Controlling polarons and polaron-vacancy interactions (PVIs) in oxides is of vital importance for their physical properties and practical applications. Here, we leverage recent improvements in $\mathrm{DFT}+\mathrm{U}$ to investigate PVI energetics, atomic geometry, and electronic structure while varying two experimentally accessible control parameters. The industrially important $\mathrm{Pb}\left({\mathrm{Zr}}_x{\mathrm{Ti}}_{1-x}\right){\mathrm{O}}_3$ (PZT) system is studied to understand how composition affects static polaron properties, while epitaxial strain is introduced on the $x-y$ plane of the ${\mathrm{PbTiO}}_3$ (PTO) lattice, allowing the $z$ axis to relax. Upon doping PTO with Zr to form PZT, low Zr content results in preferential hybridization of $\mathrm{Zr}-4{\mathrm{d}}_{\mathrm{t}2\mathrm{g}}$ and $\mathrm{Ti}-3{\mathrm{d}}_{\mathrm{t}2\mathrm{g}}$ orbitals and unstable polaron-vacancy complexes (PVCs), despite the similarity between the PZT and PTO lattices. A crossover point occurs at $\sim 29\%$ Zr, where PVCs become stable as $\mathrm{Zr}-4{\mathrm{d}}_{\mathrm{t}2\mathrm{g}}$ and $\mathrm{Ti}-3{\mathrm{d}}_{\mathrm{eg}}$ states begin to separate rather than hybridize. In PTO, we find that increasing compressive strain generally increases polaron stability both in the bulk and in PVCs, while increasing tensile strain has little effect on polaron trapping. We show this is the result of competition between the strain energy and electronic transition energy: Under compressive strain, the electronic transition energy change outcompetes the strain energy, while tensile strain leaves both energies largely unchanged. Thereby, we demonstrate that significant changes to the electronic structure because of orbital hybridization with dopant states are the dominant effect on polaron stability, while the smaller effect of epitaxial strain may be used to more finely tune the polaron stability.

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• Point defects
• Polarons
• Oxides
• Perovskites
• DFT+U