A depth-resolved electron-microscopy study suggests that a familiar-looking swirl in a polar material can hide several different structures stacked through its thickness. In the examined PbTiO3/SrTiO3 superlattice, atomic displacements and polarization patterns changed with depth, while an image integrated across the full thickness still retained an apparent vortex-like pattern.
Projection images combine signals from different depths into one view. In the selected reconstruction, that depth integration could obscure changes that became visible when narrower sections of the material were examined.
A layered sample, examined slice by slice
The material was a [(PTO)15/(STO)15]15 superlattice, a repeating stack of PbTiO3 and SrTiO3, grown epitaxially on (001)pc DyScO3 by 90-degree off-axis radio-frequency magnetron sputtering. The study then examined selected regions at different depths.
The imaging workflow combined two scanning transmission electron microscopy modes, LAADF-STEM and HAADF-STEM, with MEP, or multislice electron ptychography, to inspect atomic structure and polarization topology at different depths. In depth-sectioning ADF-STEM, the probe was sequentially focused through the specimen in steps of 3 nanometres.
The selected MEP reconstruction region was approximately 16 nanometres thick, with thickness assessed using EELS measurements and PACBED simulations.
To build polarization maps, the researchers extracted the positions of lead, titanium and oxygen columns from reconstructed phase images with a custom Python workflow based on Atomap. They then calculated local displacement fields from the relative positions of those atomic columns.
Different elements told different parts of the story
In simulated PTO data, the displaced titanium signal was localized near approximately 25 Å, the lead signal emerged around 50 Å, and the lead signal vanished near approximately 75 Å. The result showed that the simulated reconstruction could place the two displacement signals at different axial positions.
The experimental depth slices also showed structural variation between selected regions. In one region, there was no significant titanium-column distortion at 5 nanometres; splitting appeared at 10 nanometres and disappeared at 13 nanometres. In a second region, split titanium and lead features appeared at 10 nanometres and remained at 13 nanometres.
The titanium displacement maps changed markedly through the reconstructed thickness. A right-side vortex-like structure appeared at approximately 3 to 5 nanometres, weakened around 7 nanometres, and had largely given way to a sinusoidal pattern by about 10 nanometres. A new left-side vortex-like feature then appeared near the bottom surface.
The lead maps showed another sequence. A weak left vortex was visible at about 4 nanometres, disappeared at 7 nanometres, and was accompanied by weakening vortex-like and sinusoidal features around 8 nanometres. At 12 nanometres, a left vortex re-emerged alongside a more complex texture on the right.
The whole image can smooth over the changes
When the analysis integrated the full reconstructed thickness from 1 to 16 nanometres, the result retained an apparent vortex-like pattern. But integrations over narrower intervals—1 to 8 nanometres, 5 to 12 nanometres, and 9 to 16 nanometres—produced different polarization configurations.
The authors interpret this contrast as a possible superposition of multiple depth-dependent polar states. That makes MEP useful for connecting local atomic displacements with buried three-dimensional polarization textures. The maps are built from relative positions of lead, titanium and oxygen columns, so the reported polarization is an inferred displacement-based texture rather than a direct measure of electrical switching.
The document is an arXiv preprint. The depth estimates should therefore be read as approximate: no formal uncertainty estimate was reported for the simulated localization result. The main experimental reconstruction was a selected region approximately 16 nanometres thick, which limits the result to the region examined rather than establishing a pattern across the full superlattice.
Simulations validate aspects of the imaging method, but they are not independent experimental confirmation of the reconstructed superlattice texture. The experimental evidence comes from selected depth slices and the displacement maps described in the reported superlattice.
What needs testing next
An important next test is whether the different configurations recur in independently grown samples and additional specimen regions. Another open question is how reconstruction uncertainty and algorithm choices influence the displacement and vorticity maps.
The authors state that all data are available in the manuscript or supplementary information and declare no competing interests.
Paper data and sources
Original title: Depth-Resolved Evolution of Buried Polar Topologies in a PbTiO3/SrTiO3 Superlattice
Authors: Xinxin Hu, Penghan Lu, Noa Varela-Dominguez et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-25
DOI: Not available
Original paper · Full text