Freeman, A. J.

Koelling, D. D.

UNT Digital Library

ROLE OF ITINERANT Sf STATES ON THE FERMI SURFACEOF Th AND POSSIBLE IMPURITY LOCAL MOMENT FORMATIONbyD. D. K o e l l i n g and A. J . Freeman- NOTICE -This report was prepared us an account of worksponsored by the United States Government. Neitherthe United States nor the United Suites EnergyResearch and Development Administration, nor any oftheir employees, nor any of their contractors,subcontractors, or their employees, makes anywarranty, express or implied, or assumes any legalliability or responsibility far the accuracy, completenessor usefulness of any information, apparatus, product orprocess disclosed, or represents that its use would notinfringe privately owned rights.Presen ted At:20th Annual^Copference on Magnetism and Magnetic Materials,San Francisco, California, December 3-6, 1974DISTRIBUTION OF THIS DOCUMENTUofC-AUA-USAECARGONNE NATIONAL LABORATORY, ARGONNE, ILLINOISROLE OF ITINERANT 5f STATES ON THE FERMI SURFACE OF ThAND POSSIBLE IMPURITY LOCAL MOMENT FORMATION*D. D. KoellingArgonne National Laboratory, Argonne, Illinois 60439andA. J. FreemanPhysics Department, Northwestern University, Evanston, Illinois 60201 andArgonne National Laboratory, Argonne, Illinois 60439ABSTRACTThe nature (itinerant vs. localized) of the 5felectrons in the actinides determines their magneticproperties. Extensive optical and de Haas-van Alphendata which exist only for Th, the simplest actinidewith no occupied 5f states, allow detailed comparisonsto be made between theory and experiment. The 5f bandswere found, by means of ab initio RAPW energy band cal-culations, to lie above the Fermi energy, to be itin-erant in character and to significantly affect thereflectivity measurements of Veal, et al. We find thatthe 5f bands when included in the RAPW calculations,give excellent agreement with the de Haas-van Alphenresults of Boyle and Gold, for all sections of theLungs, Dumbell and Superegg Fermi surfaces, in contrastwith calculations based on artificially removing the 5fresonance. Simple overlap charge density impurityscattering potential model calculations are used todiscuss the possible occurrence of impurity localmoment formation in Th based alloys.INTRODUCTION. Theoretical studies of the actinide metals haveshown that their magnetic and other properties are de-termined by the nature of their 5f elections—itin-erant for the light actinides (Th-Pu) ai>d localizedfor the heavy actinides (Am and beyond). Unfortu-nately, the low temperature phases of the light acti-nides are structurally complex making extremely diffi-cult both the band calculations and interpretations ofexperimental data. Thorium, at the beginning of theseries, with no occupied 5f states, has the fee struc-ture as its low temperature phase and thus appears tobe an ideal candidate for theoretical and experimentalinvestigations. The availability of high purity singlecrystals has permitted accurate de Haas-van Aiphen(dHvA) measurements tc be made.Gupta aud Loucks2 artifically removed the 5fbands from their RAPW calculations, in order to over-coment the difficulties found by Keeton and Loucks3in their full Slater exchange (a = 1) calculations, andobtained reasonable agreement with the dHvA measure-ments. By contrast, Koelling and Freeman1 >"* arguedthat the 5f electrons in the lighter actinides aresufficiently delocalized to significantly overlapneighboring atoms and to hybridize strongly with the6d and 7s bands. As in the case of the lighter acti-nides, the f electrons have small Coulomb correlationenergy (relative to the now large effective band width)and hence must be considered itinerant; i.e., are to beincluded in and described by band calculations unlikethe case of the 4f electrons in the rare earths.Recently normal incidence reflectivity measure-ments on thorium by Veal, et al.,5 showed the existenceof band-like f states 1-5 eV above Ep. Because of theimportance of this result as providing strong confirm-ing evidence for the prediction that the occupied 5fstates in the lighter actinide metals are itinerant,a highly precise determination of the FS of Th appearsnecessary as a severe test of the itinerant model.We have found that the itinerant model (f statesincluded) gives Fermi surface dimensions in excellentagreement with the dHvA measurements unlike the pre-dictions of the localised (f state removed) model. Inaddition, we have used the overlapping charge densityimpurity potential scattering model to calculate forthe dilute impurity in Th problem some informationabout the possible f resonance states on the impuri-ties and to discuss the possibility of impurity localmoment formation.INFLUENCE OF UNOCCUPIED 5f STATES ON THE FERMI SURFACEThe relativistic energy band structure of fee Thconsists of s and d-like states as in any high Z fcctransition metal.1"11 For the itinerant model, thereare in addition f bands located in the range of 1 to5 eV above Ep. In both models the Fermi Surface (FS)consists