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The antiferroquadrupolar ordering in DyB2C2 has been investigated using the x-ray resonant scattering technique. The dependence of the intensities of two superlattice peaks on temperature, azimuthal angle, and energy of the incident x-rays was measured. The results show that the antiferroquadrupole ordering, which accompanies a structural phase transition, exists below TQ = 25 K. A structural model for the antiferroquadrupole ordering, for which the propagation vectors are (0,0,1/2) and (0,1,1/2), is presented.

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We determined the magnetic structures of the antiferroquadrupolar (AFQ) ordering material with a tetragonal crystal structure, Ho 11 B 2 C 2 , by neutron diffraction technique. The ground state of Ho 11 B 2 C 2 below T Q shows a characteristic magnetic structure due to competitive coexistence of AFQ and antiferromagnetic (AFM) interactions, which is basically the same as that of the other tetragonal AFQ material DyB 2 C 2 . An angle of 70 • between adjacent magnetic moments along [0 0 1] indicates that the main component of magnetic couplings along [0 0 1] in the ground state is ferromagnetic one, which is strongly affected by AFQ interactions. The existence of the intermediate magnetic ordered phase, phase IV, above T Q indicates that the AFQ ordering in HoB 2 C 2 at T Q is a rare case which is realised in a magnetic ordered state. The magnetic structure in phase IV is a long period one caused by a short range magnetic ordering with a characteristic energy of about 9 K which is higher than T N . The suppressed magnetic entropy at T N is, therefore, attributed to the short range magnetic ordering.KEYWORDS: HoB 2 C 2 , DyB 2 C 2 , antiferroquadrupolar ordering, antiferromagnet, magnetic structure, short range magnetic ordering, neutron powder diffraction §1. IntroductionRecently, Yamauchi et al. found that DyB 2 C 2 with the tetragonal LaB 2 C 2 type crystal structure 1) is the first compound which undergoes an antiferroquadrupolar (AFQ) ordering among tetragonal compounds with well-localised 4f states. 2) DyB 2 C 2 undergoes the AFQ ordering at T Q = 24.7 K and a further transition to an antiferromagnetic (AFM) state with a weak ferromagnetic component at T C = 15.3 K. 2) It should be pointed out that T Q of DyB 2 C 2 is nearly ten times higher than those in other AFQ compounds, for instance, T Q = 1.8 K in TmTe 3) and T Q = 3.3 K in the Kondo compound, CeB 6 . 4) From the experimental point of view, the AFQ ordering in DyB 2 C 2 was confirmed from the characteristic magnetic structure in the ground state which is caused by effects of competitive coexistence of AFQ and AFM interactions; the magnetic moments which lie in the c-plane are fixed to be perpendicular to those of adjacent Dy atoms along the [0 0 1] direction, and are canted from the [1 1 0] direction to the [1 0 0] direction in the c-plane by a canting angle of 28 • . 2) To describe the fundamental structure of this characteristic magnetic structure, two propagation vectors of k 1 = [1 0 0], k 2 = [0 1 1/2] are needed, besides k 3 = [0 0 0] and k 4 = [0 0 1/2] for the canting structure in the c-plane. 2) Very recently, the AFQ ordering in DyB 2 C 2 at T Q was also confirmed by Tanaka et al. and Hirota et al. independently by means of the resonant X-ray diffraction technique. 5, 6) 3401Onodera et al. reported another remarkable compound HoB 2 C 2 which also undergoes an AFQ ordering at T Q = 5.0 K. 7) The temperature dependence of magnetic susceptibility of HoB 2 C 2 shows an apparent anomaly along each direction at T Q , and a broad peak was also observ...