Octahedral rotations in Ruddlesden-Popper layered oxides under pressure from first principles

The combination of reduced dimensionality and tunable structural distortions in layered perovskite oxides makes these materials ideal platforms for designing novel properties and functionalities. One example is hybrid improper ferroelectricity in $n=2$ Ruddlesden-Popper oxides, where the combination of a layered crystal structure and rotations of the metal-oxide octahedra break symmetry and induce a polarization. Precisely controlling the octahedral rotation distortions, for example by the application of hydrostatic pressure, provides a pathway to tune and optimize the properties of these materials. We combine group theoretic methods, density functional theory calculations, and Landau theory analysis to investigate how octahedral rotations respond to pressure in the hybrid improper ferroelectrics ${\mathrm{Sr}}_{3}{\mathrm{Zr}}_{2}{\mathrm{O}}_{7}, {\mathrm{Ca}}_{3}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$, and ${\mathrm{Sr}}_{3}{\mathrm{Sn}}_{2}{\mathrm{O}}_{7}$. We find that factors that are known to control the pressure response of $\mathrm{A}\mathrm{B}{\mathrm{O}}_{3}$ perovskites---the formal charge of the $A$- and $B$-site cations, tolerance factor, and $B$-site chemistry---also impact the pressure response of these layered perovskites. We also show that coupling between the octahedral rotation and strain order parameters plays a key role in determining the overall pressure response. Despite some similarities, we find that these layered perovskites display a distinct pressure response compared to their $\mathrm{A}\mathrm{B}{\mathrm{O}}_{3}$ perovskite analogs. By identifying trends and underlying mechanisms that control octahedral rotations in Ruddlesden-Popper oxides under pressure, this work lays the foundation for tailoring the structure and properties of these materials.