Magnetic Orderings and Phase Separations in the Zero-Bandwidth Limit of the Extended Hubbard Model with Intersite Magnetic Interactions

A simple effective model for a description of magnetically ordered insulators is analysed. The tight binding Hamiltonian consists of the effective on-site interaction (U) and intersite magnetic exchange interactions $(J^{z}, J^{xy})$ between nearest neighbours. The phase diagrams of this model have been determined within the variational approach, which treats the on-site interaction term exactly and the intersite interactions within the mean-field approximation. We show that, depending on the values of interaction parameters and the electron concentration, the system can exhibit not only homogeneous phases: (anti-)ferromagnetic $(F_α)$ and nonordered (NO), but also phase separated states $(PS_α: F_α-NO)$.