochalcogenides tosemimetallic, with tiny Fermi surface portions. This findinis consistent with recent resistivity and optical measuments.12,13 There is a quasigap in the band structure, whbecomes a real band gap for the lattice constant corresping to the Pu21 ion. From the calculated total energy anband structures, we then consider the possible phase trtions that could take place and compute the optical reflec
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ity spectra. A particular point that we address is the possiity of a magnetic phase transition in the Pmonochalcogenides in an applied magnetic field under psure. Such a phase transition leads to drastically altetransport properties, and we predict that such a phase tration is accompanied by a giant magnetoresistance.
II. SELF-CONSISTENT BAND-STRUCTURECALCULATIONS
A. The electronic ground state
Our band-structure calculations are based upon the lspin-density approximation~LSDA! to density-functionaltheory. The LSDA Kohn-Sham equation has been solveding a relativistic version of the augmented-spherical-wa~ASW! method.14 In this energy-linearized band-structuscheme first the scalar-relativistic Kohn-Sham equationssolved and then the SO interaction is included in a secvariational procedure in every self-consistent iteration stThe potential is treated in the spherical approximation, acombined correction terms are used. In practice, the resof this approach are indistinguishable from calculatiobased on the Dirac equation. For the exchange-correlapotential we have chosen the parametrization of von Baand Hedin.15 The sphere radii used in the calculations wedetermined by minimizing the charge transfer betweentwo atoms, which gives sphere radii similar to those obtainfrom minimizing the Hartree-Coulomb energy. In particulawe have verified that the calculated energy bands are insitive to reasonable changes of the relative sphere radii.reciprocal space integrations were carried out using 243cial k points in 1/16th part of the Brillouin zone. Test calclations have been performed also with 646 specialk points,but no detectable changes of the band structure couldobserved. The core states have been relaxed within eself-consistent iteration step. The Pu 6p states are treated acore states.
Figure 2 shows the calculated energy bands of PuS, Pand PuTe, computed for the experimental lattice constai.e., 5.530 Å, 5,793 Å, 6.190 Å, for PuS, PuSe, and Purespectively.8,13 The quotients of the Pu and chalcogenisphere radii used in the calculations are 1.180, 1.122,1.037, for PuS, PuSe, and PuTe, respectively. For all thchalcogenides, there are clearly two sets of flat bands, onabove and the other set below the Fermi energy with a seration of about 1 eV~see also Refs. 10 and 11!. These sets ofbands are primarily 5f in character and the splitting betweethem is due to the SO interaction.
We have verified the influence of the SO interactionmultiplying the SO interaction for the 5f states by a constanprefactor equal to 0.2, 1.0, and 2.0. The calculated densof state~DOS! of PuS for the three cases are shown in Fig.The pseudogap, which leaves a small DOS at the Fermiergy, disappears when the prefactor is set equal to 0.reduce the spin-orbit interaction by a factor of 5, and whthe magnitude of the spin-orbit interaction is doubled therea real band gap. In the latter case, with a gap between5 f 5/2- and 5f 7/2-derived bands six valence electrons fill bothe bonding and antibonding orbitals of the 5f 5/2 bands. Inthe former case, where there is no gap, there is a groufourteen 5f bands to be filled and the six electrons enter
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PRB 61 12 827ELECTRONIC STRUCTURE OF PLUTONIUM . . .
bonding bands, leaving the antibonding bands empty. Ocpation of antibonding bands increases the lattice constand since this occupation increases with spin-orbit intertion, the 5f spin-orbit interaction can increase the latticonstant when the 5f occupation is about six—a situatiorealized in the plutonium chalcogenides.
