membranes: a first-principles investigation*

CaTiO₃ is the prototypical ABO₃ perovskite oxide, which crystallizes in the orthorhombic Pnma structure. Although bulk CaTiO₃ is non-polar, past theoretical and experimental work has unveiled that it transitions into a polar phase when biaxial strain is applied to a thin film via lattice mismatch with a substrate. Recently, the development of freestanding perovskite oxide membranes, whereby a perovskite oxide is lifted off from a water-soluble substrate and then transferred to a polymer sheet, opens up new possibilities for designing novel strain states. For example, the membrane can be stretched in one (uniaxial strain), two (biaxial strain), or even multiple directions by different amounts, producing unique strain states not previously accessible in other oxide platforms. However, our understanding of how these novel strain states impact targeted properties or phases remains relatively limited. In this work, we combine density functional theory calculations with group theoretic analysis to examine the effect of uniaxial strain applied along different crystallographic directions of CaTiO₃ and investigate the impact of these strains on the octahedral rotation amplitudes in the Pnma structure. We also explore the properties of CaTiO₃ when strains of distinct amplitudes are applied along different axes, and examine instabilities to different polar subgroups of Pnma. Our study offers new insight into tuning structural distortions and stabilizing polar structures under strain in CaTiO₃. We also discuss the applicability of our results to other ABO₃ perovskite oxides.