Spin-Polarization-Induced Structural Selectivity in Pd {3}X and Pt {3}

VOLUME 75, NUMBER 7 PHYSICAL REVIEW LETTERS 14 AvrvsT 1995

Spin-Polarization-Induced Structural Selectivity in Pd3X and Pt3X (X=3d) Compounds

Z. W. Lu, Barry M. Klein, and Alex Zunger Department of Physics, University of California, Davis, California 95616 National Renewable Energy Laboratory, Golden, Colorado 80402 (Received 20 December 1994) Spin polarization is known to lead to important magnetic and optical effects in open-shell atoms and elemental solids, but has rarely been implicated in controlling structural selectivity in compounds and alloys. Here we show that spin-polarized electronic structure calculations are crucial for predicting the correct T = 0 crystal structures for Pd3X and PtiX compounds. Spin polarization leads to (i) stabilization of the L12 structure over the D022 structure in Pt3Cr, Pd3Cr, and Pd3Mn, (ii) stabilization of the DOz2 structure over the Llz structure in PdiCo, and (iii) ordering (rather than phase separation) in Pt3Co and Pd3Cr. The results are analyzed in terms of first-principles local spin density calculations.

PACS numbers: 61.66.Dk, 71.20.Cf, 75.50.Cc

Crystal structure compilations [1,2] reveal that the most Fermi level N(EF) Local d.ensity approximation (LDA) commonly occurring structures among intermetallic bi- [9] band structure and total energy calculations [6,7] have nary compounds with a 3:1 stoichiometry (A&B) are the later substantiated this relation. To examine such a rela- cubic Llz and the tetragonal DOzz (Fig. 1). The crystal- tion for intertransition metal A3B compounds rather than lographic difference between the L12 and D022 structures aluminides we have calculated N(E) (Fig. 2) and total en- is rather subtle: The two structures have identical first ergy difference 6E = E(Llz) —E(DOzz) [Fig. 3(a) and neighbor coordination (each A has 8A + 4B neighbors Table I] for PdsX with 3d atom X = Sc through Cu us- and each B has 12A neighbors), while a difference exists ing the NM linearized augmented plane wave (LAPW) in the second shell (see Fig. 1). The manner in which method [10]. We see that the structure with the lower particular A3B compounds select the L12 or the D022 calculated NM total energy (Table I) indeed has a lower configuration appears to be rather interesting. For exam- calculated NM N(EF) (Fig. 2), thus substantiating ear- ple [2], the 4d trialuminides AlsM show the sequence lier trends for aluminides [5—7]. For example, for Pd3X L12 L12 D022 as M varies across the 4d row with X = V, Cr, and Mn, the Fermi energy, EF, falls Y ~ Zr ~ Nb, while the 3d palladium alloys Pd3X show near a DOS maximum for L1~ but near a DOS mini- L lp L12 D022 L12 L12 L12 as one pro- mum for DOzz, correspondingly, E(DOzz) is lower than ceeds in the 3d row X = Sc ~ Ti ~ V ~ Cr ~ Mn ~ E(Llz). Unfortunately, while the magnitude of N(EF) Fe [3] (for X = Co and Ni, the systems phase separate). is indicative of the stability of the calculated structure, The origin of such regularities was the subject of nurner- these nonmagnetic calculations incorrectly predict the ob- ous investigations including the d-electron "generalized served stable crystal structure in several cases: While perturbation method" (GPM) [4], and first-principles cal- Pd3V is correctly predicted to be more stable in the D022 culations [5—7]. However, these calculations failed to re- structure, the observed [2] stable structure for Pd3Cr, produce the observed structural trends. These calculations Pd3Mn [3], and Pd3Fe is the L1z structure, not the were nonmagnetic (NM), i.e., without spin polarization. This appeared to be a reasonable assumption, since one (b) DOzz that an rich in expects alloy a nonmagnetic component 4E 4E JE 4E %F 0 0 (e.g. , Pd3Cr) or one without any magnetic components 1F %F (e. will not have significant magnetic ef- g. , Pd3V) any 0 0 o 0 0 o fects. We demonstrate here that spin polarization has a o o 4E crucial infIuence on the structural stability of Pd3X and o ~ p) Pt3X compounds: It stabilizes the observed L12 struc- wr 0 0 0 0 ture over the D022 structure in Pt3Cr, Pd3Cr, and Pd3Mn, 0 0 0 A10 4E the DO~2 structure over the L12 structure in Pd3Co, and o is responsible for compound formation (rather than phase separation) in Pt3Co and Pd3Cr. 1st A: 8A+4B 1st A: 8A+4B,8A+4B 1st B:12A+OB The key insight to stability in compounds and alloys 1st B:12A+OB 2nd A: 6A+OB 2nd A: 6A+OB, 4A+2B has traditionally been the association of stability with 2nd B:OA+6B 2nd B:2A+4B low density of states (DOS) at the Fermi energy EF [8]. FIG. 1. The crystal structures of the L12 and Nicholson et al. noted that for transition metal alu- (a) (b) D022 [5] structures. The inset shows the atomic coordination about A minides the more stable of the two structures (Llz or and 8 sites in the first (1st) and second (2nd) atomic shells. Ai DOzz) corresponds to the one with smaller DOS at the and A2 indicate two distinct A sites in the D022 structure.