The following broad picture of the Pu monochalcogenidin the NaCl structure emerges. The chalcogenidep bands arecompletely filled. These are the three filled bands extendfrom about27 eV to about23 eV for all three compoundsThe chalcogenide anions are thus in the 22 ionic state. Note,that the chalcogenidep bands shift up in energy going fromthe sulfide to the teluride. This is the normal behavior,lated to the increase of the lattice parameter, which wasfound for the uranium monochalcogenides.16 AboveEF thereare mostly the Pu 6d bands. The bands of primarily 5f char-acter are thus placed energetically in between the chalcoide p bands and the 6d bands, which are separated at theGpoint by an energy of about 4 eV. The plutonium 5f bandshybridize with the 6d bands. In the absence of SO splittinof the 5f states the hybridized 5f -6d states straddle theFermi energy, and the chalcogenides would, in this casemagnetic metal since the Stoner criterion is easily fulfilljust as in uranium and neptunium chalcogenides. In the p
FIG. 2. Calculated energy bands of PuS, PuSe, and PuTambient lattice constant. The Fermi energy is at 0 eV.
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ence of the SO interaction, there is, however, a lapseudogap due essentially to a splitting between5 f 5/2-derived bands and the 5f 7/2-derived bands of about 1eV. In these compounds there are 12 valence electronsformula unit, six of which fill the chalcogenidep bands. Theremaining six electrons are nearly enough to fill t5 f 5/2-derived bands, except for a small portion of thebands at theG point. Close to theX point there is the nextenergy band, which also crossesEF . The Fermi energy liesthus in a pseudogap, yet there are two small hole Fesurface pockets about theG point and a small electron Fermsurface at theX point. The result is that the Pu monochalcgenides are calculated to be compensated metals, havitiny Fermi surface. Next to the SO splitting of the 5f sub-bands there is a second, more subtle, mechanism that isponsible for the formation of the quasigap. The Pu 5f and6d bands hybridize such that a hybridization gap is formwhere these bands would otherwise cross. In Fig. 2 it canseen that for all three chalcogenides there is at theX point thelowest energy band of the hybridized 5f -6d complex. Thisband originates from a band of 6d character aboveEF at theG point. The hybridization of this band with the SO-sp
atFIG. 3. The pseudogap in the density of states~DOS! of PuS as
a function of the scaled spin-orbit interaction. The fully relativiscalculation is labeled by ‘‘Scale51.0.’’ The pseudogap vanishewhen the spin-orbit interaction is made 5 times smaller~‘‘Scale50.2’’!.
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12 828 PRB 61P. M. OPPENEER, T. KRAFT, AND M. S. S. BROOKS
5 f -derived bands is such that instead of band crossinquasigap is formed alongG-X. One of the hybridized bandbecomes very flat and squeezed on the Fermi energy fabove. Below we shall examine the formation of thybridization-related pseudogap in detail as a function oflattice constant, which sensitively modifies thef -d hybrid-ization.
The band structure of other actinide monochalcogeniis similar to that of PuS, PuSe, and PuTe, but with the Feenergy falling below the quasigap and the 5f 5/2-derivedbands partially unfilled, leading to normal metallic behaviIt is therefore the position ofEF relative to the overall bandstructure that makes the Pu monochalcogenides uniquehave also studied, therefore, the NaCl-type Am monopntides ~for which there is little experimental data!, since theyare isoelectronic with the Pu monochalcogenides. Althouthep-derived valence bands in the pnictides are closer toconduction bands than in the chalcogenides, the electrstructure is found to be similar. The Fermi energy is againthe top of the 5f 5/2-derived conduction bands and we finthese compounds to be semimetallic when the 5f 5/2 electronsare delocalized. The latter condition is most likely to be ffilled for AmN, which has an anomalously small lattice costant.
B. The ground-state energy and lattice constant
The calculated total energy of PuTe as a function oftice constant is shown in Fig. 4. The calculated energy mmum corresponds to a lattice constant of 6.07 Å, whichabout 2% less than the measured lattice constant of 6.1Within the LSDA, a deviation of 2% of the experimentlattice constant is normal, as is also the fact that the calated lattice constant is smaller. The latter occurs becauseLSDA has a tendency to overbind, i.e., make the bondtances shorter. The correct prediction of the lattice paramis a strong indication that the LSDA electronic structure aproach is applicable to describe the anomalous propertiethe Pu chalcogenides. Wachteret al. have examined theanomalous lattice parameter of PuTe by comparing it toparameters that are expected~from the ionic radii! for Pu21
and Pu31.2 The lattice parameter expected for PuTe w
FIG. 4. Calculated total energy of PuTe as a function of lattconstant. The arrow at 6.72 Å indicates the lattice constantwhich Pu is expected to have the Pu21 valency.
