Development of the high-temperature phase of hexagonal manganites

Reports about the ferroelectric ordering temperatures in the multiferroic hexagonal RMnO₃ system are controversial: transition temperatures varying between ≈900K and ≈1300K 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 P6₃/mmc to the low-temperature symmetry P6₃cm. 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 TmMnO₃, based on this group-theoretical analysis, reveal two phase transitions: We extrapolate a polar to nonpolar transition temperature of Tₙₚₜ=1433(27)K, where the hexagonal bitetrahedra start to tilt, while the ferroelectric distortion appears at TFE=1050(50)K. For R=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.