Study of ground state phases for spin-1/2 Falicov-Kimball model on a triangular lattice

The spin-dependent Falicov-Kimball model (FKM) is studied on a triangular lattice using numerical diagonalization technique and Monte-Carlo simulation algorithm. Magnetic properties have been explored for different values of parameters: on-site Coulomb correlation $U$, exchange interaction $J$ and filling of electrons. We have found that the ground state configurations exhibit long range Ne\`el order, ferromagnetism or a mixture of both as $J$ is varied. The magnetic moments of itinerant ($d$) and localized ($f$) electrons are also studied. For the one-fourth filling case we found no magnetic moment from $d$- and $f$-electrons for $U$ less than a critical value.Comment: 6 pages, 8 figure

An extended Falicov-Kimball model on a triangular lattice

The combined effect of frustration and correlation in electrons is a matter of considerable interest of late. In this context a Falicov-Kimball model on a triangular lattice with two localized states, relevant for certain correlated systems, is considered. Making use of the local symmetries of the model, our numerical study reveals a number of orbital ordered ground states, tuned by the small changes in parameters while quantum fluctuations between the localized and extended states produce homogeneous mixed valence. The inversion symmetry of the Hamiltonian is broken by most of these ordered states leading to orbitally driven ferroelectricity. We demonstrate that there is no spontaneous symmetry breaking when the ground state is inhomogeneous. The study could be relevant for frustrated systems like $GdI_2$, $NaTiO_2$ (in its low temperature C2/m phase) where two Mott localized states couple to a conduction band.Comment: 6 pages, 8 figure