Journal of the Physical Society of Japan
Vol. 76, No. 7, July, 2007, 073710#2007 The Physical Society of JapanLETTERSA Novel Ordered Phase in SrCu2 (BO3 )2 under High Pressure
Takeshi W AKI1 , Koichi ARAI1 y, Masashi T AKIGAWA1 z, Yuta S AIGA1;2 ,Yoshiya U WATOKO1 , Hiroshi K AGEYAMA3 , and Yutaka U EDA1
1

Institute for Solid State Physics, The University of Tokyo, Kashiwa, Chiba 277-8581
Graduate School of Science and Engineering, Saitama University, Saitama 338-8570
3
Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502
2(Received May 2, 2007; accepted May 31, 2007; published July 10, 2007)

We report results of 11 B NMR and susceptibility measurements on the quasi two-dimensional
frustrated dimer spin system SrCu2 (BO3 )2 under high pressure. At 2.4 GPa and in a magnetic ﬁeld of 7 T,
NMR lines split with decreasing temperature in two steps. A gradual splitting below T ¼ 30 K breaking
the four-fold symmetry of magnetic response is followed by a further sudden splitting below 3.6 K. The
latter indicates a magnetic phase transition, which is also marked by a kink in the susceptibility at
1.44 GPa. From the magnetic hyperﬁne shift data, we conclude that the low-T phase has a doubled unit
cell containing two types of dimers, one in a nearly singlet state and the other with a ﬁnite magnetization
down to T ¼ 0.
KEYWORDS: SrCu2 (BO3 )2 , Shastry–Sutherland model, high pressure, NMR, phase transition
DOI: 10.1143/JPSJ.76.073710

A variety of exotic phenomena has been discoveredin the quasi two-dimensional (2D) dimer spin system
SrCu2 (BO3 )2 .1,2) It has an alternating stack of the magnetic
CuBO3 layers [Figs. 1(a) and 1(b)] and the non-magnetic Sr
layers.3,4) The magnetic layer containing orthogonal arraysof spin-1/2 Cu2þ dimers is a realization of the 2D Shastry–
Sutherland model,5)X
X
H¼J
Si  Sj þ J 0
Si  Sj ;
ð1Þ
n.n.

(a)
B3
B1
B2 J



E-mail: twac@issp.u-tokyo.ac.jp
Present address: Hitachi Medical Corporation, Kashiwa, Chiba.
zE-mail: masashi@issp.u-tokyo.ac.jp
y

B2s
B4b

(b)
B2

B1

B1s

B3b

B2b
B4s

B3s

B1b

[110]

0

where J (J ) is the intradimer (interdimer) Heisenberg
exchange interaction. The ground state of this model isobvious in two limiting cases: the dimer singlet phase
for J 0 =J  1 and the Néel ordered phase for J 0 =J  1. The
dimer singlet phase is known to be stable up to ðJ 0 =JÞc ¼
0:68.6–8) Various experiments have established that
SrCu2 (BO3 )2 has a dimer singlet ground state at ambientpressure and zero magnetic ﬁeld1,9,10) with the energy gapof 33 K11–13) and J 0 =J ¼ 0:60 { 0:64.14,15)
Frustration in the Shastry–Sutherland model strongly
suppresses the kinetic energy of triplets.6) Indeed SrCu2 (BO3 )2 has an extremely small width of the triplet dispersion(0:2 meV12,13)). Such localized nature of triplets leads toformation of various bound states of two triplets15,16) as
observed by Raman17) and neutron18) scattering. It also
leads to the magnetization plateaus at 1/8, 1/4, and 1/3of the saturated magnetization in high magnetic ﬁelds,19)
where triplets crystalize in commensurate superlattices due
to mutual repulsion.20–23)
Since J 0 =J in SrCu2 (BO3 )2 is close to the criticalvalue, tuning the exchange parameters, e.g., by applying
pressure, might enable us to explore the phase diagram of
the Shastry–Sutherland model, which is still an open issue. A
plaquette singlet phase was proposed to exist between the
dimer singlet and the Néel ordered phase.8,24) Alternatively,
instability of two-triplet bound states25) may lead to a spinJ' [110] [110]B4cn.n.n.

