Another thin-film limit of micromagnetics

Robert Kohn, Valeriy V. Slastikov

Research output: Contribution to journalArticle

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

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Micromagnetics
Variational Problem
Film thickness
Thin Films
Aspect ratio
Anisotropy
Magnetic fields
Thin films
Boundary Integral
Time Constant
Aspect Ratio
Small Parameter
Limiting
Asymptotic Behavior
Magnetic Field

ASJC Scopus subject areas

  • Mechanics of Materials
  • Computational Mechanics
  • Mathematics(all)
  • Mathematics (miscellaneous)

Cite this

Another thin-film limit of micromagnetics. / Kohn, Robert; Slastikov, Valeriy V.

In: Archive for Rational Mechanics and Analysis, Vol. 178, No. 2, 11.2005, p. 227-245.

Research output: Contribution to journalArticle

Kohn, Robert ; Slastikov, Valeriy V. / Another thin-film limit of micromagnetics. In: Archive for Rational Mechanics and Analysis. 2005 ; Vol. 178, No. 2. pp. 227-245.
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