Multipole tensor analysis of the resonant X-ray scattering by quadrupolar and magnetic order in DyB₂C₂

Resonant x-ray scattering (RXS) experiment has been performed for the (3 0 1.5) superlattice reflection in the antiferroquadrupolar and antiferromagnetic phase of DyB₂C₂. Azimuthal-angle dependence of the resonance enhanced intensities for both dipolar (E1) and quadrupolar (E2) resonant processes has been measured precisely with polarization analysis. Every scattering channel exhibits distinctive azimuthal dependence, differently from the symmetric reflection at (0 0 0.5) which was studied previously. We have analyzed the results using a theory developed by Lovesey et al. [J. Phys.: Condens. Matter 8 (1996) 10983], which directly connects atomic tensors with the cross-section of RXS. The fitting results indicate that the azimuthal dependences can be explained well by the atomic tensors up to rank 2. Rank 4 tensor is not reflected in the RXS data. In addition, the coupling scheme among the 4f quadrupolar moment, 5d ortital, and the lattice has been determined from the interference among the Thomson scattering from the lattice distortion and the resonant scatterings of E1 and E2 processes. It has also been established from the RXS of the (3 0 1.5) reflection that the canting of the 4f quadrupolar moments exists up to T_Q. We also discuss a possible wavefunction of the ground state and the existence of the rank 4 moment.