Decoding of complex magnetic structures from Hall-effect measurements*

It is generally accepted that the Hall response of complex
spin-textures is given in terms of the linear superposition of the ordinary (OHE),
the anomalous (AHE) and the topological Hall effect (THE). This addition is not
questioned and is experimentally used to relate Hall responses to magnetic textures.
Here, using a simple and transparent multiple scattering approach, we show that
this relation is incomplete. We introduce a missing contribution, the non-collinear Hall
effect (NHE). The angular form of this term depends on the underlying crystal structure.
The presence of the NHE may results in a substantial Hall response in non-collinear
magnets without invoking the presence of non-coplanar spin textures or magnetic
skyrmions and enables the decoding of exotic non-collinear magnetic textures that
have been observed in itinerant magnets [1,2].
[1] A. Neubauer et al. PRL 102, 186602 (2009)
[2] Takashi Kurumaji et al. Science 365, 6456 (2019)