Oxygen tilt driven polar superorders in BiFeO3 -based superlattices

Ferroelectric-dielectric superlattices have attracted renewed interest for their ability to frustrate the polar order, leading to the emergence of exotic polar textures. The electrostatic depolarization, thought to be responsible for the complex polar textures in these superlattices, can be alleviated by replacing the dielectric layer with a metallic one. One would thus expect that a close to uniform polarization state be recovered in the ferroelectric layer. However, here we show, using density-functional theory calculations, that metastable antipolar motions may still appear in superlattices combining multiferroic ${\mathrm{BiFeO}}_{3}$ and metallic ${\mathrm{SrRuO}}_{3}$ perovskite layers. We find that a complex oxygen octahedra tilt order, a so-called nanotwin phase, exists in ${\mathrm{BiFeO}}_{3}/{\mathrm{SrRuO}}_{3}$ superlattices and competes with a more conventional phase. It leads to a doubling of the chemical period along the out-of-plane direction, owing to the presence of an oxygen octahedra tilt-wave pattern and antipolar motions caused by trilinear energy couplings. We also show that out-of-plane polar displacements in the ${\mathrm{BiFeO}}_{3}$ layer may reverse the (anti)polar displacements thanks to a strong quadrilinear coupling term. The oxygen tilt-driven couplings identified here may open new ways to engineer and control polar displacements in superlattice-based polar metals and hybrid improper (anti)ferroelectrics.