Magnetic Skyrmions at Critical Coupling

Bruno Barton-Singer, Calum Ross, Bernd J. Schroers*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

31 Citations (Scopus)
48 Downloads (Pure)


We introduce a family of models for magnetic skyrmions in the plane for which infinitely many solutions can be given explicitly. The energy defining the models is bounded below by a linear combination of degree and total vortex strength, and the configurations attaining the bound satisfy a first order Bogomol’nyi equation. We give explicit solutions which depend on an arbitrary holomorphic function. The simplest solutions are the basic Bloch and Néel skyrmions, but we also exhibit distorted skyrmions and anti-skyrmions as well as line defects and configurations consisting of skyrmions and anti-skyrmions.

Original languageEnglish
Pages (from-to)2259-2280
Number of pages22
JournalCommunications in Mathematical Physics
Issue number3
Early online date20 Jan 2020
Publication statusPublished - May 2020

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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