# A reduced model for domain walls in soft ferromagnetic films at the cross-over from symmetric to asymmetric wall types

Lucas Döring; Radu Ignat; Felix Otto

Journal of the European Mathematical Society (2014)

- Volume: 016, Issue: 7, page 1377-1422
- ISSN: 1435-9855

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topDöring, Lucas, Ignat, Radu, and Otto, Felix. "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 016.7 (2014): 1377-1422. <http://eudml.org/doc/277655>.

@article{Döring2014,

abstract = {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 $m^\pm _\alpha \in \mathbb \{S\}^2$ that differ by an angle $2\alpha $. 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 $\mathbb \{S\}^2$ by an angle $2\theta $, and a contribution from two symmetric, logarithmically decaying tails, each of which completes the rotation from angle $\theta $ to $\alpha $ in $\mathbb \{S\}^1$. The angle $\theta $ 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]. Our reduced model is the starting point for the analysis of a bifurcation phenomenon from symmetric to asymmetric domain walls. Moreover, it allows for capturing asymmetric domain walls including their extended tails (which were previously inaccessible to brute-force numerical simulation).},

author = {Döring, Lucas, Ignat, Radu, Otto, Felix},

journal = {Journal of the European Mathematical Society},

keywords = {$\Gamma $-convergence; concentration-compactness; transition layer; bifurcation; micromagnetics; -convergence; concentration-compactness; transition layer; bifurcation; micromagnetics},

language = {eng},

number = {7},

pages = {1377-1422},

publisher = {European Mathematical Society Publishing House},

title = {A reduced model for domain walls in soft ferromagnetic films at the cross-over from symmetric to asymmetric wall types},

url = {http://eudml.org/doc/277655},

volume = {016},

year = {2014},

}

TY - JOUR

AU - Döring, Lucas

AU - Ignat, Radu

AU - Otto, Felix

TI - A reduced model for domain walls in soft ferromagnetic films at the cross-over from symmetric to asymmetric wall types

JO - Journal of the European Mathematical Society

PY - 2014

PB - European Mathematical Society Publishing House

VL - 016

IS - 7

SP - 1377

EP - 1422

AB - 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 $m^\pm _\alpha \in \mathbb {S}^2$ that differ by an angle $2\alpha $. 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 $\mathbb {S}^2$ by an angle $2\theta $, and a contribution from two symmetric, logarithmically decaying tails, each of which completes the rotation from angle $\theta $ to $\alpha $ in $\mathbb {S}^1$. The angle $\theta $ 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]. Our reduced model is the starting point for the analysis of a bifurcation phenomenon from symmetric to asymmetric domain walls. Moreover, it allows for capturing asymmetric domain walls including their extended tails (which were previously inaccessible to brute-force numerical simulation).

LA - eng

KW - $\Gamma $-convergence; concentration-compactness; transition layer; bifurcation; micromagnetics; -convergence; concentration-compactness; transition layer; bifurcation; micromagnetics

UR - http://eudml.org/doc/277655

ER -

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