Dipolar Nematic State in Relaxor Ferroelectrics

Relaxor ferroelectrics exhibit exceptional dielectric and electromechanical properties, yet their microscopic origins remain elusive due to the interplay of hierarchical polar structures and chemical complexity. While models based on polar nanoregions or nanodomains offer valuable phenomenological insights, they often lack the first-principles predictive capability necessary for quantitatively describing functional properties such as piezoelectric coefficients. Here, we use large-scale molecular dynamics simulations, enabled by a universal first-principles-based machine-learning interatomic potential, to investigate atomic-scale polar dynamics in canonical Pb-, Bi-, and Ba-based relaxors. Across all systems, we uncover a universal dipolar nematic state, characterized by long-range orientational order of local polarizations without local alignment, challenging conventional polar-cluster-based paradigms. We introduce a universal order parameter, derived from the skewness of the distributions of the local polarization autocorrelation functions, that captures the thermal evolution of both lead-based and lead-free systems within a single master curve. This nematic order, and its robust structural memory under electric field cycling, underpins key relaxor phenomena, including diffuse phase transition, frequency-dependent dielectric dispersion, and reversible giant piezoelectricity. Our findings establish a unified microscopic framework for relaxors and present a broadly applicable statistical approach to understanding complex disordered materials.