Power-law temperature dependence of the conductivity of disorder-tuned magnetic thin films

Using a specialized high vacuum deposition/characterization chamber, we study the \textit{in situ} temperature-dependent conductivity \textit{$\sigma $}($T$,$R_{0})$~of thin magnetic films (Fe, Gd and Cr) prepared at different stages of disorder where disorder is characterized by the sheet resistance $R_{0}$ measured at $T$~=~5~K. Our observation of power-law dependences of the form, $\sigma $(T,R$_{0})$~=~A~+~BT$^{P}$ , has also been noted in numerous experiments on other materials including indium oxide, 2D Si inversion layers and amorphous NiSi alloys. For our samples, the fitting parameters $A$, $B$ and $P$ vary systematically with increasing disorder. We discuss two regimes of behavior: In the first weak disorder regime, the power-law dependence represents a quantum correction to the classical Boltzmann conductivity due to spin-wave scattering. This contribution can appear either alone (Cr) or simultaneously (Gd) with the well-known logarithmic corrections due to weak localization. In the second regime with greater disorder, we utilize $T$-dependent reduced activation energy plots of \textit{$\sigma $}($T)$ for sets of films spanning a large range of disorder strengths to show that there are narrow regions of disorder strength where pure power-law behavior (A~=~0) dominates.