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arXiv · 2212.03500

Emergent Magneto-multipoles and Nonlinear Responses of a Magnetic Hopfion

Yizhou Liu·Hikaru Watanabe·Naoto Nagaosa
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Abstract

The three-dimensional emergent magnetic field $\textbf{B}^e$ 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 ${T}^e_z = \frac{1}{2}\int (\textbf{r}\times \textbf{B}^e)_z dV$ and emergent magnetic octupole component ${\it Γ}^e =\int [(x^2+y^2)B^e_z - xz B^e_x - y z B^e_y] dV$. The hopfion exhibits nonreciprocal dynamics (nonlinear hopfion Hall effect) under an ac driving current applied along (perpendicular to) the direction of ${T}^e_z$. 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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Yizhou Liu, Hikaru Watanabe, Naoto Nagaosa. 2022-12-07. Emergent Magneto-multipoles and Nonlinear Responses of a Magnetic Hopfion. https://doi.org/10.1103/physrevlett.129.267201

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