The effect of core-valence intra-atomic quadrupolar interaction in resonant x-ray scattering at the Dy M4,5 edges in DyB2C2

The dependences on energy of the resonant soft x-ray Bragg diffraction intensities in DyB2C2 for the (00 1/2) reflection at the Dy M-4,M-5 edges have been calculated with an atomic multiplet Hamiltonian including the effect of the crystal field and introducing an intra-atomic quadrupolar interaction between the 3d core and 4f valence shell. These calculations are compared with experimental results (Mulders et al 2006 J. Phys.: Condens. Matter 18 11195) for the antiferroquadrupolar and antiferromagnetic phases of DyB2C2. We reproduce all the features appearing in the (0012) 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. These calculations show that a detailed description of the energy dependences of resonant x-ray scattering signals at the M edges in 4f and 5f systems with multipolar ordering may require the inclusion of an aspherical intra-atomic Coulomb interaction.