Collins, Eric M.

Cooper, Bernard R.

Kioussis, Nicholas

Lim, Say Peng

English

The Research Repository @ WVU (West Virginia University)

Faculty Scholarship2000Competition of exchange and crystal fieldinteractions in cerium monopnictides andmonochalcogenidesEric M. CollinsNicholas KioussisSay Peng LimBernard R. CooperFollow this and additional works at: https://researchrepository.wvu.edu/faculty_publicationsThis Article is brought to you for free and open access by The Research Repository @ WVU. It has been accepted for inclusion in Faculty Scholarshipby an authorized administrator of The Research Repository @ WVU. For more information, please contact ian.harmon@mail.wvu.edu.Digital Commons CitationCollins, Eric M.; Kioussis, Nicholas; Lim, Say Peng; and Cooper, Bernard R., "Competition of exchange and crystal field interactionsin cerium monopnictides and monochalcogenides" (2000). Faculty Scholarship. 94.https://researchrepository.wvu.edu/faculty_publications/94Competition of exchange and crystal field interactions in cerium monopnictides andmonochalcogenidesEric M. Collins, Nicholas Kioussis, Say Peng Lim, and Bernard R. Cooper  Citation: Journal of Applied Physics 87, 5143 (2000); doi: 10.1063/1.373276 View online: http://dx.doi.org/10.1063/1.373276 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/87/9?ver=pdfcov Published by the AIP Publishing  Articles you may be interested in Heavy fermion Ce3Co4Sn13 compound under pressure J. Appl. Phys. 117, 17E307 (2015); 10.1063/1.4913304  First-principles study of electronic structure and magnetic properties of Cu-doped CeO2 J. Appl. Phys. 112, 083702 (2012); 10.1063/1.4759359  Magnetic-field-induced effects in the electronic structure of itinerant d - and f -metal systems Low Temp. Phys. 35, 638 (2009); 10.1063/1.3224723  Crystal field effects in Ce Os 4 Sb 12 as determined by inelastic neutron scattering Appl. Phys. Lett. 89, 082508 (2006); 10.1063/1.2264336  Enlarged paramagnetism by electron–electron exchange interactions in n-type modulation doped Cd 1−x Mn xTe/Cd 1−x−y Mn x Mg y Te single quantum wells J. Appl. Phys. 85, 5947 (1999); 10.1063/1.370000    Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Download to IP:  130.166.29.139 On: Wed, 15 Jun2016 18:27:39Competition of exchange and crystal field interactions in ceriummonopnictides and monochalcogenidesEric M. Collins, Nicholas Kioussis,a) and Say Peng LimDepartment of Physics and Astronomy, California State University Northridge, Northridge,California 91330-8268Bernard R. CooperDepartment of Physics, West Virginia University, Morgantown, West Virginia 26506We have applied twoab initio based methods to study the dramatic change of magnetic propertiesacross a series of strongly correlated electron systems consisting of cerium monopnictides andmonochalcogenides. While, the fullyab initio method gives good results for the magnetic momentsin the lighter chalcogenides, it entirely fails to give, even qualitatively, the trend of their unusualmagnetic behavior. On the other hand, the second approach, which explicitly takes into account theinterplay between the hybridization, the Coulomb exchange, and the crystal-field interactions, givesresults in excellent agreement with experiment for all compounds in the series, including themoment collapsefrom CeSb to CeTe and the trend of moments and ordering temperatures across theseries. ©2000 American Institute of Physics.