Multiscale Electric Field Imaging in Ferroelectric Vortices

The discovery of polarization vortices in PbTiO₃/SrTiO₃ superlattices [1] has drawn significant interest due to their unique structure. For example, previous studies of the electric field in these vortex structures using a large probe size revealed the presence of confined regions of negative capacitance within the lattice [2]. However, changing the length scale of measurement can reveal new properties in materials. Using a highly convergent electron probe in a scanning transmission electron microscope with sub-Å resolution, we have studied the electric field at the scale of individual atoms and unit cells, revealing a different pattern in the local electric field than what is observed when using a nanometer scale probe. We find that the atomic scale electric field pattern follows the same vortex structure as the atomic dipole distribution while the nanometer scale electric field does not. This divergence in the electric field patterns results from the highly convergent probe interacting with the charge dipoles of individual unit cells which do not generate a coherent shift in the larger nanometer scale probe.

[1] A.K. Yadav et al., Nature 530, 198 (2016)
[2] A.K. Yadav et al., Nature 565, 468(2019)