Electronic scattering off a magnetic hopfion

Abstract

We study scattering of itinerant electrons off a magnetic hopfion in a three-dimensional metallic magnet described by a magnetization vector $\mathbf{S}(\mathbf{r})$. A hopfion is a confined topological soliton of $\mathbf{S}(\mathbf{r})$ characterized by an {\it emergent} magnetic field $B_{\gamma }(\mathbf{r})\equiv {\epsilon }_{\alpha \beta \gamma }\mathbf{S}\cdot ({\nabla }_{\alpha }\mathbf{S}\times {\nabla }_{\beta }\mathbf{S})/4\ne 0$ with vanishing average value $⟨\mathbf{B}(\mathbf{r})⟩=0$. We evaluate the scattering amplitude in the opposite limits of large and small hopfion radius $R$ using the eikonal and Born approximations, respectively. In both limits, we find that the scattering cross-section contains a skew-scattering component giving rise to the Hall effect within a hopfion plane. That conclusion contests the popular notion that the topological Hall effect in non-collinear magnetic structures necessarily implies $⟨\mathbf{B}(\mathbf{r})⟩\ne 0$. In the limit of small hopfion radius $pR\ll 1$, we expand the Born series in powers of momentum $p$ and identify different expansion terms corresponding to the hopfion anisotropy, toroidal moment, and skew-scattering.

8+4 pages, 3+1 figures

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Cited by in corpus (8)

• Magnetic particle-antiparticle creation and annihilation
• Emergent Magneto-multipoles and Nonlinear Responses of a Magnetic Hopfion
• Magnonic Hall Effect and Magnonic Holography of Hopfions
• Magnetic parity violation and parity-time-reversal-symmetric magnets
• Microscopic Theory of Nonlinear Hall Effect in Three-dimensional Magnetic Systems
• Static and Dynamics of Twisted Skyrmion Tubes in Frustrated Magnets
• Riemannian geometric classification and emergent phenomena of magnetic textures
• Construction of Hopfion Crystals