Sinusoidal and cycloidal F-type spin structures in multiferroic orthomanganites

We performed resonant x-ray scattering on F-type (0 $q$ 0) reflections of TbMnO$_3$ and Eu$_{0.75}$Y$_{0.25}$MnO$_3$ at Mn $L$-edge, where modulation $q$ are near 0.28 and 0.25, respectively. By using circularly and linearly polarized light, we could confirm that F-type spin structure in TbMnO$_3$ is $c$- axis sinusoid above ferroelectric $T_C$ and $bc$-plane cycloid below $T_C$, while F-type spin structure in Eu$_{0.75}$Y$_{0.25} $MnO$_3$ is not cycloid but $c$-axis sinusoid down to base temperature. F-type spin structures in multiferroic orthomanganites can be explained as canted spin moment developed by Dzyaloshinskii-Moriya interaction and are also consistent in symmetric analysis.