Progress of Theoretical Physics Supplement No. 159, 2005

39

S = 1/2 Square-Lattice Antiferromagnets: (CuX)LaB2 O7 and(CuCl)A2 B3 O10 (X = Cl, Br; A = Ca, Sr; B = Nb, Ta)
Hiroshi Kageyama,1,2 Taro Kitano,1 Ryu Nakanishi,1 Jun Yasuda,1Noriaki Oba,1 Yoichi Baba,1 Masakazu Nishi,2 Yutaka Ueda,2 Yoshitami Ajiro1
and Kazuyoshi Yoshimura1
1 Department of Chemistry, Graduate School of Science, Kyoto University,

Kyoto 606-8502, Japan
2 Institute for Solid State Physics, The University of Tokyo,

Kashiwa 277-8581, Japan
A series of magnetic compounds with the formula (CuX)LaB2 O7 and (CuCl)A2 B3 O10(X = Cl, Br; A = Ca, Sr; B = Nb, Ta) have been prepared through a low-temperature
topochemical route starting from nonmagnetic double- (n = 2) and triple- (n = 3) layered
perovskites, respectively. The magnetic susceptibility of these compounds typically exhibitsa broad maximum at low temperatures, characteristic of low-dimensional antiferromagnetic
compounds. However, depending on the choice of the parameters, X, A, B and n, physicalquantities such as the Weiss temperature and the temperature at a maximum susceptibility
vary to a great extent, which enables us to study the phase diagram of the S = 1/2 frustrated
square-lattice antiferromagnets (the so-called J1 -J2 model). In particular, (CuCl)LaNb2 O7 ,possibly having a ferromagnetic J1 and an antiferromagnetic J2 , shows a spin-liquid behavior
with the spin gap of 27 K.

§1.

Introduction

Low-dimensional antiferromagnetic (AFM) quantum spin systems with a spinsinglet ground state and an energy gap in the magnetic excitation spectrum haverecently received considerable attention. These features arise from quantum spin
ﬂuctuations in low-dimensional structures, as exempliﬁed by the spin-Peierls compound CuGeO3 , where the spin-singlet ground state is stabilized by a modulationor doubling of the underlying lattice.1) Other spin-gap compounds range from theinteger-spin chain (Haldane system) Ni(C2 H8 N2 )2 NO2 (ClO4 )2) to the two-leg spinladder SrCu2 O3 3) and the alternating spin chain Cu(NO3 )2 ·2.5H2 O.4) After intensive
experimental and theoretical study with corresponding model compounds, it is fair tostate that the one-dimensional (1D) case is rather well understood. By contrast, little is known about 2D case. Among 2D models, the S = 1/2 frustrated square lattice
antiferromagnet (J1 -J2 model) is of special importance in the light of the relevanceto the CuO2 plane in high-Tc superconducting cuprates along with a pseudo spin-gap
behavior.5) An interesting phase diagram with unusual ground states is predicted
as a function of the ratio J2 /J1 between the ﬁrst-nearest-neighbor (J1 ) and secondnearest-neighbor (J2 ) exchange interactions.6) – 8) For 0 < J2 /J1 < 0.38 a normalNéel order state is the ground state, while for J2 /J1 > 0.55 a collinear order should
develop. The most interesting phase, a quantum disordered phase with a ﬁnite gap
is expected for 0.38 < J2 /J1 < 0.55. Three compounds are suggested as prototypesof the J1 -J2 model with a signiﬁcant coupling between J1 and J2 , Li2 VOSiO4 (J1 =40

H. Kageyama et al.

0.56, J2 = 6.3 K), Li2 VOGeO4 (J1 = 0.82, J2 = 4.1 K)9), 10) and Pb2 VO(PO4 )2 (J1 =−6 K, J2 = 9.8 K),11) all of which are, however, magnetically ordered at low temperatures. Very recently we have reported that a double-layered Dion-Jacobson phase(CuCl)LaNb2 O7 , prepared from the topochemical ion-exchange reaction between
RbLaNb2 O7 and CuCl2 , is the long-time awaited spin-liquid phase for the J1 -J2model.12) Magnetic susceptibility of (CuCl)LaNb2 O7 exhibits a thermal-activatedbehavior. The analysis of the magnetic data together with structural considerations
gave a ferromagnetic J1 (< 0), an antiferromagnetic J2 (> 0) and the relation J1 + J2
= 9.6 K. Moreover, neutron scattering experiments provided explicit evidence for aspin-singlet ground state with an energy gap of 2.3 meV (∼26.7 K). A sizable geometrical frustration was derived from the almost Q independent one-triplet excitation,
as in the case of SrCu2 (BO3 )2 .13) Using the same synthetic strategy, it is possible toobtain a series of S =1/2 square-lattice antiferromagnets (CuX)An−1 Bn O3n−1 (X= halogen; A = alkaline earth metal or rare earth metal, B= niobium and tantalum;n = 2, 3).14) – 16) These parameters A, B, X and n may oﬀer eﬀective routes to systematically tune the sign and magnitude of exchange constants, and dimensionality.
Our ultimate goal is to reveal the phase diagram for the (quasi 2D) J1 -J2 modelexperimentally. In this paper, we report on the structural and magnetic propertiesof (CuX)An−1 Bn O3n−1 , some of which have been newly synthesized. It turned outthat they indeed exhibit, depending on the tuning parameters, a variety of magnetic
behaviors ranging from a long-range ordered to a spin-liquid phases.
§2.