of three distinct pieces: (1) a hole surfaceat the center of the Brillouin zone (BZ) shaped like arounded cube called "superegg"; (2) electron surfaceson symmetry lines rK<110> shaped like pairs of "lungs";and (3) the hole surfaces on the symmetry linesFL<111> shaped like "dumbbells" with triangular ends.In comparing their model with experiment,6 Gupta andLoucks concluded that their model was "only inqualitative agreement with the experimental results".In many ways, the agreement obtained is rather remark-able but may be understood in terms of the potentialinsensitivity of the underlying transition-elementband structure found by us from comparisons of theFermi surfaces resulting from four different calcula-tions: (1) the Gupta-Loucks (GL) calculation(d s, a = 1, f states removed); (2) the calculationfor the d 2s 2, a = 2/3 potential with the f statesremoved; (3) the calculation for the d2s2, a = 2/3potential with the f states included; ard (4) the cal-culation for the d3s1, a = 2/3 potential with f statesincluded.The FS showed a very clear separation between thecalculations with the f states included and those withthe f states excluded. The two FS resulting from thecalculations (3) and (4) with the f states includedand with the configuration varied were close to iden-tical. (This tends to give one confidence that theseresults will not differ greatly from a fully self-consistent calculation.) The two FS for the f statesremoved calculations give some index of the small butobservable sensitivity to exchange approximation ofthe underlying transition—element band structure.Further, we find that the effect of changing a is tomove the f states relative to the remaining bands.Thus the parameter a mainly affects these other bandsand their Fermi surface via the f states and theirhybridization with these bands.Having (briefly) described the effects of self-consistency (through configuration) and exchangeapproximation, we examine the effect on the FS ofincluding or omitting the f states. This effect wasfound to be larger than that due to change of con-figuration or exchange. The effect on the hole sur-faces was to move volume froti the superegg to thedumbbell. The superegg shows somewhat more structurein addition to being smaller. The dumbbell increasedin size primarily on the ball portion, the rod sectiontoward L remaining relatively unchanged. The electronsurface (the lungs) is not centered on a high-symmetrypoint but on a line and thus can change its position.The inclusion of the f states moves this surfaceslightly in the direction of T. The tube which con-nects the two lobes across the £ line is reduced insize. The lobes themselves are taller and narrower.Qualitatively, these changes are all in the correctdirection to improve the agreement between theory andexperiment.However, in order to obtain a more quantitativecomparison, one must actually perform the area inte-grals. The results of these calculations give dHvAareas in excellent agreement with the experiment forall the experimental orbits observed by Boyle andGeld6 (provided their orbits c and d are interchanged).The effect of including the f-states was to reduce thelargest discrepancies on the hole surfaces from over100% to less than 15%. In addition, comparing thecalculated values of m* with the few experimentalnumbers give reasonable enhancement factors (0.4 to0.7)—again provided orbits c and d are interchanged.This excellent agreement with experiment adds strongconfirmation to the itinerant nature of 5f states inthe lighter actinides.POSSIBLE LOCAL MOMENTS OF DILUTE IMPURITIES IN ThA number of striking effects are observed if di-lute impurities are alloyed with Th metal.7"10 As anideal BCS superconductor with a transition temperatureof 1.36°K, Th has been used as a host for a number ofalloy experiments which focus on the magnetic (pair-breaking) properties of the impurities since theirdramatic effect on superconducting properties gives asensitive test for magnetic moment formation. Thusthe experimental results have been compared withKaiser's11 theory for the effect of nonmagnetic reso-nant impurity states on the superconductivity of theiOt metal and/or with the Abrikosov-Gorkov (AG) theoryfor the pairing breaking effect of a localized mag-netic moment. It is found that: Ce behaves as a non-magnetic impurity and fits the Kaiser theory; Gd, as amagnetic impurity fits the AG theory; and U is anintermediate case which is associated with localizedspin fluctuations.In order to understand the results of these ex-periments, we have examined the overlapping chargedensity model for a single impurity in a Th host.Within this model (which is not necessarily self-con-sistent) , we can then hope to see the nature of anyfT-resonances which might form, and relate them to thepossibility of local moment formation. Thus we super-pose (overlap) the impurity charge density ?.nd thehost atom charge densities, construct a muffin tin (MT)potential and solve the radial