Infrared longitudinal and Hall conductivity of SrRuO$_3$ and Ga$_{1-x}$Mn$_x$As films obtained by magneto-polarization measurements*

By measuring the changes in the polarization of transmitted (Faraday effect) and reflected (Kerr effect) mid-infrared (MIR: 115-366 meV) light induced by an external magnetic field, we determine the complete complex magneto-conductivity tensor in SrRuO$_3$ and Ga$_{1-x}$Mn$_x$As films. Thick film transmission and reflection equations are used to convert the measured complex Faraday and Kerr angles into the MIR complex longitudinal conductivity $\sigma_{xx}$ and the complex transverse (Hall) conductivity $\sigma_{xy}$. The resulting $\sigma_{xx}$ is consistent with the values obtained from conventional transmittance and reflectance measurements on these films, as well as the results from Kramers-Kronig analysis of reflectance measurements on similar films.