1320 0031-9007/95/75(7)/1320(4)$06. 00 1995 The American Physical Society VOLUME 75, NUMBER 7 PHYSICAL REVIEW LETTERS 14 AvovsT 1995

I I I I I I I I — — X=Sc Ti V Cr Mn Fe Co Ni CU 2 L12 DO . eel- I PdpSc * 1 Q.341 22 1 o. 100— o 0 I D I I I I I I I I 2 -p T * : 2al- 50- 1 o. E

C CV 0 04 M I I I I o Ch 2 -Pd3V 441- ) 1 o. LLI I -50 3X I nmngnetic 0 I I I rromagnetic CO 2 -p 13Cr LYI 1 o.eel -100- onmagnetic X 1 X$ CL 0 I I I I CP I 0.2 ~~ 2 0- -Pd3Mn :: 1 o.711 Yp o C CO CS C5 ) p E I I I I I I E 2 ~ -100— O -Pd3Fe 11.141 R a LLI 0) 0 I L I i— I I I I I -200- 0 2 -Pd3Co ' ' Cl * 11421: 11.7al- LL LLI

0 I I I I I I I I ~I I I I I -300 2 -Pd3Ni 8.0 8.5 9.0 9.5 1 0.0 10.5 Number of Valence Electrons/Atom

0 I I I I I I I I I I FIG. 3. LDA and GPM (Ref. calculated I I (a) (present) [4]) 2 -Pd C : difference = — for 1 o.e21 energy BE E(L12) E(D02q) [Eq. (2)] Pd3X compounds. Note the reversal of sign for 6F due to spin polarization for Pd3Cr, Pd3Mn, and Pd3Co (nearly so for p I I I -8 -6 -4 -2 0 2 4 -8 -6 -4 -2 0 2 4 Pd3Fe). Part (b) gives the magnetization energies BM(cr) = Energy (eV) EI:M(o) —EFM(o) [Eq. (3)] for cr = Llq (empty circles) and o = D02q (solid squares) structures and shows the local FIG. 2. LDA calculated NM total DOS for Pd3X in the L12 magnetic moment for the X atom (numbers above or below and DOq2 structures. The insets denote N(EF). An asterisk the symbols). denotes the more stable structure predicted by total energy calculations in the absence of magnetic ordering. Note that I.12 and D022 structures using the LDA in both the spin- the more stable structure has a lower N(EF) polarized and spin-unpolarized versions [12] of the full- nonmagnetically predicted D022 structure. Thus, while potential LAPW method [10]. In order to accurately the correlation between the calculated quantities N(EF) obtain the small energy difference between two fairly vs E(Llz) —E(DOzz) holds, it leads to incorrect predic- similar crystal structures, the calculations were carried tions for the stability of Pd3Cr, Pd3Mn, and Pd3Fe. The out consistently using the same muffin-tin radii RMT generalized perturbation method calculations [4], based on and basis set energy cutoffs Em». The Brillouin zone similar DOS arguments [diamond symbols in Fig. 3(a)] summations were done using the geometrically equivalent likewise predict Pd3Cr, PdsMn, and Pd3Fe (and even k-point sampling scheme [13(a)], in which 20 (40) k Pd3Sc and Pd3Ti) to be