Skyrmions and Hopfions in 3D Frustrated Magnets

Abstract

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 non-linear sigma model on a squashed sphere which 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 model and the Skyrme model is reconsidered and it is shown that energies of the solitons obey a linear BPS bound. The 3D Skyrmions in the frustrated magnetic model are found and compared to the rational map ansatz.

33 pages, 6 figures; major update with additional numerical results

References in corpus (9)

• The 2020 Skyrmionics Roadmap
• Stationary ring solitons in field theory - knots and vortons
• Creation and confirmation of Hopfions in magnetic multilayer systems
• Skyrmion knots in frustrated magnets
• Skyrmions, instantons and holography
• Knots in the Skyrme-Faddeev model
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• A Smörgåsbord of Skyrmions
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• Magnon dynamics in a Skyrmion-textured domain wall of antiferromagnets
• Microscopic Theory of Nonlinear Hall Effect in Three-dimensional Magnetic Systems
• Static and Dynamics of Twisted Skyrmion Tubes in Frustrated Magnets
• Classification and correlation signatures of chiral spin liquids on the pyrochlore lattice