  According to earlier first-principles calculations, the spin-disorder
contribution to the resistivity of rare-earth metals in the paramagnetic state
is strongly underestimated if Matthiessen's rule is assumed to hold. To
understand this discrepancy, the resistivity of paramagnetic Fe and Gd is
evaluated by taking into account both spin and phonon disorder. Calculations
are performed using the supercell approach within the linear muffin-tin orbital
method. Phonon disorder is modeled by introducing random displacements of the
atomic nuclei, and the results are compared with the case of fictitious
Anderson disorder. In both cases the resistivity shows a nonlinear dependence
on the square of the disorder potential, which is interpreted as a resistivity
saturation effect. This effect is much stronger in Gd than in Fe. The
non-linearity makes the phonon and spin-disorder contributions to the
resistivity non-additive, and the standard procedure of extracting the
spin-disorder resistivity by extrapolation from high temperatures becomes
ambiguous. An "apparent" spin-disorder resistivity obtained through such
extrapolation is in much better agreement with experiment compared to the
results obtained by considering only spin disorder. By analyzing the spectral
function of the paramagnetic Gd in the presence of Anderson disorder, the
resistivity saturation is explained by the collapse of a large area of the
Fermi surface due to the disorder-induced mixing between the electronic and
hole sheets.
