Collinear to Spiral Spin Transformation without Changing the Modulation Wavelength upon Ferroelectric Transition inTb1−xDyxMnO3

Lattice modulation and magnetic structures in magnetoelectric compounds ${\mathrm{Tb}}_{1-x}{\mathrm{Dy}}_x{\mathrm{MnO}}_3$ have been studied around the ferroelectric (FE) Curie temperature $T_C$ by x-ray and neutron diffraction. Temperature-independent modulation vectors through $T_C$ are observed for the compounds with $0.50\le x\le 0.68$. This indicates that ferroelectricity with a polarization ($P$) along the $c$ axis in the $R{\mathrm{MnO}}_3$ series cannot be ascribed to such an incommensurate-commensurate transition of an antiferromagnetic order as was previously anticipated. A neutron diffraction study with $x=0.59$ shows that the FE transition is accompanied by the transformation of the Mn-spin alignment from sinusoidal (collinear) antiferromagnetism into a transverse-spiral structure. The observed spiral structure below $T_C$ is expected to produce $P$ along the $c$ axis with the “inverse” Dzialoshinski-Moriya interaction, which is consistent with observation.