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Asymptotic behavior of the Landau—Lifshitz model of ferromagnetism

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Abstract

According to the classical theory of Weiss, Landau, and Lifshitz, on a microscopic scale a ferromagnetic body is magnetically saturated (i.e., |M| =ℳ: constant) and consists of regions in which the magnetization is uniform, separated by thin transition layers. Any stationary configuration corresponds to a minimum point of an energy functional in which a small parameterε is present. The asymptotic behavior asε → 0 is studied here. It is easy to see that any sequence of minimizers contains a subsequenceM εj that converges to a fieldM. By means of a Γ-limit procedure it is shown that this fieldM is a minimizer of a new functional containing a term proportional to the area of the surfaces separating different domains of uniform magnetization. TheC 1,γ-regularity of these surfaces, forγ < 1/2, is also proved under suitable assumptions for the external magnetic field.

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Authors and Affiliations

  1. Dipartimento di Matematica, Universitá di Trento, 38050, Povo (Trento), Italy

    G. Anzellotti & A. Visintin

  2. Scuola Normale Superiore, 56100, Pisa, Italy

    S. Baldo

  3. Istituto di Analisi Numerica del C.N.R., Pavia, Italy

    A. Visintin

Authors
  1. G. Anzellotti
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  2. S. Baldo
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  3. A. Visintin
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Communicated by David Kinderlehrer

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Anzellotti, G., Baldo, S. & Visintin, A. Asymptotic behavior of the Landau—Lifshitz model of ferromagnetism. Appl Math Optim 23, 171–192 (1991). https://doi.org/10.1007/BF01442396

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  • DOI: https://doi.org/10.1007/BF01442396

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