A new symmetry-based framework for discovering minimum energy pathways

TL;DR

This paper introduces a symmetry-based framework using distortion symmetry groups to systematically discover minimum energy pathways in physical systems, reducing user bias and revealing hidden pathways.

Contribution

The novel framework leverages group theory to classify and explore all possible pathways, enabling automatic discovery of previously hidden minimum energy paths.

Findings

Discovered new pathways in ferroelectric switching

Systematic classification reduces search bias

Applicable to various physical phenomena

Abstract

Physical systems evolve from one state to another along paths of least energy barrier. Without a priori knowledge of the energy landscape, multidimensional search methods aim to find such minimum energy pathways between the initial and final states of a kinetic process. However in many cases, the user has to repeatedly provide initial guess paths, thus ensuring that the reliability of the final result is heavily user-dependent. Recently, the idea of "distortion symmetry groups" as a complete description of the symmetry of a path has been introduced. Through this, a new framework is enabled that provides a powerful means of classifying the infinite collection of possible pathways into a finite number of symmetry equivalent subsets, and then exploring each of these subsets systematically using rigorous group theoretical methods. The method is shown to lead to the discovery of new, previously hidden pathways for the case studies of bulk ferroelectric switching and domain wall motion in proper and improper ferroelectrics, as well as in multiferroic switching. This approach is applicable to a wide variety of physical phenomena ranging from structural, electronic and magnetic distortions, diffusion, and phase transitions in materials.