Magnetic ordering of itinerant systems; the role of kinetic exchange   interaction
  The possibility of ferromagnetic ordering is revisited in the band model. The coherent potential approximation decoupling has been used for the strong on-site Coulomb interaction. The driving forces towards the ferromagnetism are the on-site and inter-site molecular fields coming from different Coulomb interactions. Another driving force is the lowering of the kinetic energy with growing magnetic moment coming from the dependence of the hopping integrals on occupation of the neighboring sites involved in hopping. This effect is described by the hopping interaction, $\Delta t$, and by what we call the exchange-hopping interaction, $t_{ex}$. The exchange-hopping interaction, which is the difference in hopping integrals for different occupation of neighboring lattice sites, acts in analogous way to the Hund's magnetic exchange interaction. The results are calculated for semi-elliptic density of states (DOS) and for the distorted semi-elliptic DOS with the maximum around the Fermi energy. They show a natural tendency towards the magnetic ordering at the end of the 3d row for the DOS with maximum density around the Fermi energy, when the hopping integrals grow with the occupation of the neighboring lattice sites. 
G. G\'orski and J. Mizia