Exploring physics of ferroelectric domain walls via Bayesian analysis of atomically resolved STEM data

• Published in: Nature communications Vol. 11; no. 1; p. 6361
• Main Authors: Nelson, Christopher T., Vasudevan, Rama K., Zhang, Xiaohang, Ziatdinov, Maxim, Eliseev, Eugene A., Takeuchi, Ichiro, Morozovska, Anna N., Kalinin, Sergei V.
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 11.12.2020; Nature Publishing Group; Nature Portfolio
• Subjects: 147/137; 639/301/119/996; 639/766/119/544; 639/766/530/2804; 639/766/930/12; Bayesian analysis; Bismuth compounds; characterization and analytical techniques; CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Domain walls; Ferroelectric domains; Ferroelectric materials; Ferroelectricity; ferroelectrics and multiferroics; Humanities and Social Sciences; Mathematical models; MATHEMATICS AND COMPUTING; multidisciplinary; Order parameters; Parameter estimation; Parameter sensitivity; Physics; Science; Science (multidisciplinary); Statistical inference; statistical physics; surfaces, interfaces and thin films; Uncertainty
• ISSN: 2041-1723; 2041-1723
• DOI: 10.1038/s41467-020-19907-2

The physics of ferroelectric domain walls is explored using the Bayesian inference analysis of atomically resolved STEM data. We demonstrate that domain wall profile shapes are ultimately sensitive to the nature of the order parameter in the material, including the functional form of Ginzburg-Landau-Devonshire expansion, and numerical value of the corresponding parameters. The preexisting materials knowledge naturally folds in the Bayesian framework in the form of prior distributions, with the different order parameters forming competing (or hierarchical) models. Here, we explore the physics of the ferroelectric domain walls in BiFeO 3 using this method, and derive the posterior estimates of relevant parameters. More generally, this inference approach both allows learning materials physics from experimental data with associated uncertainty quantification, and establishing guidelines for instrumental development answering questions on what resolution and information limits are necessary for reliable observation of specific physical mechanisms of interest. Ferroelectric domain wall profiles can be modeled by phenomenological Ginzburg-Landau theory, with different candidate models and parameters. Here, the authors solve the problem of model selection by developing a Bayesian inference framework allowing for uncertainty quantification and apply it to atomically resolved images of walls. This analysis can also predict the level of microscope performance needed to detect specific physical phenomena.