Theory of the electronic and magnetic structure of cerium pnictides under pressure

Solid State Communications,

Vol. 102, No. 6, pp. 473-477, 1997 @ 1997 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0038-1098197 $17.00 + .OO

Pergamon

PII: SOO38-1098(97)00002-l

THEORY OF THE ELECTRONIC

AND MAGNETIC STRUCTURE UNDER PRESSURE

OF CERIUM PNICTIDES

A. Svane,a Z. Szotek, b W. M. Temmerman b and H. WinterC a Institute of Physics and Astronomy, University of Aarhus, DK-8000 Aarhus C, Denmark b Daresbury Laboratory, Warrington WA4 4AD, United Kingdom c Forschungszentrum Karlsruhe, INFP, Postfach 3640, Karlsruhe, Germany (Received 12 December

1996; accepted 20 December 1996 by PH. Dederichs)

The electronic structures of the cerium pnictides CeN, CeP, CeAs, CeSb and CeBi are calculated within the self-interaction corrected local-spin density approximation. This method allows a description of the Ce f-electrons as either localized or delocalized. We find that the isostructural phase transition in CeP is associated with the delocalization of the f-electron under pressure. Similar structural phase transitions in CeAs, CeSb and CeBi are also well described by this theory. Moreover, in agreement with recent experiments we obtain a very low carrier type-1 antiferromagnetic groundstate for CeP and CeSb. 01997 Elsevier Science Ltd Keywords: D. electronic states (localized), D. phase transitions, A. magnetically ordered materials.

The Cerium Pnictides CeN, CeP, CeAs, CeSb and CeBi have peculiar properties as a function of applied hydrostatic pressure. At ambient conditions they all crystallize in the rocksalt (Bl) crystal structure. With the exception of CeN the lattice constants indicate a trivalent nature of the Ce ions. [l] CeN is closer to a tetravalent Ce configuration, but photoemission experiments reveal significant mixed-valence characteristics. [24] Thus, CeN is similar to the collapsed (x phase of pure cerium, where the cerium f-electron contributes actively to the cohesive properties, while the other Ce pnictides at ambient conditions are more similar to the y phase of cerium, characterized by ‘localized’, i.e. atomic-like, f-electrons. When pressure is applied discontinuous structural phase transitions occur, [1,5-lo] again with the exception of CeN, where to the best of our knowledge no pressure experiment has been reported. In CeP an isostructural transition is observed at a temperature of 300 K and at a pressure of Pi 90 kbar accompanied by a volume collapse of AVi 3% [5,11]. At low temperature this transition pressure has been determined to be 55 kbar [6]. This transition is similar to the isostructural o( - y phase transition in cerium metal, and is usually attributed to a change

from trivalent to tetravalent behavior of the cerium ions. At a higher pressure of Pz - 150 f 40 kbar, [l l] a second transition to the CsCl (B2) structure is observed, with a volume collapse of AV2 - 11%. [5] In CeAs, only a single Bl -B2 phase transition occurs at a pressure of P - 140+20 kbar with a volume collapse ofAV - 11%. [7] While some authors have claimed that no substantial change in Ce valency occurs at this transition [7], others conclude a significant change. [S] In CeSb and CeBi a high pressure tetragonal phase is observed, at P = 80 f 20 and P = 90 + 40, respectively, with volume collapses of AV - 10% [9] in CeSb and AV - 8% [lo] in CeBi. The tetragonal phase may be viewed as a uniaxial compression of the CsCl structure with a c/a ratio of 0.82 in CeSb [9] and 0.84 in CeBi. [lo] In both cases the Ce ions are considered to remain trivalent across the phase transition. The magnetic properties of the cerium pnictides are quite complicated with several antiferromagnetically ordered phases and phase transitions as a function of pressure, temperature and applied magnetic field. [6,12,13] For CeP and CeAs the ground state configuration in zero field and at zero pressure and temperature is the AFI structure, which consists of an antifer-

