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

TL;DR

This study uses resonant x-ray scattering and tensor analysis to investigate quadrupolar and magnetic order in DyB2C2, revealing detailed atomic tensor contributions and coupling schemes in the material.

Contribution

It introduces a detailed tensor analysis of RXS data in DyB2C2, clarifying the roles of atomic tensors and coupling among quadrupolar moments, lattice, and electronic states.

Findings

Azimuthal dependence explained by atomic tensors up to rank 2.

Coupling scheme among 4f quadrupolar moments, 5d orbitals, and lattice established.

Existence of canting of 4f quadrupolar moments up to T_Q confirmed.

Abstract

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., 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 3 and rank 4 tensors are reflected in the data very little. In addition, The coupling scheme among the 4f quadrupolar moment, 5d ortitals, 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 from the point-charge model calculation.