X-ray resonant magnetic scattering study of multiferroic $R$MnO$_{3 }(R$~=~Dy, Ho, Er) compounds

Element specific x-ray resonant magnetic scattering (XRMS) investigations were undertaken to determine the magnetic structure of multiferroic hexagonal RMnO$_{3}$ compounds. In the intermediate temperature phase (ITP) (8-68~K for the Dy$^{3+}$ and 4.5-40~K for Ho$^{3+})$ the moments are aligned and antiferromagnetically correlated in the \textbf{c }direction according to the same magnetic representation $\Gamma _{3}$. Below the ITP, the Dy$^{3+}$/Ho$^{3+}$ moments order differently and according to the magnetic representations $\Gamma _{2 }$/$\Gamma _{1}$. The temperature dependence of the observed intensity in the ITP can be modeled assuming the splitting of ground-state doublet/quasi-doublet crystal-field levels of Dy$^{3+}$/Ho$^{3+ }$by the exchange field of Mn$^{3+}$. No resonant signals could be found for Er$^{3+}$ from 2-80~K. Specific magnetic representations can be excluded for the magnetic order of Er$^{3+}$ moments but can not be uniquely determined within the sensitivity of XRMS. -- The support by U.S. DOE (DE-AC02-07CH11358 and DE-AC02-06 CH11357) is acknowledged.