Hall angle in ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ epitaxial films: Comparison between oxygen reduction and Pr doping

We have investigated the temperature dependence of the Hall angle in oxygen-deficient and Pr-doped ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ epitaxial films. The cotangent of the Hall angle follows a universal ${\mathit{T}}^2$ dependence in all superconducting samples, i.e., cot${\mathrm{\theta }}_{\mathit{H}}$=α${\mathit{T}}^2$+C. In the ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ system the slope α increases monotonically with δ while the quantity C remains almost constant. Most important, there exists a linear correlation between ${\mathit{T}}_{\mathit{c}}$ and α. In the ${\mathrm{Pr}}_{\mathit{x}}$ ${\mathrm{Y}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Ba}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$ series both α and C increase with x. Combined with previous studies we conclude that the changes of α and C are related to two distinct mechanisms for suppressing superconductivity. While the increase of C corresponds to a reduction of mobility, the change of α reflects the variation in true carrier density.