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 MO sub(6) octahedra are analyzed. In this geometry, we consider the form of the spin-orbital Hamiltonian for transition-metal ions with double (e super()[sigma] sub(g)) or triple (t sub(2g)) orbital degeneracy. Trigonal distortions typical of the structures with face-sharing octahedra lead to splitting of t sub(2g) orbitals into an a sub(1)g singlet and e super([pi]) sub(g) doublet. For both doublets (e super()[sigma] sub(g) and e super([pi]) sub(g)), 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 ("KugelKhomskii") exchange interaction for three typical situations: those of MO sub(6) octahedra with common corner, common edge, and the present case of common face, which has not been considered yet.