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  • Open Access

Dipolar Nematic State in Relaxor Ferroelectrics

Yuan-Jinsheng Liu1, Tyler C. Sterling2, and Shi Liu1,3,*

  • 1Department of Physics, School of Science, Westlake University, Hangzhou 310030, China
  • 2Department of Physics, University of Colorado, Boulder, Boulder, Colorado 80309, USA
  • 3Institute of Natural Sciences, Westlake Institute for Advanced Study, Hangzhou 310024, China

  • *Contact author: liushi@westlake.edu.cn
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Phys. Rev. X 16, 021022 – Published 29 April, 2026

DOI: https://doi.org/10.1103/1p6v-lgv7

Abstract

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.

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Popular Summary

Ferroelectric materials change polarization in response to an electric field, with relaxor ferroelectrics being a specific class that is particularly useful for a range of technologies. We discovered a universal organizing principle that governs relaxor ferroelectrics, while also providing a powerful methodological example of how deep neural network-based universal interatomic potentials can uncover fundamental mechanisms across broad chemical spaces. We find a dipolar nematic state, characterized by long-range orientational order without local polar alignment, which marks a fundamental shift from the decades-old paradigm of polar nanoregions and nanodomains for explaining relaxor ferroelectrics. This establishes a unified framework for understanding these complex systems with diverse chemical compositions. Our framework provides a foundational basis for rational design of these functional materials, important for an array of applications from advanced energy technologies to sensing and diagnostics.

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Phys. Rev. X 16, 021022– Published 29 April, 2026
  • Received 2 October 2025
  • Accepted 31 March 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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