Competing polar and antipolar phases in n=2 Ruddlesden-Popper niobates and tantalates from first principles

The Li-based layered perovskites ${\mathrm{Li}}₂A{B}₂{\mathrm{O}}₇$ $(A=\mathrm{Ca},\mathrm{Sr};B=\mathrm{Nb},\mathrm{Ta})$ host competing ferroelectric and antiferroelectric states which arise from coupled octahedral rotation distortions and (anti)polar instabilities. We combine density functional theory (DFT) calculations with group theoretic analysis to unravel the mechanism that controls the relative energies of these competing states. We identify transition paths between the competing polar and antipolar states with very low-energy barriers (3 meV/f.u.), and show that stacking domain walls can facilitate an antipolar-polar transition. We furthermore show that epitaxial strain tunes the relative energy between the polar and antipolar phases. We compare the ${\mathrm{Li}}₂A{B}₂{\mathrm{O}}₇$ materials to other families of layered perovskite oxide (anti)ferroelectrics.