A Reduced Theory for Thin-Film Micromagnetics

Antonio DeSimone, Robert Kohn, Stefan Müller, Felix Otto

Research output: Contribution to journalArticle

Abstract

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
Volume55
Issue number11
DOIs
StatePublished - Nov 2002

Fingerprint

Micromagnetics
Ground state
Thin Films
Magnetization
Minimizer
Thin films
External Field
Ground State
Nonconvex Variational Problems
Limiting Behavior
Variational Problem
Imply
Three-dimensional

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

A Reduced Theory for Thin-Film Micromagnetics. / DeSimone, Antonio; Kohn, Robert; Müller, Stefan; Otto, Felix.

In: Communications on Pure and Applied Mathematics, Vol. 55, No. 11, 11.2002, p. 1408-1460.

Research output: Contribution to journalArticle

DeSimone, Antonio ; Kohn, Robert ; Müller, Stefan ; Otto, Felix. / A Reduced Theory for Thin-Film Micromagnetics. In: Communications on Pure and Applied Mathematics. 2002 ; Vol. 55, No. 11. pp. 1408-1460.
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