Development of the high-temperature phase of hexagonal manganites

Abstract

Reports about the ferroelectric ordering temperatures in the multiferroic hexagonal $R{\mathrm{MnO}}_{3}$ system are controversial: transition temperatures varying between $\ensuremath{\approx}900\mathrm{K}$ and $\ensuremath{\approx}1300\mathrm{K}$ are reported for the same material. To elucidate the structural changes leading to ferroelectric distortions in hexagonal manganites, we calculate the irreducible representations of the distortions from the possible high-temperature symmetry ${P6}_{3}/mmc$ to the low-temperature symmetry ${P6}_{3}\mathrm{cm}.$ There are four different orthogonal modes, of which only one allows a spontaneous electric polarization. Structure refinements and an accurate statistical analysis of neutron powder-diffraction data of ${\mathrm{TmMnO}}_{3},$ based on this group-theoretical analysis, reveal two phase transitions: We extrapolate a polar to nonpolar transition temperature of ${T}_{\mathrm{npt}}=1433(27)\mathrm{K},$ where the hexagonal bitetrahedra start to tilt, while the ferroelectric distortion appears at ${T}_{\mathrm{FE}}=1050(50)\mathrm{K}.$ For $R=\mathrm{Lu},$ Yb the tilt of the bitetrahedra and the buckling of the R layers as well as the ferroelectric distortion were extrapolated to comparable temperatures.