Percolation nature of the metal-to-insulator transition in La$_{0.8}$Ba$_{0.2}$MnO$_3$

For a La$_{0.8}$Ba$_{0.2}$MnO$_3$ single crystal, the temperature dependences of its resistivity, magnetization, and differential magnetic susceptibility are studied in the vicinity of the metal-to-insulator transition and near the ferromagnetic-paramagnetic phase transition. The critical temperatures corresponding to these transitions are determined independently from the experiment. These temperatures are found to coincide within $2$–$3\%$. The results are discussed within the framework of percolation theory.