Observation of persistent centrosymmetricity in the hexagonal manganite family

The controversy regarding the ferroelectric behavior of hexagonal InMnO$_3$ 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 $P6_3cm$ 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 $P\bar{3}c$ 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-$R$-site covalency, with an absence of covalency favoring the ferroelectric phase.