Model of the Interplay of Band J-T Effect with Magnetic Order Mediated by Exchange Interaction

A model calculation is presented with the aim to study the interplay between magnetic and structural transitions. The model consists of an orbitally doubly degenerate conduction band and a periodic array of local moments. The band electrons interact with the local spins via the s-f interaction. The interaction of the band electrons with phonons is introduced by including band Jahn-Teller (J-T) interaction. The model Hamiltonian, including the above terms, is solved for the single particle Greens function. In doing this an ansatz for selfenergy of electrons, which was developed earlier has been utilized. The quasiparticle density of states (QDOS) and hence the orbital populations are calculated treating the ferromagnetism of local moments in the mean field approximation. The critical value of electron-phonon interaction ($G$) for the appearance of the band J-T distortion is higher in the ferromagnetic state. The strain appears at a critical temperature ($T_s$) when $G$ is greater than the critical value. The onset of ferromagnetism at $T_C$ ($<T_s$) arrests the growth of the strain. It is concluded that the magnetization hinders the structural transition. The quasiparticle density of states are presented to interpret these results.