Hall effect in the mixed state of ${\mathrm{Y}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Pr}}_{\mathit{x}}$${\mathrm{Ba}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ single crystals

The magnetic field and the temperature dependence of the mixed-state Hall effect have been measured on single crystals in the system ${\mathrm{Y}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Pr}}_{\mathit{x}}$ ${\mathrm{Ba}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ (0.0≤x≤0.3) with the magnetic field perpendicular to the ab plane and the current flowing in the ab plane. A sign change of the Hall resistivity is observed at low Pr concentrations, with the negative Hall resistivity disappearing between the concentrations of x=0.1 and x=0.2. The field dependence of the Hall resistivity for various Pr concentrations can be qualitatively explained by incorporating a finite pinning force ${\mathbf{F}}_{\mathit{p}}$ in the Nozières and Vinen (NV) model.