We examine the problem of two holes in an otherwise filled band, or two electrons in an empty band, by the method of configuration interaction, using Wannier functions, asking which state lies lower, the triplet or singlet. If the triplet lies lower, it would indicate that the spins set themselves parallel, favoring ferromagnetism. We find that if the band is nondegenerate, the singlet will always lie lower, so that ferromagnetism requires a degenerate band, such as the fivefold degenerate $d$ band. With a degenerate band ferromagnetism can arise under some circumstances, provided the band is not too broad. The cause of the ferromagnetism is an intra-atomic exchange effect, causing the two electrons or holes to prefer to align themselves with parallel spin when they happen to lie on the same atom. The model leads to a treatment of correlation, showing that with increasing interatomic distance the likelihood of finding the two electrons or holes on the same atom decreases, vanishing at infinite internuclear distance. The ferromagnetic interaction depends both on an intra-atomic exchange integral, which persists to infinite distance, and the probability of finding the electrons or holes on the same atom, which vanishes in the limit.

Close

PrevNext

View figure in article