Effect of core-valence intra-atomic quadrupolar interaction in resonant x-ray scattering at the Dy M$_{4,5}$ edges in DyB$_2$C$_2$

TL;DR

This study models the energy dependence of resonant soft x-ray diffraction in DyB$_2$C$_2$, highlighting the impact of intra-atomic quadrupolar interactions and matching experimental data across different magnetic phases.

Contribution

It introduces an atomic multiplet Hamiltonian including core-valence quadrupolar interactions to accurately simulate resonant x-ray scattering in DyB$_2$C$_2$.

Findings

Reproduces energy profile features in antiferroquadrupolar phase.

Matches scattering intensity behavior near Dy M$_5$ edge in antiferromagnetic phase.

Validates the role of intra-atomic quadrupolar interactions in resonant scattering.

Abstract

The dependence with energy of the resonant soft x-ray Bragg diffraction intensity in DyB$_2$C$_2$ for the $(00{1/2})$ reflection at the Dy M$_{4,5}$ edges have been calculated by using an atomic multiplet hamiltonian including the effect of crystal field and introducing an intra-atomic quadrupolar interaction between the 3d core and 4f valence shell. These calculations are compared with the experimental results (Mulders et al., J. Phys.: Condens. Matter 18 (2006) 11195) in the antiferroquadrupolar and antiferromagnetic phases of DyB$_2$C$_2$. We reproduce all the features appearing $(00{1/2})$ reflection energy profile in the antiferroquadrupolar ordered phase, and we reproduce the behaviour of the resonant x-ray scattering intensity at different energies in the vicinity of the Dy M$_5$ edge when the temperature is lowered within the antiferromagnetic phase.