Unraveling the Suppression of Oxygen Octahedra Rotations in A3B2O7 Ruddlesden-Popper Compounds: Engineering Multiferroicity and Beyond

The competition between polar distortions and ${B\text{O}}_{6}$ octahedra rotations is well known to be critical in explaining the ground state of various $AB{\mathrm{O}}_{3}$ perovskites. Here, we show from first-principles calculations that a similar competition between interlayer rumpling and rotations is playing a key role in layered Ruddlesden-Popper (RP) perovskites. This competition explains the suppression of oxygen octahedra rotations and hybrid improper ferroelectricity in ${A}_{3}{B}_{2}{\mathrm{O}}_{7}$ compounds with rare-earth ions in the rocksalt layer and also appears relevant to other phenomena like negative thermal expansion and the dimensionality determined band gap in RP systems. Moreover, we highlight that RP perovskites offer more flexibility than $AB{\mathrm{O}}_{3}$ perovskites in controlling such a competition and four distinct strategies are proposed to tune it. These strategies are shown to be promising for designing new multiferroics. They are generic and might also be exploited for tuning negative thermal expansion and band gap.