Non-linear Hall resistivity in overdoped Pr$_{1.82}$Ce$_{0.18}$CuO$_{4 + \delta}$ electron-doped cuprate

The Hall coefficient $R_\mathrm{H}$ as a function of temperature for Pr$_{2-x}$Ce$_{x}$CuO$_{4}$ (PCCO) at $x = 0.17$ shows two sign changes between 0 and 300K that can be explained qualitatively using the two-carrier model. Using this two-carrier model, one predicts the presence of a nonlinear $B^{3}$ contribution to the Hall resistivity $\rho_{yx}$ that should be easily observed when the linear coefficient $R_{H}$ is approaching zero. We present the measurement of this nonlinear Hall resistivity for overdoped PCCO thin films at $x=0.18$. We show that this weak nonlinear term persists at all temperatures despite being dominated by the linear term ($R_{H}B$). It is strongly temperature dependent and, analyzing it with the two-carrier model, we conclude that the density of electron carriers is larger than the hole density, but that the hole mobility is larger than that of the electrons. This nonlinear Hall resistivity should be observable for similar materials for which $R_{H}(T)$ goes through sign reversals as does overdoped PCCO.