Geodesic
Asymptotic formulas for magnetization and chemical potential of ferromagnetic metals at low temperatures
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXV", Voronezh, April 26-30, 2024, Part 1, Tome 235 (2024), pp. 78-86

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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.
Keywords: magnetization, temperature dependence, ferromagnetic metals, Fermi integral, Sommerfeld expansion, Riemann zeta function 
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N. B. Melnikov; B. I. Reser. Asymptotic formulas for magnetization and chemical potential of ferromagnetic metals at low temperatures. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXV", Voronezh, April 26-30, 2024, Part 1, Tome 235 (2024), pp. 78-86. http://geodesic.mathdoc.fr/item/INTO_2024_235_a6/