Singular stress field induced two-dimensional topological polar structures in SrTiO3: Topological number manipulation via loading modes

Abstract

Topological structures in condensed matter attract much attention of the scientific community due to their unique and significant properties. In contrast to the well-explored topological spin structures such as meron, and skyrmion in ferromagnetic materials, ferroelectrics face challenges in forming topological polar structures due to the absence of a spontaneous driving force. Nevertheless, the coupling effect between polarization and strain (gradient), e.g. piezoelectricity and flexoelectricity, provides a mechanical approach to induce topological polar structures that reflect the intricate features of the strain (gradient) field. This study demonstrates the creation of a topological polar structure through a mode II crack-induced singular stress field in SrTiO3 by using phase-field simulations. Furthermore, under mixed-mode loading of mode I and mode II, alterations in the mode ratio induce a variety of topological structures, including a novel structure (winding number nv=4) that is absent under the single-mode loading. Our study demonstrates that topological strain field can be a general and effective tool to generate and control topological polar structures.