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Oxide heterostructures exhibit a vast variety of unique physical properties.Examples are unconventional superconductivity in layered nickelates andtopological polar order in (PbTiO$_3$)$_n$/(SrTiO$_3$)$_n$ superlattices.Although it is clear that variations in oxygen content are crucial for theelectronic correlation phenomena in oxides, it remains a major challenge toquantify their impact. Here, we measure the chemical composition inmultiferroic (LuFeO$_3$)$_9$/(LuFe$_2$O$_4$)$_1$ superlattices, revealing aone-to-one correlation between the distribution of oxygen vacancies and theelectric and magnetic properties. Using atom probe tomography, we observeoxygen vacancies arranging in a layered three-dimensional structure with alocal density on the order of 10$^{14}$ cm$^{-2}$, congruent with theformula-unit-thick ferrimagnetic LuFe$_2$O$_4$ layers. The vacancy order ispromoted by the locally reduced formation energy and plays a key role instabilizing the ferroelectric domains and ferrimagnetism in the LuFeO$_3$ andLuFe$_2$O$_4$ layers, respectively. The results demonstrate the importance ofoxygen vacancies for the room-temperature multiferroicity in this system andestablish an approach for quantifying the oxygen defects with atomic-scaleprecision in 3D, giving new opportunities for deterministic defect-enabledproperty control in oxide heterostructures.

3D oxygen vacancy order and defect-property relations in multiferroic (LuFeO$_3$)$_9$/(LuFe$_2$O$_4$)$_1$ superlattices