Kugel–Khomskii coupling explained

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 = (t ^{2})/(U) \sum _{\langle} \left[ 4 \left(\overrightarrow{S _{i} ⋅ \overrightarrow{S} _{j}\right)\left(\tau} - ^{\alpha} _{i} (1)/(2) \right)\left(\tau ^{\alpha} _{j} - (1)/(2) \right) + \left(\tau ^{\alpha} _{i} + (1)/(2) \right)\left(\tau ^{\alpha} _{j} + (1)/(2) \right) -1 \right].

References

• Spin and orbital excitation spectrum in the Kugel-Khomskii model. https://web.archive.org/web/20110819135507/http://kotliar6.rutgers.edu/udo/prof/profd/papers/prb56_14243.pdf. dead. 19 August 2011. Physical Review B. G. Khaliullin and V. Oudovenko. 1 Dec 1997. 56. 22. R14243–R14246 . 10.1103/PhysRevB.56.R14243. cond-mat/9710070. 1997PhRvB..5614243K . 119360845 .
• 10.1070/PU1982v025n04ABEH004537. K. I. Kugel and D. I. Khomskii. Soviet Physics Uspekhi. 25. 231. 1982. The Jahn-Teller effect and magnetism: transition metal compounds. 4 .