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Archive for Rational Mechanics and Analysis

, Volume 220, Issue 2, pp 889–936 | Cite as

Asymmetric Domain Walls of Small Angle in Soft Ferromagnetic Films

  • Lukas DöringEmail author
  • Radu Ignat
Article

Abstract

We focus on a special type of domain wall appearing in the Landau–Lifshitz theory for soft ferromagnetic films. These domain walls are divergence-free \({\mathbb{S}^2}\)-valued transition layers that connect two directions \({m_\theta^\pm \in \mathbb{S}^2}\) (differing by an angle \({2\theta}\)) and minimize the Dirichlet energy. Our main result is the rigorous derivation of the asymptotic structure and energy of such “asymmetric” domain walls in the limit \({\theta \downarrow 0}\). As an application, we deduce that a supercritical bifurcation causes the transition from symmetric to asymmetric walls in the full micromagnetic model.

Keywords

Domain Wall Eikonal Equation Wall Angle Rigorous Derivation Internal Length Scale 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Lehrstuhl I für MathematikRWTH AachenAachenGermany
  2. 2.Institut de Mathématiques de ToulouseUniversité Paul SabatierToulouseFrance

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