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Using multiple scattering theory, we show that the generally acceptedexpression of transverse resistivity in magnetic systems that host skyrmions,given by the linear superposition of the ordinary (OHE), the anomalous (AHE)and the topological Hall effect (THE), is incomplete and must be amended by anadditional term, the "non-collinear" Hall effect (NHE). Its angular form isdetermined by the magnetic texture, the spin-orbit field of the electrons, andthe underlying crystal structure, allowing to disentangle the NHE from thevarious other Hall contributions. Its magnitude is proportional to thespin-orbit interaction strength. The NHE is an essential term required fordecoding two- and three-dimensional spin textures from transport experiments.

Transverse Transport in Two-Dimensional Relativistic Systems with Non-Trivial Spin Textures