  Magnetic textures like skyrmions and domain walls coupled to itinerant
electrons give rise to rich transport phenomena such as anomalous Hall effect
and nonreciprocal current. An interesting case is when the transport
coefficient is related to the global (or topological) property of the magnetic
texture, e.g., skyrmion and domain wall numbers. Such phenomena are also
interesting from applications, in which the transport phenomena are potential
probes for electrically detecting magnetic textures in nano-scale devices.
Here, we show that an anomalous Hall effect proportional to the net magnetic
monopole charge occurs from skew scattering when the magnetic texture couples
to itinerant electrons in a non-centrosymmetric system with spin-orbit
interaction. This mechanism 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 also discuss the relation between the magnetic
texture contributing to the anomalous Hall effect and the crystal symmetry. The
results demonstrate rich features arising from the interplay of spin-orbit
interaction and magnetic textures and their potential for detecting various
magnetic textures in nanoscale devices.
