Orbital Ordering in a Two-Dimensional Triangular Lattice

Abstract

We discuss the role of orbital ordering in a two-dimensional triangular lattice. Usually, this lattice is considered as “frustrated.” We show that a peculiar type of orbital ordering can remove this frustration if we allow for orbital degeneracy. We pay special attention to the $d^2$ case, for which we present mean field calculations for possible orbital orderings and an exact diagonalization study of a three-site cluster within a degenerate Hubbard model. The results support the possibility of an orbitally ordered singlet ground state. In particular, it provides new insight to the magnetic phase transition and the low temperature phase of ${\mathrm{LiVO}}_2$.