- Letter
Anomalous Hall effect by chiral spin textures in the two-dimensional Luttinger model
Phys. Rev. B 109, L060407 – Published 22 February, 2024
DOI: https://doi.org/10.1103/PhysRevB.109.L060407
Abstract
Long-range magnetic textures, such as magnetic skyrmions, give rise to rich transport properties in magnetic metals, such as the anomalous Hall effect related to spin chirality, aka topological Hall effect. In addition to the topological Hall effect, recent studies on noncentrosymmetric magnets have found that the spin-orbit interaction of itinerant electrons gives rise to unique contributions related to spin chirality, i.e., the chiral Hall effect. In this paper, we discuss that the spin-orbit interaction has a distinct yet significant effect on the anomalous Hall effect related to spin chirality in centrosymmetric magnets. Using a scattering theory method, we find that the anomalous Hall effect related to scalar spin chirality in a two-dimensional Luttinger model is suppressed by more than one order of magnitude compared to the quadratic dispersion, and the contributions similar to the chiral Hall effect in Rashba models vanishes. At the same time, a unique term related to vector spin chirality occurs, which gives different Hall conductivities for the Bloch and Neel skyrmions, thereby enabling detection of the skyrmion helicity. The striking differences demonstrate the rich effect of crystal symmetry on the chirality-related anomalous Hall effect in materials with strong spin-orbit interactions.
