Ferromagnetism in the Transition Metals

Abstract

An outline is given of a proposed theory for the behavior of electrons in transition metals. This is based on considering corrections to a supposed self-consistent band calculation which arise from the intra-atomic electron-electron Coulomb repulsion. The resulting interaction energy is considered to occur only between electrons with similar Bloch wave functions and to depend on the shape of those functions. An important element in the discussion is the one-electron $s-d$ admixture term in the Hamiltonian which arises when the $d$ band and conduction band are worked out using different potentials. The behavior of dilute alloys of non-transition metals in transition metals can then be understood in terms of the hybridized $s-d$ band. It is suggested that the effect of the nontransition impurity (Cu, Zn, etc., are here to be regarded as transition metals) is to lower the conduction band, thus changing the $s-d$ band. In terms of a theory parallel to the localized-moment calculation of Anderson, this reduces the magnetic moment by moving the spin-up and spin-down $d$ bands with respect to each other. Because of the increased $s$-like character, the true $s-d$ electrons have become more mobile and this reduces the effectiveness of the exchange splitting. It is shown that this model leads to reasonable agreement with the experimental reduction in the saturation magnetization. It is further shown that if the interaction energy is regarded as a dominant factor in determining which is the stable lattice structure in these metals, one can obtain correct ranges of stability as the electron-per-atom ratio changes for all three transition series. The second and third series are supposed to be nonferromagnetic because of a large band width and small interaction energy. The paper is entirely qualitative, such calculations as are presented being of an illustrative nature.