Geodesic
A reduced model for domain walls in soft ferromagnetic films at the cross-over from symmetric to asymmetric wall types
Journal of the European Mathematical Society, Tome 16 (2014) no. 7, pp. 1377-1422

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We study the Landau-Lifshitz model for the energy of multi-scale transition layers – called "domain walls'' – in soft ferromagnetic films. Domain walls separate domains of constant magnetization vectors mα±​∈S2 that differ by an angle 2α. Assuming translation invariance tangential to the wall, our main result is the rigorous derivation of a reduced model for the energy of the optimal transition layer, which in a certain parameter regime confirms the experimental, numerical and physical predictions: The minimal energy splits into a contribution from an asymmetric, divergence-free core which performs a partial rotation in S2 by an angle 2θ, and a contribution from two symmetric, logarithmically decaying tails, each of which completes the rotation from angle θ to α in S1. The angle θ is chosen such that the total energy is minimal. The contribution from the symmetric tails is known explicitly, while the contribution from the asymmetric core is analyzed in [7].
DOI : 10.4171/jems/464
Classification : 49-XX, 35-XX, 78-XX
Keywords: Γ-convergence, concentration-compactness, transition layer, bifurcation, micromagnetics 
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     author = {Lukas D\"oring and Radu Ignat and Felix Otto},
     title = {A reduced model for domain walls in soft ferromagnetic films at the cross-over from symmetric to asymmetric wall types},
     journal = {Journal of the European Mathematical Society},
     pages = {1377--1422},
     publisher = {mathdoc},
     volume = {16},
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     year = {2014},
     doi = {10.4171/jems/464},
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Lukas Döring; Radu Ignat; Felix Otto. A reduced model for domain walls in soft ferromagnetic films at the cross-over from symmetric to asymmetric wall types. Journal of the European Mathematical Society, Tome 16 (2014) no. 7, pp. 1377-1422. doi: 10.4171/jems/464

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