Physics:Kugel–Khomskii coupling

Kugel–Khomskii coupling describes a coupling between the spin and orbital degrees of freedom in a solid; it is named after the Russian physicists Kliment I. Kugel (Климент Ильич Кугель) and Daniel I. Khomskii (Daniil I. Khomskii, Даниил Ильич Хомский). The Hamiltonian used is:

$H=\frac{t^2}{U}\sum _{⟨i,j⟩}[4(\overrightarrow{S_i}\cdot \overrightarrow{S_j})({\tau }_i^{\alpha }-\frac{1}{2})({\tau }_j^{\alpha }-\frac{1}{2})+({\tau }_i^{\alpha }+\frac{1}{2})({\tau }_j^{\alpha }+\frac{1}{2})-1]$

References

• G. Khaliullin and V. Oudovenko (1 Dec 1997). "Spin and orbital excitation spectrum in the Kugel-Khomskii model". Physical Review B 56 (22): R14243–R14246. doi:10.1103/PhysRevB.56.R14243. Bibcode: 1997PhRvB..5614243K. http://kotliar6.rutgers.edu/udo/prof/profd/papers/prb56_14243.pdf. 
• K. I. Kugel and D. I. Khomskii (1982). "The Jahn-Teller effect and magnetism: transition metal compounds". Soviet Physics Uspekhi 25 (4): 231. doi:10.1070/PU1982v025n04ABEH004537.