Faraday rotation and the Hall constant in strongly correlated Fermi systems

We observe that the semiclassical Hall constant for a strongly correlated Fermi system is most directly related to the high frequency Hall conductivity. For the square lattice, the sign of the latter is found to be holelike (while the Fermi surface is electronlike) for fillings close to half, and electronlike for almost empty bands. For the t-J model on the square lattice in two dimensions the change of sign occurs at roughly 1/3 hole filling in good agreement with measurements on ${\mathrm{La}}_{2\mathrm{-}\mathit{x}}$${\mathrm{Sr}}_{\mathit{x}}$${\mathrm{CuO}}_4$ compounds, and is weakly temperature dependent. We suggest that the high frequency Hall constant can be directly measured in a Faraday rotation experiment.