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romagnetic stacking of ( 100) planes, within which the Ce spins are ferromagnetically coupled. In CeSb and CeBi the stacking of ferromagnetically ordered (100) planes follows the sequence (+ + --) (AFIA). The NCel temperatures are quite low, S-30 K, [14] and at high temperatures their susceptibilities show characteristic Curie-Weiss behavior indicative of local moments. Only CeN behaves more as a Pauli enhanced paramagnet. The resistivity of CeN is metallic. In these two respects, CeN is again similar to o+Ce. The resistivity of the other cerium pnictides is semimetallic with extremely low carrier density, of the order of O.l3%. [14] Here we undertake a systematic theoretical study of Ce pnictides concentrating on the structural phase transitions and magnetic structures. We use the selfinteraction corrected (SIC) local-spin-density (LSD) approximation, [15] which provides an ab-initio electronic structure scheme, which is capable of describing localization phenomena in solids. [16-201 In this scheme the spurious self-interaction of each occupied electron orbital is subtracted from the conventional LSD approximation to the total energy functional, which leads to a greatly improved description of static Coulomb correlation effects over the LSD approximation. Two different, [ 18,211 yet equivalent, implementations of the SIC-LSD approach, based on the linear muffin-tin-orbital (LMTO) method [22,23] in the atomic sphere approximation (ASA) have been used. In addition, a full-potential version of the LMTO method [24] has also been applied for some of our calculations in the local-density approximation (LDA). In the SIC-LSD approximation [15] one subtracts from the LSD total energy functional the selfCoulomb energy and self-exchange-correlation energy for each occupied electron state:

U[n] + E,L,SD[fi]+ Vrxt[n] - 2 6,.

(1)

a

Here, Es” is given in terms of a set of occupied orthonormal single electron wavefunctions +a. ii is the total spin density of the system: E(r) = (n’(r), n’ (r)), n(r) = n’(r) + n’(r). U[rz], E~?[ii] and VC,..[n] are the Hartree energy, the exchange-correlation energy, and the interaction energy with the ion lattice, respectively, and 5, = UIn, 3 -t E,“Ifi,]

(2)

represents the total self-interaction correction for the orbital qa with spin density ii,. If the last term in

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the total energy functional in Eq. (1) were omitted we would have the LSD energy functional ELsD. For periodic solids the SIC-LSD approximation is a genuine extension of the LSD approximation since the selfinteraction correction is only finite for localized states, which means that for Bloch-like single-particle states EsIc coincides with ELSD. Therefore, the LSD minimum is also a local minimum of EsIc. In some cases another set of single-particle states can be found, not all being in Bloch form, to provide a local minimum for Estc. For this to happen some states must exist which can benefit from the self-interaction term without loosing too much band formation energy. This will usually be the case for rather well localized states like the 3d states in transition metal oxides or the 4f states in rare earth compounds. Thus, EsIc is a single density functional, which may be used to describe localized as well as delocalized electron states. As we will demonstrate in the following, the relative position of the two minima may be influenced by external parameters such as hydrostatic pressure allowing for a localization - delocalization transition to occur. We have performed total energy calculations as a function of volume for CeN, CeP, CeAs. CeSb and CeBi for Bl and B2 phases, in the ferromagnetic (F) arrangement of Ce moments, and with the f -electron treated as either delocalized (LSD) or localized (SICLSD). Empty spheres were introduced in the Bl structure, and the calculations were fully converged with 95 (165) k-points in the irreducible Brilouin zone for the Bl (B2) structure. Spin orbit coupling was not considered. Our main results for the relevant transition pressures and volumes, together with the experimental data, are summarized in Table 1. For CeP, from the common tangent construction, a phase transition is predicted at a pressure of 71 kbar with a volume collapse of Av/ VO= 8% which agrees well with the experimental values of 55 and 90 kbar. The B2 structure is not favorable for the CeP compound, since the calculated energy is substantially higher than that of the Bl structure. This holds for both localized and delocalized

f-electronsis found. The transition pressure is calculated to be 113 kbar and the volume collapse 12%, while experimentally the Bl -B2 phase transition occurs at 150+40 kbar with a volume collapse of 11%. [l l] Some uncertainty is associated with comparing the total energies calculated for the Bl and B2 phases in the ASA. Therefore we have also investigated the high pressure transition in CeP with the full-potential LMTO method. [24] In this case we have found a transition pressure of 167 kbar, which is somewhat higher,

