Model of charge and magnetic order formation in itinerant electron systems

We propose a simple model of charge and/or magnetic order formation in systems containing both localized and itinerant electrons coupled by the on-site, spin-dependent interaction that represents Coulomb repulsion and Hund's rule (a generalized Falicov-Kimball model). Ground state properties of the model are analyzed on the square lattice on a basis of the phase diagrams that have been constructed rigorously, but in a restricted configurational space. For intermediate values of the coupling constants there are considerable ranges of itinerant electron densities where phases with complex charge and magnetic structures of the localized electrons have lower energy than the simplest antiferromagnetic and ferromagnetic ones. A strong tendency towards the antiferromagnetic coupling between spins of localized electrons has been observed close to half-filling for any density of localized electrons, including situations where the magnetic ions are diluted. For small band fillings the ferromagnetic coupling between localized spins is predominant.