Competing Structural Instabilities in the Ruddlesden-Popper Derivatives HRTiO₄ (R = Rare Earths): Oxygen Octahedral Rotations Inducing Noncentrosymmetricity and Layer Sliding Retaining Centrosymmetricity

We report the observation of noncentrosymmetricity in the family of HRTiO₄ (R = Eu, Gd, Dy) layered oxides possessing a Ruddlesden-Popper derivative structure, by second harmonic generation and synchrotron X-ray diffraction with the support of density functional theory calculations. These oxides were previously thought to possess inversion symmetry. Here, inversion symmetry is lifted by rotations of the oxygen-coordinated octahedra, a mechanism that is not active in simple perovskites. We observe a competition between rotations of the oxygen octahedra and sliding of a combined unit of perovskite-rocksalt-perovskite blocks at the proton layers. For the smaller rare earth ions, R = Eu, Gd, and Dy, which favor the octahedral rotations, noncentrosymmetricity is present but the sliding is absent. For the larger rare earth ions, R = Nd and Sm, the octahedral rotations are absent, but the sliding at the proton layers is present to optimize the length and direction of hydrogen bonding in the crystal structure. The study reveals a new mechanism for inducing noncentrosymmetricity in layered oxides, and chemical-structural effects related to rare earth ion size and hydrogen bonding that can turn this mechanism on and off. We construct a phase diagram of temperature versus rare earth ionic radius for the HRTiO₄ family.