Magnetoresistance of YBa2Cu3O7 in the "cold spots" model

We calculate the in-plane magnetoresistance $\mathrm{\Delta }{\rho }_{xx}\mathrm{/}{\rho }_{xx}$ of YBa${}_2$Cu${}_3$O${}_7$ in a magnetic field applied perpendicular to the $Cu{O}_2$ planes for the ``cold spots’’ model. In this model, the electron relaxation time ${\tau }_2\propto 1\mathrm{/}{T}^2$ at small regions on the Fermi surface near the Brillouin zone diagonals is much longer than the relaxation time ${\tau }_1\propto 1\mathrm{/}T$ 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 $\mathrm{\Delta }{\rho }_{xx}\mathrm{/}{\rho }_{xx}{\tan }^2{\theta }_H$, 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.