Quadrupole and hexadecapole ordering inDyB2C2:Direct observation with resonant x-ray diffraction

Abstract

Direct evidence of the spatial ordering of Dy $4f$ quadrupole and hexadecapole moments in ${\mathrm{DyB}}_2{\mathrm{C}}_2$ is demonstrated by resonant x-ray diffraction enhanced by an electric quadrupole event $(E2\mathrm{}$ resonance) at the Dy $L_{\mathrm{III}}$ absorption edge. The diffraction data show that the structural phase transition at $T_{\mathrm{Q}}=24.7\mathrm{}\mathrm{K}$ is accompanied by a reduction in the symmetry of the Dy site to $2/m,$ from $4/m,$ and the spatial ordering of the time-even Dy multipoles with $A_g$ character. Below $T_{\mathrm{Q}}$ the crystal structure is described by the space group ${P4\mathrm{}}_2/mnm$ and Dy ions occupy sites $\mathrm{}\left(4c\right).$ The distortion at $T_{\mathrm{Q}}$ involves the lattice occupied by B and C ions, and it amounts to a buckling of B-C planes that are normal to the two-fold rotation axis of $2/m.$ An immediately plausible model of low-energy Dy states correlates data on the specific heat, our x-ray diffraction signals, and magnetic ordering below 15.3 K which has been observed in magnetic neutron diffraction.