Experimental details

For the synthesis of the n = 2 members, mother compounds RbLaB2 O7 (B= Nb, Ta) were initially prepared by a solid-state reaction method from Rb2 CO3(99.99%, La2 O3 (99.99%), and B2 O5 (99.999%). RbLaB2 O7 were mixed with 2fold molar excess of ultra dry CuX2 (X = Cl, Br) (99.99%) and then pressed into
pellets inside the Ar-ﬁlled glove box (MBRAUN). Reaction (1) was carried out insealed, evacuated (< 10−3 Torr) Pyrex tubes at 320 ˚C for one week. Final productwas washed with water to eliminate the excess copper chloride and alkali-metal
byproduct, and dried at 120˚C. Similarly, the n = 3 members (CuCl)A2 B3 O10 (A =Ca, Sr; B = Nb, Ta) were able to obtain but using host compounds RbA2 B3 O10 . Xray powder diﬀraction data were collected on a Mac Science M18XHF diﬀractometerequipped with a graphite monochromator and Cu Kα (λ = 1.5406 Å). Elemental
analysis was carried out by energy dispersive spectroscopy (EDX) on a series ofindividual crystallines on a JEOL scanning electron microscope (SEM) equippedwith an EDAX microanalytical system. Magnetic susceptibility measurements were
performed on a powder sample with a superconducting quantum interference device(SQUID) magnetometer (Quantum Design, MPMS) over the temperature range T= 2 – 300 K, typically in an applied ﬁeld of H = 0.1 T.

S = 1/2 Square-Lattice Antiferromagnets§3.

41

Structural properties

As shown in Fig. 1, the single-step ion-exchange reaction for the synthesis of,e.g., the n = 3 members is expressed as
RbA2 B3 O10 + CuCl2 → (CuCl)A2 B3 O10 + RbCl,(1)

which involves the replacement of rubidium cation of the perovskite host by [CuCl]+ .
The S = 1/2 copper ion is octahedrally coordinated, bridging between apical oxygens
from the perovskite layer and surrounded by four chlorines in the CuCl plane. The
CuO2 Cl4 octahedra corner-share with the BO6 octahedra of the perovskite slabs
while edge-sharing with other CuO2 Cl4 octahedra in the ab plane. In the CuCl plane,copper ions form the square lattice, while chlorines are located at the center of the2NN copper bonds, as shown in Fig. 2. Figures 3 and 4 represent X-ray diﬀraction
patterns at room temperature for (CuX)LaB2 O7 and (CuCl)A2 B3 O10 , respectively,
relative to those for the mother compounds. All proﬁles could be readily indexedon tetragonal unit cells and no trace of the impurity phase was found within theexperimental resolution of the present experiment. The ﬁnal products are green andbrown for the Cl and Br compounds, respectively. The EDX experiment revealed
that no residual alkali metal is present in the products and the Cu : X : A : B
compositions were found approximately to be 1 : 1 : 1 : 2 for n = 2 and 1 : 1 : 2 : 3
for n = 3. As seen in Table I, the spacing between the perovskite layers is expanded
signiﬁcantly on the ion-exchange reaction relative to the starting compounds. For
the known compounds unit cells obtained from the analysis are consistent with thosereported.14) – 16) It is to be noted that the A = Sr compounds, (CuCl)Sr2 Nb3 O10 and(CuCl)Sr2 Ta3 O10 , have been obtained for the ﬁrst time in the present study. The
observed diﬀraction patterns without any extinct reﬂections are quite similar to thoseof the known (CuCl)Ca2 B3 O10 with the space group P 4/mmm.15), 16) Therefore
it is likely that the all n = 3 compounds are isostructural with respect to eachother. Reﬂecting the diﬀerence in ionic radius, the replacement of Sr for Ca leads toexpansion of the lattice parameters a and c.
Table I. Tetragonal unit cell parameters for the parents and the exchange products.
compounds
RbLaNb2 O7(CuCl)LaNb2 O7(CuCl)LaTa2 O7(CuBr)LaNb2 O7(CuCl)LaTa2 O7
RbSr2 Ta3 O10(CuCl)Sr2 Ta3 O10(CuCl)Sr2 Nb3 O10(CuCl)Ca2 Ta3 O10(CuCl)Ca2 Nb3 O10

