We define a gauged non-linear sigma model for a 2-sphere valued field and a $SU(2)$ connection on an arbitrary Riemann surface whose energy functional reduces to that for critically coupled magnetic skyrmions in the plane, with arbitrary Dzyaloshinskii-Moriya interaction, for a suitably chosen gauge field. We use the interplay of unitary and holomorphic structures to derive a general solution of the first order Bogomol'nyi equation of the model for any given connection. We illustrate this formula with examples, and also point out applications to the study of impurities.
Cited by 3
Masaru Hongo et al., Instantons in chiral magnets
Phys. Rev. B 101, 104417 (2020) [Crossref]
Ricardo Zarzuela et al., Stability and dynamics of in-plane skyrmions in collinear ferromagnets
Phys. Rev. B 101, 054405 (2020) [Crossref]
Bruno Barton-Singer et al., Magnetic Skyrmions at Critical Coupling
Commun. Math. Phys., (2020) [Crossref]
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- 1 2 Bernd Schroers