Dirac equa'.ion to de-termine the (logarithmic derivatives and the) scat-tered-wave phase shifts. To define the quantities ofinterest we note that this procedure applied to a puremetal (and excluding hybridization) would yieldeJ. and £J (relative to E~) for which the maximumof the wave function and its zero (which would be atinfinity for the free atom) occur at the MT radius.These would be upper and lower bounds for the stateswith a given j-character and so give some idea of theenergy range over which f resonances will have arappreciable effect. The other two parameter eJ and FJare obtained from the expansion in energyE3 - ecot 6 = r + ... (1)3 rJof the cotangent of the phase shift near the energy forwhich it is zero. This expansion has been used ex-tensively in deriving combined basis representationsfrom the Green's function formalism;12 e^ is theresonant energy (center of the band for a collectionof such potentials) and TJ is the Born transitionprobability. [To establish the scale of I1,'we notethat T = 0.044 Ry for the d-states in bcc Fe.] Clearlyit will be the difference of the impurity values fromthe Th values which are significant since if the im-purity scattered like Th it would have no effect onthe electron states.Our results for Ce, Gd and U are given in Table I,for j = 5/2 and 7/2 of each impurity. The results forGd show quite clearly that since the transition prob-ability r is small and the resonance lies well belowthe E F one will obtain a local moment on the impuritysite. (Because of the large Coulomb correlationenergy, U e f f, an occupied f8 configuration would movefar above the Fermi energy; thus these one-electronenergies must be used with care when the states arebeginning to localize.) The results show quite clearlythat Ce will not support any f states but that one willget considerable scattering. Since the "clear-cut"cases of Gd and Ce are seen to fit well into our model,we now consider the case of U.It is interesting to note that U (f :'d2s1) yieldsnearly the same scattering parameters as Th. Thus, ifU were to remain in this configuration, it would havevery little effect on the Th host. However, as thiswould require the occupied f-states to remain in theirenergy states well above the Fermi energy, this cannotbe the ground state of the system. If, instead, welook at D (f2d3s1), the f levels are lowered by 0.16 Ry(which gives an estimate of the Coulomb correlationenergy) and can be occupied. Here we notice that thewidths A = (eJ - EJ. ) and/or transition probabili-max minties T3 are reduced to 40% of their U (f3d2s1) valuesbecause the atomic f states have contractetl by roughly10%. Hence, for the case of U impurities, the f statesare located at Ep as required by the specific heatdata10 and self-consistency requirements, aS:e muchmore localized than with the trivalent conf.Lguration,and strongly correlated (Ueff = A). |Table I. f-state parameters (in Ry) for impurities "'in ThImpurityTh(dV)Gd(f7d2s>)Ce(f'dV)Ce(dV)U(f3dV)U(f2dV)£5/2 £5/2 e5/2 r5/2min max r0.06 0.30 0.19 0.031-0.13 -0.09 -0.10 0.0010.11 0.20 0.15 0.0090.10 0.20 0.15 0.0110.10 0.30 0.20 0.025-0.06 0.09 0.02 0.010Jft J/2 \JI2 r7/2tun nax :•"0.09 0.37 .0,24 0.038-0.07 -0.04 -U.06 0.0020.12 0.22 0 ]8 0.0120.12 0.22 0.3..' 0.0120.15 0.36 O.*6 0.032-O.OJ 0.16 o.o;; 0.015IREFERENCESSupported by the AEC, the NSF and the AFOSR.1. See the review article by A, J. Freeman andD. D. Koelling, in the Actinides; ElectronicStructure and Properties, A. J. Freeman andJ. B. Darby, Jr., Eds. (Academic Press, N.Y. , 1974),Vol. I, p. 51.2. R. P. Gupta and T. L. Loucks, Phys. Rev. Letters2£, 458 (1969).3. S. C. Keeton and T. L. Loucks, Phys. Rev. 146, 429(1966).4. D. D. Koe.lling and A. J. Freeman, Solid State CommunCommun. £, 1369 (1971).5. B. W. Veal, D. D. Koelling, and A. J. Freeman,Phys. Rev. Letters 30, 1061 (1973).6. D. J. Boyle and A. V. Gold, Phys. Rev. Letters22, 461 "(1969).7. W. R. Decker and D. K. Finnemore, Phys. Rev. 172,430 (1968).8. J. G. Huber and M. B. Maple, J. Low Temp. Phys.2, 537 (1970).9. M. B. Maple, J. G. Huber, B. R. Coles, and A. C.Lawson, J. Low Temp. Phys. _3> 1 3 7 (1970); H. L.Watson, D. T. Peterson, and D. K. Finnemore, LowTemperature Physii-.s-LT 13, K. D. Timtnerhaus, W. J.0'Sullivan, and E. F. Hammel, Eds. (Plenum Press,N.Y., 1974), Vol. II, p. 590.10. C. A. Luengo, J. M. Cotignola, J. Sereni, A. R.Sweedler, and M. B. Maple, Low TemperaturePhysics-LT 13, K. D. Timmerhause, VI. J. 0'Sullivan,and E. F. Hammel, Eds. (Academic Press, N.Y.,1974), Vol. II, p. 585.11. A. B. Kaiser, J. Phys. C 3> 409 (1970).12. D. G. Pettifor, J. Phys. C 2. 367 (1970).

Role of itinerant 5f states on the Fermi surface of Th and possible impurity local moment formation

https://digital.library.unt.edu/ark:/67531/metadc1023742/m2/1/high_res_d/4215104.pdf

Role of itinerant 5f states on the Fermi surface of Th and possible impurity local moment formation

Abstract

Similar works

Full text

Available Versions

UNT Digital Library