d−fCoulomb and quadrupole-strain interactions inDyB2C2

Abstract

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.

Competition of Magnetic and Quadrupolar Order Parameters in HoB4

“…In DyB 2 C 2 , the quadrupolar interaction is stronger than the magnetic one, resulting in the successive phase transitions of an antiferroquadrupolar (AFQ) order at T Q ¼ 24:7 K and an antiferromagnetic (AFM) order at T N ¼ 15:3 K. Although the magnetic interaction favors a parallel stacking of [110]-oriented magnetic moments along the c-axis, the AFQ order confines the orientation of the moments to be perpendicular to adjacent moments. 6,9,10) In HoB 2 C 2 , the Ruderman-Kittel-Kasuya-Yoshida (RKKY)-type magnetic interaction is considered to be slightly stronger than the AFQ interaction, and the system initially exhibits an AFM order at T N ¼ 5:8 K. However, because of the underlying AFQ interaction, a first-order transition into the AFQ phase occurs at T Q ¼ 5:0 K. 7,11,12) The AFM and AFQ interactions are also competitive in TbB 2 C 2 . Although TbB 2 C 2 exhibits only an AFM order at zero magnetic field, the same AFQ phase as that in DyB 2 C 2 and HoB 2 C 2 appears in a magnetic field of only 1 T. 8,13,14) What is more intriguing in TbB 2 C 2 is its magnetic structure at zero magnetic field described by q ¼ ð0; 0; 1=2Þ, which is different from the q ¼ ð0; 0; 0Þ-type structure realized commonly in the RB 2 C 2 series.…”

Resonant X-ray Scattering Experiments on the Ordering of Electronic Degrees of Freedom

“…The solid lines show the calculated azimuthalangle dependences of the geometrical factor P ð2Þ E1 for the O 22 moment. 86,88) The coincidence between the calculation and the data shows that the O 22 -type AFQ order is actually realized. Although the illustration in Fig.…”

“…[82][83][84][85][86][87][88][89][90] In the AFQ state, only the quadrupole moments are ordered, whereas the magnetic degree of freedom remains paramagnetic. DyB 2 C 2 is a tetragonal compound exhibiting two successive phase transitions at T Q ¼ 25 and T N ¼ 15 K. 91) Since the AFM order is observed only below T N , the intermediate phase between T N and T Q was ascribed to an AFQ-ordered phase.…”

“…18 includes detailed distributions including up to the rank-6 component, the signal observed by RXS actually reflects up to the rank-2 moment, and it is considered that the effects of the rank-4 and rank-6 moments are not reflected in the data. 88,89) Although the azimuthal dependence can be well reproduced by the rank-2 term, care should be taken with respect to the real mechanism of the resonant peak, especially for E1, which probes the 5d state. In the case of DyB 2 C 2 , displacements of the B and C atoms take place by the AFQ order below T Q .…”

“…51) Our results indicate that the Jahn-Teller mechanism is more responsible than the Coulomb mechanism in the e g electron system (La 0:5 Sr 0:5 MnO 3 thin films) of 3d transition-metal oxides, 18) and vice versa in the t 2g electron system (YTiO 3 ) of 3d transition-metal oxides 25) and a 4f electron system (DyB 2 C 2 ). 88) In this paper, we review recent applications of RXS to various developments in d and f electron systems. First, in Sect.…”