Intrinsic polar vortex crystals in A-site layer-ordered perovskites

This Related Signal Note (RSN) documents and evaluates the empirical result reported by Xu et al. (Nature, 29 April 2026, doi:10.1038/s41586-026-10470-2), demonstrating the spontaneous formation of a two-dimensional polar hedgehog/vortex lattice in bulk A-site layer-ordered perovskites. The reported structure exhibits a periodicity down to ~4 nm and arises intrinsically, without reliance on external boundary conditions such as interfaces, strain, or applied fields. The stabilising mechanism is attributed to cooperative coupling of in-phase and out-of-phase octahedral rotation modes, consistent with hybrid improper ferroelectricity. These coupled lattice modes—describable via phonon interactions—constrain the…