Ferromagnetic Anisotropy and the Itinerant Electron Model

Abstract

The purpose of the present investigation is to explore the possibilities of the "itinerant" or "collective" electron picture in the theory of metals to explain the quenching of orbital angular momentum in solids and, through the introduction of $l$,$s$ coupling, the phenomenon of ferromagnetic anisotropy in cubic crystals. The approach used is that of the Bloch "approximation of tight binding" in the theory of metals, the exchange energy being treated as a Weiss internal field as in the work of Stoner and Slater, and the spin-orbit coupling being introduced as a perturbation. The anisotropy is shown to appear in the fourth approximation, and to have the correct order of magnitude for iron and nickel. The model also predicts the correct sign of $K_1$ in nickel and iron, but this prediction is not entirely satisfactory because computational difficulties prevent the inclusion of all the $d$-wave functions in the calculation. A qualitative discussion of the behavior of iron-nickel alloys is given. The chief weakness of the model is its failure to take account adequately of Russell-Saunders coupling within the atom, and the dependence of many of its predictions on details of the model which are not very well established.