arXiv subjects

Lukas Döring

Publications and source records attributed to Lukas Döring.

3 recordsLinked to original sources

arXiv2016

Compactness results for static and dynamic chiral skyrmions near the conformal limit

We examine lower order perturbations of the harmonic map prob- lem from $\mathbb{R}^2$ to $\mathbb{S}^2$ including chiral interaction in form of a helicity term that prefers modulation, and a potential term that enables decay to a uniform background state. Energy functionals of this type arise in the context of magnetic systems without inversion symmetry. In the almost conformal regime, where these perturbations are weighted with a small parameter, we examine the existence of relative minimizers in a non-trivial homotopy class, so-called chiral skyrmions, strong compactness of almost minimizers, and their asymptotic limit. Finally we examine dynamic stability and compactness of almost minimizers in the context of the Landau-Lifshitz-Gilbert equation including spin-transfer torques arising from the interaction with an external current.

math.AP↗

arXiv2014

Asymmetric domain walls of small angle in soft ferromagnetic films

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 $S^2$-valued transition layers that connect two directions in $S^2$ (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.

math.AP↗

arXiv2013

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

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 $m^\pm \in \mathbb{S}^2$ 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 $\mathbb{S}^2$ 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 $\mathbb{S}^1$. 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]. 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).

math.AP↗