Origin of the large recoverable electrostrain in relaxor ferroelectrics

We investigate the mechanisms responsible for the distinct characteristics of certain relaxor ferroelectrics, which display pinched polarization hysteresis loops and recoverable electrostrains, in contrast to the rectangular-like polarization hysteresis loops and irrecoverable butterfly-shaped electrostrains observed in typical ferroelectrics. Despite the large number of experimental reports on these materials, the origin of their recoverable electrostrains has remained elusive until now. Using a phase-field model, we study a doped ferroelectric system, considering both local electric fields and local phase-transition temperature variations induced by the local compositional heterogeneity. The directions of local electric fields are randomly distributed along one of the four directions of the spontaneous polarizations in the system. The resulting phase diagram reveals the existence of both normal ferroelectrics and relaxor ferroelectrics, with pinched polarization hysteresis loops and recoverable electrostrains appearing only in the latter. Our simulations shed light on the crucial role of strong local electric fields along spontaneous polarization directions caused by point defects in facilitating nucleation of domains with polarization along the same direction. This, in turn, explains the recoverability of the polarization and electrostrain in certain relaxors, as these local fields can help restore the initial domain-structure, polarization, and strain. These findings provide new insights into the origin of recoverable electrostrains in relaxors, which could have implications for the design of relaxors with large recoverable electrostrains.