On the Nature of the Magnetic Couplings in Transitional Metals

Abstract

This paper suggests a simple model of magnetism for transitional metals which is somewhat intermediate between Heisenberg's atomic model and Stoner's band model. Starting with a paramagneticd band, described in the tight-binding approximation and with equal population of both spin directions, exchange interactions are introduced. They are shown able to produce localized magnetic moments, by attracting locally the (traveling) electrons of one spin direction at the expense of the others. A simple condition is obtained for such magnetic moments to appear spontaneously;it is shown to be fulfilled in many transitional metals. With the use of general results obtained recently by the authors and by others, it is then shown that each of these magnetic moments, if produced alone, should extend over a certain region in space, and should be surrounded by “fringes” of spin polarization with an alternating sign. The size of the central region and the wavelength of the fringes are related to an average wavelength of the Fermi electrons, and thus to the filling of the d band. The sign and the strength of the coupling between magnetic moments centered on neighboring atoms is deduced from the extent of their overlap. The magnetic couplings observed in the first transitional series are shown to be in fair agreement with this model. The conditions prevailing in the other series and in alloys are also discussed. This model is compared to those put forward by Zener, Yoshida, and Slater. It is emphasized that it leads to the equivalent of chemical exchange integrals between the moments of neighboring atoms without losing the characteristic features of the d band, especially its high electronic specific heat and Pauli paramagnetism.