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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2024, Volume 235, Pages 78–86
DOI: https://doi.org/10.36535/2782-4438-2024-235-78-86 (Mi into1310) 		 
Asymptotic formulas for magnetization and chemical potential of ferromagnetic metals at low temperatures

N. B. Melnikova, B. I. Reserb

a Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics
b Institute of Metal Physics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
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DOI: https://doi.org/10.36535/2782-4438-2024-235-78-86
Abstract: 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
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 122021000039-4
This work was supported by the Ministry of Science and Higher Education of the Russian Federation (project No. 122021000039-4).
Document Type: Article
UDC: 51-72, 511.331.1, 537.611.44
MSC: 41A60, 82D40
Language: Russian
Citation: N. B. Melnikov, B. I. Reser, “Asymptotic formulas for magnetization and chemical potential of ferromagnetic metals at low temperatures”, 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, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 235, VINITI, Moscow, 2024, 78–86
Citation in format AMSBIB
\Bibitem{MelRes24}
\by N.~B.~Melnikov, B.~I.~Reser
\paper Asymptotic formulas for magnetization and chemical potential of ferromagnetic metals at low temperatures
\inbook 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
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2024
\vol 235
\pages 78--86
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into1310}
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