Metallic ferromagnetism in a single-band model

It is pointed out that certain off-diagonal matrix elements of the Coulomb interaction between Bloch electrons are likely to play a fundamental role in metallic ferromagnetism. These matrix elements lower the energy when the two interacting electrons are in states of opposite bonding character, thus favoring a situation where up and down electron bands have different fillings. It is proposed that this effect can explain the occurrence of metallic ferromagnetism in solids, without band degeneracy playing an essential role.