Metal-insulator transition in the mixed-valence manganites

It is found that the sharp resistivity peak observed near the Curie temperature $T_C$ in the manganites $R_{1-x}{A}_x{\mathrm{MnO}}_3$ is closely correlated to the residual resistivity ${\rho }_0$ of the sample, suggesting that nonmagnetic randomness plays an important role in determining their anomalous properties. Using the one-parameter scaling theory to study the electronic localization due to both the nonmagnetic randomness and the double exchange spin disorder, we show that the sharp resistivity peak is caused by the Anderson metal-insulator (M-I) transition and that ${\rho }_0>{\rho }_c$ (a critical value) is a prerequisite to the occurrence of the M-I transition. $T_C$ as a function of ${\rho }_0$ has also been calculated. These results are in good agreement with experimental measurements.