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Boundary Vortices for Thin Ferromagnetic Films

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Abstract.

We consider a simplified version of the micromagnetic energy for ferromagnetic samples in the shape of thin films. We study (a) stationary, stable critical points, and (b) solutions of the corresponding Landau-Lifshitz equation under a stability condition. We determine the asymptotic behaviour of solutions of these variational problems in the thin film limit. A characteristic property of the limit is the development of Ginzburg-Landau-type vortices at the boundary.

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Acknowledgments.

This work was carried out while I was at the Max Planck Institute for Mathematics in the Sciences in Leipzig. It was supported by the Deutsche Forschungsgemeinschaft through SPP 1095. I would like to thank S. Müller and A. Desimone for their interest and many fruitful discussions.

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  1. Courant Institute, 251 Mercer Street, New York, NY, 10012, USA

    Roger Moser

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  1. Roger Moser
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Correspondence to Roger Moser.

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Communicated by F. Otto

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Moser, R. Boundary Vortices for Thin Ferromagnetic Films. Arch. Rational Mech. Anal. 174, 267–300 (2004). https://doi.org/10.1007/s00205-004-0329-2

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