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Materials near structural phase transitions find applications in a wide range of devices. Typically, phase transitions are determined macroscopically through measurements of relevant order parameters and related property coefficients. Here, a method for understanding electric field induced phase transitions in ferroelectrically active materials at the nanometer scale via acoustic detection with band-excitation piezoresponse force microscopy (BE-PFM) is introduced. Specifically, the field-induced rhombohedral (R) to tetragonal (T) phase transition in single crystal 0.72PbMg1/3Nb2/3O3-0.28PbTiO3 (PMN-PT) is mapped. It is shown that due to sample heterogeneity, some regions are more prone to the R–T transition, and display signatures in the acquired piezoresponse loops, as well as pronounced softening in the elastic modulus (monitored via the resonant frequency and calibrated with models of cantilever dynamics) that occurs just prior to phase switching. Landau–Devonshire thermodynamic theory confirms the stability of the tetragonal phase under applied fields in PMN-PT, while phase-field modeling suggests that the transition evolves smoothly in the probed volume of the tip, both in agreement with the BE-PFM results. These results confirm the validity and utility of utilizing acoustic changes at phase transitions to detect their onset in nanoscale probed volumes, allowing spatial mapping of their onset with unprecedented resolution.

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.