Revealing the Three-Dimensional Arrangement of Polar Topology in Nanoparticles

TL;DR

This paper uses atomic electron tomography to visualize and analyze three-dimensional topological polar structures in ferroelectric BaTiO3 nanoparticles, revealing size-dependent topological transitions and confirming theoretical predictions.

Contribution

It introduces a novel atomic-scale 3D imaging method to classify and understand topological polar structures in ferroelectric nanoparticles, advancing nanoscale ferroelectric research.

Findings

Revealed 3D topological polar structures in BaTiO3 nanoparticles.

Observed size-dependent transition from single to multiple vortices.

Confirmed theoretical predictions of topological orderings in nanoscale ferroelectrics.

Abstract

In the early 2000s, low dimensional systems were predicted to have topologically nontrivial polar structures, such as vortices or skyrmions, depending on mechanical or electrical boundary conditions. A few variants of these structures have been experimentally observed in thin film model systems, where they are engineered by balancing electrostatic charge and elastic distortion energies. However, the measurement and classification of topological textures for general ferroelectric nanostructures have remained elusive, as it requires mapping the local polarization at the atomic scale in three dimensions. Here we unveil topological polar structures in ferroelectric BaTiO3 nanoparticles via atomic electron tomography, which enables us to reconstruct the full three-dimensional arrangement of cation atoms at an individual atom level. Our three-dimensional polarization maps reveal clear topological orderings, along with evidence of size-dependent topological transitions from a single vortex structure to multiple vortices, consistent with theoretical predictions. The discovery of the predicted topological polar ordering in nanoscale ferroelectrics, independent of epitaxial strain, widens the research perspective and offers potential for practical applications utilizing contact-free switchable toroidal moments.