Journal of the Physical Society of Japan
Vol. 78, No. 4, April, 2009, 043702#2009 The Physical Society of JapanLETTERS

Field Induced Lattice Deformation in the Quantum Antiferromagnet SrCu2 (BO3 )2Yasuo N ARUMI, Noriki T ERADA1 , Yoshikazu TANAKA2 , Masahiro IWAKI, Koichi K ATSUMATA2 ,Koichi K INDO, Hiroshi K AGEYAMA3 , Yutaka U EDA, Hidenori T OYOKAWA4 ,Tetsuya I SHIKAWA2 , and Hideo K ITAMURA2ISSP, University of Tokyo, Kashiwa, Chiba 277-8581
National Institute for Materials Science, Tsukuba, Ibaraki 305-0044
2RIKEN SPring-8 Center, Harima Institute, Sayo, Hyogo 679-5148
3
Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502
4
SPring-8/JASRI, Sayo, Hyogo 679-5198
1(Received December 22, 2008; accepted February 6, 2009; published March 25, 2009)

The results of synchrotron X-ray diﬀraction by the coupled dimer compound SrCu2 (BO3 )2 subjected toa pulsed high magnetic ﬁeld are reported. We ﬁnd the lattice constant, a, contracts with increasing
magnetic ﬁeld. This change in the lattice constant scales with the magnetization change. We argue thatthe nearest neighbor exchange interaction between Cu2þ spins is an antiferromagnetic one through an
oxygen and its strength depends on the bond angle Cu2þ –O2 –Cu2þ . The bond length between the Cu
ions in a triplet becomes shorter to make the bond angle smaller and to diminish the antiferromagnetic
exchange interaction. We propose this mechanism as a main source of the lattice contraction.
KEYWORDS: SrCu2 (BO3 )2 , synchrotron X-ray diffraction, high magnetic field, magneto-elastic coupling, exchangeinteraction
DOI: 10.1143/JPSJ.78.043702

Magnetic systems with a non-magnetic ground state andan energy gap to the lowest excited state, have attracted
much attention in recent years. A simple example of such
quantum antiferomagnets is found in a dimer, in which two
S ¼ 1=2 spins interact with an antiferromagnetic exchangeinteraction constant, J. The compound, SrCu2 (BO3 )2 (abbreviated SCBO, hereafter) has a non-magnetic ground state
and an energy gap as evidenced by the temperaturedependence of the magnetic susceptibility and nuclear
quadrupole resonance measurements.1) The crystal structure2) of SCBO allows one to discuss the magnetism basedon a model with interacting dimers in two dimension.1,3)
A novel feature found in SCBO is the appearance ofmagnetization plateaux: when an external magnetic ﬁeld, B,
is applied, this material shows magnetization plateaux at
1/8, 1/4, and 1/3 of the saturation magnetization at low
temperatures.1,4,5) The origin of these magnetization plateaux
has been studied theoretically by several authors.3,6–11) With
increasing magnetic ﬁeld, the energy of the lowest excitedstate with Sztot ¼ 1 decreases and it becomes the ground state
above a critical ﬁeld, Hc (20 T). We call this ﬁeld induced
triplet state a ‘‘triplet’’, in which each spin of a Cu2þ dimer
has Sz ¼ 1=2. As discussed by Miyahara and Ueda,3) this
triplet is heavily localized and so an arrangement of these
triplets with a unique pattern is expected to occur at eachplateau phase. From a nuclear magnetic resonance (NMR)
study performed on SCBO at a temperature, T ¼ 35 mK,
Kodama et al. found at least eleven distinct sites for Cu inthe 1/8 plateau phase.12) They proposed a pattern with arhomboid unit cell containing one triplet at the corners andseven dimers with diﬀerent magnetic moments inside.
Tsujii et al. reported that a ﬁnite energy gap exists at Hcfrom their heat capacity, Cp , measurements on SCBO.13)
Therefore, the energy level scheme is more complex thanthat described above.14,15) Nonetheless, it may be a good
approximation to describe the magnetism of SCBO above Hc
as a collection of the triplets. They have also found a sharp
peak in Cp below 1 K at ﬁelds 27:5  B  33 T andinterpreted this ﬁnding as due to a freezing of the triplets.13)
The magnetization of SCBO changes gradually in theﬁeld regions between the plateaux.1,4,5) The nature of theintermediate states between the plateaux has not been fully
understood. Momoi and Totsuka9) argued that a supersolidstate will appear in the intermediate states. In recent years,
extensive theoretical studies have been done on this supersolid.16–18) Takigawa et al. reported that a freezing of thetriplets still exists in the intermediate state between the 1/8
and 1/4 plateaux from their NMR measurements.19)
In this paper, the results of synchrotron X-ray diﬀraction
measurements by SCBO under pulsed, high magnetic ﬁelds
are reported. We ﬁnd that the lattice constant shrinks withincreasing magnetic ﬁeld. This result clearly shows acoupling of spin and lattice degrees of freedom. A spin–lattice coupling has been found in SCBO by ultrasonicexperiments.20) Here, we report the ﬁrst direct observation of
the lattice distortion associated with the emergence of thetriplets. We discuss the origin of the lattice distortion in anatomic level.
The compound, SrCu2 (BO3 )2 has the tetragonal crystal
structure (space group I 4 2m) at room temperature and thelattice constants are a ¼ 8:995 Å and c ¼ 6:649 Å.2) The
crystal structure projected onto the ab-plane is shown inFig. 1. Copper, oxygen and boron atoms sit on a plane
perpendicular to the c-axis. The Cu–O–B plane and the plane
containing Sr are stacked alternately along the c-axis and weexpect that the magnetic interaction between the planes isvery weak. The Cu dimers coupled by J are shown by twoﬁlled circles connected by dashed line in Fig. 1. Thesedimers interact with the neighboring orthogonal dimers withan exchange interaction constant, J 0 . Writing the exchangeinteraction between spins Si and Sj as, JSi  Sj , the valuesof the exchange constants in SCBO are, J=kB ¼ 85 K and
J 0 =kB ¼ 54 K,21) where, kB is the Boltzmann’s constant. The
value of the spin gap, , is =kB ’ 35 K.21)
The single crystal sample of SCBO used in this study wasgrown by a traveling solvent ﬂoating zone method22) and cut

