Gauged sigma models and magnetic Skyrmions

Bernd Johannes Schroers

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Abstract

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.
Original languageEnglish
Article number030
JournalSciPost Physics
Volume7
Issue number3
DOIs
Publication statusPublished - 10 Sep 2019

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Schroers, Bernd Johannes. / Gauged sigma models and magnetic Skyrmions. In: SciPost Physics. 2019 ; Vol. 7, No. 3.
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Schroers, BJ 2019, 'Gauged sigma models and magnetic Skyrmions', SciPost Physics, vol. 7, no. 3, 030. https://doi.org/10.21468/SciPostPhys.7.3.030

Gauged sigma models and magnetic Skyrmions. / Schroers, Bernd Johannes.

In: SciPost Physics, Vol. 7, No. 3, 030, 10.09.2019.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Gauged sigma models and magnetic Skyrmions

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PY - 2019/9/10

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N2 - 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.

AB - 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.

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DO - 10.21468/SciPostPhys.7.3.030

M3 - Article

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JO - SciPost Physics

JF - SciPost Physics

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IS - 3

M1 - 030

ER -

Schroers BJ. Gauged sigma models and magnetic Skyrmions. SciPost Physics. 2019 Sep 10;7(3). 030. https://doi.org/10.21468/SciPostPhys.7.3.030

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