First-principles study to identify heterostructures of (Pb, Sr)TiO$_{3}$ with enhanced ferroelectric polarisation

A first-principle cluster expansion method is employed to study the ferroelectric (FE) polarisation properties of Pb$_{x}$Sr$_{1-x}$TiO$_{3}$ perovskite oxide grown on SrTiO$_{3}$ (001)-substrate. Our results indicate that some heterostructures can significantly enhance polarisation in comparison with the (001) superlattice and the random alloy structures. At $x=0.5$, an (110) A/B mono-layer superlattice is identified as the structure with the most enhanced polarisation, and at $x=0.25$, the optimal structure is determined to be a body-centred superstructure. Detailed structural analysis reveals the atomic configurational patterns in the (001) plane that benefit the off-centering of Pb and Sr cations. Explanation is provided in terms of dipole interactions. Our results should apply to other multicomponent FE perovskites as well and they could have a significant impact in the design of FE materials.