@S0021-8979~00!65008-9#The isostructural~rock-salt structure! series of the ce-rium monopnictides CeX (X5P, As, Sb, Bi) and monochal-cogenides (X5S, Se, Te) have become prototype model sys-tems for study, because of their unusual magnetic properties.This series of strongly correlated electron systems offers theopportunity to vary systematically, through chemical pres-sure, the lattice constant and the cerium separation on goingdown the pnictogen or chalcogen column, and hence tailorthe degree of 4f localization from the strongly localizedlimit in the heavier systems to to the weakly localized limitin the lighter systems.1–7 The sensitivity of the hybridization,Coulomb exchange, and crystal-field~CF! interactions to thechemical environment gives rise to a variety of unusual mag-netic properties.This class of systems exhibits strong magnetic anisot-ropy which changes from thê001& direction in the pnictidesto the^111& direction in the chalcogenides. The low tempera-ture magnetic moment increases with increasing lattice con-stant for the pnictides from 0.80mB in CeP to 2.1mB inCeBi,1–2 and decreases with increasing lattice constant forthe chalcogenides from 0.57mB in CeS to 0.3mB in CeTe.3–5The magnetic moment collapsefrom CeSb to CeTe, withboth systems having about the same lattice constant, is in-dicative of the sensitivity of the exchange interactions to thechemical environment. The ordering temperature increasesfrom 8 K in CeP to 26 K inCeBi for the pnictides, whereasit decreases from 8.4 K in CeS to an unusually low 2.2 K inCeTe.1–5An unusual feature of the cerium series is thelarge sup-pressionof the CF splitting of the Ce31 free-ion 4f 5/2 mul-tiplet from values expected from the behavior of the heavierisostructural rare-earth monopnictides.8 In both the ceriummonopnictides and monochalcogenides, the CF splitting be-tween theG7 doublet and theG8 quartet decreases with in-creasing anion size, from 150 K for CeP to 8 K in CeBi andfrom 140 K for CeS to 32 K for CeTe, and it is about thesame in both series, a rather surprising result in view of theadditional valence electron on the chalcogen ion.9 Neutronscattering experiments have shown10 that theG7 doublet isthe CF ground state in all the cerium monopnictides andmonochalcogenides.The purpose of this work is to understand the underlyingmechanisms responsible for the unusual magnetism in thisclass of systems and to investigate the interplay of exchangeand crystal field interactions. We have employed twoab ini-tio based approaches to calculate the magnetic properties ofthese compounds. First, we have carried outab initio spinpolarized electronic structure calculations based on the fullpotential linear muffin tin orbital~FPLMTO! method11 using~1! only the spin polarization, with the orbital polarizationincluded only through spin-orbit coupling, and~2! both thespin and orbital polarization correction.12 Second, we applyan ab initio based approach synthesizing~1! a phenomeno-logical theory oforbitally driven magnetism based on theAnderson and Kondo lattice model which incorporates ex-plicitly the hybridization induced, the Coulomb exchange,and the crystal field interactions on an equal footing, and~2!FPLMTO electronic structure calculations allowing a firstprinciples evaluation of all the parameters entering the modelHamiltonian, except for the crystal field interaction. To date,our attempts13 to determine the CF splitting for this class ofsystems on a fullyab initio basis have not proven successful,and thus we use the experimental10 CF value for each com-pound. In contrast to the first method, in the FPLMTO evalu-ation of the parameters entering the model Hamiltonian, the4 f states are treated aslocalized, atomic-like, states and areplaced in the core not being allowed to hybridize with thenon-f states, in order to be consistent with the treatment ofthe f states in the Anderson–Kondo Hamiltonian.14–16 Itshould be emphasized that in the second method the bandenergies, thef-state energies, the on-site Coulomb repulsiona!Author to whom correspondence should be addressed; electronic mail:nkioussi@newton.csun.eduJOURNAL OF APPLIED PHYSICS VOLUME 87, NUMBER 9 1 MAY 200051430021-8979/2000/87(9)/5143/3/$17.00 © 2000 American Institute of Physics Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Download to IP:  130.166.29.139 On: Wed, 15 Jun2016 18:27:39U, the hybridization matrix elements,Vkm , and the band-fCoulomb exchange Jmm8(k,k8)5^fk* (r 1)cm* (r 2)u1/r 12ucm8(r 1)fk8(r 2)& are evaluated from nonspin polarizedFPLMTO