Abstract
The nonlinear response of a ferroic to an applied stimulus (e.g. electric field, mechanical stress) is a fundamental characteristic that underpins a number of technologically significant applications[1-3]. It is also the driving feature in numerous physical phenomena, such as interfacial motion[4,5], spin glasses[6], relaxors[7] and phase transitions[8]. In particular, nonlinearity associated with minor hysteresis loops is an extremely useful avenue to explore energy dissipation and losses in such systems. This knowledge is necessary for the design of future materials with enhanced low-field properties. Quantitatively, the macroscopic nonlinear response of ferroic systems at low to mid-range amplitudes of driving fields is given by the phenomenological Rayleigh law[9], first conceived in 1887 for magnetic materials. Yet, the applicability of the Rayleigh law at small length scales has not been extensively studied. Here, we show using a combination of scanning probe techniques and phase field modeling, that nanoscale response appears to follow a non-Rayleigh regime. However, through statistical analysis, we find that a distribution in the individual responses can lead to directly to Rayleigh-like behavior of the strain on a macroscale. The studies shed light on the nanoscale origins of nonlinear behavior in disordered ferroics.
