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Oxygen vacancies in two-dimensional metal-oxide structures garner muchattention due to unique conductive, magnetic and even superconductivefunctionalities they induce. Ferroelectric domain walls have been a prominentrecent example because they serve as a hub for topological defects that enableunusual symmetries and are relevant for low-energy switching technologies.However, owing to the light weight of oxygen atoms and localized effects oftheir vacancies, the atomic-scale electrical and mechanical influence of oxygenvacancies has remained elusive. Here, stable individual oxygen vacancies werefound and engineered in situ at domain walls of seminal titanate perovskiteferroics. The atomic-scale strain, electric-field, charge and dipole-momentdistribution around these vacancies were characterized by combining advancedtransmission electron microscopy and first-principle methodologies. 3-5 %tensile strain was observed at the immediate surrounding unit cells of thevacancies. The dipole-moment distribution around the vacancy was found to be analternating head-to-head $-$ tail-to-tail $-$ head-to-head structure, givingrise to a quasi-linear quadrupole topology. Reduction of the nearby Ti ion aswell as enhanced charging and electric-field concentration near the vacancyconfirmed the quadrupole structure and illustrated its local effects on theelectrical and structural properties. Significant intra-band states were foundin the unit cell of the vacancies, proposing a meaningful domain-wallconductivity. Oxygen-vacancy engineering and controllable quadrupoles thatenable pre-determining both atomic-scale and global functional properties offera promising platform of electro-mechanical topological solitons and deviceminiaturization in metal oxides.

Establishing quasi-linear quadrupole functional topology by oxygen-vacancy engineering at a ferroelectric domain wall