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divalent Pu is 6.72 Å. Our calculated lattice parametermuch smaller than the divalent PuTe lattice parameter, csistent with the observation that Pu is not in the divalestate.
A lattice constant less than that expected from a locali5 f configuration may be attributed to 5f bonding, whereas alattice constant greater than that expected for a normalerant system is at least partially explained by the effect ofinteraction. This effect is illustrated in Fig. 5, which showthe calculated electronic pressure~or derivative of the totalenergy with respect to volume! as a function of SO scalingfactor. Since SO coupling splits the 5f bands into 5f 5/2 and5 f 7/2 bands the center of all the 5f bands is not affected, buthe preferential filling of the 5f 5/2 increases the electronipressure by 80 kbar, which corresponds to a change in laconstant of 2%. The SO interaction has little effect uponcontribution of other states to the pressure. The fact that5 f contribution to the electronic pressure, and therebylattice constant, changes so much with SO coupling consis therefore due to the filling of the 5f 5/2-derived bands.
As the lattice constant is increased the 5f -5 f , 5f -6d, and5 f -p hybridization decreases. In order to understand thefect of this hybridization and its dependence upon lattconstant it is useful to start from the extreme case of purefbands. Pure SO-split 5f bands separate into 5f 5/2 and 5f 7/2bands. If the SO splitting is very large the intra-atomic hbridization between the 5f 5/2 and 5f 7/2 components is smallthe result being that the 5f 5/2 bands are very narrow. Hybridization within the 5f 5/2 states is determined by the expansiof tails of the 5f 5/2 orbitals at a given Pu site about other Psites. The multipole expansion of the 5f orbitals results inwave functions at the other site with angular momentatained by adding an angular momentum of up to 2l 56 to thej 55/2 angular momentum. The addition of angular mome
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FIG. 5. The change in electronic pressure of PuS as a funcof the spin-orbit scaling factor, for a fixed value of lattice constaThe calculation for zero spin-orbit coupling corresponds to the sing factor 0.0, while the normal relativistic calculation corresponto 1.0.
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PRB 61 12 829ELECTRONIC STRUCTURE OF PLUTONIUM . . .
restricts the expanded multipoles tol 517/2, . . . ,7/2. Thereis therefore no 5f 5/2 component and the interatom5 f 5/2-5 f 5/2 hybridization vanishes. The SO interaction in Pis not large enough to drive this extreme case and the 5f 5/2bands obtain width through hybridization with the 5f 7/2bands. Hybridization in general decreases with increaslattice constant, but the above-mentioned effect amplifiesinfluence of lattice constant upon the width of the 5f 5/2bands and the size of the pseudogap. In Fig. 6 we haveted the state density of PuS with hybridization between5 f and 6d and sulfurp states removed. This was done bsetting the appropriate structure constant blocks to zeromodel calculation. The hybridization gap is removed ands-p-d states produce a free-electron-like background sdensity with the SO-split 5f state density superimposeThus it is thecombinationof SO splitting of the 5f statesand the hybridization withd and p states that producespseudogap.
The 5f -5 f and 5f -6d hybridization is sensitively dependent upon the lattice constant. In Fig. 7 the changes ofquasigap in PuTe are shown for three expanded latticestants. For the experimental lattice constant there is theband that, without hybridization, would extend from aboEF at theG point to belowEF at theX point ~see Fig. 2!.Particularly this band changes as the lattice is expandedposition in energy atX increases rapidly, whereas minimchanges occur in the bands atK-G-L. Note that although thisband changes substantially, the quasigap itself remstable. An examination of the orbital occupation numbfurther illustrates how the electronic structure changes wthe lattice constant: Only the relative Pu 5f and 6d occupa-tion numbers are continuously altered, their sum remainconstant, which relates to the anion 2-valency staying cstant. The Pu configuration is thus 5f 62x6dx, wherex is the6d occupation number, the value of which decreases wincreasing lattice constant. Near the experimental lattice cstantx is approximately 0.4–0.5. We note, though, that tLSDA approach probably tends to overestimate hybridition.
