Extended frequency dependence of the infrared Hall Effect in electron-doped high T$_c$ cuprate Pr$_{2-x}$Ce$_x$CuO$_4$

Although the infrared longitudinal conductivity $\sigma_{xx}$ in Pr$_{2-x}$Ce$_x$CuO$_4$ can be modeled using a Drude model which includes density wave (DW) excitations at low temperatures and low doping concentrations (Zimmers, PRB 2004), the infrared Hall conductivity $\sigma_{xy}$ exhibits behavior (Zimmers, cond-mat/0510085) that is not consistent with this model even outside of the DW phase. By measuring the rotation and ellipticity of the polarization of transmitted light through a sample in magnetic fields up to 7 T, the infrared Faraday angle is determined in the 115 to 366 meV (930-3000 cm$^{-1}$) energy range. The Faraday angle is closely related to the Hall angle and $\sigma_{xy}$, which provide a sensitive test of the many-body interactions that could lead to deviations from Drude behavior. Three samples with doping levels of $x =$ 0.12, 0.15 and 0.18 are probed at temperatures ranging from 50 K to 300 K. Non-Drude behavior is observed in the Faraday angle, which also changes sign as a function of frequency and temperature from electron-like to hole-like as expected from the hole-like underlying Fermi surface. Supported by the Research Corporation Cottrell Scholar Award (UB), NSF CAREER Award (UB), NSF DMR-0352735 (UMCP) and NSF DMR-0303112 (UMCP).