Temperature Dependence of the Conductivity in (La,Sr)MnO$_3$

Using the Kondo lattice model with classical spins in infinite dimension, conductivity in the perovskite-type $3d$ transition-metal oxide (La,Sr)MnO$_3$ is theoretically studied. Green's functions as well as spontaneous magnetization are obtained exactly on the Bethe lattice as a function of temperature. Conductivity is calculated from the Kubo formula. Below the Curie temperature, resistivity as a function of magnetization is in a good agreement with the experimental data. Anomalous behaviour in the temperature dependence of the optical conductivity observed in (La,Sr)MnO$_3$ is also explained.