When the lattice is expanded to a constant of 6.75 Åbands cross the Fermi energy; see Fig. 7. At this point5 f 5/2 bands are filled, the 5f 7/2 bands are empty, and PuTea semiconductor. If there were no SO interaction the copound would remain a metal. The lattice constant of ab6.72 Å at which PuTe becomes a semiconductor correspo
FIG. 6. The state density of PuS with hybridization betweenPu 5f states and 6d states and sulfurp states removed. Thes-p-dfree-electron background is the dotted line.
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The total energy around this lattice constant showsanomaly17 ~see Fig. 4! that would lead to an increased compressibility for lattice constants just less than 6.72 Å. Wnote, with respect to the discussion of which model desction is applicable to PuTe, that the LSDA approach thpredicts the lattice parameter at which the transition to Pu21
is expected. We also note that the occurrence of a real sconductor gap in expanded PuTe is reminiscent of the cductivity behavior of SmS.18 SmS is, at ambient pressure,semiconductor with Sm in the divalent state, which makthe transition to the IV metallic state under pressure. Hoever, in contrast to the theory of localizedf configurations,we emphasize once more that although the 5f 5/2 bands arefilled the energy dispersion of these 5f bands is an order omagnitude greater than for 4f states.
C. Optical properties
A more detailed examination of the quasigap upon phycal properties is facilitated by an examination of the optiproperties. To calculate the optical spectrum we have eployed the linear-response expression for the optical condtivity s(v):
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FIG. 7. Energy bands of PuTe in the vicinity of the Fermi eergy for lattice constants that are 7%, 8%, and 9% expandedrespect to the experimental lattice constant.
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12 830 PRB 61P. M. OPPENEER, T. KRAFT, AND M. S. S. BROOKS
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where f (enk) is the Fermi function,\vnn8(k)[enk2en8k ,the energy difference of the Kohn-Sham energiesenk , andt21 is the lifetime parameter, which is included to descrithe finite lifetime of excited electron states. ThePn8n(k) arethe matrix elements of the relativistic momentum operaDetails of the computation ofs andP can be found in Refs19 and 16.
The calculated absorptive part of the interband opticonductivity is shown in Fig. 8 in the photon energy ran0–0.3 eV as a function of lattice constant close tosemimetal-semiconductor transition. For comparison we aincluded the spectrum calculated for the ambient lattice cstant. For the latter lattice constant two optical gapspresent, one of about 20 meV and a larger one of abouteV. The smaller one slightly increases with increasing lattconstant. The spectral intensity at 0.05 eV decreasesincreasing lattice constant, until at a lattice constant of 6Å, corresponding to the semimetal-semiconductor transitthis intensity and the smaller gap completely disappear, leing only the semiconducing gap of 0.2 eV. The large gcorresponds to the pseudogap between the 5f 5/2- and5 f 7/2-derived bands, whereas the smaller gap of aboutmeV corresponds to the separation of the two bands at thGpoint ~see Fig. 7!. In the calculation ofs we have not takenthe intraband contribution to the optical conductivity inaccount. The small Fermi surface leads to a Drude-typetraband conductivity. Very similar spectra have been callated for PuS and PuSe, and thus we shall not show thseparately.
The reflectivity spectrum of PuTe was recently measuby Mendik et al.3 From the calculated optical conductivitthe theoretical reflectivity can straightforwardly be obtainand compared to experiment. In Fig. 9 the experimental
FIG. 8. Calculated optical conductivitysxx(1) of PuTe for the
experimental lattice constants, and for three lattice constants,8%, and 9% expanded, at about which the semimesemiconductor transition occurs.
