Enhanced ferroelectric polarization by induced Dy spin-order in multiferroic DyMnO$_{3}$

Neutron powder diffraction and single crystal x-ray resonant magnetic scattering measurements suggest that Dy plays an active role in enhancing the ferroelectric polarization in multiferroic DyMnO$_{3}$ above $T_{N}^{\rm Dy}$=~6.5~K. We observe the evolution of an incommensurate ordering of Dy moments with the same periodicity as the Mn spiral ordering. It closely tracks the evolution of the ferroelectric polarization. Below $T_{N}^{\rm Dy}$, where Dy spins order commensurately, the polarization decreases to values similar for those of TbMnO$_{3}$. The higher $P_{s}$~found just above $T_{N}^{\rm Dy}$~arises from the contribution of Dy-spins so as to effectively increase the amplitude of the Mn spin-spiral.