Infrared anomalous Hall effect: Faraday and Kerr measurements in calcium strontium ruthenium(VI) oxide

The dc anomalous Hall effect (AHE) is observed in many itinerant ferromagnets, but its origin which can be intrinsic or extrinsic is still not resolved in many cases. We have measured the complex Faraday and Kerr angles, the complex Hall angle, as well as the complex Hall conductivity in CaxSr1-xRuO3 films in the mid- and near-infrared energy range (115 -- 1400 meV) to study the infrared AHE in the itinerant ferromagnets (x < 0.7) and paramagnets (x > 0.75). To obtain high accuracy and high sensitivity infrared Hall measurements, a unique magneto-polarimetry system along with a number of new calibration and analysis techniques have been developed. We have explored the magnetic field, the temperature, and probe energy dependence of the infrared Hall responses in CaxSr 1-xRuO3. Strong features in probe energy and temperature dependence of the AHE appears and systematic changes in Ca-doping dependence of the AHE are shown. For SrRuO3, the energy dependence of the AHE above 200 meV is consistent with predictions from a band calculation for the intrinsic AHE. Temperature dependence of the AHE below 200 meV is similar to the dc AHE and shows the Hall sign reversal which can be explained by either extrinsic or intrinsic AHE models. For CaxSr1-xRuO 3, Ca doping makes a significant change in the Hall conductivity sigma xy at low energies, but sigmaxy is less sensitive to Ca composition at higher energies. The infrared Hall sign reversals with temperature occur only in the 0% -- 13% Ca compositions, which is narrower than the range at dc (0% -- 30%). These results will provide the opportunity to test the band structure of CaxSr 1-xRuO3 and theoretical models of the energy dependent AHE.