Emergence of non-trivial polar topologies hidden in singular stress field in SrTiO₃: topological strain-field engineering

Abstract

Discovery of non-trivial topological structures in condensed matters holds promise in novel technological paradigms. In contrast to ferromagnetics, where a variety of topological structures such as vortex, meron, and skyrmion have been discovered, only few topological structures can exist in ferroelectrics due to the lack of non-collinear interaction like the Dzyaloshinskii-Moriya interaction in ferromagnetics. Here, we demonstrate that polarization structures with a wide range of topological numbers (winding number n from −3 to +1) can be mechanically excited and designed by the mode-I singular stress field formed near the crack-tip in incipient ferroelectric SrTiO 3 . Our phase-field simulations based on Ginzburg-Landau theory successfully reveals that the near-tip polar topology is driven by the flexoelectric coupling with intense strain gradient at the tip, while a variety of the far-field topological structures is triggered by a collaboration between the electrostrictive and flexoelectric effects. The strain (gradient) field analysis further shows that the unexpected topological characters are implied in the singular stress field, which develops a variety of polar topologies near the crack tip. Therefore, our work provides a novel insight into the unusual interplay between mechanical-and ferroelectric-topologies, i.e. 'topological strain-field engineering', which paves the way to the mechanical design of functional topologies in the matter.

Strain‐Driven Mixed‐Phase Domain Architectures and Topological Transitions in Pb1−xSrxTiO3 Thin Films

“…[26] The different regions including: 1) pure c/a domains, 2) a 1 /a 2 droplets in a c/a matrix, 3) connected-labyrinth structure of c/a domains, 4) broken-labyrinth structure of c/a domains, 5) c/a droplets in an a 1 /a 2 matrix, and 6) pure a 1 /a 2 domains can be identified using this method. This approach provides novel insight into the strain-field tuning of domain structures and ferroelectric topological nanostructures and helps open the door for the new field of "topological strain-field engineering" [62] and "topological defectronics." [63,64] Building from these observations, we focused specifically on the continuous-labyrinth structure which showed local ordering up to a certain finite length and also exhibited the most types of pattern defects in its as-grown state.…”

Discovery of Ultrasmall Polar Merons and Rich Topological Phase Transitions: Defects Make 2D Lead Chalcogenides Flexible Topological Materials

“…This 2D polarization distribution is also a nontrivial polarization structure that can be characterized by the topological quantity of winding number 1. [ 44 ] Therefore, polar topological phase transitions (i.e., polaron meron‐skyrmion and 2D topology of the polarization field) can also be manipulated by the vertical electric field and mechanical strain.…”

Theoretical Understanding of Polar Topological Phase Transitions in Functional Oxide Heterostructures: A Review

“…One of the first theoretical predictions of the topological polar phase was made in the 2000s, where the polar vortex phase was predicted in the low dimensional ferroelectric system (i.e., PZT nanodisks, nanorods, and thin films) via ab initio calculations (Figure 3a). [ 101,102 ] Consequently, other theoretical studies have been reported on the vortex structure, [ 103–125 ] switching dynamics, [ 126–141 ] and properties [ 142–146 ] in various low‐dimensional ferroelectric systems. In particular, in 2006, using phase‐field simulations, J. Wang et al predicted the formation of polar vortex‐like structure in a ferroelectric nanodot (Figure 3b).…”