a (Å)
3.884(3)3.8773(4)3.876(4)3.8929(3)3.894(1)3.857(6)3.881(3)3.882(4)3.829(7)3.844(5)c (Å)
10.963(2)11.726(2)11.739(4)11.690(1)11.707(2)15.044(1)15.996(8)15.990(3)15.533(2)15.659(6)cell vol. (Å3 )
165.4
176.3
176.4
177.2
177.5
223.8
240.9
241.0
227.8
231.4

42

H. Kageyama et al.
(a)

(b)

+ CuCl2− RbClcbaFig. 1. The ion-exchange reaction of RbA2 B3 O10 (A = Ca, Sr; B = Nb, Ta) and CuCl2 for thesynthesis of (CuCl)A2 B3 O10 , where the large dark spheres are rubidiums, the large gray spheres
are A cations, the small closed spheres are copper cations, the intermediate gray spheres arechlorines, and the octahedra represent BO6 .

J1

J2

b

a
Fig. 2. The CuCl layer viewed along the tetragonal c axis. The bold broken and solid lines represent,
respectively, the J1 and J2 bonds.

§4.

Magnetic properties

Among thus obtained eight compounds, the magnetic properties had been investigated for only three compounds (CuCl)LaNb2 O7 ,12), 14) (CuCl)Ca2 Nb3 O10 15) and(CuCl)Ca2 Ta3 O10 .16) In Figs. 5–7, we present the magnetic susceptibilities χ of all
the compounds, plotted against temperature. In high temperature region, all themagnetic susceptibilities exhibit the Curie-Weiss behavior, i.e., χ = C/(T + θ), with

S = 1/2 Square-Lattice Antiferromagnets

43(CuCl)Ca2Nb3O10(CuBr)LaTa2O7(CuCl)Ca2Ta3O10

20

30

40

60

102
004100102

1020

2θ (degree)1
H = 0.1T

40

60 80
T (K)

100 120

Fig. 5. The temperature variation of magnetic susceptibility for (CuCl)LaNb2 O7and (CuCl)LaTa2 O7 measured at H = 0.1
T.

χ (x10-3 emu/mol)χ (x10-2 emu/mol): (CuCl)LaTa2O7: (CuCl)LaNb2O7

20

104
110

40

50

60

Fig. 4. The X-ray diﬀraction patterns for then = 3 family (CuCl)A2 B3 O10 relative tothe mother compound RbSr2 Ta3 O10 .

2

0

30

RbSr2Ta3O102θ (degree)

Fig. 3. The X-ray diﬀraction patterns for then = 2 family (CuX)LaB2 O7 relative to themother compound RbLaNb2 O7 .

0

(CuCl)Sr2Ta3O10

103
104 110

003
003

002

001

RbLaNb2O7

50

103

004
100

(CuCl)Sr2Nb3O10002(CuCl)LaNb2O7

113

012
003

001

10

110
111

003
101 110
102
004
110
111
112
104

002

001

(CuCl)LaTa2O7001

Intensity (arb. units)

Intensity (arb. units)(CuBr)LaNb2O7

10: (CuBr)LaTa2O7: (CuBr)LaNb2O7

5

H = 0.1T

0

0

20

40

60 80
T (K)

100 120

Fig. 6. The temperature variation of magnetic susceptibility for (CuBr)LaNb2 O7and (CuBr)LaTa2 O7 measured at H = 0.1
T.

the eﬀective magnetic moment being nearly consistent with that expected for S =1/2. In addition, a broad maximum at low temperatures in the χ-T curve is commonly observed (except for the A = Sr case), which is a characteristic feature for the
low-dimensional antiferromagnets. It is easy to ﬁnd a great diversity in the magnetic
properties as a function of A, B, X and n. For example, the Weiss temperature θ= 9.6 K for (CuCl)LaNb2 O7 is smaller than θ = 15.6 K for (CuCl)LaTa2 O7 , despite

