Journal of the Physical Society of Japan
Vol. 75, No. 11, November, 2006, 113601#2006 The Physical Society of JapanLETTERS

Collinear Order in Frustrated Quantum Antiferromagnet
on Square Lattice (CuBr)LaNb2 O7
Noriaki O BA1 , Hiroshi K AGEYAMA1 , Taro KITANO1 , Jun Y ASUDA1 , Yoichi BABA1 ,Masakazu N ISHI2 , Kazuma H IROTA2 , Yasuo N ARUMI2 , Masayuki H AGIWARA3 ,Koichi K INDO2;3 , Takashi SAITO4 , Yoshitami AJIRO1;5 and Kazuyoshi YOSHIMURA1
1

Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502
2
Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581
3
Center for Quantum Science and Technology under Extreme Conditions, Osaka University,
Toyonaka, Osaka 560-8531
4
Institute for Chemical Research, Kyoto University, Uji, Kyoto 611-0011
5
CREST, Japan Science and Technology Agency (JST)(Received August 28, 2006; accepted September 15, 2006; published November 10, 2006)

Magnetic susceptibility, heat capacity, high-ﬁeld magnetization and neutron diﬀraction measurements
have been performed on a two-dimensional S ¼ 1=2 square-lattice system (CuBr)LaNb2 O7 , preparedby a topotactic ion-exchange reaction of a nonmagnetic double-layered perovskite RbLaNb2 O7 .
(CuBr)LaNb2 O7 exhibits a second-order magnetic transition at 32 K, in marked contrast to a spin-singlet
nature for its Cl-based counterpart (CuCl)LaNb2 O7 , despite nearly identical structural parameters. The
magnetic structure is a novel collinear antiferromagnetic (CAF) ordering characterized by a modulation
vector q ¼ ð; 0; Þ with a reduced moment of 0.6B . Mixed ferromagnetic nearest-neighbor (J1 ) andantiferromagnetic second-nearest-neighbor (J2 ) interactions are of comparable strength (J1 =kB ¼
35:6 K and J2 =kB ¼ 41:3 K), placing the system in a more frustrated region of the CAF phase than everreported.
KEYWORDS: (CuBr)LaNb2 O7 , square lattice, J1 –J2 model, ion exchange, collinear order, frustration
DOI: 10.1143/JPSJ.75.113601

Quantum ﬂuctuations that are expected to develop nearquantum critical points are recognized as primary sources of
unconventional phenomena found in condensed matterphysics and have been central to intensive research studies.
In particular, frustrated square-lattice S ¼ 1=2 Heisenberg
antiferromagnets with the nearest-neighbor exchange constant J1 and second-nearest-neighbor exchange constant J2 ,referred to as the antiferromagnetic (AF) J1 –J2 model[Fig. 1(b)], have received considerable attention, especially
due to the discovery of high-Tc superconducting cuprates
whose undoped parent materials are S ¼ 1=2 square-lattice
antiferromagnets. There are indeed a great deal of controversial theoretical calculations on the AF J1 –J2 model,1–3)
but the general consensus is that there exist several
interesting phases as a function of the ratio  ¼ J2 =J1 ;increasing  results in the quantum phase transition fromthe q ¼ ð; Þ Néel antiferromagnetic (NAF) state to thequantum spin-liquid (QSL) state around   0:5, and further
increasing  drives an order by disorder stabilizing the
q ¼ ð; 0Þ or (0, ) collinear antiferromagnetic (CAF) state,with spins aligned ferromagnetically along the b axis andantiferromagnetically along the a axis, or vise versa.
Shannon et al. extended the phase diagram to the ferromagnetic (F) J1 (< 0) regime, predicting a new gapless QSL
state for a region around   0:5 in the F J1 –J2 regime, assummarized in Fig. 1(c).4,5)
On the other hand, only a limited number of compounds
were discovered experimentally as prototypes, but relatively
large values of  indicating weak frustration were obtained: ¼ 3:5, 2.5, and 1:64 for Li2 VOSiO4 ,6–8) Li2 VOGeO4 ,6)
and Pb2 VO(PO4 )2 ,9,10) respectively. These are far above thecritical ratio |c j  0:5 [see Fig. 1(c)], and as theoretically
expected, the occurrence of CAF ordering was detected at
low temperatures. For probing enhanced quantum ﬂuctuations, new prototype compounds with much stronger
frustration are awaited. Low-temperature syntheses may
oﬀer promising routes to innovate low-dimensional magnetic compounds, as nonequilibrium phases that are notproduced by ordinary solid-state reactions but remain stable
under ambient conditions. In fact, reacting a double-layered
nonmagnetic Dion-Jacobson phase RbLaNb2 O7 with CuX2
yields a perovskite/metal halide intergrowth structure(CuX)LaNb2 O7 (X ¼ Cl, Br), where the interlayer Rbþ ionsare replaced by the [CuX]þ layer with an S ¼ 1=2 squarelattice, as shown in Fig. 1(a).11) We have recently reported
that the ground state of (CuCl)LaNb2 O7 is described by the
QSL, where no long-range order exists down to 20 mK andthe spin-singlet ground state is separated from the triplet
excited states by a gap of 2.3 meV.12,13) Moreover, fascinating features have been observed in (CuCl)LaNb2 O7 , including the localized nature of triplet excitations (possibly as aconsequence of competition between J1 and J2 ), thepresence of an excitation at 5.0 meV presumably consistingof several elementary triplets, and an anomalously small
critical ﬁeld (10 T) implying the existence of yet unknown
states. This letter is motivated by the aforementioned
theoretical evolutions for the J1 –J2 model and unusual
magnetic properties in (CuCl)LaNb2 O7 . We will demonstrate the magnetic properties of isostructural (CuBr)LaNb2 O7 synthesized by a similar method, and discuss theresults in terms of the F J1 –J2 model.
The synthesis of (CuBr)LaNb2 O7 is expressed by thefollowing ion-exchange reaction:

