The anomalous Hall effect (AHE) of epitaxial SrRuO$_3$ films with varying lattice parameters is investigated, and analyzed according to the Berry-phase scenario. SrRuO$_3$ thin films were deposited on SrTiO$_3$ substrates directly, or using intermediate buffer layers, in order to finely control the epitaxial strain. The AHE of the different films exhibits intrinsic features such as the sign change of the Hall resistivity with the temperature, even for small thicknesses of SrRuO$_3$. However, the anomalous Hall conductivity is greatly reduced from its intrinsic value as the carrier scattering is increased when the epitaxial strain is released. We argue that the AHE of fully strained SrRuO$_3$ film with low residual resistivity represents the intrinsic AHE of SrRuO$_3$.
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