The low temperature magnetization of ferromagnetic metals

The dependence of the magnetization on the temperature T for ferromagnetic metals is obtained in the random phase approximation at low temperatures. The magnetization is expressed as a sum of terms proportional to T 3/2 , T 5/2 and T 2 for weak ferromagnets, which are derived from excitations of spin waves, interactions between spin waves and individual electrons, ordinary excitations of individual electrons and spin fluctuations. For very weak ferromagnets, it is shown that the dominant dependence of the magnetization on T comes from spin fluctuations and it is conjectured that the Curie temperature is inversely proportional to the enhancement factor of the susceptibility.