Bridging experiment and theory of relaxor ferroelectrics at the atomic scale with multislice electron ptychography

Introducing structural and/or chemical heterogeneity into otherwise ordered crystals can dramatically alter material properties. Lead-based relaxor ferroelectrics are a prototypical example, with decades of investigation having connected chemical and structural heterogeneity to their unique properties. While theory has pointed to the formation of an ensemble of ``slush''-like polar domains, the lack of direct, spatially resolved volumetric data comparable to simulations presents a significant challenge in measuring the spatial distribution and correlation of local chemistry and structure with the physics underlying relaxor behavior. Here, we address this challenge through three-dimensional volumetric characterization of the prototypical relaxor ferroelectric \ce{0.68Pb(Mg$_{1/3}$Nb$_{2/3}$)O3-0.32PbTiO$_3$} using multislice electron ptychography. Direct comparison with molecular dynamics simulations reveals the intimate relationship between the polar structure and unit-cell level charge imbalance induced by chemical disorder. Further, polar nanodomains are maintained through local correlations arising from residual short-range chemical order. Acting in concert with the chemical heterogeneities, it is also shown that compressive strain enhances out-of-plane correlations and ferroelectric-like order without affecting the in-plane relaxor-like structure. Broadly, these findings provide a pathway to enable detailed atomic scale understanding for hierarchical control of polar domains in relaxor ferroelectric materials and devices, and also present significant opportunities to tackle other heterogeneous systems using complementary theoretical and experimental studies.