On the possibility to detect multipolar order in URu${}_2$Si${}_2$ by the electric quadrupolar transition of resonant elastic X-ray scattering

Abstract

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 URu${}_2$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 ultra-clean single crystals of URu${}_2$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 URu${}_2$Si${}_2$ in the current experimental setup.

9 pages, 4 figures, Accepted for publication in PRB

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• Chiral charge as hidden order parameter in URu${}_2$Si${}_2$
• Antiferromagnetic real-space configuration probed by dichroism in scattered x-ray beams with orbital angular momentum
• Anisotropic Resonant Scattering from uranium systems at the U M4 edge
• Efficient Method for Prediction of Meta-stable/Ground Multipolar Ordered States and its Application in Monolayer $\alpha$-\ce{RuX3} (X=Cl,I)
• Magnetic X-ray imaging using a single polarization and multimodal-ptychography