Determination of magnetic-moment directions using x-ray resonant exchange scattering

We present determinations of the magnetic structures of ${\mathrm{NdNi}}_2$${\mathrm{B}}_2$C and ${\mathrm{SmNi}}_2$${\mathrm{B}}_2$C by means of x-ray resonant exchange scattering (XRES). The integrated intensity of a number of magnetic reflections was measured as a function of the Bragg angle and compared to model calculations for various magnetic structures. The two compounds were found to have the same magnetic modulation wave vector but different moment directions. A resonant feature observed below the Sm ${\mathrm{L}}_3$-absorption edge, similar to unexplained effects found in other light rare-earth compounds, is identified as quadrupolar XRES and is used to refine the details of the moment direction.