A -site cation size effect on oxygen octahedral rotations in acentric Ruddlesden-Popper alkali rare-earth titanates

Abstract

We demonstrate inversion symmetry breaking induced by oxygen octahedral rotations in layered perovskite oxides $\mathrm{K}{A}_{R}{\mathrm{TiO}}_{4}$ (${A}_{R}$ = rare earth) using a combined experimental and theoretical approach including synchrotron x-ray diffraction, optical second harmonic generation, and first-principles lattice dynamics calculations. We experimentally find an interesting but counterintuitive phenomenon, i.e., the acentric-to-centric phase transition temperatures for K family are higher than those for previously reported Na family, in contrast to expectations based on the Goldschmidt tolerance factor, where the octahedral rotation instability toward the acentric phases would reduce with an increase in the radius of $A$-site alkali metal ions. Our detailed analysis of first-principles calculations for ${A}_{A}{A}_{R}{\mathrm{TiO}}_{4}$ (${A}_{A}=\mathrm{Na}$, K, Rb) reveals that the alkali metal and rare-earth ions play quite different roles in driving the octahedral rotations. Since rare-earth ions attract oxide ions more strongly than alkali metal ions due to the higher valence of the former in comparison with the latter (${A}_{R}^{3+}$ vs ${A}_{A}^{+}$), the optimization of coordination environment of rare-earth ions is the primary driving force of the octahedral rotations. Alkali metal ions serve to impose ``bond strains'' parallel to the layers, playing a secondary role in the octahedral rotations. Incorporation of large alkali metal ions generates a significant in-plane biaxial bond strain in ${A}_{R}\mathrm{O}$ and ${\mathrm{TiO}}_{2}$ layers through the expanded ${A}_{A}\mathrm{O}$ layers, and thereby facilitates the octahedral rotations because of the otherwise highly underbonding of rare-earth ions. Thus, the effect of $A$-site alkali metal size on the octahedral rotation instability can be explained in terms of the interlayer lattice mismatch. This understanding allows us to propose a geometric descriptor governing the structural instability in ${A}_{A}{A}_{R}{\mathrm{TiO}}_{4}$ layered perovskites. We believe that control over the interlayer lattice mismatch could be a useful strategy to tune the octahedral rotations in layered compounds.