Infrared Hall conductivity of Na${}_{0.7}$CoO${}_2$

We report infrared Hall conductivity ${\sigma }_{xy}(\omega )$ of Na${}_{0.7}$CoO${}_2$ thin films determined from Faraday rotation angle ${\theta }_F$ measurements. ${\sigma }_{xy}(\omega )$ exhibits two types of hole conduction, Drude and incoherent carriers. The coherent Drude carrier shows a large renormalized mass and Fermi liquid-like behavior of Hall scattering rate, ${\gamma }_H\sim a{T}^2$. The spectral weight is suppressed and disappears at T = 120K. The incoherent carrier response is centered at mid-IR frequency and shifts to lower energy with increasing T. Infrared Hall constant is positive and almost independent of temperature in sharp contrast with the dc-Hall constant.