Crystal Distortion in Magnetic Compounds

A theoretical overview of the cooperative Jahn-Teller effect in the insulating phase is given. We obtain an effective Hamiltonian of an interaction between the orbital states of the Jahn-Teller ions through a canonical transformation, which associates each electronic state with a local lattice distortion, and by use of the mean field approximation. The effective Hamiltonian yields a simple unified picture of cooperative distortions of various types. The competing effect of the spin-orbit coupling is discussed also. Electron itinerancy is briefly discussed at the end.