calculations. Comparison of the two methods teststhe limitations of theseab initio based calculations as thedegree of 4f localization is varied across the series, and re-veals the failure of standardab initio electronic structurecalculations based on density functional theory within thelocal density approximation to predict, even qualitatively, thetrend of magnetic properties in these strongly correlated elec-tron systems. In the past, we have applied the second methodto investigate the effect of hybridization-induced exchangeinteractions14,15 and the effect of both the hybridization andCoulomb exchange interactions16 on the magnetic propertiesof the heavier cerium pnictides and chalcogenides~CeBi,CeSb, and CeTe!. However, these calculations did not takeinto account the crystal field interaction and employed awarped muffin-tin LMTO calculation for the parameters en-tering the model. The very good agreement found16 withexperiment for the low-temperature magnetic moment andordering temperature is due to the fact that the CF interactionin the heavier systems is smaller~about 8 K! than the ex-change interactions. We have generalized ourab initio basedmethod to include the exchange~both hybridization andCoulomb exchange! and crystal field interactions on an equalfooting and to employ a full potential LMTO evaluation ofthe exchange parameters. While the effect of the full poten-tial on both the hybridization and Coulomb exchange inter-actions is small, the inclusion of the CF interaction will beshown to play a role as important as the exchange interac-tions for understanding and predicting the unusual magneticproperties, as one tunes the degree of 4f localization acrossthis series of strongly correlated electron systems. Becausethe size of both the hybridization and Coulomb exchangematrix elements are much smaller~about 2 meV! than theintra-atomic cerium Coulomb interactionU ~6 eV!, one canapply the perturbation theory and evaluate the anisotropictwo-ion exchange 636 matrices.14–16The exchange interac-tions have three contributions: the pure Coulomb exchangeinteraction term proportional to Jmm82 (k,k8), thehybridization-mediated exchange interaction term propor-tional to Vkm4 , and the cross term proportional toVkm2 Jmm8(k,k8).We next discuss the necessity of including the CF inter-action term in the phenomenological Hamiltonian, so we caninvestigate the interplay of exchange and CF interactions onan equal footing as wechemically tunethe various pertinentinteractions across the series. In the second approach, the 4fstates are treated as core states, and as such, they interactonly with the spherical component of the effective one-electron potential. Thus, the interaction of theatomic-like4 fstate with thenonsphericalcomponents of the potential, giv-ing rise to the CF splitting, is not explicitly included. Thus,the CF interaction is included in the phenomenologicaltheory through the inclusion of the CF interaction,HCF5B4(O4015O44) where theO40 and O44 are Stevens equiva-lence operators.17 ~A positive B4 value gives theG7 groundstate, experimentally observed.! In the absence of anab ini-tio value of the CF interaction in this class of strongly cor-related electron systems,13 the CF splitting,DCF5360B4 , isset to the experimental values, listed in Table III.10 With thetwo-ion interactions having been determined, the low-temperature magnetic moment and the ordering temperaturecan be determined by means of a mean field calculation.In Table I we present the calculated values of the zero-temperature cerium magnetic moment from the FPLMTOelectronic structure calculations. Listed in the table are val-ues both with and without the orbital polarization correctiontaken into account. Note, the importance of including theorbital polarization in these 4f correlated electron systems.In all cases, the orbital polarization is found to be opposite tothe spin polarization, as expected. Comparison of the totalenergies gives that the magnetic anisotropy changes