(c)
Cu
O
B

Fig. 1. (Color online) The magnetic layer of SrCu2 (BO3 )2 viewed along(a) the c-direction and (b) the [1 10]-direction. (c) A possible orderedstructure in the low-T phase. Shaded circles represent the ‘‘magnetic’’
dimers.

nematic phase. Further variation may arise from the
Dzyaloshinski–Moriya interaction beyond the Shastry–
Sutherland model.26)
In spite of such interest, only a few experiments underpressure have been reported to date. Magnetic susceptibility
data up to P ¼ 0:7 GPa indicates reduction of the energy gap
extrapolating to zero near P ¼ 2:5 { 3:0 GPa.27) The X-ray
study shows a tetragonal to monoclinic structural transition
at 4.7 GPa.28) In this letter, we report results of the nuclear
magnetic resonance (NMR) experiments on 11 B nuclei at
P ¼ 2:4 GPa and the susceptibility measurements up to P ¼
1:44 GPa. Our data provide evidence for a magnetic
phase transition below 4 K into an ordered phase with two
distinct types of dimers.
A single crystal of SrCu2 (BO3 )2 prepared by the traveling-solvent-ﬂoating-zone method29) was cut into a thin plate(2:0  2:8  0:3 mm3 ) for NMR measurements to reduce
distribution of demagnetizing ﬁeld. It was placed in a pistoncylinder-type pressure cell made of NiCrAl and BeCu alloys
ﬁlled with 1 : 1 mixture of N-pentane and isoamyl-alcohol.
The pressure was calibrated against the load applied at room
temperature by separate measurements of the superconducting transition temperature of Sn metal. The pressure cell was

073710-1

LETTERS

J. Phys. Soc. Jpn., Vol. 76, No. 7(a)

T. WAKI et al.

(b) B1, B2

H || cH || [110]B3, B4

Intensity (arb. units)

70 K

150 K

4.2 K
10 K
3.6 K
B1, B2
B3, B4

3.5 K
B3s, B4s

4.0 K

B1s, B2s
3.2 K

B1s, B2s

B3s, B4s

B1b, B2b
B3b, B4b

B3b, B4b
2.1 K

94.0

2.1 K

94.5

95.5
96.5
Frequency (MHz)

97.0

94.5

95.0

95.5
96.0
Frequency (MHz)96.5

Fig. 2. (Color online) Variation of the NMR spectra with temperature at 2.4 GPa for (a) H k c and (b) H k ½110 at the magnetic ﬁeld H ¼ 7:006 T,
The peaks assigned to B1 and B2 (B3 and B4) are marked by the dashed (solid) lines.

