Quadrupolar, structural, and magnetic ordering in DyB₂C ₂ studied by symmetry analysis and neutron diffraction

Antiferroquadrupolar (AFQ) and antiferromagnetic (AFM) order in DyB ₂C₂ have been investigated by theoretical symmetry analysis and neutron single crystal diffraction experiment with 0 to 4 T applied magnetic field along [100]. New symmetry arguments indicate that the AFQ ordering below T_Q = 24.7 K is accompanied by structural distortions involving boron and carbon atoms, but not dysprosium ions. In the AFQ phase a new arrangement of quadrupoles is proposed based on symmetry analysis of the long-range quadrupolar ordering, neutron diffraction study of the field-induced dipolar magnetic structure, and other available observations. This is a 90° arrangement of quadrupoles of neighboring atoms in the xy plane, and along z. For the zero-field AFM phase, the refinement of neutron single crystal diffraction data of Dy¹¹B₂C₂ against models proposed by Yamauchi et al. [J. Phys. Soc. Jpn. 68, 2057 (1999)] (model A) and by van Duijn, Attfield, and Suzuki [Phys. Rev. B 62, 6410 (2000)] (model B) allows to give preference to modified model A. The magnetic moments of the four Dy sublattices are equal and are confined in the xy plane. The tilt of the Dy moments from the x axis is 36(4)° at (0 0 0) and -112(4)° at the (1/2 1/2 0) site. The angle between the Dy moments adjacent along z is 76(6)° and not 90° as proposed originally.