We developed an original fully relativistic ab initio theory of anomalous Hall effect for disordered ferromagnetic alloys with simple and complex lattice structure. The theory was applied to elementary ferromagnets (Fe, Co, Ni), their alloys (NiFe, FeSi), to partially ordered FePt alloys and to selected Heusler alloys in a good agreement with experiment. Anomalous Hall effect in Heusler alloys is important for prospective applications in spintronics.
The anomalous Hall resistivity ρxy vs. longitudinal resistivity ρxx for all values of LRO parameter S. The dependence ρxy/ρxx vs. ρxx is shown in the inset to demonstrate a quadratic relation of ρxy as a function of ρxx valid over a broad range of LRO parameters S. The empty circles denote the experimental data. The experimental values of LRO parameter S are attached to points for clarity.