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Table I. Calculated transition pressures for the electronic and structural phase transitions in the cerium pnictides. Also quoted are the specific volumes on the two sides of the transition [1 I]. The notation (d) and (1) refers to calculations with delocalized or localized Ce f-electrons, i.e. tetravalent or trivalent Ce atoms. B2* denotes the distorted B2 structure (see text for discussion) P, (kbar) vh expt. theo. theo. I48 620 Bl(d) - B2(d) 325 90” 55b Bl(l) - Bl(d) 71 288 150[40) II3 Bl(d) - B2(d) 332 II4 I40(20)’ Bl(l) - B2(d) 400 85(25)d Bl(l) - B2*(I) 70 311 252 B2*(l) - B2*(d) 90(40)’ 427 Bl(l) - B2*(I) 88 317 370 B2*(1) - B2*(d) [5]. b Ref. [6]. (’ Ref. [7]. d Ref. [9]. e Ref. [IO].

compound CeN CeP CeP CeAs CeSb CeSb CeBi CeBi 0 Ref.

transition

(a03)

expt. 308” 285” 31Y 39gJ 399e -

VI

theo I41 297 246 265 353 295 376 304

(a07

expt. 298O 247” 274r 354d 36Or -

to a substantial increase of the Madelung energy by respectively 23 mRy and 25 mRy in comparison with CeP the AFI and the AFII structures. On the other hand -65.91 the magnetic moment is lowest in the F structure: 1.OO pe per CeP, compared with 1.07 /.QJin the AFII and 1.04 pE in the AFI. In short, the f-electron is more -65.92 localized in the AFI and AFII structures than in the F structure. In the case of delocalized f-electrons, we -65.93 find that the ferromagnetic structure is the structure ^x 5 of lowest energy at the experimental lattice constant. w However, at high pressure the AFII structure wins over -65.94 the F structure. Therefore, we predict that a change of magnetic structure occurs in the high pressure phase. The AFII structure of CeP is insulating and has a -65.95 gap of 0.1 eV, whilst the AFI structure is semi-metallic 340 380 260 300 V (a.u.) with a density of states at Ef of 0.066 state&e and Ry. The electron pockets are situated both at the I’ and X Fig. 1. Total energy of CeP (in Ry/formula unit) as points, whilst the compensating holes are found along a function of specific volume (in &formula unit) in the direction starting at the X point and running in the Bl crystal structure with three different magnetic parallel to the c-axis. By comparison, for CeSb in the structures: AFI (solid curves), AFII (dashed curves), and ferromagnetic (dash-dotted curves). The lower set AFI structure the number of states is slightly increased of curves corresponds to the calculations treating one to 0.1 state&e and Ry, and more strikingly, due to Ce f-electron as localized, whilst the upper set refers a reduction of the separation between the Ce d states to the calculations with delocalized S-electron. The and the P p states, the holes occur at the I’ point. common tangent marks the isostructural phase tranThe stability of the localized with respect to the desition. localized phase is increased slightly when going from CeP to CeAs due to the somewhat larger specific volbut in good accord with the experimental value. ume caused by the larger ligand ion. As a consequence To address the important question of the magnetic the common tangent construction leads to only one structure we also performed calculations for AFI and phase transition, from the localized Bl structure diAFII antiferromagnetic arrangements in the rocksalt rectly to the delocalized B2 structure. The transition Bl crystal structure. The AFII structure consists of pressure is calculated to be 114 kbar with a 18 % an antiferromagnetic stacking of ( 111) planes, within volume collapse. This is in accord with the experiwhich the Ce moments are ferromagnetically coupled. mental situation, where a Bl-B2 transition is obIn the calculations with localized f-electrons all the served at 140+20 kbar, with a volume collapse of 11 magnetic structures are very close in energy as can be ‘l/u.There has been some dispute over the nature of seen from Figure 1: at the experimental lattice constant the f-electrons in the high pressure phase. [7.8] The the AFI is lower by 0.5 mRy than the AFII and 1.8 present calculations rule out the presence of localized mRy than the F structure. In the F structure, the Ce f-electrons in the B2 phase of CeAs. The theoretical atomic sphere looses 0.0046 electrons in comparison pictures offered by the present work is rather idealwith the AFI and the AFII structures. This gives rise

