Observation of persistent centrosymmetricity in the hexagonal manganite family

The controversy regarding the ferroelectric behavior of hexagonal InMnO₃ is resolved by using a combination of x-ray diffraction (XRD), piezoresponse force microscopy (PFM), second harmonic generation (SHG), and density functional theory (DFT). While XRD data show a symmetry-lowering unit-cell tripling, which is also found in the multiferroic hexagonal manganites of P6₃cm symmetry, PFM and SHG do not detect ferroelectricity at ambient or low temperature, in striking contrast to the behavior in the multiferroic counterparts. We propose instead a centrosymmetric P3̄c phase as the ground-state structure. Our DFT calculations reveal that the relative energy of the ferroelectric and nonferroelectric structures is determined by a competition between electrostatics and oxygen--rare-earth covalency, with an $absence$ of covalency favoring the ferroelectric phase.