Applying Distortion Symmetries to the Calculation of Minimum Energy Pathways in Ferroelectric Switching

The nudged elastic band method is a commonly used algorithm to determine the minimum energy path between the initial and final state of a kinetic process. However, these calculated pathways are critically dependent on the choice of the initial path, necessitating many trials with different starting points in order to obtain accurate minimum energy pathway predictions. Most commonly, these have been produced by applying perturbations to individual structures along the initial path. Recently, a better approach to the problem has been formulated by considering a path’s distortion symmetry group.[1] Using these, exploration of additional pathways is enabled through the generation of symmetry-adapted perturbations to the initial path. This new approach has been implemented into a Python module, and the open-source Quantum-ESPRESSO software package. It has then been used in the calculation of minimum energy pathways for bulk polarization switching and domain-wall motion in various ferroelectric materials including Ca₃Ti₂O₇, BiFeO₃, and LiNbO₃. The method not only successfully reproduces previously reported paths, but has also led to the discovery of hidden pathways that reveal a variety of notable physical phenomena.

[1] VanLeeuwen, B. K. & Gopalan, V. Nat. Comm. 6, 8818 (2015).