Magnetic order and ferroelectricity in RMnO₃multiferroic manganites: coupling between R- and Mn-spins

Abstract

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 TbMnO 3 and DyMnO 3 show an induced ordering of the R-ion with a propagation vector clamped to the Mn ordering. While in TbMnO 3 this clamping leads to a ground state in which the two propagation vectors Tb and Mn obey the relation 3 Tb - 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.