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A reduced theory for thin‐film micromagnetics
Author(s) -
Desimone Antonio,
Kohn Robert V.,
Müller Stefan,
Otto Felix
Publication year - 2002
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3028
Subject(s) - micromagnetics , limit (mathematics) , degenerate energy levels , convergence (economics) , limiting , ground state , magnetization , mathematics , regular polygon , field (mathematics) , ferromagnetism , variational inequality , mathematical analysis , condensed matter physics , physics , magnetic field , quantum mechanics , geometry , pure mathematics , mechanical engineering , engineering , economics , economic growth
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. © 2002 Wiley Periodicals, Inc.