Fig. 3. Polar structures and Pontryagin density of (BFO₇/STO₄)₈ superlattices calculated by phase-field simulations.

a Planar view of the in-plane polarization magnitude. b Magnified view of the in-plane polar vector plot, showing a bimeron structure. c Plot of the Pontryagin density for the same region as shown in (a). d Magnified view of the Pontryagin density of the bimeron structure. Surface integration of the Pontryagin density for the bimeron gives a topological charge of −1. e Cross-section view of the out-of-plane polarization magnitude, showing alternating positive and negative polarization. f Magnified view of the out-of-plane polar vector plot, showing a vortex-like structure, with a mixture of R-like and T-like polar regions.