Ferromagnetism of an Electron Gas

Abstract

Magnetism, especially ferromagnetism, of an electron gas is studied on the basis of the Bohm-Pines collective description of electron interactions. Exchange interactions are derived from the screened Coulomb interaction, the interaction obtained from the second-order perturbation of the screened Coulomb interaction, and the weak interaction coming from the interaction between plasma and individual electrons. We assume effective mass for the electron mass. The total energy of the electron gas in the ferromagnetic state is compared with that in the non-ferromagnetic state, and the conditions of ferromagnetism for the electron gas are discussed. The one-electron approximation being adopted, the effective number of magnetic carriers in the electron gas is expressed as a function of temperature and magnetic field. Using the Weiss approximation, we express the spontaneous magnetization at an arbitrary temperature in terms of this effective number and the molecular field obtained from the proper average of the exchange interactions. At low temperatures, the spin-wave approximation is adopted. The Curie temperature, the paramagnetic susceptrbility above the Curie point, and the temperature variation of spontaneous magnetization at low temperatures are determined as functions of the effective mass and the electron mean distance. Using the effective masses determined so as to explain the experimental values of the electronic heats, we make a comparison with experimental values for Ni, Co and Fe. It shows satisfactory agreement in the case of positive hole gas. The strong paramagnetism of γFe, Pd and Pt are also satisfactorily explained, and the inverse of their susceptibilities is well expressed as the sum of a constant term and the term proportional to T² at comparatively lower temperatures.