Journal of the Physical Society of Japan
Vol. 74, No. 6, June, 2005, pp. 1702–1705#2005 The Physical Society of JapanLETTERS

Spin-Singlet Ground State in Two-Dimensional S ¼ 1=2
Frustrated Square Lattice: (CuCl)LaNb2 O7
H. K AGEYAMA, T. KITANO, N. O BA, M. N ISHI1 , S. N AGAI1 , K. H IROTA1 ,L. V ICIU2 y, J. B. W ILEY2 , J. Y ASUDA, Y. B ABA, Y. A JIRO and K. Y OSHIMURA
Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502
1
Neutron Science Laboratory, Institute for Solid State Physics, University of Tokyo,
106-1 Shirakata, Tokai, Ibaraki 319-1106
2
Department of Chemistry and the Advanced Materials Research Institute,
University of New Orleans, New Orleans, LA 70148-2820, U.S.A.
(Received February 25, 2005; accepted April 6, 2005)

We report on the magnetic properties of double-layered perovskite (CuCl)LaNb2 O7 with a squarelattice of S ¼ 1=2 Cu2þ ions, prepared by topotactic ion-exchange reactions. Magnetic susceptibility
exhibits a thermal-activated behavior, and the analysis of the data suggests competing ferro- andantiferromagnetic exchanges for ﬁrst- and second-nearest-neighbor bonds, respectively. Neutron
scattering experiments provide explicit evidence for a spin-singlet ground state with an energy gap of
2.3 meV. The well-deﬁned low-lying triplet mode is almost independent of Q despite densely packed
magnetic ions in the CuCl plane. In addition, on the basis of the isolated dimer model, we found that the which corresponds to the fourth-nearest-neighbor bond. These
intradimer distance is as long as 8.8 A,
results indicate a sizable geometrical frustration that should impose severe constraints on the propagationof the triplet excitation, as in the case of SrCu2 (BO3 )2 . This argument is further reinforced by theobservation of a collective-triplets bound state at 5.0 meV.
KEYWORDS: spin gap, square lattice, J1 –J2 model, ion-exchange reaction, neutron scattering, bound state,(CuCl)LaNb2 O7
DOI: 10.1143/JPSJ.74.1702

In recent years, much attention has been given to lowdimensional antiferromagnetic (AFM) quantum spin systems
that have a ground state with no long-range magnetic orderand an energy gap in the magnetic excitation spectrum.
Among them, the S ¼ 1=2 frustrated square lattice AFM
system (J1 –J2 model) is of special importance in light ofAnderson’s resonating valence bond (RVB) concept to
explain high-Tc superconductivity in doped layered cuprates.1) An interesting phase diagram with unusual groundstates is predicted as a function of the ratio J2 =J1 between
the ﬁrst- (J1 ) and second- (J2 ) nearest-neighbor exchangeinteractions.2–4) For 0 < J2 =J1 < 0:38, a normal Néel orderstate is the ground state, while for J2 =J1 > 0:55, a collinear
order should develop. For 0:38 < J2 =J1 < 0:55, where theeﬀect of the frustration is stronger, a quantum disorderedphase with a ﬁnite gap is expected. However, so far there has
been no experimental veriﬁcation of the spin-liquid phase in
the J1 –J2 model, apart from CaV4 O9 5) and SrCu2 (BO3 )2 6)
structures, which are derivatives of the square lattice. As far
as the authors know, three compounds have been suggested
as prototypes of the J1 –J2 model with signiﬁcant coupling
between J1 and J2 : Li2 VOSiO4 (J1 ¼ 0:56, J2 ¼ 6:3 K),
Li2 VOGeO4 (J1 ¼ 0:82, J2 ¼ 4:1 K)7–9) and Pb2 VO(PO4 )2(J1 ¼ 6, J2 ¼ 9:8 K).10) All of these are, however, magnetically ordered at low temperatures.
Low-temperature topotactic strategies such as intercalation/deintercalation oﬀer eﬀective routes for the design andconstruction of new two-dimensional (2D) magnetic materials.11–13) In this letter, we will demonstrate that a doublelayered Dion-Jacobson phase (CuCl)LaNb2 O7 , preparedE-mail: kage@kuchem.kyoto-u.ac.jp
Present address: Department of Chemistry and Princeton Materials
Institute, Princeton University, NJ 08544, U.S.A.

