Magnetoresistance ofYBa2Cu3O7in the cold spots model

We calculate the in-plane magnetoresistance $\Delta {\rho }_{\mathrm{xx}}/{\rho }_{\mathrm{xx}}$ of ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_7$ in a magnetic field applied perpendicular to the ${\mathrm{CuO}}_2$ planes for the “cold spots” model. In this model, the electron relaxation time ${\tau }_2\propto {1/T}^2$ at small regions on the Fermi surface near the Brillouin zone diagonals is much longer than the relaxation time ${\tau }_1\propto 1/T$ at the rest of the Fermi surface ($T$ is temperature). In qualitative agreement with the experiment, we find that Kohler’s rule is strongly violated, but the ratio $\Delta {\rho }_{\mathrm{xx}}/{\rho }_{\mathrm{xx}}{\tan }^2{\theta }_H,$ where $\tan {\theta }_H$ is the Hall angle, is approximately temperature independent. We find the ratio is about 5.5, which is of the same order of magnitude as in the experiment.