E-mail: kage@kuchem.kyoto-u.ac.jp

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LETTERS

J. Phys. Soc. Jpn., Vol. 75, No. 11(a)

N. OBA et al.

(b)
J2
J1
Cu

Br

Fig. 1. (a) Schematic representation of crystal andmagnetic structures for (CuBr)LaNb2 O7 . Spins on
the Cu2þ ions point to the b-axis. (b) J1 –J2 model onsquare lattice. (c) General phase diagram for J1 –J2model,4) where FM, NAF and CAF denote, respectively, (0; 0) F, (; ) NAF and (; 0) CAF phases.
The shaded areas correspond to the QSL phases.4,5)
The locations of (CuBr)LaNb2 O7 , Pb2 VO(PO4 )2 ,9)
Li2 VOGeO4 ,6) and Li2 VOSiO4 6) on the phase
diagram are indicated by the arrows.

J2(c)
NbO6 (CuBr)LaNb2O 7
Pb 2VO(PO 4)2
La

Li 2VOGeO4
Li 2VOSiO4

CAF

−0.5

0.5

J1
FM
NAF

c
a
J2 /J1= −∞

-5

12
10
8

10
800
0

10

20
30
T (K)

600

40

6

400

1/χ (mol/emu)

The mother compound RbLaNb2 O7 was prepared via a
conventional high-temperature route, using Rb2 CO3(99.9%), La2 O3 (99.99%), and Nb2 O5 (99.99%) as starting
reagents. RbLaNb2 O7 was then mixed with a two-fold molar
excess of ultradry CuBr2 (99.9%) and pressed into pellets
inside a dry box (<1 ppm O2 /H2 O). The reaction in eq. (1)was carried out in sealed, evacuated (<103 Torr) Pyrex
tubes at 320  C for 7 d.14) The ﬁnal product was washed with
distilled water to eliminate the excess CuBr2 and RbBr, anddried at 120  C. An X-ray diﬀraction study conﬁrmed thetetragonal symmetry with room-temperature cell constants
a ¼ 3:9025 Å and c ¼ 11:7168 Å, in good agreement withthose previously reported.11) Energy dispersive spectroscopy(EDS) gave the stoichiometric composition of the ﬁnal
product, assuring complete ion-exchange reactions.
The magnetic susceptibility was studied using a superconducting quantum interference device (SQUID) magnetometer (Quantum Design, MPMS) in the temperature range
of T ¼ 2 { 300 K in a magnetic ﬁeld H ¼ 0:1 T. High-ﬁeld
magnetization measurements up to 65 T were conductedusing a pulse magnet installed at Osaka University. A
speciﬁc-heat measurement was performed by the heatrelaxation method in a T-range from 3.5 to 100 K in theabsence of magnetic ﬁeld using a QD-PPMS at the Institutefor Chemical Research, Kyoto University. A hand-pressedpellet was attached to an alumina platform by a small
amount of Apiezon N grease. Neutron powder diﬀraction
experiments were conducted using the IMR-HERMES
diﬀractometer (T1-3) and the ISSP-PONTA triple-axis
spectrometer (5G), both installed at the JRR-3M reactor of
the Japan Atomic Energy Agency (JAEA), Tokai. For themeasurements at 5G, a polycrystalline sample of 10 g mass
was placed into a vanadium cylinder and neutrons witha wavelength of 2.3618 Å were obtained by the (002)
reﬂection of pyrolytic graphite (PG), and a horizontal
collimation of open-400 -sample-800 -800 in combination witha PG ﬁlter placed before the sample to eliminate higherorder beam contaminations.
In Fig. 2, we compare the temperature dependence of themagnetic susceptibility ðTÞ of (CuBr)LaNb2 O7 with that of1000
dχ/dT (10 emu/mol K)

