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• W2038815348 endingPage "479" @default.
• W2038815348 startingPage "466" @default.
• W2038815348 abstract "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 ${M}_{L}=0, ifmmodepmelsetextpmfi{}1$. 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 $b>{b}_{c}$, where ${b}_{c}$ 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 Nb${mathrm{S}}_{2}$ and W${mathrm{S}}_{2}$, 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 LaMn${mathrm{O}}_{3}$. The competition between spin-orbit-coupling and Jahn-Teller stabilizations is dramatically illustrated by the system $mathrm{Ni}{mathrm{Fe}}_{t}{mathrm{Cr}}_{2ensuremath{-}t}{mathrm{O}}_{4}$. Whereas superexchange energies maintain a Jahn-Teller stabilization below ${T}_{c}$ in Cu${mathrm{Cr}}_{2}$${mathrm{O}}_{4}$, despite collinear ${mathrm{Cu}}^{2+}$-ion spins, magnetostrictive distortions below ${T}_{N}$ occur in FeO and CoO. Elastic restoring forces favor trigonal ($ensuremath{alpha}>60ifmmode^circelsetextdegreefi{}$) symmetry for octahedral-site ${mathrm{Fe}}^{2+}$, but tetragonal ($frac{c}{a}<1$) symmetry for ${mathrm{Co}}^{2+}$ and ${mathrm{V}}^{2+}$. In trigonal FeO, superexchange interactions also help stabilize the trigonal distortion, whereas in tetragonal CoO they do not. The compound LaV${mathrm{O}}_{3}$ also has a spin-orbit coupling stabilization that is enhanced by a magnetostrictive distortion to tetragonal ($frac{c}{a}<1$) symmetry below ${T}_{N}$. However, the isoelectronic compound PbCr${mathrm{O}}_{3}$ shows no such distortion, presumably because it illustrates band antiferromagnetism together with spin-orbit-coupling stabilization. The low-spin ions ${mathrm{Fe}}^{4+}$ and ${mathrm{Co}}^{4+}$ also form collective $d$ orbitals in oxides with perovskite structure; electric, magnetic, and crystallographic data for SrFe${mathrm{O}}_{3}$ and LaSr${mathrm{Co}}_{2}$${mathrm{O}}_{6}$ indicate collective $d$ electrons having transfer integrals in the narrow range ${b}_{c}<b<{b}_{m}$, where ${b}_{m}$ is the maximum transfer integral for spontaneous band magnetism." @default.
• W2038815348 created "2016-06-24" @default.
• W2038815348 creator A5056531495 @default.
• W2038815348 date "1968-07-10" @default.
• W2038815348 modified "2023-09-27" @default.
• W2038815348 title "Spin-Orbit-Coupling Effects in Transition-Metal Compounds" @default.
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• W2038815348 doi "https://doi.org/10.1103/physrev.171.466" @default.
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