  The floating-zone method with different growth ambiances has been used to
selectively obtain hexagonal or orthorhombic DyMnO$_{3}$ single crystals. The
crystals were characterized by X-ray powder diffraction of ground specimen and
a structure refinement as well as electron diffraction. We report magnetic
susceptibility, magnetisation, and specific heat studies of this multiferroic
compound in both the hexagonal and the orthorhombic structure. The hexagonal
DyMnO$_{3}$ shows magnetic ordering of Mn$^{3+}$ (S =2) spins on a triangular
Mn lattice at $T^{\mathrm {Mn}}_{N}$ = 57 K characterized by a cusp in the
specific heat. This transition is not apparent in the magnetic susceptibility
due to the frustration on the Mn triangular lattice and the dominating
paramagnetic susceptibility of the Dy$^{3+}$ (S=9/2) spins. At $T^{\mathrm
{Dy}}_{N}$ = 3 K, a partial antiferromagnetic order of Dy moments has been
observed. In comparison, the magnetic data for orthorhombic DyMnO$_{3}$ display
three transitions. The data broadly agree with results from earlier neutron
diffraction experiments, which allows for the following assignment: a
transition from an incommensurate antiferromagnetic ordering of Mn$^{3+}$ spins
at $T^{\mathrm {Mn}}_N$ = 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 the
orthorhombic crystals show magnetic anisotropy and complex magnetic properties
due to 4$f-4f$ and 4$f-3d$ couplings.