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calculated reflectivities are shown. A constant lifetime prameter\t2150.2 eV has been applied in the calculatioThe reflectivity calculated for the ambient lattice constanin overall agreement with experiment, except for a smpeak at 2 eV, which is not observed in the experiment.the LSDA approach tends to too strong a hybridization,expect that the 5f -6d hybridization can be reduced bysmall lattice expansion. The influence of a 3% lattice expsion is also shown in Fig. 9: the agreement with experimbecomes excellent. This result definitely supports the LSdescription of the electronic structure. Very recently it hbecome clear from several computational investigationsoptical and magneto-optical spectra that the appropriatescription of the electronic structure will provide an accuraexplanation of the measured spectra.20–22
D. Semiconducting properties and specific heat
As mentioned before, three effective energy gaps hbeen determined from the temperature-dependresistivity.1,2,4 Our energy-band calculations predict, however, the Pu monochalcogenides at ambient pressure tsemimetallic, due to the existence of tiny Fermi surfacesscrupulous analysis of the available data shows, in our oion, that the Pu monochalcogenides are not truly semicducting materials. The smallest, low-temperature gaphas been identified is of the order of 0.5 meV to 3 meV1,2
Yet, the low-temperature resistivity is not correspondinghigh. We may, for example, compare to the thoroughly stied compound SmB6, which is an IV semiconductor with anestablished energy gap of 4–5 meV~see Ref. 18!. The resis-tivity of SmB6 rises appreciably at low temperatures,about 1V cm, a value that is 1000 times higher than tmeasured low-temperature resistivity of PuTe.1 Furthermore,the occurrence of a Drude-like edge in the near-infraredflectivity spectrum has been considered as an indicationfree carriers.3,13 Also, photoemission spectroscopy reveale5 f -related peak in the vicinity ofEF .6 Due to final-stateeffects the photoemission spectrum need not be in a one
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FIG. 9. Calculated and measured reflectivity of PuTe. The toretical spectra are obtained for the experimental lattice consa56.19 Å, and for a 3% expanded lattice constant. The experimtal data (s) are from Ref. 3.
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PRB 61 12 831ELECTRONIC STRUCTURE OF PLUTONIUM . . .
one correspondence with single-particle state densinonetheless, an energy gap atEF could not be detectedFrom these data we infer that the Pu monochalcogenidessemimetallic, in agreement with the band-structure resThe experimentally observed resistivity behaviorunusual,1,12 but as shown above, there is a gap of aboutmeV in the optical conductivity spectrum. While an opticgap is not straightforwardly related to a thermal gap, itnevertheless reasonable to anticipate that a signature ooptical gap becomes visible in the resistivity.
A very recent investigation of the resistivity behaviorPuTe under pressure revealed an anomalous upturn olow-temperature resistivity.12 Under pressure conduction anvalence bands normally broaden, which should therebycrease any semiconducting gap. Obviously the resistivityPuTe does not follow the standard behavior. The quasigaPuTe arises in a usual manner from the SO interactionthe 5f -6d hybridization, which we expect to be the reasonthe pressure-increased resistivity. To examine this conjecwe have calculated the zero-temperature conductivitys0,which is given by
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as follows from Eq.~1! for v50. The relaxation timet isunknown and may result from various complex manparticle interactions. We adopt here the constant relaxatime approximation, which is sufficient for a qualitative uderstanding. From Eq.~2! we find that the resistivity of PuTeincreases by 53% in going from the 3% expanded latticethe ambient lattice constant. An even further decrease oftice parameter, from the 3% expanded lattice to a 3% ctracted lattice, leads to a resistivity increase of 141%. Tanomalous resistivity increase in PuTe is thereby indeed cfirmed as a peculiarity of the quasigap. Here we have chothe 3% expanded lattice constant in order to mimic bestcalculated electronic structure of PuTe to the experimeelectronic structure, in accordance with the conclusionrived from the reflectivity spectrum.
