Subunit cell–level measurement of polarization in an individual polar vortex

Recently, several captivating topological structures of electric dipole moments (e.g., vortex, flux closure) have been reported in ferroelectrics with reduced size/dimensions. However, accurate polarization distribution of these topological ferroelectric structures has never been experimentally obtained. We precisely measure the polarization distribution of an individual ferroelectric vortex in PbTiO(3)/SrTiO(3) superlattices at the subunit cell level by using the atomically resolved integrated differential phase contrast imaging in an aberration-corrected scanning transmission electron microscope. We find, in vortices, that out-of-plane polarization is larger than in-plane polarization, and that downward polarization is larger than upward polarization. The polarization magnitude is closely related to tetragonality. Moreover, the contribution of the Pb─O bond to total polarization is highly inhomogeneous in vortices. Our precise measurement at the subunit cell scale provides a sound foundation for mechanistic understanding of the structure and properties of a ferroelectric vortex and lattice-charge coupling phenomena in these topological ferroelectric structures.