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


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.


Domain Wall Eikonal Equation Wall Angle Rigorous Derivation Internal Length Scale 
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© 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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