Photon Factory Activity Report 2004 #22 Part B (2005)
Materials Science

16A2/2001G063

Evidence for d-f Coulomb mechanism in the resonant x-ray scattering of DyB2C2
Takeshi MATSUMURA*1, Daisuke OKUYAMA1, Hironori NAKAO1, Youichi MURAKAMI1,Yusuke WAKABAYASHI2
1
Department of Physics, Tohoku University, Sendai 980-8578, Japan
2
KEK-PF, Tsukuba, Ibaraki 305-0801, Japan

Results and Analysis
Figure 1 shows the energy dependence of the (0 0 2.5)
resonant reflection of DyB2C2 for σ- σ' and σ-π' polarization channels. The peak at 7.792 and 7.782 keVcorresponds to the E1 (2p-5d) and E2 (2p-4f) resonance,
respectively. These resonances have been considered to becaused by the AFQ order of the 4f electrons. However,since the surrounding B and C atoms are also distorted
below TQ, the 5d state could be influenced by the B and Catoms; this means that the E1 resonance do notnecessarily reflect the AFQ order of the 4f state, but thedisplacements of B and C atoms.

Intensity x µ [arb. units]

300(0 0 2.5)
Ψ=45°
σ−σ'

DyB2C2200

T=16 KDyB2C2(3 0 1.5)
T=20 K

10000
σ−σ'5000

Ψ=180°
Ψ=270°

050
0

σ−π'

Ψ=180°
Ψ=270°
7.75

7.80

7.85

Energy [keV]

100

Figure 2: Energy dependence of the (3 0 1.5) resonant
reflection. For σ- σ', there is a contribution of Thomson
scattering from the lattice distortion.

0100(0 0 2.5)
Ψ=0°
σ−π'

50

0

7.76

7.78

7.80

7.82

Energy [keV]
Figure 1: Energy dependence of the (0 0 2.5) resonant
reflection originating from the AFQ order.

138

One mystery in this experimental result is that the E2resonance is well separated in the σ-π' channel but ishidden in the tail of the E1 resonance for σ-σ'. In order tosolve this mystery, we have analyzed the data by utilizinga theory developed by Lovesey et al., which directly
connects the atomic tensors with the scattering amplitude.
The calculation described in Refs. 1 and 2 shows thatthe structure factors for the E1 and E2 resonances have
opposite sign for σ-σ' and same sign for σ-π', respectively.
Furthermore, it is shown that this difference in sign iscaused by the fact that the rank 2 atomic tensors for the 4f
and 5d shells have opposite signs. This means clearly thatthe charge distributions of the 4f and 5d electrons are
orthogonal to each other because of the Coulombinteraction. This is the direct evidence for the Coulomb
mechanism in RXS for an AFQ system.

Intensity x µ [arb. units]

Introduction
Resonant x-ray scattering (RXS) has now become apowerful technique to observe orderings of orbital andquadrupolar moments. However, there have been acriticism that RXS do not observe the orderings directly.
For example, in the K-edge resonance in d-electronsystems, RXS utilizes the p-state as the intermediate stateof the E1 process. Although we expect the p-state
contains information on the d-shell, it can also be
influenced by the surrounding ions. The same criticism
also applies to f-electron systems if the LIII-edge isutilized. The present study on the antiferroquadrupolar(AFQ) order in DyB2C2 shows that the d-f Coulombinteraction is responsible for the resonance.

Users' Report

Analysis of another reflection at (3 0 1.5) also confirm
the above interpretation. In addition, it is concluded thatthe displacement of B and C atoms prefer to avoid thecharge distribution of 4f, and not that of 5d.
References[1] T. Matsumura et al., Phys. Rev. B 71, 012405 (2005).
[2] T. Matsumura et al., J. Phys. Soc. Jpn. 74, 1500 (2005).
* tmatsu@iiyo.phys.tohoku.ac.jp