The specific-heat coefficient measured for PuTe isproximately 30 mJ/mol K2.5 From the DOS at the Fermenergy we obtain theoretical specific-heat coefficientsg'5–6 mJ/mol K2 for all three chalcogenides. Theseg ’s arethus about 5 times smaller than the measuredg. We note,however, that there is the one very flat band close toFermi energy~see Fig. 2!. The flatness of this particular bancauses a peak in the DOS at energies up to 4–5 meV aEF . This high DOS would correspond to ag of 20 to 30mJ/mol K2, depending somewhat on the energy distanceEF . At finite temperatures the effect of the peak would beincrease the theoreticalg over the 0 K value. In combinationwith an anticipated many-body enhancement factor of ab2 for actinides, the measured specific heat could thenaccounted for.
E. Magnetic form factor
The induced magnetic form factor of PuTe has been msured by Landeret al.7 There can be a significant differencin the induced magnetic form factor of a paramagnetic m
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and that of a magnetic metal when the magnetic electronsitinerant and the SO interaction is large.23 When a light ac-tinide is magnetic and the spin density large, the SO intertion induces a large orbital moment antiparallel to the smoment, leading to a magnetic form factor for which torbital effects are visible as a long tail,24 such as in PuSb.7 Inuranium metal, in contrast, the induced form factor fallsrapidly with scattering vector, the explanation being thatinduced spin density is so small that the SO interactionless effect than the applied field, which tends to align orband spin moments parallel. In fact, the effects of the appfield and SO interaction tend to cancel, leading to a smainduced orbital moment parallel to the spin moment, whis difficult, if not impossible, to observe. We have calculatthe induced form factors for PuS and PuTe by applying smmagnetic fields to the results of a paramagnetic calculaand verified that both the induced spin and orbital momewere proportional to the applied field. For small applifields the spin and orbital moments are parallel and thebital moment is a factor of 5 larger than the spin momeThe resulting magnetic form factors, which are shown in F10, decreases monotonically with scattering vector, indicing that there is no cancellation of spin and orbital momein PuS or PuTe. The calculated form factor is in good agrment with the experimental result for PuTe~see Fig. 10!from which the same conclusions were drawn.7 Otherwise,when the spin and orbital magnetic moments are antiparaand of about the same magnitude, the general shape oform factor is different, and it must resemble the form facof UN,24 which is typical for most actinide compounds. Ithe present calculation the induced moment contains a Pcontribution since the DOS at the Fermi energy is not zbut also a significant Van Vleck contribution since highelying states are mixed into the ground state by the appfield.
F. Possible magnetic phase transition
The above-discussed properties of the Pu monochagenides are all based on paramagnetic electronic struccalculations, extended with a small applied magnetic fi
FIG. 10. The calculated induced magnetic form factors of Pand PuTe. The solid line depicts the calculated form factor of Pand the dots that of PuTe. The vertical bars give the experimedata points for PuTe after Ref. 7.
