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The floating-zone method with different growth ambiances has been used toselectively obtain hexagonal or orthorhombic DyMnO$_{3}$ single crystals. Thecrystals were characterized by X-ray powder diffraction of ground specimen anda structure refinement as well as electron diffraction. We report magneticsusceptibility, magnetisation, and specific heat studies of this multiferroiccompound in both the hexagonal and the orthorhombic structure. The hexagonalDyMnO$_{3}$ shows magnetic ordering of Mn$^{3+}$ (S =2) spins on a triangularMn lattice at $T^{\mathrm {Mn}}_{N}$ = 57 K characterized by a cusp in thespecific heat. This transition is not apparent in the magnetic susceptibilitydue to the frustration on the Mn triangular lattice and the dominatingparamagnetic susceptibility of the Dy$^{3+}$ (S=9/2) spins. At $T^{\mathrm{Dy}}_{N}$ = 3 K, a partial antiferromagnetic order of Dy moments has beenobserved. In comparison, the magnetic data for orthorhombic DyMnO$_{3}$ displaythree transitions. The data broadly agree with results from earlier neutrondiffraction experiments, which allows for the following assignment: atransition from an incommensurate antiferromagnetic ordering of Mn$^{3+}$ spinsat $T^{\mathrm {Mn}}_N$ = 39 K, a {\textit{lock--in}} transition at $T_{\mathrm{lock-in}}$ = 16 K and a second antiferromagnetic transition at $T^{\mathrm{Dy}}_N$ = 5 K due to the ordering of Dy moments. Both the hexagonal and theorthorhombic crystals show magnetic anisotropy and complex magnetic propertiesdue to 4$f-4f$ and 4$f-3d$ couplings.

Phase transitions and rare-earth magnetism in hexagonal and orthorhombic DyMnO$_{3}$ single crystals