Anomalous Hall effect in thin films of ${\mathrm{Pr}}_{0.5}$${\mathrm{Sr}}_{0.5}$${\mathrm{MnO}}_3$

We report on the type and density of charge carriers obtained from Hall-effect measurements in the three different magnetic phases of ${\mathrm{Pr}}_{0.5}$ ${\mathrm{Sr}}_{0.5}$ ${\mathrm{MnO}}_3$ . The field dependence of the Hall resistivity has two contributions of opposite sign: one is related to skew scattering and dominates in low magnetic fields; the other one is due to the Lorentz-force contribution which prevails at higher fields. This second contribution corresponds to a temperature-independent carrier density in the order of 0.8 holes per chemical unit cell. The skew-scattering contribution is related to the susceptibility of the material and is maximum at the transition temperature from the ferro- to the antiferromagnetic state.