Multiorbital exchange Hamiltonians: Derivation and examples

Journal of Magnetism and Magnetic Materials. 2023. Vol. 587. Article 171315.

Igoshev P., Streltsov S., Kliment I. Kugel

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.

Keywords: обменное взаимодействие, exchange interaction, модель Хаббарда, Hubbard model, модель Кугеля-Хомского, orbital ordering, орбитальное упорядочение, Kugel–Khomskii model