Atomic scale crystal field mapping of polar vortices in oxide superlattices

Polar vortices in oxide superlattices exhibit complex polarization topologies. Using a combination of electron energy loss near-edge structure analysis, crystal field multiplet theory, and first-principles calculations, we probe the electronic structure within such polar vortices in [(PbTiO₃)₁₆/(SrTiO₃)₁₆] superlattices at the atomic scale. The peaks in Ti [Formula: see text]-edge spectra shift systematically depending on the position of the Ti⁴⁺ cations within the vortices i.e., the direction and magnitude of the local dipole. First-principles computation of the local projected density of states on the Ti [Formula: see text] orbitals, together with the simulated crystal field multiplet spectra derived from first principles are in good agreement with the experiments.