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

16A2/2004G235

Geometrical frustration of quadrupolar moments in DyB4
Takeshi MATSUMURA*, Daisuke OKUYAMA, Hironori NAKAO, Youichi MURAKAMI
Department of Physics, Tohoku University, Sendai 980-8578, Japan

50 (a) (1 0 0)

σ-π'

4030
20
100

1.2x10-3

HWHM [Å-1]x4
E=7.79 keV
Ψ=0º
Ψ=90º

1.0
0.8
0.6

Intensity [cps]Results, Analysis, and Discussion
Resonant x-ray scattering experiment has been
performed at BL16A2 and the (1 0 0) forbidden reflectionhas been investigated in detail. Only the σ-π’ scattering
was observed at any azimuthal angle. Azimuthal angle isdefined to be zero when the c-axis is parallel to thescattering plane. Figure 2 shows the temperaturedependence of the integrated intensity of the rocking scanat the E1 resonance and its half width at half maximum.

At Ψ=0°, the intensity rises up steeply below TN1 andHWHM is very small though it slightly decreases withdecreasing temperature. Contrastingly, at Ψ=90°, theintensity exhibits a sudden increase below TN2 andHWHM is clealy broader than the resolution limit; it also
exhibits a sudden drop below TN2.
A simple magnetic structure assuming only the c-axis
component as shown in Fig. 1 cannot explain the nonzero
intensity at Ψ=90°. It is necessary to introduce in-planemagnetic and quadrupolar components. A detailed
analysis shows that the structure factor at Ψ=0° is
proportional to <Jz>, whereas at Ψ=90° it is proportional
to <Jx> and <Ozx>. In view of the results of ultrasonicmeasurements, it is likely that the quadrupolar degree of
freedom plays an important role. Broad peak width at
Ψ=90° indicate that the <Ozx> quadrupolar moment has
short range correlation because of the geometricalfrustration, whereas the <Jz> magnetic moment observedat Ψ=0° has a long range order. Elastic softening indicatethat there is no static order of <Ozx>; but, it is possible toobserve the short range correlation by RXS because thetime scale of observation is very short. These results
suggest that the <Ozx> moment is fluctuating.
Integrated Intensity [a. u.]

Introduction
A tetragonal rare-earth compound DyB4 has been
attracting growing interest as a system where the quadrupolar moment of Dy might be fluctuating because of thegeometrical frustration. The lattice of Dy is illustrated inFig. 1; note that this is equivalent to the ShastrySutherland lattice. The Dy lattice here can be regarded as
a combination of square and triangular connections
because the nearest neighbor (orange) and the next
nearest neighbor (pink) connections have almost the samedistance.
DyB4 interestingly exhibits two phase transitons atTN1=20.3 K and at TN2=12.7 K. It is established by neutron
powder diffraction that an antiferromagnetic order occurs
at TN1 with magnetic moments align along the c-axis andpropagate along the [100] direction. Also shown in Fig. 1
is this c-axis magnetic moment. What is intriguing is thatthe entropy of Rln2 still remain and that the elastic
softening and absorption are enhanced for TN2 < T < TN1.
These results indicate that the quadrupolar degeneracy issomehow not lifted even below TN1.

150

T=7 K
T=15 Kx4

100
500-0.005(b) (1 0 0) σ-π'E=7.79 keV

0.005

k [r. l. u]

0.4
0.200510152025

Temperature [K]Figure 2: (top) Temperature dependence of theintegrated intensity at Ψ=0° and 90°. (bottom) Half widthat half maximum of the rocking scan. Inset shows thepeak profile at Ψ=90°. Dotted line is the resolution limit.
Figure 1: Lattice of Dy within the ab-plane of DyB4. Blueand red circle represent Dy with up and down spins along
the c-axis, respectively.

References[1] D. Okuyama et al., to be submitted.
* tmatsu@iiyo.phys.tohoku.ac.jp

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