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

Abstract

The dependence with energy of the resonant soft x-ray Bragg diffraction intensity in DyB${}_2$C${}_2$ for the $(001/2)$ 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 $(001/2)$ 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.