Another Thin-Film Limit of Micromagnetics |
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Authors: | Email author" target="_blank">Robert V?KohnEmail author Valeriy V?Slastikov |
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Institution: | (1) Courant Institute, 251 Mercer Street, New York, NY, 10012 |
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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) w2/l2≫(t/l)| log (t/l)| or (b) w2/l2∼(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. |
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