Lattice Distortion and Resonant X-Ray Scattering in DyB2C2

TL;DR

This paper investigates the resonant x-ray scattering spectra in DyB2C2, revealing that lattice distortions primarily influence the spectra rather than quadrupole order, through a detailed theoretical model considering crystal field effects.

Contribution

The study introduces a model that accounts for lattice distortion effects on RXS spectra, highlighting the dominant role of lattice distortion over quadrupole order in DyB2C2.

Findings

Lattice distortion significantly affects RXS intensities.

Main peak of RXS spectra is mainly controlled by lattice distortion.

Both lattice distortion and quadrupole charge anisotropy influence RXS, but distortion dominates.

Abstract

We study the resonant x-ray scattering (RXS) spectra at the Dy $L_{\rm III}$ absorption edge in the quadrupole ordering phase of DyB$_2$C$_2$. Analyzing the buckling of sheets of B and C atoms, we construct an effective model that the crystal field is acting on the $5d$ and $4f$ states with the principal axes different for different sublattices. Treating the $5d$ states as a band and the $4f$ states as localized states, we calculate the spectra within the dipole transition. We take account of processes that (1) the lattice distortion directly modulates the $5d$ states and (2) the charge anisotropy of the quadrupole ordering $4f$ states modulates the $5d$ states through the $5d$-$4f$ Coulomb interaction. Both processes give rise to the RXS intensities on $(00\frac{\ell}{2})$ and $(h0\frac{\ell}{2})$ spots. Both give similar photon-energy dependences and the same azimuthal-angle dependences for the main peak, in agreement with the experiment. The first process is found to give the intensities much larger than the second one in a wide parameter range of crystal field. This suggests that the main-peak of the RXS spectra is not a direct reflection of the quadrupole order but mainly controlled by the lattice distortion.