Magnetic order and ferroelectricity in RMnO(3) 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 RMnO(3), R = Tb and Dy. Polarized neutron diffraction reveals the moment orientation associated with the various modes describing the complex magnetic ordering observed in TbMnO(3), 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 DyMnO(3) 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 tau(Tb) and tau(Mn) obey the relation 3 tau(Tb) - tau(Mn) = 1, in DyMnO(3) 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