Orbital-only models: ordering and excitations

Abstract

We consider orbital-only models in Mott insulators, where the orbital–orbital interactions are either due to Jahn–Teller distortions or due to the Kugel–Khomskii superexchange. This leads to highly anisotropic and frustrated orbital Hamiltonians. For two-fold degenerate e g systems, both types of orbital interactions lead to the same form of the Hamiltonian—the 120° model. In both cases, the predicted symmetry of the orbital ordering is the same, although different from the one observed experimentally. The orbital operators that appear in the two kinds of orbital-only Hamiltonians are different. In the case of superexchange, the orbital degrees of freedom are represented by quantum pseudo-spin 1/2 operators. But when the interactions are Jahn–Teller mediated and the coupling with the lattice is strong, the orbital operators are essentially classical pseudospins. Thus as a function of the relative coupling strengths, a quantum-to-classical crossover is expected. For three-fold degenerate t 2g orbitals, the Jahn–Teller coupling gives rise to a particular type of orbital compass models. We point out that fluctuations—whether due to quantum effects or finite temperature—are of prime importance for ordering in the 120° and orbital compass models. The fluctuations generally generate a gap in the orbital excitation spectrum. These orbital excitations—orbitons—are hybrid excitations that carry both a lattice Jahn–Teller and a magnetic Kugel–Khomskii character.