Emergent Magneto-multipoles and Nonlinear Responses of a Magnetic Hopfion

Abstract

The three-dimensional emergent magnetic field ${\text{B}}^e$ of a magnetic hopfion gives rise to emergent magneto-multipoles in a similar manner to the multipoles of classical electromagnetic field. Here, we show that the nonlinear responses of a hopfion are characterized by its emergent magnetic toroidal moment $T_z^e=\frac{1}{2}\int (\text{r}\times {\text{B}}^e{)}_{z}dV$ and emergent magnetic octupole component ${\Gamma }^e=\int [(x^2+y^2)B_z^e-xz{B}_x^e-yz{B}_y^e]dV$. The hopfion exhibits nonreciprocal dynamics (nonlinear hopfion Hall effect) under an ac driving current applied along (perpendicular to) the direction of $T_z^e$. The sign of nonreciprocity and nonlinear Hall angle is determined by the polarity and chirality of hopfion. The nonlinear electrical transport induced by a magnetic hopfion is also discussed. This work reveals the vital roles of emergent magneto-multipoles in nonlinear hopfion dynamics and could stimulate further investigations on the dynamical responses of topological spin textures induced by emergent electromagnetic multipoles.

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Cited by in corpus (13)

• Topologically controlled multiskyrmions in photonic gradient-index lenses
• Symmetry analysis with spin crystallographic groups: Disentangling effects free of spin-orbit coupling in emergent electromagnetism
• Magnonic Hall Effect and Magnonic Holography of Hopfions
• Space-Time Hopfion Crystals
• Stability of Hopfions in Bulk Magnets with Competing Exchange Interactions
• Signatures of hidden octupolar order from nonlinear Hall effects
• Emergent magnetic field and vector potential of the toroidal magnetic hopfions
• Magnetic parity violation and parity-time-reversal-symmetric magnets
• Lifetime, collapse and escape paths for hopfions in bulk magnets with competing exchange interactions
• Emergent Magnetic Field and Nonzero Gyrovector of the Toroidal Magnetic Hopfion
• Microscopic Theory of Nonlinear Hall Effect in Three-dimensional Magnetic Systems
• Construction of Hopfion Crystals
• Riemannian geometric classification and emergent phenomena of magnetic textures