mounted on the NMR probe with a double-axis-goniometerto enable arbitrary alignment of the crystal in magnetic
ﬁelds. The 11 B NMR spectra were obtained by Fouriertransforming the spin-echo signal. The demagnetizing
ﬁeld was corrected by comparing the NMR frequencies atambient pressure to the published data obtained on a nearly
spherical crystal.10,26) The susceptibility was measured on adiﬀerent crystal with a SQUID magnetometer (Quantum
Design, MPMS) equipped with a BeCu pressure cell30) using
Daphne Oil 7373 as the pressure transmitting ﬂuid.
Figure 2 shows the NMR spectra under pressure(P ¼ 2:4 GPa) at various temperatures (T) in the ﬁeld H ¼
7:006 T applied along (a) the c- and (b) the [110]-directions.
As 11 B nuclei have spin 3/2, frequencies of the quadrupolesplit three NMR lines are given as,31)m$m1 ¼ ð1 þ K ÞH þ m  1=2 Q þ ð2Þ
ð2Þ
m ;m ¼ 3=2, 1/2, or 1=2. Here  ¼ 13:66 MHz/T is thenuclear gyromagnetic ratio and K is the magnetic hyperﬁne
shift caused by the coupling between nuclei and magnetization on neighboring Cu sites. The second term is the ﬁrst
order quadrupole shift with Q proportional to the electricﬁeld gradient (EFG) along the magnetic ﬁeld direction. This
term vanishes for the central line (m ¼ 1=2). The third term,
the second order quadrupole shift, is identical for the twosatellite lines (m ¼ 3=2 and 1=2).
SrCu2 (BO3 )2 has tetragonal structure with the space group
I 4 2m at ambient pressure and temperatures below 395 K.3,4)
The Cu and B atoms both occupy a unique 8i site locatedon the (110) or (1 10) mirror plane [Fig. 1(a)]. A unit cell
contains two magnetic CuBO3 layers related by the translation tð1=2; 1=2; 1=2Þ. The four B atoms in a unit cell per
layer, B1–B4 in Fig. 1(a), give distinct NMR frequencies
for general ﬁeld directions. The number of NMR lines isreduced for symmetric directions. When the ﬁeld H is in the
ð1 10Þ mirror plane containing the c- and the [110]-directions,B3 and B4 sites are equivalent but B1 and B2 are not due

to buckling of CuBO3 layers [Fig. 1(b)].26) Then B1, B2 and(B3, B4) give three sets of quadrupole split three lines. For
H k ½110 , B1 and B2 also become equivalent resulting
in two sets of lines. For H k c, all four sites are equivalent.
The NMR spectra at ambient pressure are indeed consistent
with these predictions at all temperatures.10,26)
At P ¼ 2:4 GPa, only one set of NMR lines is observed athigh temperatures for H k c [Fig. 2(a)], consistent with the
crystal symmetry at ambient pressure. Upon cooling below
30 K, however, each line begins to split gradually andgets broadened. All three quadrupole split lines show clear
double peak structure at 10 and 4 K [Fig. 2(a)]. In order tomake site assignment for the split peaks, we examinedvariation of the spectra with the ﬁeld rotated in the ð1 10Þplane at 10 K. We found that one of the split peaks further
splits into two lines, while the other peak remains unsplit.
The unsplit peak was then assigned to (B3, B4) and each of
the split lines to B1 or B2. We repeated the measurements
for the ﬁeld rotated in the (110)-plane. The lines assigned toB3 and B4 split but lines from B1 and B2 do not, as
expected.
The value of Q determined from the spacing between thetwo satellite lines is plotted against the angle  between H
and the c-direction in Fig. 3(c) for H k ð1 10Þ and in Fig. 3(d)for H k ð110Þ. The -dependence of K is then determinedfrom the average frequency of the two satellite lines after
32)
subtracting ð2Þ
as shown
m calculated from the Q ðÞ data
in Figs. 3(a) and 3(b).
The distinction between (B1, B2) and (B3, B4) revealedby the line splitting for H k c must be ascribed to the lossof four fold symmetry (4 ) around the c-direction. Thissymmetry requires that Q ðÞ and KðÞ at B1 and B2 (B3 andB4) for H k ð1 10Þ be identical to those at B3 and B4 (B1 and
B2) for H k ð110Þ. The data in Fig. 3 show that thiscondition is grossly violated for the magnetic shift K but
not for the quadrupole coupling Q . This strongly suggeststhat the symmetry change is primarily due to magnetic origin

073710-2

LETTERS

c

K (%)

0.0

0.1

-

H || (110)
B1

(a)

B2

-0.1

νQ (MHz)-0.2

B3, B41.0

B3, B4

0.5

B2
B1
H || (110)

0.0

(c)

-0.5
-30

0

0.0

90

[110]
H || (110)
B3

(b)

(e)