stable in the DOzz structures, in points in the irreducible zone for the L12 (DOzz) structure conllict with experiment [2]. is mapped into the same 60 special k points [13(b)] in the In this paper we explain this puzzle by noting that, fcc structure. We optimized the total energy as a function while a large N(EF) indeed implies a destabilizing factor of volume, as well as the c/a ratio in the D02z structure. for the one-electron ("band") energy, it also leads (in The estimated LAPW error for the E(L12) —E(D02z) open-shell systems) to spin polarization and magnetic energy difference is -5 meV jatom, and the neglected moment formation which, in turn, is a stabilizing factor. zero-point energy difference between the two similar Thus despite their large N(EF) in the L lz structure structures should be even smaller. (suggesting one-electron instability), Pt3Cr, Pd3Cr, and At zero temperature, the absolute stability of a com- Pd3Mn (nearly so for Pd3Fe) are correctly predicted pound in a structure o with respect to phase separation is to be more stable in this structure once spin-polarized given by its formation enthalpy 6 H(cr) total energy calculations [11] are done. Thus magnetic AH~(o) = E~(tr) —xgEp(Vg) —xeEe(Ve), (1) ordering changes the predictions of NM total energy calculations and restores agreement with experiment. where E~(V~) and Ee(Ve) are the energies of the con- We have calculated the total energies of Pd3X, for stituents A and B in their respective ground states (e.g., for X = Sc through Cu as well as Pt3Cr and Pt3Co in the Pd3Ni, it is nonmagnetic fcc for Pd and ferromagnetic fcc 1321 VOLUME 75, NUMBER 7 PH YS ICAL REVIEW LETTERS 14 AUGUsT 1995

TABLE I. LDA calculated total energy difference (in meV/atom) BE = E(Llz) —E(DOzz) and the ferromagnetic (FM) DOS at Fermi energy N(EF) (in states/eV spin) for the Llz and DOzz structures. Note that the spin polarization (included in the FM state) reverses the relative stability of nonmagnetic (NM) Llz and DOzz structures for those compounds marked by an asterisk, thus restoring agreement with experiment [2,3]. PS denotes phase separation. Expt. structure 6FFM L12 NFM(EF) +O22 &FM(EF) Pd3Sc L12 —102 —102 0.34 0.65 Pd3 Ti L12 —48 —48 0.14 0.28 Pd3V 71 40 0.64 0.38 Pd3Cr* L12 74 —20 0.57 0.60 Pd3Mn* L12 48 —45 0.59 0.80 Pd3Fe Llp 14 1 0.42 0.34 Pd3CO* PS 15 0.79 0.46 Pd3Ni PS —2 0 0.95 0.93 Pd3Cu Llp —8 —8 0.52 0.92 Pt3Cr* L12 71 —23 0.56 0.54 Pt3Co L12 —11 —16 0.66 0.65