14

ð1Þ

-3

RbLaNb2 O7 þ CuBr2 ! (CuBr)LaNb2 O7 þ RbCl:

χ (10 emu/mol)b

4(CuBr)LaNb2O7

200

2
0
0

50

100

150

200

250

0
300

T (K)
Fig. 2. Magnetic susceptibility  (solid circles) and inverse susceptibility
1/ (open circles) of (CuBr)LaNb2 O7 measured at 0.1 T. The broken
line is a ﬁt to the Curie–Weiss law. The ðTÞ of (CuCl)LaNb2 O7 having
the QSL ground state is plotted for comparison purposes by the dottedline.12) The inset shows the diﬀerential susceptibility d=dT to illustrate
the anomaly at TN .

(CuCl)LaNb2 O7 .12) At high temperatures above 100 K, thetwo lines nearly coincide with respect to each other, fromwhich it is readily determined that the sum of the exchange
constants (i.e., J1 þ J2 ) is of the same order of magnitude forboth compounds. The ﬁt of the bromine data with the Curie–
Weiss formula ðTÞ ¼ C=ðT  Þ resulted in  ¼ 5:1 
0:5 K, where C and  [¼ ðJ1 þ J2 Þ=kB ] represent the Curie
constant and the Weiss temperature. It is close to the value
obtained for the chlorine sample ( ¼ 9:6 K). The veriﬁcation of the completion of the ion-exchange reaction ismade again by ﬁnding C ¼ 0:393 emu/(K mol), which isquite reasonable for 1 mol of Cu2þ ions in (CuBr)LaNb2 O7 .
Despite the apparent similarity between the high-T
behaviors of ðTÞ of the two samples, a marked diﬀerence
becomes discernible for T < 100 K. ðTÞ for X ¼ Br showsa round maximum at TM ¼ 36:0 K, which is expected for

113601-2

LETTERS

J. Phys. Soc. Jpn., Vol. 75, No. 11

low-dimensional magnetic systems but is much higher than
TM ¼ 16:0 K for X ¼ Cl.12) This fact is an implication thatthe former has greater magnitudes of both J1 and J2 , which
will be conﬁrmed later by the magnetization curve. The ratio
TM =jj is equal to 7.06 and is considerably larger than 0.935
expected for the nonfrustrated case.15) It implies, together
with the structural characteristics of the CuX layer, that for
X ¼ Br, J2 is AF while J1 is F, as in the case for X ¼ Cl12,13)
and for Pb2 VO(PO4 )2 .9)
ðTÞ for the bromine sample reveals a tiny kink at 30 K
pointing to a transition into a magnetically ordered state. It isbetter shown if one plots the derivative susceptibility d=dT,
as seen in the inset of Fig. 2. The upturn in ðTÞ at around
15 K is attributed to impurities or defects and corresponds
approximately to what one would expect for 1.5% of
noninteracting paramagnetic one-half spins. The subtractionof the extrinsic term resulted in a ﬁnite susceptibility3  103 emu/mol at 0 K. This is in stark contrast to thethermally activated behavior in the chlorine sample, i.e., ! 0 as T ! 0. The heat capacity divided by temperature(CuBr)LaNb2O7

10
CpT (x10 J K/mol)2

Cp /T (J/mol K )

1.0

5

2

4

0.5

0

0.0
0

10

20

0

5

30

10
15
5
7 5
T (x10 K )

40

20

50

60

T (K)

m (μB)

(b)

1.2

0.5

0.0
0

10

20

30

T (K)

4.5

(c)

(d)

(1/2 0 1/2)

40 1.01.0(1/2 0 3/2)

3

3

5.0

1.0

0.5

17

18

19

20

23

24

25

26

2θ (degree)
113601-3

3

0.0

0.0

Difference (x10 cnt.)

