Another thin-film limit of micromagnetics

Robert V. Kohn, Valeriy V. Slastikov

Research output: Contribution to journalArticlepeer-review

Abstract

We consider the variational problem of micromagnetics for soft, relatively small thin films with no applied magnetic field. In terms of the film thickness t, the diameter l and the magnetic exchange length w, we study the asymptotic behavior in the small-aspect-ratio limit t/l → 0, when either (a) w 2/l 2 ≫(t/l)|log(t/l)| or (b) w 2/l 2 ∼ (t/l)|log(t/l)|. Our analysis builds on prior work by Gioia & James and Carbou. The limiting variational problem is much simpler than 3D micromagnetics; in particular it is two-dimensional and local, with no small parameters. The contribution of shape anisotropy reduces, in this limit, to a constant times the boundary integral of (m•n) 2.

Original languageEnglish (US)
Pages (from-to)227-245
Number of pages19
JournalArchive for Rational Mechanics and Analysis
Volume178
Issue number2
DOIs
StatePublished - Nov 2005

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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