yfrom topochemical ion exchange, provides a new class of
2D Heisenberg spin systems, where a spin-singlet groundstate with a ﬁnite energy gap is achieved in the S ¼ 1=2
frustrated square lattice. The structure of (CuCl)LaNb2 O7 ,determined using Rietveld analysis of X-ray powder diffraction data,11) revealed that the lattice is tetragonal (spacegroup P4=mmm), the room-temperature cell constants being
 and c ¼ 11:728 A.
 As shown in Fig. 1, thea ¼ 3:879 A
structure consists of magnetic CuCl planes widely separated
by nonmagnetic double perovskite slabs. Hence 2D magnetic properties are strongly expected. The S ¼ 1=2 copper
ion is octahedrally coordinated, bridging apical oxygen ions

(a)

(b)
J1
F
E

E'

b

J2

C

D
B'

c

B
A

a

b
a

Fig. 1. (a) Structure of (CuCl)LaNb2 O7 . The closed spheres are Cu2þ , thegray spheres are Cl , the open spheres are La3þ , and the octahedra
represent NbO6 .11) (b) The CuCl layer viewed along [001]. The Cu2þ ionsconnected by the dotted line correspond to a 4NN dimer. The bold broken
and solid lines represent, respectively, the J1 and J2 bonds. Later
structural investigation14) has suggested disorder of Cl ions from 1a(0, 0, 1/2) to 4m (x, 0, 1/2), as indicated by the arrows.

1702

LETTERS

where N, B , and kB denote Avogadro’s number, the Bohrmagneton, and Boltzmann’s constant, respectively. Here, equals the strength of intradimer interaction J and is the only
adjustable parameter in eq. (1). The value of  wasdetermined so as to make the temperatures at maximum s

1703

(a)
χ (x10-3 emu/mol)

1010χ (x10-3 emu/mol)of the perovskite layer and surrounded by four chlorine ionsin the CuCl plane. The CuO2 Cl4 octahedra share corners
with the NbO6 octahedra of the perovskite slabs and edges
with other CuO2 Cl4 octahedra in the CuCl plane. Later
structural analysis on the basis of neutron diﬀraction
suggests disorder of the chlorine ions within the CuCl
plane.14)
The ion-exchange reaction for the synthesis of (CuCl)LaNb2 O7 is expressed as RbLaNb2 O7 + CuCl2 ! (CuCl)LaNb2 O7 + RbCl. The details of the synthesis are given inref. 11. The powder X-ray diﬀraction pattern indicated asingle-phase product with cell parameters consistent withthose previously reported.11) The energy dispersive spectroscopy (EDS) conﬁrmed a stoichiometric composition.
Magnetic susceptibility measurements were performed on a
powder sample with a SQUID magnetometer (Quantum
Design, MPMS) over the temperature range T ¼ 2{300 K in
an applied ﬁeld of H ¼ 0:1 T. Inelastic neutron scatteringexperiments were carried out on the ISSP-PONTA tripleaxis spectrometer installed at a 5G beam port of JRR-3M at
the Japan Atomic Energy Research Institute. A powder
sample of 12.6 g was put into an aluminum cylinder. Most of
the data were collected using a ﬁxed ﬁnal energy Ef of 1 ) and a horizontal collimation of
14.7 meV (kf ¼ 2:67 A
000
open-40 -S-80 -80 in combination with a pyrolytic graphite(PG) ﬁlter placed after the sample to eliminate higher-orderbeam contaminations. This setup yields an energy resolution 1 and E ¼ 0, as determined byof 1.21 meV at Q ¼ 1:38 A
measuring the incoherent scattering from the sample.
Figure 2 shows the magnetic susceptibility  for(CuCl)LaNb2 O7 . At high T above 50 K, the raw data rexhibit a Curie–Weiss (CW) behavior. On cooling, rexhibits a broad maximum at around 16.5 K (Tmax), which ischaracteristic of low-dimensional AFM system, and decreases rapidly with decreasing T. This decrease suggests a
spin-singlet ground state separated from the excited state bya ﬁnite energy gap. It should be noted that neutron
diﬀraction experiments revealed no sign of 3D order. Apartfrom the pronounced thermal-activated character, a Curie
tail is seen below 4 K, most likely due to residual impurities
and/or defects of Cu2þ ions in (CuCl)LaNb2 O7 . The amountof impurities/defects was estimated to be about 2.6% of free
S ¼ 1=2 Cu2þ ions. After subtracting this upturn, one
obtains the spin susceptibility s . Subsequently, the analysisof s using the CW formula,  ¼ C=ðT þ Þ, resulted ins ¼ 9:6 K and Cs ¼ 0:385 [emu K/mol]. Assuming the
stoichiometric composition, as supported by EDS, a reasonable value of 2.03 from the g-factor for a Cu2þ ion, gs , isobtained.15)
As a starting point, in order to estimate mainly the spin
gap , we ﬁrst analyzed the s data using a S ¼ 1=2 isolated
AFM dimer model, where the susceptibility d is precisely
expressed as1
Ng2 2B1
d ¼
ð1Þ
1 þ expð=TÞ ;3
3kB T

