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

TL;DR

This paper analyzes the spin--orbital structure of transition metal compounds with face-sharing octahedra, revealing a highly symmetric SU(4) model applicable to real materials and comparing it with other geometries.

Contribution

It introduces a symmetric SU(4) spin--orbital model for face-sharing octahedra, expanding the understanding of exchange interactions in these geometries.

Findings

Derivation of a high-symmetry SU(4) Hamiltonian for face-sharing octahedra.

Identification of orbital splitting into $a_{1g}$ and $e_g^{\pi}$ due to trigonal distortions.

Comparison of spin--orbital interactions across different octahedral geometries.

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.