Skyrmions and hopfions in three-dimensional frustrated magnets

Carlos Naya, Daniel A Schubring, Mikhail Shifman, Zhentao Wang

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A model of an inversion-symmetric frustrated spin system is introduced which hosts three-dimensional extensions of magnetic skyrmions. In the continuum approximation, this model reduces to a nonlinear sigma model on a squashed sphere that has a natural interpolating parameter. At one limit of the parameter, the model reduces to a frustrated magnetic system earlier considered by Sutcliffe as a host to hopfions, and in the other limit, it becomes very similar to the 3D Skyrme model. To better understand the relation between hopfions and 3D skyrmions, a model interpolating between the Faddeev-Niemi and the Skyrme models is reconsidered and it is shown that energies of the solitons obey a linear Bogomol'nyi-Prasad-Sommerfeld bound. The 3D skyrmions in the frustrated magnetic model are found and compared to the rational map ansatz.

Original languageEnglish (US)
Article number094434
JournalPhysical Review B
Issue number9
StatePublished - Sep 1 2022

Bibliographical note

Funding Information:
We would like to acknowledge Cristian Batista for helpful discussions. D.S. was supported in part by the U of MN Doctoral Dissertation Fellowship. During the writing of this paper, Z.W. was supported by the U.S. Department of Energy through the University of Minnesota Center for Quantum Materials, under Award No. DE-SC-0016371. C.N. was supported by the Olle Engkvist foundation, Grant No 204-0185. M.S. is supported in part by DOE Grant No. DE-SC0011842.

Publisher Copyright:
© 2022 American Physical Society.


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