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We use density functional theory (DFT) calculations to show that oxygenvacancies ($v_\mathrm{O}$) and mobility induce noncentrosymmetric polarstructures in SrTi$_{1-x-y}$Fe$_{x}$Co$_{y}$O$_{3-\delta}$ ($x=y=0.125$) with$\delta = \{0.125, 0.25\}$, enhance the saturation magnetization and give riseto large changes in the electric polarization $\vert\Delta P\vert$. We presentan intuitive set of rules for SrTiFeCoO$_{3-\delta}$ (STFC), which are based onthe interplay between (Co/Fe)-$v_\mathrm{O}$ defects, magnetic cationscoordination and topological vacancy disorder. STFC structures convey layeredcrystals with sheets of linear organized O$_{4,5,6}$-coordinated Fe-Co pairs,sandwiched with layers of O$_{5}$-coordinated Ti. Co,Fe-$v_\mathrm{O}$ defectsare the source of the crystal distortions, cations off-centering and bending ofthe oxygen octahedra, which added to the charge redistribution mediated by$v_\mathrm{O}$, the cations electronegativity and valence states trigger aneffective electric polarization. Oxygen migrations for $\delta=0.125$ providesus with $\vert\Delta \mathbf{P}\vert$ $>\sim10 \mu$C/cm$^2$ due to aquantum-of-polarization differences between $\delta=0.125$ structures.Increasing the deficiency to $\delta=0.25$ yields $\vert\Delta \mathbf{P}\vert$whose O-migration resolved polarization for $\delta=0.25$ is $>\sim3\mu$C/cm$^2$ in the worst case scenario. Magnetism is dominated by the Fe,Cospin states for $\delta=0.125$ while there is a raid of Ti magnetic moments($\sim1\mu_{B}$) for $\delta=0.25$. Magnetic and electric order parameterschange for variations of $\delta$ or oxygen migrations for a given deficiency.Our results capture characteristics observed in the end-members of the seriesSrTi(Co,Fe)O$_{3}$, and suggest the existence of a broader set of rules foroxygen deficient multiferroic oxides.

Oxygen deficiency and migration mediated electric polarization in Fe,Co-substituted SrTiO$_{3-\delta}$