Breakdown of Matthiessen's Rule in Gold Alloys

The resistivities of alloys of gold with magnetic (Fe, Mn, Co) and nonmagnetic (Ni, Ti) impurities have been measured in the temperature range 0.5-60°K. Using suitable extrapolation formulas for the impurity resistivity, it is found that large departures from Matthiessen's rule occur in these alloys. At low temperatures the deviations are shown to be proportional to the phonon resistivity, or $T^n$, where $4<n<\mathrm{}5\mathrm{}$, in contrast to a recent theory which predicts an initial $T^3$ temperature dependence. The results are interpreted in terms of the differing anisotropies of the relaxation times for phonon and impurity scattering over the Fermi surface.