Correlation between piezoresponse nonlinearity and hysteresis in ferroelectric crystals at the nanoscale

The nonlinear response of a ferroic to external fields has been studied for decades, garnering interest for both understanding fundamental physics, as well as technological applications such as memory devices. Yet, the behavior of ferroelectrics at mesoscopic regimes remains poorly understood, and the scale limits of theories developed for macroscopic regimes are not well tested experimentally. Here, we test the link between piezo-nonlinearity and local piezoelectric strain hysteresis, via AC-field dependent measurements in conjunction with hysteresis measurements with varying voltage windows on (K,Na)NbO₃ crystals with band-excitation piezoelectric force microscopy. The correlation coefficient between nonlinearity amplitude and the amplitude during hysteresis loop acquisition shows a clear decrease with increasing AC bias. Further, correlation of polynomial fitting terms from the nonlinear measurements with the hysteresis loop area reveals that the largest correlations are reserved for the quadratic terms, which is expected for irreversible domain wall motion contributions that impact both piezoelectric behavior as well as minor loop formation. This study suggests applicability at local length scales of fundamental principles of Rayleigh behavior, with associated implications for future nanoscale ferroic devices.