Infrared Hall Effect in High-TcSuperconductors: Evidence for Non-Fermi-Liquid Hall Scattering

Infrared ( $20--120$ and $900--1100{\mathrm{cm}}^{\ensuremath{-}1}$) Faraday rotation and circular dichroism are measured in high- ${T}_{c}$ superconductors using sensitive polarization modulation techniques. Optimally doped ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7}$ thin films are studied at temperatures in the range ( $15lTl300\phantom{\rule{0ex}{0ex}}\mathrm{K}$) and magnetic fields up to 8 T. At $1000{\mathrm{cm}}^{\ensuremath{-}1}$ the Hall conductivity ${\ensuremath{\sigma}}_{\mathrm{xy}}$ varies strongly with temperature in contrast to the longitudinal conductivity ${\ensuremath{\sigma}}_{\mathrm{xx}}$ which is nearly independent of temperature. The Hall scattering rate ${\ensuremath{\gamma}}_{\mathrm{H}}$ has a ${T}^{2}$ temperature dependence but, unlike a Fermi liquid, depends only weakly on frequency. The experiment puts severe constraints on theories of transport in the normal state of high- ${T}_{c}$ superconductors.