KugelKhomskii

Kugel-Khomskii refers to a theoretical model in condensed matter physics that describes the coupled spin and orbital degrees of freedom in Mott insulators with degenerate electronic orbitals. It was introduced by Kirill I. Kugel and Dmitrii I. Khomskii in the early 1980s to explain how electron correlations tie together magnetic and orbital order in transition metal compounds.

The model arises from a strong-coupling expansion of a multi-orbital Hubbard Hamiltonian, yielding an effective spin-orbital superexchange Hamiltonian. In this framework, each lattice site carries both a spin degree of freedom and an orbital (or orbital pseudospin) degree of freedom. The exchange interactions depend on the specific orbitals occupied and on the bond direction, leading to interdependent spin and orbital dynamics. As a result, the system can exhibit complex phase diagrams with various magnetic and orbital ordering patterns, and in some cases orbital fluctuations can influence magnetic properties or even drive novel states.

Applications of the Kugel-Khomskii model include a range of transition metal oxides with orbital degeneracy, such as certain perovskites. Classic examples discussed in the literature include KCuF3, LaMnO3, and related compounds, where observed magnetic structures and orbital orderings can be understood within the spin-orbital coupling framework. The model has inspired numerous extensions that incorporate lattice effects, Jahn-Teller distortions, and additional orbital flavors, broadening its relevance to correlated electron systems.

See also: spin-orbital model, superexchange, Jahn-Teller effect, transition metal oxides.