The anomalous Hall effect (AHE) of ferromagnetic thin films of ${\mathrm{S}\mathrm{r}}_{1-x}{\mathrm{C}\mathrm{a}}_x{\mathrm{R}\mathrm{u}\mathrm{O}}_3$ ($0\le x\le 0.4$) is studied as a function of $x$ and temperature $T$. As $x$ increases, both the transition temperature $T_c$ and the magnetization $M$ are reduced and vanish near $x\sim$ 0.7. For all compositions, the transverse resistivity ${\rho }_H$ varies nonmonotonously with $T$, and even changes sign, thus violating the conventional expression ${\rho }_H=R_{o}B+4\pi R_{s}M\left(T\right)$ ($B$ is the magnetic induction, while $R_o$ and $R_s$ are the ordinary and anomalous Hall coefficients). From the rather complicated data of ${\rho }_H$, we find a scaling behavior of the transverse conductivity ${\sigma }_{xy}$ with $M\left(T\right)$, which is well reproduced by the first-principles band calculation assuming the intrinsic origin of the AHE.

• Received 20 November 2003

DOI:https://doi.org/10.1103/PhysRevLett.93.016602