Metallic ferromagnetism in a single-band model: Effect of band filling and Coulomb interactions

A single-band tight-binding model with on-site repulsion and nearest-neighbor exchange interaction has been proposed as a simple model to describe metallic ferromagnetism. Here we extend previously obtained exact-diagonalization studies for a one-dimensional 1/2-filled band system to other band fillings, and consider the effect of including various other Coulomb matrix elements in the Hamiltonian that are expected to be of appreciable magnitude in real materials. Results of exact diagonalization and mean-field theory for the one-dimensional case are compared. As the band filling decreases from 1/2, the tendency to ferromagnetism is found to decrease in exact diagonalization, while mean-field theory predicts the opposite behavior. A nearest-neighbor Coulomb repulsion term is found to suppress the tendency to ferromagnetism; however, the effect becomes small for large on-site repulsion. A pair hopping interaction enhances the tendency to ferromagnetism. A nearest-neighbor hybrid Coulomb matrix element breaks electron-hole symmetry and causes metallic ferromagnetism to occur preferentially for more than half-filled rather than less-than-half-filled bands in this model. Mean-field theory is found to yield qualitatively incorrect results for the effect of these interactions on the tendency to ferromagnetism. The implications of these results for the understanding of ferromagnetism in real materials is discussed.