Observation of the antiferroquadrupolar order in DyB 2 C 2 by resonant x-ray scattering

We have investigated the antiferroquadrupolar (AFQ) order in ${\mathrm{DyB}}_{2}{\mathrm{C}}_{2}$ 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 0), (1 0 1/2), and (0 0 1/2) 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 $\ensuremath{\beta}$ is deduced to be 0.35, not far from the three-dimensional Heisenberg system. We have also succeeded in detecting the diffuse scattering above ${T}_{Q}.$