  Transport properties of permalloy doped with V, Co, Pt, and Au are explored
via ab-initio calculations. The Kubo-Bastin formula is evaluated within the
fully relativistic Korringa-Kohn-Rostoker Green function formalism. Finite
temperature effects are treated by means of the alloy analogy model. It is
shown that the fact that the host is disordered and not crystalline has a
profound effect on how the conductivities characterizing the anomalous Hall
effect and the spin Hall effect depend on the dopant concentration. Several
relationships between quantities characterizing charge and spin transport are
highlighted. The decrease of the longitudinal charge conductivity with
increasing doping depends on the dopant type, following the sequence
Co-Au-Pt-V. The dependence of the anomalous Hall and spin Hall conductivities
on the dopant concentration is found to be non-monotonic. Introducing a finite
temperature changes the overall trends significantly. The theoretical results
are compared with available experimental data.
