Extended Kohler's Rule of Magnetoresistance in TaCo$_2$Te$_2$

TaCo$_2$Te$_2$ is recently reported to be an air-stable, high mobility Van der Waals material with probable magnetic order. Here we investigate the scaling behavior of its magnetoresistance. We measured both the longitudinal ($\rho_{xx}$) and Hall ($\rho_{xy}$) magnetoresistivities of TaCo$_2$Te$_2$ crystals in magnetic fields parallel to the c-axis and found that the magnetoresistance violates the Kohler's rule $MR \sim f[H/\rho_0]$ while obeying the extended Kohler's rule $MR \sim f[H/(n_T\rho_0)]$, where $MR \sim [\rho_{xx}(H)-\rho_0]/\rho_0$, $H$ is the magnetic field, $n_T$ is a thermal factor, $\rho_{xx}(H)$ and $\rho_0$ are the resistivities at $H$ and zero field, respectively. While deviating from those of the densities of electrons ($n_e$) and holes ($n_h$) obtained from the two-band model analysis of the magnetoconductivities, the temperature dependence of $n_T$ is close to that of the Hall carrier densities $n_H$ calculated from the slopes of $\rho_{xy}(H)$ curves at low magnetic fields, providing a new way to obtain the thermal factor in the extended Kohler's rule.