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

Specific features of orbital and spin structure of transition-metal compounds in the case of the face-sharing MO6 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 alpha(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 the spin-orbital ("Kugel-Khomskii") exchange interaction for three typical situations: those of MO6 octahedra with common corner, common edge, and the present case of common face, which has not been considered yet.