H. KAGEYAMA et al.

5

5
0

0

10

20

30

40

T (K)

0
800

χ-1 (mol/emu)

J. Phys. Soc. Jpn., Vol. 74, No. 6, June, 2005

(b)

600
400

0.1 T
(CuCl)LaNb2O7

200
0
0

50

100

150

200

250

300

T (K)
Fig. 2. (a) The T variation of the magnetic susceptibility in (CuCl)LaNb2 O7 measured at 0.1 T. There is no diﬀerence between ZFC/FC
susceptibilities. The open and closed circles represent, respectively, r
and s , while the dotted line represents the Curie term. The solid line is dwith  ¼ 26:5 K. The enlarged plot is presented in the inset. (b)Reciprocal susceptibilities, 1=s and 1=d .

and d coincide with each other. As a result, we obtained
 ¼ 26:5 K. Despite the densely arranged magnetic ions in
the CuCl layers, d appears to agree well with s . Yet, asseen at around 15 K, a quantitative discrepancy exists
between s and d . Furthermore, the 1= vs T plots in
Fig. 2(b) clearly exhibit a disagreement between experimentand theory at high T.
It is known that  is equal to J1 þ J2 for the J1 –J2 model.
In the limit of J1  J2 (J2  J1 ),  should be that of the
Heisenberg AFM system on the square lattice with only one
coupling constant J1ð2Þ and the maximum occurs at Tmax
16)
0:935J1ð2Þ (¼ 0:935). The experimental ratio Tmax =s ¼
1:72, which is much larger than that for the nonfrustrated
case, indicates the presence of signiﬁcant frustration. It is
worth pointing out that the J2 bonds are always frustrated by
the geometry as long as J2 is AFM. The chlorine ions in the
CuCl plane are arranged at the center of 2NN bonds, not
1NN bonds, so that J2 need not be smaller in magnitude thanJ1 . The Cu2þ –Cl–Cu2þ angle of 180 for the J2 bondactually supports a sizable AFM interaction (J2 > 0), whilethat of 90 for the J1 bond points to a ferromagnetic (FM) J1(<0). Direct evidence for the FM J1 is given by the large
value of Tmax
=s . This is the second example of FM J1 ,following Pb2 VO(PO4 )2 .10) However, Pb2 VO(PO4 )2 exhibitsa transition to an ordered state at 3.8 K in contrast with thepresent compound that shows no 3D order. To date, most of
the existing theories based on the J1 –J2 model concern thecases with AF interactions. There is only one theoretical
paper that deals with FM J1 ,17) in which it was suggested that
there should also be a spin-liquid phase occurring for

1704

J. Phys. Soc. Jpn., Vol. 74, No. 6, June, 2005

LETTERS

H. KAGEYAMA et al.

1500

6500
-1

4

I (1.7K) −I (20K)

I (Counts/600s)

