Asymptotic formulas for magnetization and chemical potential of ferromagnetic metals at low temperatures

Explicit expressions for the coefficients in the $T^2$-law for the magnetic moment and chemical potential in Stoner's theory are obtained in the case of an arbitrary electron density of states. A generalization of Stoner's ferromagnetism criterion is given in terms of spin-polarized electron densities of states. The proof is based on the asymptotic expansion of the integral with the Fermi function, which was previously used for free electrons.