. for Ni), E (o)is the energy of structure o., and u = NM concomitant magnetic stabilization energy BM [Fig. 3(b)]: or FM denotes whether structure o. is in the nonmagnetic A larger energy stabilization 6M due to spin polariza- or ferromagnetic state. The relative stability of two dif tion relates to a larger N(EF) and with a larger local- ferent ordered structures is ized magnetic moment p,~ on the X atom [Fig. 3(b)]. For example, while the Pd3X compounds with X = Sc, Ti, BE = E (Llz) —E (DOzz), and Cu are nonmagnetic (so BM = 0), when X = Mn while the magnetic stabilization energy of a given struc and Fe, one sees in Fig 3(b) large energy lowering due ture o (Llz or DOzz) is to spin polarization (BM ——200 meV/atom), and concomitantly large magnetic moments of 3.5p, z (X = Mn) BM(~r) EFM(o ) ENM(o ) . (3) and 3.1p,p (X = Fe) in both the Llz and DOzz structures Table I and Fig. 3(a) give BENM and BEFM, while (as a comparison, bcc Fe has a magnetic moment value of Fig. 3(b) shows the magnetic stabilization energies only 2.2p~). Thus spin polarization induces a local mag- BM(Llz) and BM(DOzz), and the local magnetic moment netic moment on the "magnetic" 3d atoms with large NM p,z on the X atom calculated numerically within the N(EF), while lowering the total energy of the compound. muffin-tin sphere (the value of p, x is rather insensitive In the case of Pt3Cr in the L12 structure for which previous to the small change in muffin-tin radius). Table II gives calculation exists, our calculated total magnetic moment in the formation enthalpies AH (Llz) and AH (DOzz) for the unit cell (2.6p, ~) agrees with a previous calculation [14] several systems. Figure 2 depicts the NM total DOS for of 2.6pe and with the experimental value [15]of 2.5p, e. Pd3X, where X = Sc ~ Cu, in the Llz (left panel) and (iii) In the NM calculations, Pd3V and Pd3Cr have DOzz structures (right panel). One notices the following. large DOS peaks at EF in the L12 structure, and are (i) In contrast to the very similar DOS for the Llz and concomitantly less stable in this structure than in the DOzz structures and the small energy difference E(Llz)— low N(EF) DOzz structure. However, as spin polarization E(DOzz) —20 meV/atom predicted by the GPM [4], one is introduced, the large DOS peak of the L12 structure sees from Fig. 2 a marked difference of the DOS in the splits, so that FF now resides in a low DOS region. This Llz and DOzz structures. (a) While the DOS of the cubic leads, simultaneously, to the formation of larger magnetic L12 structure resembles that of fcc Pd, having three major moments on V and Cr in the L12 structure relative to the peaks, the DOS of the D02q structure are more smeared, DO22 structure. This selective magnetization thus lowers refiecting a loss of cubic symmetry in the DO2z structure. the energy of the L12 structure more significantly than in (b) The DOS of the more stable Llz structure for Pd3Sc the DOzz structure [Fig. 3(b)]. and Pd3Ti shows a "pseudogap" near the Fermi level ab- (iv) Table I shows that the more stable of the two sent in the DOzz structure. (c) In the Llz structure, the structures generally (and weakly) relates to a smaller Fermi level of Pd3V, Pd3Cr, and Pd3Mn falls on a DOS value of the ferromagnetic DOS at the Fermi level peak (made mostly of d orbitals of the X atom), while in NFM(EF). Thus the trend of total energy stability with the D022 structure the Fermi level falls on a relatively Oat N(EF) does exist, but for the spin-polarized quantities. portion of the DOS. Indeed, these materials are more sta- (v) The magnetic stabilization energy BM reverses the ble in the D022 structure in a NM LDA description. As a relative stability predicted by NM calculations in several result of these differences, the values of N(EF) (given in cases: Spin polarization stabilizes the experimentally the insets of Fig. 2) and its shape near the Fermi level are observed [2] Llz structure of Pd3Cr, Pd3Mn, and Pt3Cr strikingly different for the L12 and D022 structures. (nearly so for Pd3Fe) over the DOzz structure, while for (ii) The above noted trends in the NM N(EF) induce a Pd3 Co spin polarization makes the D 02& structure more 1322 VOLUME 75, NUMBER 7 PH YS ICAL REVIEW LETTERS 14 AUGUsT 1995

TABLE II. Nonmagnetic (NM) and ferromagnetic (FM) for- We thank Professor Alan Ardell for pointing out the mation enthalpies, hH [in meV/atom, Eq. (1)], of some com- fact that Pd3Cr orders in the L12 structure. Z. W. L. pounds. AH's are taken with respect to the NM fcc Pd, Pt, FM and B.M. K. acknowledge the support by the Univer- fcc Ni, FM fcc Co, and anti-FM bcc Cr, respectively. sity Research Funds of the University of California at b, H(L12) AH(DOpg) Davis and San Diego Supercomputer Center for com- NM FM FM puter time. A. Z. acknowledges the DOE, the Office of Pd3Cr 126 —9 51 11 Energy Research, Basic Energy Sciences, Division of Ma- Pd3Co 155 64 160 49 terials Science for support under Contract No. DE-AC36- Pd3Ni 61 43 62 44 83CH 10093. Pt3Cr —68 —185 —139 —161 Pt3Co 31 —42 42 —26