10

1000

3

10
500

Q = 0.4 Å

0

2

4
6
E (meV)800

E = 2.2 meV
E = 4.9 meV

6000

700

5500

I (Counts/1800s)

I (counts/600s)(CuCl)LaNb2O7
1.7 K
20 K

8
5000

0

5

10

15

20

25

30

600
35

T (K)

0

2

(CuCl)LaNb2O7

4

6

8

E (meV) 1 , T ¼ 1:7 K (circles) and 20 K
Fig. 3. Inset: constant-Q scan at 0.8 A(triangles). The circles in the main panel are the diﬀerence, Ið1:7 KÞ 
Ið20 KÞ. The full curve represents the least-squares ﬁt, where the peaks
were approximated by two Gaussians.

J2 =J1  0:5 between the FM and collinear ordered phases.
It is exciting if (CuCl)LaNb2 O7 can be an experimental
correspondence of this model.
Let us move onto the result of the neutron scatteringexperiments. Typical constant-Q scans collected at T ¼ 1:7
and 20 K are shown in the inset of Fig. 3. Due to the use of apowder sample and elastic incoherent scattering which
progresses moderately below 6 meV and rapidly below
2 meV, relatively weak magnetic scattering from the sample
in this E range can be better recognized when the intensity at
20 K, I(20 K), is subtracted from that at 1.7 K, I(1.7 K) (seethe main panel of Fig. 3). There are two symmetric inelastic
peaks indicating magnetic scattering from the spin-singlet
ground state, which we call transitions I and II. No otherfeatures were observed for energy transfer up to 18 meV.
The least-squares ﬁt to the experimental data, where thepeaks are approximated by multi-Gaussians, gave theexcitation energies of 2:31  0:05 and 5:0  0:3 meV andfull widths at half maximum of 1:3  0:1 and 1:2  0:7 meVfor transitions I and II, respectively. The widths are as large
as the instrumental resolution. The ﬁrst gap of  ¼ 2:3 meV(26:7 K) agrees well with that estimated from the –T
data. The discrepancy below 1 meV, in other words, negativevalues of Ið1:7 KÞ  Ið20 KÞ, most probably reﬂects paramagnetic scattering which is negligible at 1.7 K but eﬀectiveat 20 K. The T dependence of the intensity at 2.2 meV and 1 is shown in Fig. 4. The intensity decreases with
Q ¼ 0:4 A
increasing T and levels oﬀ at a constant value above
approximately 20 K, a temperature comparable to that of thespin gap. These results are consistent with the interpretationthat transition I is a one-triplet excitation from the spinsinglet ground state. The origin of transition II will be
discussed later.
In order to gain an insight into the dynamical properties ofthe one-triplet mode, a number of constant-Q scans were 1 . In general, for 2D
performed for 0:4 < Q < 3:2 A
systems having a spin-singlet ground state, the magnetic

excitations have a wide band and thus a strong dispersion
along the magnetic plane. The spectrum shapes at constant E
and constant Q depend, to a large extent, on the shape of thedispersion relation. In particular, constant-Q scans throughthe gap show an extended tail in the high-E region, giving
rise to an asymmetric peak shape. However, our results for(CuCl)LaNb2 O7 obviously exhibit diﬀerent behavior fromconventional 2D systems; the most prominent features of theinelastic scattering are that the spectrum shapes in constantQ scans for transition I are completely symmetric (Fig. 3)
and that it is almost independent of Q (E is 0.2 meV atmost) [Fig. 5(a)]. This means that there is, at least
empirically, no strong two-dimensionality in the magnetic
excitations, although the crystal structure reveals a distinct
square-lattice arrangement of Cu2þ ions. Such a dispersionless band has been typically observed in isolated or weakly
coupled AFM clusters, as in dimers,18,19) and a four-spincluster.20) We believe that in (CuCl)LaNb2 O7 , the geometrical frustration should play a crucial role in making the
one-triplet excitation extremely localized, thus giving rise to
the ﬂat dispersion. A similar ﬂat dispersion associated withthe frustrated geometry has been observed in the Shastry–
Sutherland compound SrCu2 (BO3 )2 .21) The one-triplet ex-

