Infrared Hall effect in the electron-doped high- T_c cuprate Pr_2−xCe_xCuO₄

The electron-doped cuprate Pr_2−xCe_xCuO₄ is investigated using infrared magneto-optical measurements. The optical Hall conductivity σ_xy(ω) shows a strong doping, frequency, and temperature dependence consistent with the presence of a temperature- and doping-dependent coherent backscattering amplitude which doubles the electronic unit cell and produces a spin density wave state. At low temperatures, the data suggest that the coherent backscattering vanishes at a quantum critical point inside the superconducting dome and is associated with the commensurate antiferromagnetic order observed by other workers. Using a spectral weight analysis, we have further investigated the Fermi-liquid-like behavior of the overdoped sample. The observed Hall-conductance spectral weight is about ten times less than that predicted by band theory, raising the fundamental question of the effect of Mott and antiferromagnetic correlations on the Hall conductance of strongly correlated materials.