The infrared complex magneto-optical conductivity tensor in Ca$_x$Sr$_{1-x}$RuO$_3$ films

We explore the complex longitudinal ($\sigma_{xx}$) and Hall ($\sigma_{xy}$) conductivities, as well as the complex Hall angle ($\theta_H$) in a series of Ca$_x$Sr$_{1-x}$RuO$_3$ films by measuring the infrared ($E$ = 115 - 1400 meV) magnetization-induced complex Faraday and Kerr angles in the 10 - 300 K temperature ($T$) range. The Hall sign reversal with $T$ at 117 meV is observed up to 20\% Ca composition. It is similar to the sign reversal in the dc $\theta_H (T)$. The sign reversal $T$ decreases with increasing Ca composition. The infrared $\sigma_{xy}(E)$ and $\theta_{H}(E)$ show strong $E$ dependence at low energies. As Ca composition increases, the magnitude of the $\mathrm{Re}(\theta_H (E))$ dip decreases while the energy and width of the $\mathrm{Im}(\theta_H (E))$ dip increases. We analyze the results in terms of intrinsic and extrinsic anomalous Hall effect models. This work was supported by the Research Corp. Cottrell Scholar Award (UB), NSF-CAREER-DMR0449899 (UB), and an instrumentation award from the CAS (UB). Oak Ridge Natl. Lab is managed by UT-Battelle, LLC for the U.S. DOE (contract DE-ACO5-00OR22725).