from the^001& direction in the pnictides to thê111& in the chalco-genides, in agreement with experiment. On the other hand,except perhaps for the lighter chalcogenides~CeS and CeSe!,comparison of theab initio and experimental values for themagnetic moment indicates thefailure of the local densityapproximation~LDA ! calculations to treat properly the cor-relation effects of the 4f states~treated as band states! in thisseries of strongly correlated electron systems. Furthermore,the pureab initio calculations fail to predict the largemo-ment collapsefrom CeSb to CeTe, the latter being describedas an incipient heavy Fermion system.In Table II, listed are values of them5m851/2 matrixelements~characteristic matrix elements of the 63 ex-change interaction matrix! for the first three nearest-neighborshells for the light~CeP and CeS! and the heavier com-pounds~CeSb and CeTe!. Listed separately in this table arethe three contributions to the exchange interaction from hy-bridization (V4), Coulomb exchange (J2), and the crossterm. It is important to note that while the Coulomb ex-change interactions dominate the magnetic behavior for theheavier, more localized, 4f systems, the opposite is true forthe lighter, more delocalized, systems where the hybridiza-tion exchange interactions dominate the magnetic behavior.This change of behavior of the exchange interactions is aresult of the sensitivity of the hybridization and Coulombexchange on the degree of 4localization. Equally impor-tant, is that while all nearest-neighbor exchange interactionsare ferromagnetic for CeSb, there is an interplay betweenferromagnetic and antiferromagnetic interactions for CeTe,TABLE I. Values of the calculated and experimental~Refs. 1–4! magneticmoments for the cerium chalcogenides and pnictides in units ofmB . Listedare the LMTO values for the spin momentmS , the orbital momentmL , andtotal momentm, for the spin polarized only calculation and for the calcula-tion with spin polarization and orbital polarization correction.FP1SP FP1SP1OP EXPTmS mL m mS mL m mCeS 21.00 0.91 20.09 21.24 1.99 0.75 0.57CeSe 21.08 1.02 20.06 21.26 2.07 0.81 0.57CeTe 21.15 1.28 0.07 21.31 2.29 0.98 0.30CeP 20.80 0.55 20.25 20.85 1.27 0.43 0.80CeAs 20.84 0.64 20.20 20.85 1.42 0.57 0.80CeSb 20.86 0.74 20.12 20.91 1.61 0.70 2.06CeBi 20.86 0.74 20.12 20.95 1.69 0.74 2.105144 J. Appl. Phys., Vol. 87, No. 9, 1 May 2000 Collins et al. Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Download to IP:  130.166.29.139 On: Wed, 15 Jun2016 18:27:39mediated from the scattering of conduction electrons, givingrise to the saturated moment for CeSb and themagneticmomentcollapse from CeSb to CeTe~see Table III!.Listed in Table III are the calculated zero-temperaturemoment and ordering temperature,TN , from the secondabinitio based method, with and without the CF interaction. Itis clear that for the heavier systems~CeBi, CeSb, CeTe! theeffect of the CF interaction on the magnetic moments issmall and slightly more pronounced on the ordering tempera-tures. This is due to the fact that for the more localizedsystems the CF interaction is smaller than the exchange in-teractions. This is the reason that previous calculations, ne-glecting the CF interaction, gave results in very good agree-ment with experiment. On the other hand, for the lightermore delocalized systems the CF interactions are muchlarger than the exchange interactions and hence dominate themagnetic behavior. The overall decrease of the magnetic mo-ments in the presence of the CF interaction in all systemsarises from the mixing of the off-diagonal angular momen-tum statesu65/2& andu73/2& states from the CF interactionwith G7 ground state. Overall, we find an excellent agree-ment with experiment for both the zero-temperature momentand the ordered temperature~a more stringent test for thetheory! using the secondab initio based approach with allthree pertinent interactions~hybridization, Coulomb ex-change, and CF interactions! treated on an