Triakontadipole and high-order dysprosium multipoles in the antiferromagnetic phase of DyB$_2$C$_2$

TL;DR

This study uses resonant soft x-ray diffraction to analyze high-order multipole moments in DyB$_2$C$_2$, revealing detailed multipolar interactions and quantifying their magnitudes relative to quadrupolar moments.

Contribution

It introduces a formalism that includes magnetic and nonmagnetic oscillator interference, enabling determination of multipole moments up to rank 6 in DyB$_2$C$_2$.

Findings

Higher order multipole moments of Dy are quantified, ranging from 7% to 78% of the quadrupolar moment.

The formalism incorporating interference effects enhances the analysis of multipolar order.

The study provides detailed insights into the multipolar structure in the antiferromagnetic phase of DyB$_2$C$_2$.

Abstract

Resonant soft x-ray Bragg diffraction at the Dy M$_{4,5}$ edges has been used to study Dy multipoles in the combined magnetic and orbitally ordered phase of DyB$_2$C$_2$. The analysis incorporates both the intra-atomic magnetic and quadrupolar interactions between the 3d core and 4f valence shells. Additionally, we introduce to the formalism the interference of magnetic and nonmagnetic oscillators. This allows a determination of the higher order multipole moments of rank 1 (dipole) to 6 (hexacontatetrapole). The strength of the Dy 4f multipole moments have been estimated at being between 7 and 78 % of the quadrupolar moment.