Hall Effect in the Presence of Strong Spin-Disorder Scattering

The Hall mobility ${\mu }_H$ of a single hole in a Mott-Hubbard band of a magnetic insulator is considered using a path formulation of the atomic limit of the Hubbard model. It is shown that within a generalization of the retraceable-path approximation, the Hall mobility and the drift mobility ${\mu }_D$ are essentially equal at high temperatures compared with the bandwidth, but that the Hall mobility becomes small compared to the drift mobility as the temperature is lowered. The ratio $\frac{{\mu }_H}{{\mu }_D}$ becomes proportional to the ratio of the temperature to the bandwidth at low temperatures.