equal footing.The research at California State University Northridge~CSUN! was supported by NSF under Grant No. DMR-9531005, by the U.S. Army Grant No. DAAH04-95, and theCSUN Office of Research and Sponsored Projects, and atWest Virginia University by the NSF under Grant No. DMR-9120333.1J. Rossat-Mignod, P. Burlet, S. Quezel, J. M. Effantin, D. Delacoˆte, H.Bartholin, O. Vogt, and D. Ravot, J. Magn. Magn. Mater.31–34, 398~1983!.2B. R. Cooper, R. Siemann, D. Yang, P. Thayamballi, and A. Banerjea, inThe Handbook of the Physics and Chemistry of the Actinidese ited by A.J. Freeman and G. H. Lander~North-Holland, Amsterdam, 1985!, Vol. 2,Chap. 6, pp. 435–500.3A. Dönni, A. Furrer, P. Fischer, and F. Hulliger, Physica B186–188, 541~1993!.4F. Hulliger, B. Natterer, and H. R. Ott, J. Magn. Magn. Mater.8, 87~1978!.5H. R. Ott, J. K. Kjems, and F. Hulliger, Phys. Rev. Lett.42, 1378~1979!.6J. Rossat-Mignod, J. M. Effantin, P. Burlet, T. Chattopadhyay, L. P. Reg-nault, H. Bartholin, C. Vettier, O. Vogt, D. Ravot, and J. C. Achart, J.Magn. Magn. Mater.52, 111 ~1985!.7N. Môri, Y. Okayama, H. Takahashi, Y. Haga, and T. Suzuki, Physica B186–188, 444 ~1993!.8R. J. Birgeneau, E. Bucher, J. P. Maita, L. Passell, and K. C. Turberfield,Phys. Rev. B8, 5345~1973!.9H. R. Ott, J. K. Kjems, and F. Hulliger, Phys. Rev. Lett.42, 1378~1979!;F. Hulliger and H. R. Ott, J. Phys. C~Paris! 40, C5 ~1979!.10J. Rossat-Mignod, J. M. Effantin, P. Burlet, T. Chattopadhyay, L. P. Reg-nault, H. Bartholin, C. Vettier, O. Vogt, D. Ravot, and J. C. Achart, J.Magn. Magn. Mater.52, 111 ~1985!.11D. L. Price and B. R. Cooper, Phys. Rev. B39, 4945~1989!.12O. Eriksson, M. S. S. Brooks, and B. Johansson, Phys. Rev. B41, 7311~1990!.13N. Kioussis~private communication!.14J. M. Wills and B. R. Cooper, Phys. Rev. B36, 3809~1987!.15N. Kioussis, B. R. Cooper, and J. M. Wills, Phys. Rev. B44, 10003~1991!.16Q. G. Sheng and B. R. Cooper, J. Appl. Phys.69, 5472~1991!; Phys. Rev.B 50, 965 ~1994!.17K. R. Lea, M. J. M. Leask, and W. P. Wolf, J. Phys. Chem. Solids23,1381 ~1962!.TABLE II. Listed below are characteristic matrix elements of the 636two-ion interaction matrix@Emama8mbmb8(Rb2Ra)# of the f electrons for a crosssection of the cerium compounds. Values of the hybridization induced(EV4), cross terms (EV2J), and pure Coulomb exchange (EJ2) interactionsare listed for the first, second, and third nearest cerium neighbors in units ofK. the listed elements are them5m8561/2.CeP CeSEV4 EV2J EJ2 EV4 EV2J EJ2R5~1212 0! 2.23 0.64 1.53 0.85 20.40 1.50R5~1 0 0! 6.39 0.27 1.65 21.60 0.04 20.80R5~11212 ! 20.08 20.02 0.16 0.38 20.16 0.13CeSb CeTeEV4 EV2J EJ2 EV4 EV2J EJ2R5~1212 0! 0.70 0.34 7.30 0.17 20.19 2.90R5~1 0 0! 2.07 0.07 10.21 20.19 0.04 21.69R5~11212 ! 20.02 20.03 0.04 0.04 20.06 20.01TABLE III. Calculated ~from the model Hamiltonian! values of the zero-temperature ordered moments (mo) and ordering temperatures, Ne´el tem-perature (TN) both without~no CF! and with the crystal field splittig term~CF!, and the correspomding experimental values for the cerium com-pounds. The experimentsl values of the crystal field splitting (DCF) are alsolisted. All moments are given in units ofmB , the temperatures and thecrystal field splitting are given in units of Kelvin.mo TNDCF No CF CF exp No CF CF expCeS 140 1.80 0.73 0.57 1.0 11.0 8.4CeSe 116 1.10 0.79 0.57 2.5 14.0 5.7CeTe 32 0.60 0.46 0.30 8.0 5.0 2.2CeP 150 2.10 0.73 0.81 14 11 8CeAs 137 2.10 0.74 0.85 16 13 8CeSb 37 2.10 1.80 2.06 20 18 17CeBi 8 2.10 2.10 2.10 40 40 265145J. Appl. Phys., Vol. 87, No. 9, 1 May 2000 Collins et al. Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Download to IP:  130.166.29.139 On: Wed, 15 Jun2016 18:27:39

Competition of exchange and crystal field interactions in cerium monopnictides and monochalcogenides

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Competition of exchange and crystal field interactions in cerium monopnictides and monochalcogenides

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