Heisenberg exchange Hamiltonian from narrow energy band theory

Abstract

An effect is described, to be called the band shift effect, which arises from the interplay of strong correlation theory and the first-order energy shift of a band calculated by means of tight-binding theory. This leads to a spin dependence of the energy which, exactly in the half-filled band case and approximately otherwise, leads to a Heisenberg exchange Hamiltonian. The coupling constant from this effect is calculated for nickel and found to be of the order of magnitude observed empirically. In the presence of this effect, it is found necessary to use a condition for ferromagnetism based on the free energy of the system rather than on the occupation numbers for different electron spins The half-filled band case usually leads (in the limit of infinitely strong correlation) to ferromagnetism, without regard to the shape of the band.