JournalsjemsVol. 16, No. 7pp. 1377–1422

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

  • Lukas Döring

    Max-Planck Institut für Mathematik in den Naturwissenschaften, Leipzig, Germany
  • Radu Ignat

    Université Paul Sabatier, Toulouse, France
  • Felix Otto

    MPI für Mathematik in den Naturwissenschaften, Leipzig, Germany
A reduced model for domain walls in soft ferromagnetic films at the cross-over from symmetric to asymmetric wall types cover
Download PDF

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 mα±S2m^\pm_\alpha\in\mathbb{S}^2 that differ by an angle 2α2\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 S2\mathbb{S}^2 by an angle 2θ2\theta, and a contribution from two symmetric, logarithmically decaying tails, each of which completes the rotation from angle θ\theta to α\alpha in S1\mathbb{S}^1. The angle θ\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).

Cite this article

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. J. Eur. Math. Soc. 16 (2014), no. 7, pp. 1377–1422

DOI 10.4171/JEMS/464