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

TL;DR

This study explores the potential of resonant elastic X-ray scattering at the U-$L_{3}$ edge to detect multipolar order in URu$_2$Si$_2$, combining theoretical calculations with experimental searches that found no detectable signals within current limits.

Contribution

The paper provides a theoretical framework and experimental assessment for using resonant elastic X-ray scattering to identify multipolar order in URu$_2$Si$_2$, highlighting the challenges in detection.

Findings

Theoretically predicts azimuthal dependence of quadrupolar transition

Experimentally finds no detectable multipolar signals at current sensitivity

Estimates the cross-section magnitude, showing detection difficulty

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.