Mid-infrared Hall conductivity in Ca$_x$Sr$_{1-x}$RuO$_3$ films

We have studied the complex longitudinal ($\sigma_{xx}$) and transverse (Hall, $\sigma_{xy}$) conductivities in a series of Ca$_x$Sr$_{1-x}$RuO$_3$ films by measuring the magnetic field induced polarization changes of mid-infrared (100 - 1000 meV) radiation in the 10~K-300~K temperature range. The infrared $\sigma_{xy}$ shows strong energy dependence and sign changes. We compare the complex magneto-conductivities $\sigma_{xx}$ and $\sigma_{xy}$ [M.-H. Kim, PRB 2007] with dc measurements and with calculations [Z. Fang, Science 2003] of the intrinsic anomalous Hall effect. To test the accuracy of these measurements and to remove the background magneto-optical response of windows and substrates, the magnetic field induced changes in the polarization of transmitted light also were measured in GaAs, ZnSe, and BaF$_2$. 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 Nat. Lab.is managed by UT- Battelle, LLC, for the U.S. DOE (contract DE-ACO5-00OR22725).