Effect of Correlation on the Ferromagnetism of Transition Metals

The wave function for the electrons is investigated when a set of narrow bands (valence states) has its energies within a wide band (conduction states). The valence states are linear combinations of localized states which are attached to each lattice site. The intra-atomic Coulomb and exchange integrals for the localized states are much larger than the bandwidths of the valence states. Some of the narrow bands are neither completely empty nor completely filled. The wave function is therefore expected to be correlated, because it is disadvantageous for the electrons to crowd into the same lattice site, or take up some configuration contrary to Hund's rule. This correlation is important in trasition metals, where it is considered to be the cause of ferromagnetism. The correlated wave function is obtained by applying to the uncorrelated antisymmetrized product of Bloch functions an operator which provides each configuration of localized valence states with an appropriate amplitude and phase factor. The procedure is worked out in detail for the case of few particles (electrons or holes) in the narrow bands with the help of a diagram analysis. The localized orbits of different lattice sites do not have to be orthogonal to on another, and the computational rules are actually simplified thereby. The example of a twofold degenerate band such as the upper part of the 3d band in Ni is treated, and the conditions for the occurrence of ferromagnetism are stated in the case of few 3d holes per lattice site.