-0.1
-0.2

B4 B1, B2

1.0

B4
B1, B2

0.5
B3

0.0
-0.5

30
60
θ (degree)

-

c

[110]

νQ (MHz)

K (%)

0.1

T. WAKI et al.

Intensity (arb. units)

J. Phys. Soc. Jpn., Vol. 76, No. 70

B2s

B3b, B4b

T=2.1 K
H || (110)

B2b

B1s
B1b

80

85

(d) H || (110)-30

B3s, B4s

θ =90deg

30
60
θ (degree)

90

94.8

95.0
95.2
95.4
Frequency (MHz)Fig. 3. (Color online) (a)–(d) Angle dependences of K and Q at T ¼ 10 K. The lines show the ﬁtting explained in the text. (e) Angular variation of
the NMR spectum at T ¼ 2:1 K with the ﬁeld in the (1 10)-plane. Only the low frequency satellite lines (m ¼ 1=2) are displayed for clarity. Intensity
is plotted in a logarithmic scale to make the broad lines clearly visible.

H || c

-0.20

K (%)

-0.15

(b)

B1, B2B1s, B2s
B1b, B2b

0.10
0.05

-0.10
0.00

B3, B4B3s, B4s
B3b, B4b-0.05
B1, B2
B3, B4B1s, B2s
B3s, B4s
B3b, B4b

0.00
0.05
0.10
1

2

4 6

2

10
T (K)

4 6

-0.05

(c)
χ (10-3emu/mol)(a)1.44 GPa (5.0T, H⊥c)
0.91 GPa (5.0T, H⊥c)
AP (1.0 T, H⊥c)

3
2
1

-0.10

-0.15
100
1

H || [110]
2

4 6

2

10
T (K)

4 6

100

0
0

4

8

12

T (K)

Fig. 4. (Color online) T-dependences of the shifts at 2.4 GPa for (a) H k c and (b) H k ½110 compared with the data at ambient pressure shown by crosses.
(c) T-dependence of the susceptibility at ambient pressure (AP), 0.91 and 1.44 GPa.

since any structural change should be better sensed by Q .
Thus we conclude that the two sublattices of orthogonal Cu
dimers shown by the solid and dashed lines in Fig. 1(a)become inequivalent with diﬀerent magnetizations. We
expect though this may accompany a slight structuralchange. Detailed structural analysis is left for future studies.
The KðÞ and Q ðÞ data can be ﬁt to the standard formulafor anisotropic shifts, u þ v cos2 ð  Þ with u, v, and 
being the ﬁtting parameters,31) as shown by the lines in
Figs. 3(a)–3(d). We found that KðÞ and Q ðÞ at B1 forH k ð1 10Þ [at B3 for H k ð110Þ] are identical to KðÞ andQ ðÞ at B2 (at B4). Thus the mirror symmetries arepreserved. The loss of 4 changes the space group from I 4 2m
to orthorhombic Fmm2. Our data indicate that the entire
crystal forms a single domain.
We now discuss the NMR spectra in Fig. 2 at lower
temperatures. For H k ½110 , (B1, B2) and (B3, B4) give
distinct lines at all temperatures. No line splitting isobserved down to 3.6 K. At 3.5 K, however, all lines develop
clear two peak structure. With further decreasing temperature, these two peaks change into one sharp and one broadlines with nearly equal intensity denoted as Bns and Bnb(n ¼ 1{ 4) in Fig. 2(b). Figure 3(e) shows the variation of
the low frequency satellite lines (m ¼ 1=2) when the ﬁeld
is rotated from [110] toward the c-direction at 2.1 K. Boththe sharp and the broad lines from (B1, B2) split in a similarmanner as observed at higher temperatures. Therefore, eachof B1 and B2 must be divided into two sites below 3.6 K,(B1s, B1b) and (B2s, B2b), yielding eight inequivalent B
sites for general ﬁeld directions. A Similar spectrum withsharp and broad lines is observed also for H k c at
2.1 K [Fig. 2(a)], although there is only one set of broadlines. We found that this belongs to (B3, B4), while thebroad lines from (B1, B2) overlap with the sharp lines,by extending the measurements shown in Fig. 3(e) tosmaller values of .
Figure 4 shows the T-dependence of the shifts at various
sites for (a) H k c and (b) H k ½110 compared with the data
at ambient pressure.10,26) Above 40 K, the results at 2.4 GPa
are nearly unchanged from ambient pressure. Line splitting
appears for H k c below 30 K as mentioned above. In spiteof a clear change of symmetry, the splitting develops
gradually without sign of a phase transition. In contrast,
the second splitting at 3.6 K occurs suddenly and clearly073710-3

