Skew scattering dominated anomalous Hall effect in $Co_{x} (MgO)_{100-x}$ granular thin films

We investigated the mechanism(s) of the anomalous Hall effect (AHE) in magnetic granular materials by fabricating 100-nm-thick thin films of $Co_{x} (MgO)_{100-x}$ with a Co volume fraction of $34 \le x \le 100$ using co-sputtering at room temperature. We measured the temperature dependence of longitudinal resistivity ($\rho_{XX}$) and anomalous Hall resistivity ($\rho_{AHE}$) from 5 K to 300 K in all samples. We found that when x decreases from 100 to 34, the values of $\rho_{XX}$ and $\rho_{AHE}$ respectively increased by about four and three orders in magnitude. By linearly fitting the data, obtained at 5 K, of anomalous Hall coefficient ($R_{s}$) and of $\rho_{XX}$ to $log({R}_{s})~ \gamma log(\rho_{XX})$, we found that our results perfectly fell on a straight line with a slope of $\gamma$ = 0.97±0.02. This fitting value of $\gamma$ in ${R}_{s} \varpropto \rho_{XX}$ clearly suggests that skew scattering dominated the AHE in this granular system. To explore the effect of the scattering on the AHE, we performed the same measurements on annealed samples. We found that although both$\rho_{XX}$ and ($\rho_{AHE}$) significantly reduced after annealing, the correlation between them was almost the same, which was confirmed by the fitted value, $\gamma$ =0.99±0.03. These data strongly suggest that the AHE originates from the skew scattering in Co-MgO granular thin films no matter how strong the scatterings of electrons by the interfaces and defects is. This observation may be of importance to the development of spintronic devices based on MgO.