Sign reversal of the Hall effect in superconducting $\mathrm{Y}{\mathrm{Ba}}_2{\left({\mathrm{Cu}}_{1-x}{\mathrm{Ni}}_x\right)}_3{\mathrm{O}}_{7-\delta }$ single crystals

For detwinned Ni-doped single crystals of $\mathrm{Y}{\mathrm{Ba}}_2{\left({\mathrm{Cu}}_{1-x}{\mathrm{Ni}}_x\right)}_3{\mathrm{O}}_{7-\delta }$ with $x=0.005, 0.015, \mathrm{and} 0.035$, we have measured the in-plane longitudinal and Hall resistivities. The residual resistivity $\rho \mathrm{}(T=0\mathrm{})\mathrm{}$ extrapolated from $\rho \mathrm{}\left(T\right)\mathrm{}$ above $T_c$ increases with Ni concentration $x$, indicating that the elastic scattering rate of conduction carriers $\frac{1}{\tau \mathrm{}(T=0\mathrm{})\mathrm{}}$ is increased. In the mixed state just below the superconducting transition temperature $T_c$, a sign reversal of the Hall resistivity is observed. The in-plane Hall conductivity ${\sigma }_{\mathrm{xy}}$ is found to be the sum of two terms, $\frac{C_1}{H}$ and $C_{2}H$. $C_1$ and $C_2$ are independent of field as in pure $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$, but dependent on both temperature and Ni concentration. The temperature dependences of $C_1$ and $C_2$ weaken with increasing Ni concentration.