Antiferroquadrupolar (AFQ) ordering has been conjectured in several rare-earth compounds to explain their anomalous magnetic properties. No direct evidence for AFQ ordering, however, has been reported. Using the resonant x-ray scattering technique near the Dy L(III) absorption edge, we have succeeded in observing the AFQ order parameter in DyB2C2 and analyzing the energy and polarization dependence. The much weaker coupling between the orbital degrees of freedom and the lattice in 4f electron systems than in 3d compounds makes them an ideal platform to study orbital interactions originating from electronic mechanisms.

We have investigated the antiferroquadrupolar ͑AFQ͒ order in DyB 2 C 2 by resonant x-ray scattering. X rays with energies near the L 3 absorption edge of Dy were employed. Superlattice peaks that correspond to three kinds of propagation vectors of ͑1 0 0͒, ͑1 0 1/2͒, and ͑0 0 1/2͒ were investigated in detail with polarization analyses. The experimental results are analyzed using a formalism of resonant x-ray scattering and a model of the AFQ order. The magnetic and quadrupolar scatterings are explained by the model satisfactorily. A detailed investigation of the critical behavior of the AFQ ordering is also reported. The critical exponent ␤ is deduced to be 0.35, not far from the three-dimensional Heisenberg system. We have also succeeded in detecting the diffuse scattering above T Q .

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Experimental evidence of the d-f Coulomb interaction responsible for the resonant x-ray scattering (RXS) from antiferroquadrupolar order in DyB2C2 is presented. The energy dependences of the RXS intensity with polarization analysis are analyzed by considering the interference between the resonances of dipolar (E1) and quadrupolar (E2) transition processes. It is found that the structure factors for the E1 and E2 processes have the same sign for σ-π ′ but the opposite sign for σσ ′ channel. This result, when compared with the calculated structure factors, means that the quadrupolar moments of the 4f and 5d electrons have opposite signs to each other. Interference between nonresonant Thomson scattering from the lattice distortion and the resonant scatterings is also studied and a direct coupling between 4f and the lattice is concluded.

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