Atomic imaging of mechanically induced topological transition of ferroelectric vortices

Abstract

Ferroelectric vortices formed through complex lattice-charge interactions have great potential in applications for future nanoelectronics such as memories. For practical applications, it is crucial to manipulate these topological states under external stimuli. Here, we apply mechanical loads to locally manipulate the vortices in a PbTiO₃/SrTiO₃ superlattice via atomically resolved in-situ scanning transmission electron microscopy. The vortices undergo a transition to the a-domain with in-plane polarization under external compressive stress and spontaneously recover after removal of the stress. We reveal the detailed transition process at the atomic scale and reproduce this numerically using phase-field simulations. These findings provide new pathways to control the exotic topological ferroelectric structures for future nanoelectronics and also valuable insights into understanding of lattice-charge interactions at nanoscale.

Fig. 1. Characterization of vortices in PbTiO₃/SrTiO₃ superlattices.

a Low-magnification scanning transmission electron microscopy (STEM) image of a (PbTiO₃)₁₁/(SrTiO₃)₁₁ superlattice along [010]_pc, showing the alternative arrangement of SrTiO₃ and PbTiO₃ on a DyScO₃ substrate. Scale bar, 25 nm. b, c Geometric-phase analysis of the STEM data showing the distribution of the out-of-plane strain Ɛ_zz and in-plane strain Ɛ_xx, respectively. Scale bar, 10 nm. d Cross-sectional high-angle annular dark-field (HAADF) STEM image with an overlay of the polar displacement vectors denoted by the yellow arrows showing the vortices in the PbTiO₃ layer. Scale bar, 1 nm. e A selected-area electron diffraction (SAED) pattern for the PbTiO₃/SrTiO₃ film. Scale bar, 2 nm⁻¹. f Enlarged (001) spots showing the satellite diffraction spots from the ordered vortex. The vortex and superlattice periods are measured to be 8.6 and 8.5 nm, respectively, denoted by d_v and d_s. Scale bar, 0.1 nm⁻¹.

Fig. 2. Mechanical manipulation of vortices by in situ transmission electron microscopy (TEM).

a Schematic image of the experimental setup, with a mobile tungsten tip acting as an indenter for the mechanical manipulation of vortices. b Chronological TEM dark-field image series formed by reflection with ɡ = (200) _pc. Under the mechanical loads, vortex contrast gradually disappears. Scale bar, 40 nm. c Corresponding transition area (blue line) and switching velocity (orange line) plotted as functions of time. d Mechanical loads as a function of time, with the blue points representing the approach branch and orange points corresponding to the retraction branch. The highlighted red stars along with labels 1–4 correspond to images in e. e Dark-field images showing the vortex evolution under certain measured mechanical stress. Scale bar, 20 nm.

Fig. 3. Structural evolution of vortices under mechanical stress.

a Three SAED images extracted from a real-time image series corresponding to before, during, and after mechanical loading. The vortex reflections disappear at 58 s and recover when the external stress is removed at 64 s. Scale bar, 2 nm⁻¹. b Chronological SAED (001)_pc images with vortex spots dimming as the mechanical force is continuously applied. Yellow box at 0 s indicates diffraction spots used in c. Scale bar, 0.1 nm⁻¹. c Line profile intensity as a function of time normalized by the center superlattice spots. d The in-plane a and out-of-plane c lattice parameters and c/a ratio as functions of time. The c/a ratio is eventually less than 1 under a continuously applied mechanical load, indicating that the vortices have transformed to a domains.

Fig. 4. Tracking stress induced vortex transition at the atomic scale.

a–d A series of HAADF-STEM images acquired with applying mechanical loads. Scale bar, 4 nm. e–h The corresponding out-of-plane lattice mapping of a–d, showing the transition process. The core of the vortex survives before the transition into a pure a domain. The rotation arrows indicate the core positions of each vortex. i A high-magnification HAADF-STEM image with the overlaid arrows showing the formed a domain after the transition. j–l HAADF-STEM images acquired during the unloading process. Scale bar, 4 nm. m–o The corresponding out-of-plane lattice mapping of j–l, indicating the spontaneous recovery of the vortex after removal of the external mechanical stress. The same scale is used for all the mapping figures. All the HAADF-STEM images were acquired in the same region indicated by the intentionally made marker using the electron probe (see the dashed yellow circles).