lacoanagth
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12 832 PRB 61P. M. OPPENEER, T. KRAFT, AND M. S. S. BROOKS
only to compute the magnetic form factor. In our calcutions we observe a peculiarity for all three Pu monochalgenides: Quite abruptly, as a function of the lattice consta transition to a ferromagnetic state is found. This ferromnetic state is predicted to have a lower total energy thanparamagnetic state. In Fig. 11 the ferromagnetic and pmagnetic total energies of PuTe as a function of latticerameter are shown. The onset of ferromagnetic order isculated to occur close toa56.15 Å. At the experimentalattice constant of 6.19 Å, a self-consistent calculation tstarted from a ferromagnetic state converges to a zeroment solution. Otherwise, the moments in the ferromagnstate are not small: the spin moment is about 5.0mB , and theorbital moment22.7mB , depending on the lattice parametand the chalcogenide anion. The moments are mainly duthe 5f states, thes-p-d states contribute a small spin moment of about 0.3mB , and an orbital moment of 0.06mB ,both parallel to the respective 5f moments. The sudden onsof ferromagnetic ordering seems anomalous.17 Nothing ofthis kind has yet been observed experimentally. In viewour above-reported results for the paramagnetic state, wcorrespond unmistakenly to the available experimental dwe are inclined to exclude the possibility that the obtainferromagnetic state is an artifact of the LSDA energy-baapproach. We remark, with respect to the computed femagnetic ground state, first, that we did not try to findantiferromagnetic state that could eventually have an elower total energy. Second, it is known that the LSDA aproach has a tendency to prefer the ferromagnetic statethe paramagnetic one. However, since the total energy oferromagnetic state is not nearly degenerate with that ofparamagnetic one, we consider it unlikely that the ferromnetic state would not be the lower-in-energy state. So famagnetic state has not been observed in the Pu monochgenides. As the agreement with experimental data is besthe 3% expanded lattice parameter, we anticipate thaexperimental detection of ferromagnetism needs to be din pressure experiments. A complication inherent to obseing a magnetic phase transition is the structural NaCl-Cphase transition, which occurs in the Pu monochalcogenunder pressure, and is rather sluggish.25,26 One of the ques-tions would therefore be if a possible magnetic phase tration would occur before the end of the structural phase tr
FIG. 11. Total energy versus lattice parameter for PuTe, calated for both paramagnetic and ferromagnetic PuTe in the Ncrystal structure.
--t,-e
a--l-
to-ic
to
fcha,dd-
n-er
hee-aco-orannev-
les
i--
sition. Recently the temperature-dependent resistivityPuTe was measured under pressure, but these initial efdid not detect an additional phase transition.12 A betterchance to detect magnetic order might be in PuS, becausPuS the NaCl-CsCl transition occurs beyond 60 GP27
whereas in PuSe and PuTe it occurs at about 35 GPa, anGPa, respectively.13,25,26On the basis of first-principles calculations we cannot adequately address the question whethe structural phase transition would occur first, becauseour current band-structure method, which uses the spherpotential approximation.14 A full-potential approach wouldbe required to calculated accurately the NaCl-CsCl transipressure.
The origin of the onset of magnetism in the Pu monocalcogenides does not rest in the Stoner criterion. The DOEF is, in the paramagnetic state, not so high that it becomreduced in the ferromagnetic state. The DOS in the fermagnetic state is, on the contrary, similar or somewhigher. Instead, to understand the magnetic phase transiwe note once more that our calculations indicate that a ctinuous shift of the 5f occupancy to the 6d occupancy takesplace under pressure. Thisf -d occupation shift corroboratewith the magnetic transition. It is therefore instructive to bgin with PuTe at an expanded lattice constant, which cosponds to a paramagnetic Pu 5f 66d0 configuration. Underpressure, the Pu configuration shifts to 5f 62x6dx, where the5 f occupation approaches a 5f 5 occupancy at high enougpressure. For Pu in the latter configuration, magnetic ording is energetically more favorable. The initially spindegenerate 5f 5/2 band becomes spin split, and part of thexchange-split bands are shifted through the Fermi eneThe Fermi surface of the ferromagnetic Pu monochalgenides is thus much bigger than the tiny portions presenthe paramagnetic state. Using again Eq.~2!, and adopting forsimplicity the constant relaxation-time approximation, wcan calculated the field-induced magnetoresistivity, from
S Dr
r D5r~B!2r~0!
r~0!, ~3!
with r(B) andr(0) the resistivity in the ferromagnetic anparamagnetic states, respectively. The calculated magnesistivities are enormous:283%, 287%, and287%, forPuS, PuSe, and PuTe, respectively. Such giant values omagnetoresistivity are sometimes observed for certainnium compounds, like, e.g., UNiGa, where287% wasmeasured.28 However, for the uranium compound the metmagnetic transition that is induced by the applied magnfield is from an antiferromagnetic ground state to a ferromnetic state. In the case of the paramagnetic Pu monochagenides the quasigap is destroyed by the field. With respto the huge resistivity changes accompanying the magntransition, we mention that also the resistivity of PuTe in tCsCl phase is much smaller than that of the NaCl ph~Refs. 12 and 29!.
