We present an ab initio theory of transport quantities of metallic ferromagnets developed in the framework of the fully relativistic tight-binding linear muffin-tin orbital method. The approach is based on the Kubo-Streda formula for the conductivity tensor, on the coherent potential approximation for random alloys, and on the concept of interatomic electron transport. The developed formalism is applied to pure 3d transition metals (Fe, Co, Ni) and to random Ni-based ferromagnetic alloys (Ni-Fe, Ni-Co, Ni-Mn). High values of the anisotropic magnetoresistance (AMR), found for Ni-rich alloys, are explained by a negligible disorder in the majority spin channel while a change of the sign of the anomalous Hall effect (AHE) on alloying is interpreted as a band-filling effect without a direct relation to the high AMR. The influence of disorder on the AHE in concentrated alloys is investigated as well.
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