J. Phys. Soc. Jpn., Vol. 76, No. 7

LETTERS

marks a phase transition. The shifts for the sharp lines
approach near zero as T ! 0, pointing to a singlet groundstate. We can indeed ﬁt the data to an activation law, þ  expð=TÞ, yielding  ¼ 11{15 K. These values aremuch smaller than the gap at ambient pressure (24 K) at
the same ﬁeld of 7 T. The shifts for the broad lines, on theother hand, maintain large values down to the lowest
temperature, pointing to a magnetic state without an
excitation gap.
These results indicate coexistence of ‘‘magnetic’’ and‘‘non-magnetic’’ Cu dimers in the low-T phase. The sharp(broad) lines should come from those B sites which couple
dominantly to the non-magnetic (magnetic) Cu dimers.
Preliminary results at diﬀerent ﬁelds show that both thehyperﬁne ﬁeld (K multiplied by H) and the line width for thebroad lines are approximately proportional to the ﬁeld,
indicating no spontaneous moment at zero-ﬁeld. The increased number of NMR lines indicates doubling of the primitive
unit cell in the low-T phase. It is most likely that each of
the Cu dimer sublattices develop spatial order of magnetic
and non-magnetic dimers, forming either a superstructurein the ab-plane [see Fig. 1(c) for an example] or alternating
magnetic and non-magnetic layers along the c-direction.
The susceptibility data are presented in Fig. 4(c). Whileno anomaly is observed at ambient pressure and at 0.91 GPa,
the data at 1.44 GPa show a clear kink at 4.0 K, providing
further evidence for bulk nature of the phase transition. The
slightly diﬀerent transition temperature is presumably due tothe diﬀerence in magnetic ﬁeld. Note that the susceptibility
approaches a ﬁnite value as T ! 0 consistent with thecoexistence of two types of Cu sites.
What is the order parameter describing the low-T phase?
Since the magnetic dimers appears to have no spontaneous
moment at zero-ﬁeld but larger susceptibility than the nonmagnetic dimers, a natural candidate would be the staggeredcomponent of the two-spin correlation hS1  S2 i within adimer. This is invariant under time-reversal and considereda bond-nematic order parameter. Recently, a bond-nematicorder has been proposed for frustrated spin systems on asquare lattice as a result of Bose condensation of twomagnon bound states.33) Whether such a scenario is relevant
for SrCu2 (BO3 )2 is an interesting issue.
To conclude, we have demonstrated that SrCu2 (BO3 )2
under pressure exhibits symmetry lowering in two steps.
A gradual loss of four-fold symmetry near 30 K is followed
by a clear phase transition below 4 K. We propose that the
low-T phase has spatial order of two types of dimers: oneis nearly in a singlet state while the other has a ﬁnite
susceptibility down to T ¼ 0.
We thank S. Miyahara, F. Mila, T. Momoi and M.
Oshikawa for stimulating discussions and T. Matsumoto forhelp in designing the pressure cell. This work was supported
by a Grant-in-Aid for COE Research (No. 12CE2004) from
the Ministry of Education, Culture, Sports, Science andTechnology of Japan.

T. WAKI et al.

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073710-4