Magnetic order and ferroelectricity in RMnO₃ multiferroic manganites: coupling between R- and Mn-spins

Combining polarized and unpolarized neutron scattering techniques with x-ray resonant magnetic scattering we have studied the coupling between the Mn- and R-spin-ordering in the multiferroic RMnO₃, R = Tb and Dy. Polarized neutron diffraction reveals the moment orientation associated with the various modes describing the complex magnetic ordering observed in TbMnO₃, while neutron diffraction in high magnetic fields allows the identification of the origin (Mn versus Tb) of the various modes. In this way we identify significant C_x and F_z contributions from Tb arising from the coupling of Tb moments to the Mn cycloidal ordering. The x-ray studies give further insight into this coupling. In the ferroelectric phase, both TbMnO₃ and DyMnO₃ show an induced ordering of the R-ion with a propagation vector clamped to the Mn ordering. While in TbMnO₃ this clamping leads to a ground state in which the two propagation vectors τ^Tb and τ^Mn obey the relation 3τ^Tb−τ^Mn = 1, in DyMnO₃ the ferroelectric polarization is effectively enhanced. The theoretical analysis of these effects not only explains the observed behavior for R = Tb and Dy but can also be applied to understand the Mn–R interaction in the related compounds with R = Gd and Ho. Finally we show both experimentally and theoretically how the Mn–R coupling can enhance the ferroelectric polarization in this manganite's multiferroics.