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at a pressure of 88 kbar with a volume collapse of 9% which is in perfect accord with the experimentally observed transition at 90+40 with a volume collapse of 8% As in CeSb, both sides of the transition are characterized by localized f-electrons. Only at a high pressure of - 370 kbar is a delocalization transition foreseen, as for CeSb with a good chance of being isostructural. In contrast to the other cerium pnictides the localization of the f-electrons is never favored in CeN. The equilibrium structure is the Bl 8 .J L..-.--_ 200 300 400 500 structure with a volume of 195 ai. The experimental V (a.u.) volume is 212 a:. The slight underestimation of the equilibrium volume may be an indication that the true Fig. 2. Cohesive energy of CeSb (in Ry/formula unit) CeN ground state is of a more complicated structure as a function of specific volume (in &formula unit). than that of itinerant f-electrons. The present calcuTwo crystal structures, the Bl and the B2, were considlations show, however, that the LDA ground state with ered, and each with two different treatments of the Ce itinerant f-electrons is a better representative of the f-electrons. The solid curves correspond to calculations with one localized f-electron per Ce atom, while CeN ground state than the SIC-LSD ground state with the dashed curves correspond to itinerant f-electrons. fully localized f-electrons.The present work predicts a structural phase transition B 1-B2 around 620 kbar. In summary, the calculations explain the experimenized, though. In reality, the ground state of CeAs at a given pressure will be a complicated fluctuating mix- tal structural facts as follows: With increasing Z of the ture of localized and delocalized f-electrons. The fact ligand, the specific volume at zero pressure increases that the Bl phase with delocalized f-electrons is very with the decrease of the ionicity of the compound. close to the transition line may imply that the Bl phase The delocalization of Ce f-electrons is less favorable at pressures just below the transition attains a signifi- at large specific volumes. The tetragonal structure observed at high pressure in CeSb and CeBi is almost decant component of delocalized f-electron character, i.e., mixed valent behavior. We take the present calcu- generate with the undistorted B2 structure. Concernlations as evidence for the high pressure phase having ing magnetic ordering, the AFI structure is found to predominantly delocalized f-electrons. be the ground state in both CeP and CeSb. We find For CeSb the phases with localized f-electrons an intricate interplay of the charge and magnetization are even further stabilized relative to those with de- densities: The groundstate is not the structure which localized f-electrons. As a consequence the first has the most localized f-electron (AFII). Moreover, transition to occur is from Bl to B2, both with lo- our calculations show that the number of carriers and calized f-electrons (see Fig. 2). The transition pres- their character is determined by the magnetic strucsure is found to be 70 kbar, while the experimental ture. This work has been partially funded by the Human Bl -B2(distorted) transition occurs at 85k2.5 kbar. The calculated volume collapse of 11% compares fa- Capital and Mobility Network on ‘Ab-initio (from vorably with the experimental value of 10%. From electronic structure) calculation of complex processes Fig. 2, it is seen that a second isostructural B2-B2 in materials’ (contract:ERBCHRXCT930369). A.S. transition is predicted to occur at high pressure, at 252 acknowledges support from the Danish Natural Scikbar, where the f-electrons are delocalizing. The as- ence Research Council (Grant no. 1l-9001-3). sociated volume collapse is 4%. Experimentally, CeSb has been investigated up to 250 kbar 191,but only one REFERENCES discontinuous phase transition was observed. It seems necessary to investigate CeSb at somewhat higher 1. Jayaraman, A., Lowe, W., Longinotti, L.D., and pressures to clarify whether a second phase transition Bucher, E., Phys. Rev. Lett. 36, 366 (1976). occurs. From the present work we can not exclude a new structure (i.e., neither Bl nor B2) at the high 2. Baer, Y, Hauger, R., Ziircher, Ch., Campagna, M., and Wertheim, G.K., Phys. Rev. B. l&4433 (1978). pressure side of a possible second phase transition. The trends observed in going from CeP over CeAs 3. Franciosi, A., Weaver, J.H., Martensson, N., and Croft, M., Phys. Rev. B. 24, 3651 (1981). to CeSb are seen to continue to CeBi, namely a preference for localized f-electronsin both the Bl and 4. Gudat, W., Rosei, R., Weaver, J.H., Kaldis, E., and the B2 phase. A transition from Bl to B2 is found Hulliger, F., Solid State Commun. 41, 37 (1982).

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