4

E (meV)0

Fig. 4. The T variation of the intensities at E ¼ 2:2 meV (left) and 1 . The broken line is a guide for the eyes.
4.9 meV (right), at Q ¼ 0:4 A

3(a)(CuCl)LaNb2O72
1
0

E = 2.1 meV (b)800

I (1.7K) −I (20K)

Q = 0.8 Å

-1

2

F (Q)
600

1-sin(QR)/QR

400
200
0
0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Q (Å-1)
Fig. 5. (a) The Q dependence of transition I. (b) Peak intensities oftransition I as a function of Q. The solid line indicates the ﬁt according to
eq. (2), which resulted in R ¼ 8:8 A.

J. Phys. Soc. Jpn., Vol. 74, No. 6, June, 2005

LETTERS

citations for the Shastry–Sutherland model can propagate
only from the sixth order in the perturbation calculations.22)
In Fig. 5(b), we demonstrate the Q dependence of thescattering intensity, Ið1:7 KÞ  Ið20 KÞ, measured at thecenter of the ﬁrst energy gap, where an oscillating behavior
is clearly seen. In analyzing this data, the use of the isolated
dimer model is possible because of the localized character of
triplet excitations irrespective of their origin.18,19,21) The
intensity of a singlet-to-triplet transition for an isolated
dimer is expressed as
sin QR
2IðQÞ / F ðQÞ 1 ;
ð2Þ
QR
where the last term is the interference term reﬂecting theseparation R within a dimer.18,19) From the qualitative pointof view, not only does the intensity decrease, as expected forF 2 ðQÞ,23) but the modulation due to the interference term isreproduced well. The surprise came from the quantitative
analysis; we obtained an extraordinarily long intradimer 24) which is far longer than 3.879 Adistance of R ¼ 8:8 A(1NN) and those in usual dimer systems.18,19) It is rather
 (4NN). This means that the spin-liquid
close to 8.674 A
phase in the present system is essentially diﬀerent from thecolumnar dimerized state for the J1 –J2 model around
J2 =J1  0:5 where the 1NN bonds are responsible for the
spin-singlet formation.2–4)
As to the conﬁguration of the 4NN spin-singlet pairs,
there are three possibilities. First, the 4NN pairs may bearranged in an ordered manner, associated with the breakingof the translational symmetry. Although no superstructure
reﬂections were observed in our neutron diﬀraction proﬁlesdown to 1.5 K, a relevant structural modulation might bevery subtle. A second scenario is a description based on thestatic but random distribution of the 4NN pairs in the layer.
The problem here is how one particular 4NN bond is chosen
out of eight equivalent sites. This may be resolved byconsidering the disorder of the chlorine ions14) because it
may diﬀerentiate otherwise uniform bonds. Last, but notleast, is the RVB state, or a resonant mixture of the 4NN
pairs, which is possible without any structural phasetransition.
Can the original J1 –J2 model with FM J1 account for the
dimerization of the 4NN bonds? As noted above, a spinliquid phase for FM J1 has been proposed to occur between
the FM and collinear order phases.17) Their justiﬁcations
largely rely on the analogy with the well-investigated spinliquid phase for AFM J1 between the Néel and collinear
order phases. Therefore, the nature of the new phase remains
mostly unidentiﬁed as of yet, including the problem of which
nearest-neighbor bond forms the spin singlet. Nevertheless,we would like to bring the attention of readers to one
important fact: The exchange routes A–(B,B0 )–C–E–F and
A–B0 –D–(E,E0 )–F (see Fig. 1(b)) are compatible with AF
correlation between 4NN sites. Alternatively, it might benecessary to consider a generalized J1 –J2 model that
includes 3NN (J3 ) and 4NN (J4 ) bonds, spin–latticecouplings, and randomness eﬀect induced by the disorderof chlorine ions.
Finally, let us brieﬂy discuss the origin of the excitation at
5.0 meV. As shown in Fig. 4, the T dependence of theintensity of transition II shows the same tendency as does