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J. Phys. Soc. Jpn., Vol. 78, No. 4

Fig. 1. The crystal structure of SrCu2 (BO3 )2 projected onto the ab-plane.
Sr atoms are omitted, for clarity.

Fig. 3. (Color online) The magnetic ﬁeld dependence of relative change
in the lattice constant, ½aðB ¼ 0 TÞ  aðBÞ=aðB ¼ 0 TÞ measured atT ¼ 1:5 K. Also shown is the magnetic ﬁeld dependence of themagnetization relative to the saturation value, Ms (red curve). Themagnetization data were taken from ref. 4. Dashed horizontal lines show
the positions of the magnetization plateaux.

θθ

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Y. NARUMI et al.

37.98

38.00
θ38.02

38.04

Fig. 4. (Color online) The magnetic ﬁeld dependence of relative change
in the lattice constant, ½aðB ¼ 0 TÞ  aðBÞ=aðB ¼ 0 TÞ measured at
T ¼ 4:2 K. Also shown is the magnetic ﬁeld dependence of themagnetization relative to the saturation value (red curve).

38.06

Fig. 2. (Color online) X-ray diﬀraction images around the (880) reciprocal lattice point in SrCu2 (BO3 )2 , obtained at (a) T ¼ 1:5 K and B ¼ 0 T,and (b) T ¼ 1:5 K and B ¼ 36:2 T. Horizontal direction in these images
corresponds to the scattering angle, 2. (c) Diﬀraction proﬁles extracted
from the images.

into a parallelepiped with dimensions ’1:5  2  3 mm3 .
Synchrotron X-ray diﬀraction measurements in pulsed, highmagnetic ﬁelds were conducted at the beamline BL19LXU
at SPring-8. The experimental details are given inrefs. 23, 24. The single crystal was mounted with its c-axis
vertical (kB) in a glass dewar which was inserted into thepulsed ﬁeld magnet. Incident and diﬀracted X-ray beams
were in the horizontal plane (?B). The incident beam wastuned to 24 keV in energy by a double-Si-crystal monochromator equipped with a cryogenic cooling system.
Figures 2(a) and 2(b) show examples of the diﬀraction
patterns obtained with the two-dimensional detector.23) We
have measured the magnetic ﬁeld and temperature depend-ence of the (880) and (660) Bragg points. In some cases, wehave observed a splitting of the diﬀraction pattern, which iscaused by the presence of two neighboring grains with asmall angle (’0:03 ) apart. In the following, we show only
the data obtained from a single grain. Figure 2(c) shows
diﬀraction proﬁles extracted from the images.
We show in Fig. 3 the magnetic ﬁeld dependence of thelattice constant, a, relative to its zero-ﬁeld value determinedfrom an analysis of the (880) Bragg peak. We also plot themagnetic ﬁeld dependence of the magnetization, M, relative
to the saturation value, Ms . All the data presented here weretaken in an increasing magnetic ﬁeld. The lattice constant isseen to decrease with increasing B, in coincidence with themagnetization changes. Figure 4 shows the corresponding
data taken at 4.2 K obtained from an analysis of the (660)
Bragg peak. Although the magnetization change at theplateaux becomes less pronounced with increasing temper-043702-2

J. Phys. Soc. Jpn., Vol. 78, No. 4LETTERS

Y. NARUMI et al.

CuO1O2Fig. 5. The magnetic ﬁeld dependence of the full width at half maximumof the (880) Bragg peak measured at T ¼ 1:5 K.

