Anomalous Hall effect sensitive to magnetic monopoles and skyrmion helicity in spin-orbit coupled systems

Abstract

Magnetic textures, such as skyrmions and domain walls, engender rich transport phenomena, including anomalous Hall effect and nonlinear response. In this work, we discuss an anomalous Hall effect proportional to the net magnetic monopole charge and dependent on the skyrmion helicity that occurs by askew scattering in a noncentrosymmetric two-dimensional magnet. This mechanism, which arises from the spin-orbit interaction, gives rise to a finite anomalous Hall effect in a ferromagnetic domain wall whose spins rotate in the $xy$ plane despite no out-of-plane magnetic moment. We show that the presence and absence of the monopole contribution is related to crystal symmetry, which gives a guideline for finding candidate materials beyond the Rashba model. The results demonstrate the rich features arising from the interplay of spin-orbit interaction and magnetic textures, and their potential for detecting various magnetic textures in micrometer devices.