Three-dimensional topological spin textures and their emergent electromagnetic dynamics

Topological spin textures (TSTs) like magnetic skyrmions host intriguing physical properties and are promising candidates for next-general spintronic applications. TSTs in one- and two-dimensions have been extensively investigated. Recently, the interest in studying three-dimensional (3D) TSTs emerges as the addition of a spatial dimension endows spin textures with diverse structures and rich physics therein. Here, I will first discuss the realization of several 3D TSTs including chiral bobber lattice, skyrmionic vortex, and magnetic hopfion via engineering magnetic interactions in chiral magnets. These 3D TSTs give rise to emergent magnetic fields with sophisticated structures in which emergent magneto-multipoles can be further identified. I will show that the emergent magneto-multipoles characterize the nonlinear responses of TSTs. As an example, the nonlinear spin dynamics and electrical transports related to a hopfion will be discussed.