Domain structure of bulk ferromagnetic crystals in applied fields near saturation

Document Type

Article

Publication Date

12-1-2011

Abstract

We investigate the ground state of a uniaxial ferromagnetic plate with perpendicular easy axis and subject to an applied magnetic field normal to the plate. Our interest is in the asymptotic behavior of the energy in macroscopically large samples near the saturation field. We establish the scaling of the critical value of the applied field strength below saturation at which the ground state changes from the uniform to a multidomain magnetization pattern and the leading order scaling behavior of the minimal energy. Furthermore, we derive a reduced sharp interface energy, giving the precise asymptotic behavior of the minimal energy in macroscopically large plates under a physically reasonable assumption of small deviations of the magnetization from the easy axis away from domain walls. On the basis of the reduced energy and by a formal asymptotic analysis near the transition, we derive the precise asymptotic values of the critical field strength at which non-trivial minimizers (either local or global) emerge. The non-trivial minimal energy scaling is achieved by magnetization patterns consisting of long slender needle-like domains of magnetization opposing the applied field. © 2011 Springer Science+Business Media, LLC.

Identifier

84855593979 (Scopus)

Publication Title

Journal of Nonlinear Science

External Full Text Location

https://doi.org/10.1007/s00332-011-9105-2

e-ISSN

14321467

ISSN

09388974

First Page

921

Last Page

962

Issue

6

Volume

21

Grant

DMS-0718027

Fund Ref

National Science Foundation

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