Percolative Conduction in the Half-Metallic-Ferromagnetic and Ferroelectric Mixture of(La,Lu,Sr)MnO3

The immiscibility between rhombohedral ${\mathrm{La}}_{5/8}{\mathrm{Sr}}_{3/8}{\mathrm{MnO}}_3$ and hexagonal ${\mathrm{LuMnO}}_3$ leads to a $\mu \mathrm{m}$-scale heterogeneous mixture of half-metallic-ferromagnetic and insulating-ferroelectric phases. Electronic conduction of the mixture exhibits nearly ideal percolation behavior in the paramagnetic state with a threshold of 0.224(5) metal volume fraction and a resistivity scaling exponent $t=2.1\pm 0.1$, consistent with the predicted universal behavior of classical percolation. However, far below $T_{\mathrm{C}}$, $t$ increases to $2.4\pm 0.1$, probably resulting from intergrain tunneling. Therefore, this system represents a unique example of the temperature-induced crossover from universal to nonuniversal behavior of $t$.