Spin--orbital interaction for face-sharing octahedra: Realization of a highly symmetric SU(4) model

Abstract

Specific features of orbital and spin structure of transition metal compounds in the case of the face-sharing MO${}_6$ octahedra are analyzed. In this geometry, we consider the form of the spin--orbital Hamiltonian for transition metal ions with double ($e_g^{\sigma }$) or triple ($t_{2g}$) orbital degeneracy. Trigonal distortions typical of the structures with face-sharing octahedra lead to splitting of $t_{2g}$ orbitals into an $a_{1g}$ singlet and $e_g^{\pi }$ doublet. For both doublets ($e_g^{\sigma }$ and $e_g^{\pi }$), in the case of one electron or hole per site, we arrive at a symmetric model with the orbital and spin interaction of the Heisenberg type and the Hamiltonian of unexpectedly high symmetry: SU(4). Thus, many real materials with this geometry can serve as a testing ground for checking the prediction of this interesting theoretical model. We also compare general trends in spin--orbital ("Kugel--Khomskii") exchange interaction for three typical situations: those of MO${}_6$ octahedra with common corner, common edge, and the present case of common face, which has not been considered yet.

10 pages, 5 figures, RevTeX, in version 2, we took into account the remarks of Referees

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