Nanoscale Origins of Nonlinear Behavior in Ferroic Thin Films

The nonlinear response of a ferroic to an applied fi eld has been studied through the phenomenological Rayleigh Law for over a hundred years. Yet, despite this, the fundamental physical mechanisms at the nanoscale that lead to macroscopic Rayleigh behavior have remained largely elusive, and experimental evidence at small length scales is limited. Here, it is shown using a combination of scanning probe techniques and phase fi eld modeling, that nanoscale piezoelectric response in prototypical Pb(Zr,Ti)O 3 fi lms appears to follow a distinctly non-Rayleigh regime. Through statistical analysis, it is found that an averaging of local responses can lead directly to Rayleigh-like behavior of the strain on a macroscale. Phase-fi eld modeling confi rms the twist of the ferroelastic interface is key in enhancing piezoelectric response. The studies shed light on the nanoscale origins of nonlinear behavior in disordered ferroics.