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:

[math]\displaystyle{ H=\frac{t^2}{U}\sum_{\langle i,j\rangle}\left[4\left(\overrightarrow{S_i}\cdot\overrightarrow{S_j}\right)(\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\right] }[/math]

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.