As I understand the anomalous Hall effect, in materials with a strong spin-orbit coupling, the intrinsic deflection effect is dominant over the side jump and skew scattering effects. In the intrinsic deflection effect, the electrons acquire an anomalous velocity due to the Berry curvature (which is not null because there is a break in the spatial inversion symmetry). The anomalous Hall effect is present in ferromagnetic materials, since the DOS is separated into two (one higher than the other), so there are more spin up electrons than spin down electrons, which travel in curved paths to different sides depending on the spin. As there is more spin up than spin down, this will generate a non-zero Hall potential difference. In the spin Hall effect, a non-magnetic material that has the same number of spin up and down electrons is used. Thus, the Hall potential is zero, but there is a current that flows due to the spins. I have a question:
Can the anomalous Hall effect only be applied to magnetic materials? Can't be applied to non-magnetic materials?
Thank you for your help.