Evidence for a disorder-dependent localization correction to the anomalous Hall conductance of ultrathin Fe films

We present an experimental study of quantum corrections to the conductivity tensor of thin ferromagnetic films when the disorder is systematically varied. Using the sheet resistance as a measure of disorder, \textit{in situ} magnetotransport studies were performed on a series of thin iron films deposited onto sapphire substrates having sheet resistance $R_{0 }\equiv $~$R_{xx}$(5K) varying over the range 140~$\Omega $ (60{\AA}) to 6250 $\Omega $ ($<$20 {\AA}). For temperatures $T$~$<$~20 K, a logarithmic temperature dependence of the longitudinal $R_{xx}$ and anomalous Hall resistances $R^{AH}_{xy}$ is observed. In the low disorder limit (R$_{0}$ $<$~150~$\Omega )$, we find that relative changes in the anomalous Hall conductivity $\delta $\textit{$\sigma $}$^{AH}_{xy}$/\textit{$\sigma $}$^{AH}_{xy }$exhibit a temperature independent behavior implying that there are no quantum corrections to \textit{$\sigma $}$^{AH}_{xy}$. As disorder increases, a finite logarithmic temperature dependence to $\delta $\textit{$\sigma $}$^{AH}_{xy}$/\textit{$\sigma $}$^{AH}_{xy}$ appears and then evolves toward a universal weak localization correction defined by the equality $\delta $\textit{$\sigma $}$^{AH}_{xy}$/\textit{$\sigma $}$^{AH}_{xy}=-\delta R^{AH}_{xy}$/$R^{AH}_{xy}$ [1]. Thus with increasing disorder, we see a crossover from a region where there are no quantum corrections to \textit{$\sigma $}$^{AH}_{xy}$ to a region dominated by weak localization corrections. These results for iron, where spin is carried by itinerant electrons, will be compared with data on thin films of gadolinium, a localized moment system. [1]. Mitra P. et al. \textit{cond-mat 0606215} (2006)