SPIN-ORBIT-COUPLING EFFECTS IN TRANSITION-METAL COMPOUNDS

Crystal-field splittings in a high-symmetry phase may leave an orbitally degenerate ground state. Three types of degeneracies are considered: (1) a twofold degeneracy that carries no orbital angular momentum, (2) a twofold degeneracy that carries an orbital angular momentum, and (3) a threefold degeneracy that carries an azimuthal angular momentum ML=0,±1. In the first type, there is a competition between ferromagnetic superexchange coupling that stabilizes dynamic Jahn-Teller vibrational modes and a static Jahn-Teller distortion that introduces anisotropic superexchange interactions. In the second type, spin-orbit coupling removes the degeneracy, and the usual empirical rules for the sign of the superexchange coupling are applicable provided that the transfer integrals with near-neighbor ions take account of the geometrical modification of the orbitals by spin-orbit coupling. In the third type, there is a competition between (a) a magnetostrictive static distortion that enhances the spin-orbit-coupling stabilization below a magnetic-ordering temperature, and (b) a pure Jahn-Teller static distortion. However, from a knowledge of the structure the orbital configurations and their transfer integrals are known, and the usual empirical rules for superexchange coupling can be applied. Further, if the transfer integrals are b>bc, where bc is sharply defined, it is necessary to use a collective-electron band model. For narrow bands, spin-orbit-coupling energies may be large enough to split degenerate bands of collective-electron orbitals. This latter splitting appears to be illustrated by NbS2 and WS2, where the cationic occupation of trigonal-bipyramidal interstices optimizes spin-orbit-coupling stabilization. Ferromagnetic superexchange via dynamic Jahn-Teller correlations is illustrated by high-temperature LaMnO3. The competition between spin-orbit-coupling and Jahn-Teller stabilizations is dramatically illustrated by the system NiFetCr2-tO4. Whereas superexchange energies maintain a Jahn-Teller stabilization below Tc in CuCr2O4, despite collinear Cu2+-ion spins, magnetostrictive distortions below TN occur in FeO and CoO. Elastic restoring forces favor trigonal (α>60°) symmetry for octahedral-site Fe2+, but tetragonal (ca<1) symmetry for Co2+ and V2+. In trigonal FeO, superexchange interactions also help stabilize the trigonal distortion, whereas in tetragonal CoO they do not. The compound LaVO3 also has a spin-orbit coupling stabilization that is enhanced by a magnetostrictive distortion to tetragonal (ca<1) symmetry below TN. However, the isoelectronic compound PbCrO3 shows no such distortion, presumably because it illustrates band antiferromagnetism together with spin-orbit-coupling stabilization. The low-spin ions Fe4+ and Co4+ also form collective d orbitals in oxides with perovskite structure; electric, magnetic, and crystallographic data for SrFeO3 and LaSrCo2O6 indicate collective d electrons having transfer integrals in the narrow range bc<b<bm, where bm is the maximum transfer integral for spontaneous band magnetism. © 1968 The American Physical Society.