III. DISCUSSION AND CONCLUSIONS
The 5f SO splitting is larger and 5f -5 f and 5f -d hybrid-ization an order of magnitude larger in the actinides thanthe rare earths. We would therefore expect that the basismodel calculations would be better provided by energy-ba
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PRB 61 12 833ELECTRONIC STRUCTURE OF PLUTONIUM . . .
calculations than by atomiclike calculations. The detaicalculations presented here already provide a reasonablplanation of many of the anomalous properties of the plunium monochalcogenides. In particular, the equilibrium ltice constant of PuTe, calculated using the LSDcorresponds quite closely to the measured one, withoutnecessity for any further assumptions. Also the lattice cstant where the transition to Pu21 is expected is nicely reproduced by the LSDA energy-band calculation. The callated induced magnetic form factor of PuTe is also closethat measured, and the computed, unenhanced, specificcoefficients compare reasonably with the measured valuePuTe. The calculated optical reflectivity of PuTe is in goagreement with experiment too, suggesting that at leastcalculated electronic structure of a semimetal with a qugap is essentially correct. The magnitude of the smalquasigap of about 20 meV in the optical conductivity sptrum is similar to that of the energy gap deduced from lotemperature resistivity measurements. Responsible forformation of the quasigap is the large SO interaction tsplits the Pu 5f 5/2 and 5f 7/2 subbands at the Fermi energy,combination with a hybridization gap being formed by tPu 5f and 6d bands. The hybridization gap is especiasensitive to modifications of the 5f -5 f , 5f -6d, and Pu-chalcogenidep hybridizations. As a consequence, the restivity is calculated to increase under moderate presswhich is unusual, but in agreement with recemeasurements.12
Our calculations show that the electronic structure lvery close to an essentially filled set of 5f 5/2-derived bandsthat contain an admixture ofd states. This suggest5 f 62x6dx configuration for Pu. Although such a configurtion corresponds to the intermediate valence suggestedthe Pu monochalcogenides,2,3 there are pertinent differenceto the theory of IV developed for rare earths. In the latter,rare earth 4f bands are dispersionless, which is not the c
r
y
.
dex---,he-
-oeator
uri-st--het
-e,t
s
for
ee
for the 5f -derived bands. In addition, the large SO interation affects the 5f bands to first order. If a localized modewere to be made that started from this calculated band strture, the localized states would be Wannier functions costructed from this filled set of bands. Such a set of localizstates, which may indeed be required to construct the lolying excited states, still differs from the localized stateused for models of intermediate-valent rare-earth copounds, since SO interaction and 5f -6d hybridization havebeen included from the outset in the energy-band calcutions. In this sense, mixed valence in the actinides mustessentially different from mixed valence in the rare earths
Previously, two phase transitions were discussed forPu monochalcogenides: the transition from the Pu21 valentstate to mixed valence,2,3 and the structural NaCl-CsCl transition under pressure.13,25,26 Our total-energy calculationspredict the possibility of a third phase transition under presure, that from a paramagnetic state to a ferromagnetic stAlthough a magnetic phase transition has not yet beenserved, we believe that under pressure, at a reduced laconstant, this should be possible. Also, our energy-bandculations predict the Pu monochalcogenides to be semimtallic, with small Fermi surface portions. A further test othis proposed electronic structure would be de Haas–vanphen measurements of the Fermi surface.
ACKNOWLEDGMENTS
We have benefited from discussions with V. Ichas, G.Lander, J. Schoenes, P. Wachter, L. Havela, T. Gouder,Eschrig, and J. M. Fournier. Part of this work has been pformed while P.M.O. and T.K. were at the Max-PlanckResearch Group ‘‘Theory of Complex and Correlated Eletron Systems.’’ Financial support from the Max-PlancSociety, and from the State of Saxony~under Contract No.4-7541.83-MP2/301! is gratefully acknowledged.
*Present address: Institute of Solid State and Materials ReseaP.O. Box 270016, D-01171 Dresden, Germany.
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