A Reduced Theory for Thin-Film Micromagnetics

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

Research output: Contribution to journalArticlepeer-review


Micromagnetics is a nonlocal, nonconvex variational problem. Its minimizer represents the ground-state magnetization pattern of a ferromagnetic body under a specified external field. This paper identifies a physically relevant thin-film limit and shows that the limiting behavior is described by a certain "reduced" variational problem. Our main result is the Γ-convergence of suitably scaled three-dimensional micromagnetic problems to a two-dimensional reduced problem; this implies, in particular, convergence 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 associated thin-film limit.

Original languageEnglish (US)
Pages (from-to)1408-1460
Number of pages53
JournalCommunications on Pure and Applied Mathematics
Issue number11
StatePublished - Nov 2002

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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