  Defect chemistry, strain, and structural, magnetic and electronic degrees of
freedom constitute a rich space for the design of functional properties in
transition metal oxides. Here, we show that it is possible to engineer polarity
and ferroelectricity in non-polar perovskite oxides via polar defect pairs
formed by anion vacancies coupled to substitutional cations. We use a
self-consistent site-dependent DFT+$U$ approach that accounts for local
structural and chemical changes upon defect creation and which is crucial to
reconcile predictions with the available experimental data. Our results for
Fe-doped oxygen-deficient SrMnO$_3$ show that substitutional Fe and oxygen
vacancies can promote polarity due to an off-center displacement of the defect
charge resulting in a net electric dipole moment, which polarizes the lattice
in the defect neighborhood. The formation of these defects and the resulting
polarization can be tuned by epitaxial strain, resulting in enhanced
polarization also for strain values lower than the ones necessary to induce a
polar phase transition in undoped SrMnO$_3$. For high enough defect
concentrations, these defect dipoles couple in a parallel fashion, thus
enabling defect- and strain-based engineering of ferroelectricity in SrMnO$_3$.
