Multiorbital exchange Hamiltonians: Derivation and examples

Abstract

We present a detailed derivation of the effective Hamiltonian for a strongly correlated electron system involving both orbital and spin degrees of freedom. This problem is relevant to a wide class of materials containing ions with the orbitally degenerate ground state (Jahn–Teller ions). We treat in detail the case of double degenerate orbitals, obtain the Kugel–Khomskii model, and then pass to a more general multiorbital case. Based on the derived Hamiltonians, we analyze possible spin and orbital configurations, which can be rather nontrivial, especially in the multiorbital case. A special emphasis is put on to a specific example of the square lattice of Jahn–Teller ions typical of layered perovskites.