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Comptes Rendus Mathématique
Volume 340, n° 1
pages 81-86 (janvier 2005)
Doi : 10.1016/j.crma.2004.10.022
Received : 21 October 2004 ;  accepted : 27 October 2004
Films courbés minces ferromagnétiques
Curved ferromagnetic thin films

Hamdi Zorgati a, b
a Laboratoire Jacques-Louis Lions, université Pierre et Marie Curie, boîte courrier 187, 75252 Paris cedex 05, France 
b CEREMADE, CNRS UMR 7534, université Paris-Dauphine, place du Maréchal de Lattre de Tassigny, 75775 Paris cedex 16, France 


On considère un film courbé mince ferromagnétique non soumis à un champ magnétique externe. Le comportement du film est décrit par une énergie dépendant de la magnétisation du film vérifiant la contrainte de saturation. Cette énergie se compose dʼune partie dʼénergie magnétostatique induite et dʼun terme dʼénergie ayant comme densité une fonction, comprenant lʼénergie dʼéchange et lʼénergie anisotrope. Nous étudions le comportement de cette énergie quand lʼépaisseur du film courbé tend vers zéro. Nous prouvons avec des arguments de Γ -convergence que les minimiseurs de lʼénergie totale convergent vers les minimiseurs dʼune énergie locale dépendant dʼune magnétisation bidimensionnelle. Pour citer cet article : H. Zorgati, C. R. Acad. Sci. Paris, Ser. I 340 (2005).

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We consider a thin curved ferromagnetic film not submitted to an external magnetic field. The behavior of the film is described by an energy depending on the magnetization of the film verifying the saturation constraint. The energy is composed of an induced magnetostatic energy and an energy term with density including the exchange energy and the anisotropic energy. We study the behavior of this energy when the thickness of the curved film goes to zero. We show with Γ -convergence arguments that the minimizers of the free energy converge to the minimizers of a local energy depending on a two-dimensional magnetization. To cite this article: H. Zorgati, C. R. Acad. Sci. Paris, Ser. I 340 (2005).

The full text of this article is available in PDF format.

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