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 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, which we name the distortion symmetry method (DSM), 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. These provide novel physical insights into the nucleation of switching pathways at experimentally observed domain walls in Ca3Ti2O7, as well as how polarization switching can proceed without reversing magnetization in BiFeO3. Furthermore, we demonstrate how symmetry-breaking from a highly symmetric pathway can be used to probe the non-Ising (Bloch and Néel) polarization components integral to transient states involved in switching in PbTiO3. 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.

Suppressing the ferroelectric switching barrier in hybrid improper ferroelectrics

“…(We refer to phases where dipole moments of each slab are zero as 'nonpolar'.) Many of these phases are observed to emerge in various A 3 B 2 O 7 oxides under biaxial strain or equivalent doping, and are also shown to be important as intermediate states in the coherent switching of polarization 5,16,[20][21][22]33 . This is in addition to single-tilt systems observed, for example, at finite temperature 7 .…”

“…It was recognized as early on as in the first HIF paper that this makes different switching pathways possible, and that the corresponding energy barriers can be tuned by strain 2 . Later, the work of Nowadnick and Fennie 21 analyzed the possible roles of different switching mechanisms, and Munro et al used the idea of distortion symmetry groups to identify other switching pathways 22,44 . Since then, the energetics of switching in various HIF compounds have been studied, for example in ref.…”

“…HIFs are shown to undergo interesting structural phase transitions under strain as well 20 , but there is no detailed study of the switching behavior of HIFs under biaxial strain. The original study on HIFs 2 showed that the lowest energy switching path and energy (which is correlated with the coercive field) is strain dependent, but the recent works that illustrate the richness of possible switching paths make it necessary to re-evaluate the polarization switching behavior of strained HIFs 21,22 .…”

Infrared nano-spectroscopy of ferroelastic domain walls in hybrid improper ferroelectric Ca3Ti2O7

“…Ferroelastic walls in Ca 3 Ti 2 O 7 are linear and separate different structural twin domains [20]. Because the boundaries connect domains with different spontaneous strain states, mechanical compatibility conditions determine their orientation [24,26,27]. These ferroelastic walls are also 90 • ferroelectric walls.…”

Implementation of distortion symmetry for the nudged elastic band method with DiSPy

“…al. 2 , where MEPs overlooked by conventional techniques are consistently and systematically generated through symmetryadapted perturbations made possible by distortion symmetry. These results agree with and extend MEPs found previously by other researchers using approaches involving physical intuition and single structure perturbations.…”