Discovering minimum energy pathways via distortion symmetry groups

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 implying 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, which we name the distortion symmetry method, is shown to lead to the discovery of 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. These provide novel physical insights into the nucleation of switching pathways at experimentally observed domain walls in ${\mathrm{Ca}}_{3}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$, as well as how polarization switching can proceed without reversing magnetization in ${\mathrm{BiFeO}}_{3}$. Furthermore, we demonstrate how symmetry-breaking from a highly symmetric pathway can be used to probe the non-Ising (Bloch and N\'eel) polarization components integral to transient states involved in switching in ${\mathrm{PbTiO}}_{3}$. The distortion symmetry method is applicable to a wide variety of physical phenomena ranging from structural, electronic and magnetic distortions, diffusion, and phase transitions in materials.