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 9
Edward Walton, On the geometry of magnetic Skyrmions on thin films
Journal of Geometry and Physics 156, 103802 103802 (2020) [Crossref]
Martin Speight et al., Skyrmions and spin waves in frustrated ferromagnets at low applied magnetic field
Phys. Rev. B 101, 134420 (2020) [Crossref]
C. Naya et al., Background fields and self-dual Skyrmions
Phys. Rev. D 102, 025007 (2020) [Crossref]
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]
Sven Bjarke Gudnason et al., Near-BPS baby Skyrmions
J. High Energ. Phys. 2020, 62 (2020) [Crossref]
Vladyslav M. Kuchkin et al., Magnetic skyrmions, chiral kinks, and holomorphic functions
Phys. Rev. B 102, 144422 (2020) [Crossref]
Nobuyuki Sawado et al., Compact, charged boson stars and shells in the
gravitating nonlinear sigma model
Phys. Rev. D 102, 045007 (2020) [Crossref]
Bruno Barton-Singer et al., Magnetic Skyrmions at Critical Coupling
Commun. Math. Phys. 375, 2259 (2020) [Crossref]
Ontology / TopicsSee full Ontology or Topics database.
Author / Affiliations: mappings to Contributors and OrganizationsSee all Organizations.
- 1 2 Bernd Schroers