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 language||English (US)|
|Number of pages||19|
|Journal||Archive for Rational Mechanics and Analysis|
|State||Published - Nov 2005|
ASJC Scopus subject areas
- Mathematics (miscellaneous)
- Mechanical Engineering