Asymmetric domain walls of small angle in soft ferromagnetic films

Lukas Döring and Radu Ignat

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Submission date: 09. Jan. 2015
Pages: 47
published in: Archive for rational mechanics and analysis, 220 (2016) 2, p. 889-936 
DOI number (of the published article): 10.1007/s00205-015-0944-0
Bibtex
MSC-Numbers: 49S05, 49J45, 78A30, 35B32, 35B36
Keywords and phrases: micromagnetics, transition layer, gamma-convergence, S2-harmonic maps, spectral gap, Eikonal equation
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Abstract:
We focus on a special type of domain walls appearing in the Landau-Lifshitz theory for soft ferromagnetic films. These domain walls are divergence-free S²-valued transition layers that connect two directions in S² (differing by an angle 2θ) 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 θ to 0. As an application, we deduce that a supercritical bifurcation causes the transition from symmetric to asymmetric walls in the full micromagnetic model.