A reduced theory for thin-film micromagnetics

Antonio DeSimone, Robert V. Kohn, Stefan Müller, and Felix Otto

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Submission date: 08. Nov. 2001
Pages: 62
published in: Communications on pure and applied mathematics, 55 (2002) 11, p. 1408-1460 
DOI number (of the published article): 10.1002/cpa.3028
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Abstract:
Micromagnetics is a nonlocal, nonconvex variational problem. Its minimizer represents the ground state magnetization pattern of a fer- romagnetic body under a specified external field. This paper identifies a physically relevant thin film limit, and shows that the limiting be- havior is described by a certain "reduced" variational problem. Our main result is the -convergence of suitably scaled 3D micromagnetic problems to a 2D reduced problem; this implies, in particular, conver- gence of minimizers for any value of the external field. The reduced problem is degenerate but convex; as a result it determines some (but not all) features of the ground state magnetization pattern in the as- sociated thin film limit.