Temperature-Dependent Cycloidal Magnetic Structure in GdRu$_{2}$Al$_{10}$ Studied by Resonant X-ray Diffraction

We have performed resonant X-ray diffraction experiments on the antiferromagnet GdRu$_{2}$Al$_{10}$ and have clarified that the magnetic structure in the ordered state is cycloidal with the moments lying in the $bc$ plane and propagating along the $b$ axis. The propagation vector shows a similar temperature dependence to the magnetic order parameter, which can be interpreted as being associated with the gap opening in the conduction band and the resultant change in the magnetic exchange interaction. Although the $S=7/2$ state of Gd is almost isotropic, the moments show slight preferential ordering along the $b$ axis. The $c$ axis component in the cycloid develops with decreasing temperature through a tiny transition in the ordered phase. We also show that the scattering involves the $\sigma$-$\sigma'$ process, which is forbidden in normal $E1$-$E1$ resonance of magnetic dipole origin. We discuss the possibility of the $E1$-$E2$ resonance originating from a toroidal moment due to the lack of inversion symmetry at the Gd site. The spin-flop transition in a magnetic field is also described in detail.