Resonant elastic x-ray scattering is a powerful technique for measuring multipolar order parameters. In this paper, we theoretically and experimentally study the possibility of using this technique to detect the proposed multipolar order parameters in ${\mathrm{URu}}_2{\mathrm{Si}}_2$ at the U-$L_3$ edge with the electric quadrupolar transition. Based on an atomic model, we calculate the azimuthal dependence of the quadrupolar transition at the U-$L_3$ edge. The results illustrate the potential of this technique for distinguishing different multipolar order parameters. We then perform experiments on ultraclean single crystals of ${\mathrm{URu}}_2{\mathrm{Si}}_2$ at the U-$L_3$ edge to search for the predicted signal, but do not detect any indications of multipolar moments within the experimental uncertainty. We theoretically estimate the orders of magnitude of the cross section and the expected count rate of the quadrupolar transition and compare them to the dipolar transitions at the U-$M_4$ and U-$L_3$ edges, clarifying the difficulty in detecting higher order multipolar order parameters in ${\mathrm{URu}}_2{\mathrm{Si}}_2$ in the current experimental setup.

• Received 26 May 2017

DOI:https://doi.org/10.1103/PhysRevB.96.085146