Acoustic Detection of Phase Transitions at the Nanoscale

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 0.72PbMg_1/3Nb_2/3O₃-0.28PbTiO₃ (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 detection of phase transitions in nanoscale volumes remains a significant challenge. Here, a method utilizing the contact resonant frequency shift of a conductive atomic force microscope tip is used to quantitatively discern the presence and spatial localization of field-induced phase transitions in a prototypical relaxor-ferroelectric, and is successfully modeled by thermodynamic theory.