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

We examine lower order perturbations of the harmonic map problem from R 2 to 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 sy...

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Bibliographic Details
Published in:Calculus of variations and partial differential equations 2017-06, Vol.56 (3), p.1-30, Article 60
Main Authors: Döring, Lukas, Melcher, Christof
Format: Article
Language:English
Subjects:
Analysis
Calculus of Variations and Optimal Control
Optimization
Control
Dynamic stability
Functionals
Helicity
Hypothetical particles
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Particle theory
Systems Theory
Theoretical
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Summary:We examine lower order perturbations of the harmonic map problem from R 2 to 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.
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-017-1172-2