Competing `soft' dielectric phases and detailed balance in thin film manganites

Using frequency dependent complex capacitance measurements on thin films of the mixed-valence manganite (La$_{1-y}$Pr$_{y}$)$_{1-x}$Ca$_{x}$MnO$_{3}$, we identify and resolve the individual dielectric responses of two competing dielectric phases. We characterize their competition over a large temperature range, revealing they are in dynamic competition both spatially and temporally. The phase competition is shown to be governed by the thermodynamic constraints imposed by detailed balance. The consequences of the detailed balance model strongly support the notion of an `electronically soft' material in which continuous conversions between dielectric phases with comparable free energies occur on time scales that are long compared with electron-phonon scattering times.