Reports about the ferroelectric ordering temperatures in the multiferroic hexagonal RMnO 3 system are controversial: transition temperatures varying between Ϸ900 K and Ϸ1300 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 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 TmMnO 3 , based on this group-theoretical analysis, reveal two phase transitions: We extrapolate a polar to nonpolar transition temperature of T npt ϭ1433(27) K, where the hexagonal bitetrahedra start to tilt, while the ferroelectric distortion appears at T FE ϭ1050(50) K. For RϭLu, Yb the tilt of the bitetrahedra and the buckling of the R layers as well as the ferroelectric distortion were extrapolated to comparable temperatures.
We report the magnetic susceptibility, specific heat and dielectric
constant for high-purity polycrystalline samples of three hexagonal
manganites: YMnO3, LuMnO3 and ScMnO3. These materials can
exhibit a ferroelectric transition at very high temperatures
(TFE>700 K). At lower temperatures there is magnetic
ordering of the frustrated Mn3+ spins (S = 2) on a triangular
Mn lattice (YMnO3: TN = 71 K; LuMnO3: TN = 90 K and
ScMnO3: TN = 130 K). The transition is characterized by a sharp
kink in the magnetic susceptibility at TN below which it
continues to increase due to the frustration on the triangular
lattice. The specific heat shows one clear continuous phase
transition at TN, which is independent of external magnetic field
up to 9 T with an entropy content as expected for Mn3+ ions.
The temperature-dependent dielectric constant displays a distinct
anomaly at TN.
Hexagonal manganites REMnO3 consist of layers of two-dimensional connected distorted MnO5 bipyramids separated by distorted layers of RE, leading to frustrated Mn3+–O2−–Mn3+ in-plane exchange paths (superexchange) and Mn3+–O2−–O2−–Mn3+ interplane exchange paths (super-superexchange). We report single-crystal diffraction experiments (RE=Ho,Er,Y) indicating magnetic 2D short-range order up to temperatures of T=150 K (TN∼74 K), and SQUID magnetization data (RE=Y) indicating short-range order up to at least 250 K. Fits of a model based on an extended mean-field theory to the single-crystal data show in-plane exchange about 3 orders of magnitude stronger than the interplane exchange, explaining the unusual strong deviation from the Curie–Weiss law of the SQUID magnetization data.
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