Rotations of oxygen octahedra are ubiquitous, but they cannot break inversion symmetry in simple perovskites. However, in a layered oxide structure, this is possible, as we demonstrate here in $A$-site ordered Ruddlesden-Popper $\mathrm{Na}R{\mathrm{TiO}}_4$ ($R$ denotes rare-earth metal), previously believed to be centric. By revisiting this series via synchrotron x-ray diffraction, optical second-harmonic generation, piezoresponse force microscopy, and first-principles phonon calculations, we find that the low-temperature phase belongs to the acentric space group $P\overline{4}{2}_{1}m$, which is piezoelectric and nonpolar. The mechanism underlying this large new family of acentric layered oxides is prevalent, and could lead to many more families of acentric oxides.

• Received 20 January 2014

DOI:https://doi.org/10.1103/PhysRevLett.112.187602