Counts (x10 /~3 min)

7K
37K

4

1.0

(a)

Cp =T (Fig. 3) reproduces the anomaly at a similar temperature 32.0 K (¼ TN ). The transition is nearly of second order,
as inferred from the small anomaly around TN without
hysteresis. No further anomaly in the Cp =T vs T plot is seen
down to 2 K, the lowest T examined in the present study.
Neutron diﬀraction analysis allows one to directly
establish the spin-ordering structure as well as the magnitudeof the ordered moment. We show, in Figs. 4(a) and 4(b),powder neutron diﬀraction patterns obtained at 5G for
temperatures below and above TN , and, in Figs. 4(c) and
4(d), the corresponding diﬀerence plots. Note that theexperiments using T1-3 essentially gave the same results.
The appearance of new reﬂections below TN is due to thebreakdown of translational symmetry and is ﬁrm evidence
for long-range magnetic ordering. The angular positions of
the observed magnetic Bragg peaks reveal that the magnetic
unit cell has a magnetic ordering vector q ¼ ð; 0; Þ. It isnatural to consider that the magnetic structure is such thatlayers of the CAF type stack along the c-axis in a staggeredmanner, as illustrated in Fig. 1(a). We found that
ð1=2; 0; 1=2Þ and ð1=2; 0; 3=2Þ reﬂections have nearly thesame magnetic structure factors, implying that the spins
point parallel to the b-axis, which is supported by the factthat reﬂections such as ð1=2; 1; 1=2Þ are not visible within theexperimental resolution. We would like to stress here that
(CuBr)LaNb2 O7 is a second experimental example of the
CAF phase in the S ¼ 1=2 square-lattice systems having
mixed F and AF exchange couplings.10)
The inset of Fig. 4 shows that the intensity of theð1=2; 0; 1=2Þ reﬂection decreases with increasing T andcontinuously becomes zero at 32 K, which is ascribed to theonset of the second-order-like transition in accordance withthe result for the heat capacity. The critical exponent  forthe magnetization below TN takes a value close to that
expected for a three-dimensional Heisenberg model (0.345)(see the inset of Fig. 3). Once given the magnetic structurein Fig. 1(a), one can determine the ordered magnetic
moment m from the intensities of the observed magnetic
reﬂections, which are proportional to the square of m. We
obtain a reduced moment (0:60  0:11B ) which is indeed

Counts (x10 /~6 min)5.5

Difference (x10 cnt.)

Fig. 3. Temperature dependence of Cp =T for (CuBr)LaNb2 O7 showing
magnetic ordering at 32 K. The inset shows the Cp T 2 vs T 5 plot, where
the solid line represents the linear ﬁt between 35 and 48 K.

N. OBA et al.

Fig. 4. (a) Powder neutron diﬀraction proﬁle for2 ¼ 16 { 20:5 for (CuBr)LaNb2 O7 at 7 K (solid),
37 K (open) and (c) diﬀerence plot, demonstratingð1=2; 0; 1=2Þ reﬂection. (b), (d) Same plot for2 ¼ 23{26:5 , demonstrating ð1=2; 0; 3=2Þ reﬂection. The solid lines in (c) and (d) represent
Gaussian ﬁts. Inset: temperature dependence ofmagnetic moment m. The line is ﬁtted with a power
law: m ¼ 0:60ð1  T=TN Þ with  ¼ 0:30.

LETTERS

J. Phys. Soc. Jpn., Vol. 75, No. 11

1.0(CuX )LaNb2O7

M (μB /f.u.)

0.8

T = 1.3 K

0.6
0.4

X = Br (raw)
X = Br (corrected)
1.5 % S = 1/2
X = Cl

0.2
0.0

0

10

20

30

40

50

60

70

H (T)
Fig. 5. Dotted line: magnetization of (CuBr)LaNb2 O7 measured at 1.3 K.
Dot-broken line: impurity term, given by Brillouin function for 1.5% of
noninteracting S ¼ 1=2 spins at 1.3 K. Solid line: corrected magnetizationof (CuBr)LaNb2 O7 after subtraction of above impurity term. Broken line:
magnetization of (CuCl)LaNb2 O7 .13)

