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

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