H. KAGEYAMA et al.

1705

that of transition I, indicating that transition II is associatedwith the collective bound state excitation of several
elementary triplets. Note that distinct multitriplet excitations
with a similar T dependence have been observed in
SrCu2 (BO3 )2 .21) Because the second energy gap 5.0 meVexceeds twice the ﬁrst energy gap (4.6 meV), transition II
should correspond to excitations of more-than-two triplets. If
the bound state consists of three elementary triplets, it has
considerable stabilization energy, i.e., 1.9 meV, implying
strong triplet-triplet interactions present in this system. The
reason for the absence of the two-triplet bound state moderemains to be solved.
To summarize, we demonstrated that (CuCl)LaNb2 O7 is a
new 2D spin gap system realized for the ﬁrst time in a
S ¼ 1=2 frustrated square lattice. The –T data indicated aspin-liquid state with competing FM J1 and AFM J2 . The
neutron scattering experiment probed two resolution-limited
peaks at 2.3 and 5.0 meV, corresponding to one- andmultitriplet excitations, respectively. The dispersion of theformer is nearly ﬂat (E < 0:2 meV) and the intensity
shows an oscillatory behavior as a function of Q. Thesephenomena are consequences of the strong geometricalfrustration present in the square lattice. It was also shownthat the dimer size is as long as the 4NN bond, but the
conﬁguration of dimerized pairs in the layer has yet to be
determined. We strongly hope that our experiments will
trigger intensive theoretical investigations on the (generalized) J1 –J2 model with FM J1 for greater understanding of
the nature of the spin-liquid phase in (CuCl)LaNb2 O7 .
Acknowledgment
We are grateful to Professor F. Mila for his usefulcomments on the J1 –J2 model. This work has been supported
partly by the National Science Foundation (DMR-0309972).

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P. W. Anderson: Science 235 (1987) 1196.
N. Read and S. Sachdev: Phys. Rev. Lett. 62 (1989) 1694.
M. P. Gelfand et al.: Phys. Rev. B 40 (1989) 10801.
F. Becca and F. Mila: Phys. Rev. Lett. 89 (2002) 037204.
K. Kodama et al.: J. Phys. Soc. Jpn. 66 (1997) 793.
H. Kageyama et al.: Phys. Rev. Lett. 82 (1999) 3168.
R. Melzi et al.: Phys. Rev. Lett. 85 (2000) 1318.
R. Melzi et al.: Phys. Rev. B 64 (2001) 024409.
H. Rosner et al.: Phys. Rev. B 67 (2003) 014416.
E. E. Kaul et al.: J. Magn. Magn. Mater. 272–276 (2004) 922.
T. A. Kodenkandath et al.: J. Am. Chem. Soc. 121 (1999) 10743.
T. A. Kodenkandath et al.: Inorg. Chem. 40 (2001) 710.
H. Kageyama et al.: J. Phys.: Condens. Matter 16 (2004) S585.
G. Caruntu et al.: Mater. Res. Bull. 37 (2002) 593.
The ﬁtting of r to the CW law gave similar values of r ¼ 9:5 K andCr ¼ 0:398 emu K/mol corresponding to gr ¼ 2:06.
J.-K. Kim and M. Troyer: Phys. Rev. Lett. 80 (1998) 2705.
N. Shannon et al.: Eur. Phys. J. B 38 (2004) 599.
A. Furrer and H. U. Güdel: Phys. Rev. Lett. 39 (1977) 657.
H. U. Güdel et al.: Inorg. Chem. 18 (1979) 1021.
M. Hase et al.: Phys. Rev. B 56 (1997) 3231.
H. Kageyama et al.: Phys. Rev. Lett. 84 (2000) 5876.
S. Miyahara and K. Ueda: Phys. Rev. Lett. 82 (1999) 3701.
International Tables for Crystallography, ed. A. J. C. Wilson,(Kluwer, Dordrecht) Vol. C, Chap. 4.4.5.
On the basis of the isolated dimer model, the cross section has a the maximum
maximum at Q ¼ 1:503  =R. Given R ¼ 8:8 A, 1 . The present experimental
should be obtained at Q ¼ 0:54 A
conditions, however, involve an increasing statistical error of the 1 .
intensity, particularly below Q  0:5 A