2021/04/19 by Sergey S. Pershoguba, Domenico Andreoli, Jiadong Zang · 1 citation
Physics and Astronomy · #cond-mat.mes-hall
paper · pdf · doi:10.1103/physrevb.104.075102
published as Phys. Rev. B 104, 075102 (2021) · 8+4 pages, 3+1 figures
arxiv created 2021/04/19 · arxiv updated 2021/08/11
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 Bγ(\mathbf r) ≡ εαβγ \mathbf S⋅(∇α\mathbf S× ∇β\mathbf S)/4 ≠ 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)⟩ ≠ 0. In the limit of small hopfion radius pR ≪ 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.