Ground states of the generalized Falicov-Kimball model in one and two dimensions

A combination of small-cluster exact-diagonalization calculations and a well-controlled approximative method is used to study the ground-state phase diagram of the spin-one-half Falicov-Kimball model extended by the spin-dependent on-site interaction between localized (f) and itinerant (d) electrons. Both the magnetic and charge ordering are analysed as functions of the spin-dependent on-site interaction (J) and the total number of itinerant (Nd) and localized (Nf) electrons at selected U (the spin-independent interaction between the f and d electrons). It is shown that the spin-dependent interaction (for Nf=L, where L is the number of lattice sites) stabilizes the fully polarized (FP) and partially polarized (PP) state, while the stability region of the non polarized (NP) phase is gradually reduced. The precisely opposite effect on the stability of FP, PP and NP phases has a reduction of Nf. Moreover, the strong coupling between the f and d-electron subsystems is found for both Nf=L as well as Nf < L.