Magnetic isotherms in the band model of ferromagnetism

Calculations are given for the dependence on temperature and magnetic field strength H of the magnetization M of ferromagnetic metals treated on the basis of the itinerant electron model. The spin wave contribution to the low temperature magnetization is considered in the limits of strong and very weak ferromagnetism. For the first limit, problems related to the well-known divergence of the zero field differential susceptibility are briefly discussed. The main part of the paper is concerned with the single particle contributions to the magnetization and associated differential susceptibility for very weak ferromagnetism. A simple equation for the magnetic isotherms is obtained in this limit and shown to be valid over a wide temperature range including 0 $^\circ$K and the Curie temperature. This equation implies that plots of M$^2$ against H/M at various temperatures in this range give a series of parallel straight lines. Recently measured isotherms for the material ZrZn$_2$ are analysed on the basis of the theory, and several characteristic properties of this material are obtained from the analysis.