Domain structure of bulk ferromagnetic crystals in applied fields near saturation

TL;DR

This paper analyzes the asymptotic behavior of the ground state and energy scaling of a uniaxial ferromagnetic plate near saturation, identifying critical fields and domain patterns using reduced sharp-interface models.

Contribution

It introduces a reduced sharp-interface energy model to precisely describe the asymptotic behavior of minimal energy and critical field values in large ferromagnetic plates near saturation.

Findings

Critical applied field scaling for domain pattern transition

Asymptotic energy behavior characterized by needle-like domains

Derived explicit critical field values for pattern emergence

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 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 branched domain 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