Resonant x-ray scattering spectra from multipole orderings: Np M_{4,5} edges in NpO2

TL;DR

This paper models resonant x-ray scattering spectra at Np M_{4,5} edges in NpO2, revealing detailed multipole orderings and matching experimental energy profiles through a localized electron approach.

Contribution

It derives a new expression for RXS amplitudes under rotational invariance, enabling accurate calculation of spectra considering intra-Coulomb and spin-orbit interactions.

Findings

Calculated spectra agree with experimental data.

Validated the localized electron model for NpO2.

Provided insights into multipole orderings in NpO2.

Abstract

We study resonant x-ray scattering (RXS) at Np M_{4,5} edges in the triple-\textbf{k} multipole ordering phase in NpO_{2}, on the basis of a localized electron model. We derive an expression for RXS amplitudes to characterize the spectra under the assumption that a rotational invariance is preserved in the intermediate state of scattering process. This assumption is justified by the fact that energies of the crystal electric field and the intersite interaction is smaller than the energy of multiplet structures. This expression is found useful to calculate energy profiles with taking account of the intra-Coulomb and spin-orbit interactions. Assuming the \Gamma_{8}-quartet ground state, we construct the triple-\textbf{k} ground state, and analyze the RXS spectra. The energy profiles are calculated in good agreement with the experiment, providing a sound basis to previous phenomenological analyses.