[1] P. Villar and L. D. Calvert, Pearson 's Handbook of Crystallographic Data for Intermetallic Phases (ASM, stable. The reversal of stability for cannot Pd3Co be Metals Park, OH, 1991). observed experimentally, since the calculated AH [Eq. (1) [2] Binary Alloy Phase Diagrams, edited by T. B. Massalski and Table II] is positive, so Pd3Co (and similarly Pd3Ni) et al. (ASM, Metals Park, OH, 1990). is predicted to phase separate rather than to order, in [3] Pd3Ti crystallizes in a hexagonal D024 structure as well as accord with the observed phase-separation behaviors for in an off-stoichiometric L12 structure. Pd3Mn is observed Pd-Co and Pd-Ni [2]. in the D023 structure, which could be characterized as a (vi) Spin polarization can stabilize ordering over phase combination of the L12 and D022 structures. separation [16]: We find that in a NM description Pt3Co [4] (a) A. Bieber et al. Solid State Commun. 39, 149 (1981); has bHNM ~ 0 so it is predicted to phase separate, (b) 45, 585 (1983); (c) A. Bieber and F. Gautier, Acta Metall. 2291 but that a strong spin-polarization effect stabilizes the 34, (1986). [5] D. M. Nicholson et al. , Mater. Res. Soc. Symp. Proc. 133, ordered Llz structure, leading to EHFM 0 in agreement ( 17 (1989); 1S6, 229 (1991). with the observed ordering behavior Similarly, spin [2]. [6] A. E. Carlson and P. J. Meschter, J. Mater. Res. 4, 1060 polarization stabilizes the experimentally observed [17] (1989). Llz structure of Pd3Cr (its magnetic behavior, however, [7] J. Xu and A. J. Freeman, Phys. Rev. B 40, 11927 (1989); has not been experimentally examined). Hence, spin J. Mater. Res. 6, 1188 (1991). polarization not only reverses the stability of the L12 and [8] N. F. Mott and H. Jones, The Theory of the Properties of D02z structures for many compounds, but it also stabilizes Metals and Alloys (Clarenden Press, Oxford, 1936). an ordered (L12) structure over phase separation for Pd3Cr [9] W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965). and Pt3Co. [10] D. J. Singh, Planewaves, Pseadopotentials, and the LAPW (vii) Interestingly, the AH for Pt3Cr are negative in Method (Kluwer, Boston, 1994). E.G. Moroni and T. Jarlborg, Phys. Rev. B 47, 3255 both the NM and FM cases, but the spin polarization ef- [11] (1993). fect gives a larger stability to the Llz structure (observed [12] We use the exchange-correlation potential of D. M. Ceper- experimentally) One also notices that the AH are [2]. ley and B.J. Alder, Phys. Rev. Lett. 45, 566 (1980) as pa- lower in the Pt alloys than in the corresponding Pd alloys. rametrized by J.P. Perdew and A. Zunger, Phys. Rev. 8 The increased stability in Pt alloys has been addressed 23, 5048 (1981). previously in Ref. [16]. [13] (a) S. Froyen, Phys. Rev. B 39, 3168 (1989); (b) H. J. In summary, we have shown that theoretically unstable Monkhorst and J.D. Pack, ibid 13, 5188 (19.76). nonmagnetic structures which involve magnetic atoms and [14] A. Szajek, Acta Phys. Pol. A S2, 967 (1992). possess large N(EF), may be stabilized by splitting the [15] S.K. Burke et al. , J. Magn. Magn. Mater. 15-1S, 505 near EF peak in the DOS and forming a local magnetic (1980). moment with a concomitant lowering of N(EF) and the [16] Z. W. Lu, S.-H. Wei, and A. Zunger, Phys. Rev. Lett. 66, 1753 these authors have also shown that relativis- total energy. Therefore theoretical studies of the stability (1991); tic effects can stabilize ordering over phase separation in of compounds with a large value of a NM should N(EF) NiPt. be carefully tested for magnetic ordering which can [17] J. C. Huang, A. J. Ardell, and O. Ajaja, J. Mater. Sci. 23, often change the predictions of the ground state crystal 1206 (1988). structure.

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