Oxygen vacancy induced electric polarization changes in Fe,Co-substituted SrTiO$_{3-delta}$

We use density functional theory (DFT) calculations to show that oxygen vacancies ($v_mathrm{O}$) induce noncentrosymmetric polar structures in SrTi$_{0.75}$Fe$_{0.125}$Co$_{0.125}$O$_{3-delta}$ (STFC) with $delta = {0.125, 0.25}$, enhance the magnetic moment and give rise to large changes in the electric polarization $vertDelta Pvert$. Variations of $delta$ or oxygen vacancy migration for a given deficiency are shown to be effective mechanisms to tune the ferroic order parameters, with the former yielding $vertDelta Pvert$ values up to $sim{8mu}$C/c$m^{2}$ while the latter yields $vertDelta Pvert$ up to $sim{23mu}$C/c$m^{2}$. The underlying mechanism is the differentiated self-regulatory-like ferroic response of Fe and Co through the (Fe/Co)-$v_mathrm{O}$ and Fe-$v_mathrm{O}$-Co interactions, which drive B-site off-centering, bending of O$_{4,5}$ incomplete octahedra and B-$v_mathrm{O}$ aligned distortions, all with characteristic charge redistributions. Our results capture characteristics observed in the end-members of the series SrTi(Co,Fe)O$_{3}$, and predict multiferroic behavior that could also be present in other ABO$_{3-delta}$ magnetic oxides.