Atomic-scale observations of electrical and mechanical manipulation of topological polar flux closure

Abstract

The ability to controllably manipulate complex topological polar configurations such as polar flux-closures via external stimuli may allow the construction of new electromechanical and nanoelectronic devices. Here, using atomically resolved in situ scanning transmission electron microscopy, we find that the polar flux-closures in PbTiO₃/SrTiO₃ superlattice films are mobile and can be reversibly switched to ordinary single ferroelectric c or a domains under an applied electric field or stress. Specifically, the electric field initially drives movement of a flux-closure via domain wall motion and then breaks it to form intermediate a/c striped domains, whereas mechanical stress first squeezes the core of a flux-closure toward the interface and then form a/c domains with disappearance of the core. After removal of the external stimulus, the flux-closure structure spontaneously recovers. These observations can be precisely reproduced by phase field simulations, which also reveal the evolutions of the competing energies during phase transitions. Such reversible switching between flux-closures and ordinary ferroelectric states provides a foundation for potential electromechanical and nanoelectronic applications.

Keywords: atomic resolution; ferroelectric; flux-closure domains; in situ (S)TEM; manipulation.

Fig. 1.

Characterization of flux-closures in PTO/STO superlattices. (A) Cross-sectional dark-field TEM image of a PTO/STO superlattice formed by reflection with g = 200, showing the alternative arrangement of STO and PTO on a GSO substrate. Flux-closure domains in the PTO layer show wave-like features. (B) Atomically resolved HAADF-STEM image showing a sharp interface between PTO and STO layers. (C) Corresponding GPA analysis showing the distribution of out-of-plane strain ε_yy. The wave-like features can be captured by GPA. (D) Enlarged view of HAADF-STEM image overlaid with polar vectors showing the flux-closure polar pattern in the PTO layer, while no substantial displacements exist in the reference cubic STO layer. The green and red dashed lines indicate the 90° and 180° domain walls, respectively. White arrows denote the polarization direction of PTO, forming alternate clockwise and counterclockwise flux-closures. (E) Flux-closure domain pattern predicted from phase field simulation, which shows good agreement with the experimental data. The polarizations are represented by blue arrows, with the 90° and 180° domain walls denoted by green and red dashed lines, respectively. (F) Out-of-plane lattice constant mapping corresponding to the image in D, showing the distribution of a and c domains in the PTO layer, analogous to GPA. The white dashed lines label the interface between PTO and STO.

Fig. 2.

Tracking the transition process of a flux-closure under increasing electrical field at the atomic scale. (A) HAADF-STEM image before application of an electric field. (B–F) Out-of-plane strain (ε_yy) maps extracted from the GPA corresponding to a sequence of HAADF-STEM images acquired in time series under different electric fields, showing the evolution of the domain pattern. (G–I) Enlarged GPA images of the representative areas outlined by yellow, orange, and green rectangles in A extracted from B–F. Thin black arrows indicate the polarization direction of PTO.

Fig. 3.

Recovery of flux-closure. (A) Atomically resolved HAADF-STEM image showing the switched area with a/c domains. Enlarged HAADF-STEM images corresponding to the areas labeled 1, 2, and 3 on the left show the polarization direction of Ti with respect to Pb. The yellow and red circles indicate the positions of Pb and Ti columns, respectively. (B) Out-of-plane lattice constant mapping series corresponding to the HAADF-STEM images acquired during gradual removal of the electric field, showing the flux-closure recovery process. Thin black arrows indicate the spontaneous polarization direction of PTO. The dashed oval highlights the growth of the c⁺ domain.

Fig. 4.

Tracking the process of flux-closure transition under mechanical stress at the atomic scale. (A) HAADF-STEM image before mechanical stress loading. (B–G) Out-of-plane strain (ε_yy) maps extracted via the GPA analysis corresponding to the series of chronologically acquired HAADF-STEM images under different mechanical stresses. The black dashed lines highlight the boundary between the transformed and untransformed areas. (H and I) Enlarged GPA images corresponding to the representative areas outlined by yellow and cyan rectangles in A extracted from B–G. Black arrows indicate the spontaneous polarization direction of PTO. (J) Mechanical load versus time. The blue points represent the approach branch and the red points represent the retraction branch. The yellow star indicates the starting point of the phase transition, and the green stars correspond to the images in SI Appendix, Fig. S8A.

Fig. 5.

Phase field simulation of flux-closure evolution. (A) Domain switching processes of a flux-closure under an electric field and under a mechanical load. The background colors denote different magnitudes of strain in the [001] direction corresponding to the out-of-plane strain (ε_yy) in GPA. (B and C) Phase diagrams of the domain structure in the PTO layer under an applied electric field and a mechanical load, respectively. The blue lines denote the gradient energy densities of PTO, which are used to determine the phase boundary. (D and E) Calculated polarization related energy profiles in the PTO layer. The green lines represent the energy profile in the flux-closure phase. The red and blue lines denote the energy profile under an applied electric field and a mechanical load, respectively.