ature, the amount of the lattice distortion is essentiallyunchanged.
Figure 5 shows the magnetic ﬁeld dependence of theradial directional full width at half maximum (FWHM) ofthe (880) Bragg peak. The width does not change muchwith magnetic ﬁeld. So, we may conclude that the crystal
symmetry remains unchanged with magnetic ﬁeld up to40 T.
Let us discuss the origin of the lattice distortion foundin this study. The ground state of a free Cu2þ ion is 2 D withtotal orbital angular momentum, L ¼ 2 and total spin,
S ¼ 1=2. In an octahedral crystal ﬁeld, the orbital states split
into a triplet, d, and a doublet, d, the latter has the lowest
energy. A Cu2þ ion in SCBO is coordinated by four O2
ions in the ab-plane as shown in Fig. 1. There is no anion
immediate above and below the Cu2þ ion along the c-axis.
In this case, the two-fold degeneracy of the d state is lifted
and the ground orbital state is predominantly the one withthe ðx2  y2 Þ symmetry.
We propose the following mechanism to explain theobservation. In Fig. 6 we show the arrangement of oxygenions around a Cu-dimer in the ab-plane of SCBO. The
nearest neighbor super-exchange interaction between Cu2þ
spins is the one through an oxygen. The bond angle Cu–O1–
Cu is 97.8 .2) Goodenough argued that the 90 superexchange interaction between Cu2þ spins is weak.25) On theother hand, we have experimental evidence that the 180
super-exchange interaction between Cu2þ spins is antiferromagnetic and strong.26,27) The increase in the bond angle
from 90 will strengthen an antiferromagnetic exchangeinteraction.
Above Hc , triplets are induced in the sample. Then, thebond length between Cu2þ ions in the triplets is expected toshrink to make the bond angle smaller resulting in a weaker
antiferromagnetic exchange interaction. Since Cu2þ has nine
3d electrons, which can be regarded as a one-hole system,
we expect that the hole orbit with the (x2  y2 ) symmetry
will attract the O2 ions to the Cu2þ ion. In this way, thelattice constant, a, becomes shorter with no detectablechange in the crystal symmetry, in accordance with theobservation (Figs. 3–5). The magnetization is proportional
to the number of triplets in the sample and so the amount of

97.8

Fig. 6. The arrangement of oxygen ions around a Cu-dimer in the abplane of SrCu2 (BO3 )2 .

the lattice distortion is proportional to the magnetization.
We see in Figs. 3 and 4 that the ﬁeld dependence of thelattice distortion is nicely correlated with that of themagnetization.
In addition to the antiferromagnetic exchange interaction
discussed above, there might be a direct exchange interaction, which is considered to be ferromagnetic. We expectthat the bond length between Cu2þ ions in the triplets will
shrink to gain the ferromagnetic direct exchange interaction.
So, the eﬀect of direct exchange interaction, if present, on
the lattice distortion is the same as that of the antiferromagnetic one.
Many Cu2þ compounds are known to exhibit lattice
distortion via the Jahn–Teller eﬀect. As explained above, thetwo-fold degeneracy of the d state in SCBO has been liftedand further gain in energy is obtained when the neighboringO2 ions move towards the Cu2þ . Because the lattice
constant does not change at the low ﬁeld region below
25 T and begins to decrease above this ﬁeld, electron spinof Cu2þ in the triplets must play an essential role in thelattice distortion. An electron spin couples to the lattice
via the spin–orbit interaction and aﬀects the Jahn–Teller
distortion. Our observation could be explained if we would
assume that the Jahn–Teller distortion was present in thetriplet state and absent in the singlet state. At the moment,
we have no reasoning to support this assumption.
In conclusion, we have studied the correlation between themagnetism and lattice degrees of freedom in the coupleddimer compound SrCu2 (BO3 )2 in applied magnetic ﬁeld bysynchrotron X-ray diﬀraction technique. We found thelattice constant, a, contracts with increasing magnetic ﬁeld.
This change in the lattice constant scales with the magnetization change. We argued that the nearest neighborexchange interaction between Cu2þ spins is the antiferromagnetic one through an oxygen and depends on the bondangle Cu2þ –O2 –Cu2þ . The bond length between the Cu
ions in a triplet becomes shorter to make the bond angle
smaller, resulting in a weaker exchange interaction. We
proposed this mechanism as a main source of the latticecontraction. It was believed that there was no chance todetect a tiny structural distortion with X-rays in highﬁelds.11) It is now possible to do X-ray diﬀraction measurements up to 40 T as demonstrated in this paper and inrefs. 23, 24, and 28.

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LETTERS

Acknowledgment
This work was supported in part by Grants-in-Aid for
Scientiﬁc Research on Priority Areas ‘‘High Field Spin
Science in 100T’’ (No. 451) and ‘‘Novel States of Matter
Induced by Frustration’’ (No. 19052004) from the Ministryof Education, Culture, Sports, Science and Technology(MEXT).

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