Magnetic properties of hexagonal YMnO$_3$, LuMnO$_3$ and ScMnO$_3$ Magnetic susceptibility, specific heat and dielectric constant of hexagonal YMnO_3, LuMnO_3 and ScMnO_3

We report the magnetic susceptibility, specific heat and dielectric constant on high purity polycrystalline samples of three hexagonal manganites: YMnO_3, LuMnO_3 and ScMnO_3. These materials can exhibit a ferroelectric transition at very high temperatures (T_{FE} > 700K). At lower temperatures there is magnetic ordering of the frustrated Mn^{3+} spins (S=2) on a triangular Mn lattice (YMnO_3:T_N=71K; LuMnO$_3:T_N=90K and ScMnO_3:T_N=130K). The transition is characterized by a sharp kink in the magnetic susceptibility at T_N below which it continues to increase due to the frustration on the triangular lattice. The specific heat shows one clear continuous phase transition at T_N, which is independent of external magnetic field up to 9T with an entropy content as expected for Mn^{3+} ions. The temperature dependent dielectric constant displays a distinct anomaly at T_N.