Scaling of the anomalous Hall effect in SrRuO${}_3$

We measure the anomalous Hall effect (AHE) resistivity ${\rho }_{xy}$ in thin films of the itinerant ferromagnet SrRuO${}_3$. At low temperatures, the AHE coefficient $R_s$ varies with ${\rho }_{xx}^2$, and at higher temperatures, $R_s$ reaches a peak and then changes sign just below $T_c$. We find that for all films studied $R_s$ scales with resistivity in the entire ferromagnetic phase. We attribute the observed behavior to the contribution of the extrinsic side jumps mechanism and the intrinsic Karplus-Luttinger (Berry phase) mechanism including the effect of finite scattering rates.