comparable to that expected from the nonfrustrated twodimensional square lattice model (0.65B ).16)
Shown in Fig. 5 is the magnetization MðHÞ measured at
1.3 K, in which the raw data was corrected by subtracting thecontribution from the impurities/defects observed in themagnetic susceptibility. Here, thermal ﬂuctuations in themagnetization are negligible at this temperature, since there
is little diﬀerence between the 1.3 and 4.2 K curves. For
0 < H < 30 T, MðHÞ varies almost linearly with H. The
linear ﬁeld dependence is subsequently followed by nonlinear growth. M(H ¼ 65 T) is 95% of the saturation
magnetization. The upward curvature should be a result of
the gradual suppression of zero-point oscillations by theexternal ﬁeld and is expected to be observed in theframework of spin-wave theory for frustrated and nonfrustrated AF square-lattice systems for all ﬁelds below thesaturation ﬁeld Hs .17,18) Possibly, the linear ﬁeld dependence
is an intrinsic nature for the frustrated F square-latticesystem. It is worth noting that a 1/2 plateau corresponding toa state with up-up-up-down spin order has been theoreticallysuggested in the frustrated CAF regime for the AF squarelattice.19) The absence of the plateau in our experimentmight be due to the fact that we deal with the F squarelattice.
Let us hereafter discuss the question of whether or not asizable frustration is present in this compound by utilizing
various methods. The magnetization curve at suﬃciently low
temperatures can be taken full advantage of to unambiguously determine the exchange constants, and hence measure
the frustration . We estimate Hs from a linear extrapolationof the M–H curve. The obtained ﬁeld of 70 T is much larger
than 30.1 T for the chlorine sample.13) On the basis of the
J1 –J2 model, the saturation ﬁeld is given by Hs ¼ 2ðJ1 þ
2J2 Þ=gB for the CAF phase. By assuming (J1 þ J2 Þ=kB ¼
5:1 K (¼ jj), we determine J1 =kB ¼ 35:6 K and J2 =kB ¼
41:3 K and hence jj ¼ 1:10, which is the smallest among
the compounds with a CAF state and places the present
compound in the most frustrated region on the phase
diagram of the J1 –J2 model.
The evaluation of  can also be discussed using thehigh-temperature expansions (HTEs) of heat capacity studied by Misguich et al.,20) who predict that at high temperatures, the magnetic heat capacity of the J1 –J2 model

N. OBA et al.

behaves as CM  0:375RðJ1 2 þ J2 2 Þ=ðkB TÞ2 [R ¼ 8:314 J/(mol K)]. Since there is a T 3 contribution from phonons at
low temperatures, Cp T 2 is plotted against T 5 [Fig. 3 (inset)].
A linear behavior is seen for 35 < T < 48 K. Then, thelinear extrapolation to T ¼ 0 gives (J1 2 þ J2 2 Þ=kB 2 6400 K2 which is larger than that obtained above roughly
by a factor of 2, but may be acceptable in view of thediﬃculty in extracting the phonon contribution from the raw
data, owing to the lack of a nonmagnetic isostructuralcompound.
A problem arises when a quantitative comparison between(CuBr)LaNb2 O7 and (CuCl)LaNb2 O7 is made with respect
to . The estimated value of 4.50 (J1 =kB ¼ 2:74 K andJ2 =kB ¼ 12:34 K) for (CuCl)LaNb2 O7 13) indicates that it isless frustrated and should be in the CAF region. From thisviewpoint, the appearance of the spin-singlet formation in(CuCl)LaNb2 O7 is an interesting puzzle to be solved in the
future. Further studies, in particular those on the solid
solution between the end members, would oﬀer better
understanding of the relationship between the QSL and CAF
phases, which will be published elsewhere.
In conclusion, we demonstrated that the two-dimensional
S ¼ 1=2 square-lattice system (CuBr)LaNb2 O7 exhibits thelong-range magnetic ordering of the CAF type at 32 K, inmarked contrast to the QSL behavior in (CuCl)LaNb2 O7 .
Strong competition between the F J1 and AF J2 interactions
is suggested. The proximity of the CAF state of(CuBr)LaNb2 O7 to the QSL state next to the F state might
be relevant to the spin-singlet formation in (CuCl)LaNb2 O7 .
We wish to point out that there have already been numerous
studies on 3 He with competing F and AF multiple spinexchange processes and on the doped colossal magnetoresistive (CMR) manganites with competing F kinetic and
AF repulsive exchange energies. On the contrary, little is
known about frustrated ferromagnets in quantum spin
systems. (CuX)LaNb2 O7 should serve in the developmentof such systems.
It is our pleasure to acknowledge fruitful discussions with
K. Totsuka, N. Shannon, M. Takigawa and M. Takano. We
thank K. Ohoyama for his help and useful discussions as tothe experiment at the IMR-HERMES. We are also gratefulto Y. Kiuchi, F. Sakai and Y. Ueda at the Institute for Solid
State Physics, University of Tokyo for the EDS experiments.
This work has been supported by Grants-in-Aid for Young
Scientists (A) (No. 17684018) and Science Research on a
Priority Area (No. 16076210 and No. 451) from the Ministryof Education, Culture, Sports, Science and Technology ofJapan, and by the 21st Century COE Program, Kyoto
University Alliance for Chemistry.
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