44

H. Kageyama et al.

χ (x10-2 emu/mol)nearly identical unit cell parameters.
With lowering temperature, the diﬀer6: (CuCl)Sr2Ta3O10
ence in the χ-T curves between the two: (CuCl)Sr2Nb3O10
compounds become even more distinct: (CuCl)Ca2Ta3O10
as seen in Fig. 5: for (CuCl)LaNb2 O7 , χ: (CuCl)Ca2Nb3O10
χtakes the maximum at 16.5 K (= Tmax
4)and then drops signiﬁcantly to zero for
T → 0, apart form the Curie-tail below 5 K due to extrinsic impurity or2
defects. The thermal-activated behavH = 0.1T
ior indicates that it has a spin-singlet
ground state with a ﬁnite energy gap.
0
On the contrary, (CuCl)LaTa2 O7 has a0
20 40 60 80 100 120
χ
somewhat smaller Tmax
) of 10.5 K andT (K)the reduction of the susceptibility below
χTmax) is much smaller. Thus the magFig. 7. The temperature variation of magnetic
netic
ground state is expected for thesusceptibility for (CuCl)A2 B3 O10 (A = Ca,
Sr; B = Nb, Ta) measured at H = 0.1 T.
tantalate. Shown in Fig. 6 are the susceptibilities for (CuBr)LaB2 O7 . Compared with the X = Cl case, the χ-T curves for X = Br exhibit a broad maximum
at much higher temperature (∼ 36 K), implying stronger exchange constants via
superexchange pathways through bromines. The long-range antiferromagnetic orχ
dering at 31 K is inferred from the curvatures below Tmax). In Fig. 7, the magnetic
susceptibilities of the n = 3 series are compared. It is interesting to point out thatfor a given A there is no appreciable diﬀerence between susceptibilities of B = Nb
and Ta, in contrast to the n = 2 case where distinct ground states are expected as
mentioned above. The magnetic properties for the n = 3 family depend only on
A: Although the ﬁts of all the χ-T data in Fig. 7 to the Curie-Weiss law led tosimilar values of θ =1 ∼ 2 K, (CuCl)Sr2 B3 O10 shows the Curie-Weiss behavior atleast down to 2 K, whereas broad maxima at 8 K are observed for (CuCl)Ca2 B3 O10 .
This may result from the change of both J1 and J2 by the expansion of the CuCl
plane for A = Sr while keeping the sum of J1 and J2 unchanged. At the present
moment, it is impossible to give complete explanations about the roles of A, B, X
and n in changing the magnetic properties. It would necessary to add other related
compounds and also to improve the sample quality.
§5.

Spin-singlet ground state in (CuCl)LaNb2 O7

The magnetic susceptibility χr of (CuCl)LaNb2 O7 is replotted by the open circles
in Fig. 8. By subtracting the Curie-tail below 5 K, one obtains the spin susceptibilityχs (solid circles). In order to mainly estimate the spin gap ∆, χs was analyzed usinga S = 1/2 isolated AFM dimer model. The value of ∆ was determined so as to makeχ
Tmax
) for χs coincide with that for the theoretical susceptibility χd (solid line). Thus
obtained value of ∆ = 26.5 K agrees well with that determined from the neutron
scattering experiment (∆ = 26.7 K).12) The discrepancy between χs and χd can be

S = 1/2 Square-Lattice Antiferromagnets

45

§6.

χ (x10 -3 emu/mol )χ (x10 -3 emu/mol)seen around 15 K (Fig. 8) and at high15
temperatures (Fig. 9). We also tried to(CuCl)LaNb 2 O 7
0.1 T
use the dimer model to ﬁt χs at hightemperatures (see broken lines), which10
however resulted in the marked discrep10
ancy at low temperatures.
5
From the structural viewpoint, it isnatural to consider that the J1 -J2 model
should be the most appropriate model
5
0
0
10
20
30
40
to interpret our experiment. In fact, theT (K)chlorines in the CuCl plane are arranged
at the center of 2NN bonds, not of 1NN,
so that J2 need not be smaller in mag0
nitude than J1 . Indeed, Cu2+ -Cl− -Cu2+
0
50
100
150
200
250
300
angle of 180˚ for the J2 bond supports aT (K)sizable AFM interaction (J2 > 0) while
Fig. 8. The temperature dependence of thethat of 90˚ for the J1 bond points tomagnetic susceptibility in (CuCl)LaNb2 O7
a ferromagnetic (FM) J1 (< 0). It ismeasured at H = 0.1 T. The open
known that θ is equal to J1 + J2 forand closed circles represent, respectively,
the J1 -J2 model. The experimental ratio
the measured susceptibility χr and theχTmax)/θs = 1.65, much larger than 0.935
spin susceptibility χs after subtracting theCurie term (dotted line). The solid andfor the nonfrustrated case of (J1 ¿ J2
broken lines are the calculated susceptibilor J2 ¿ J1 ),17) indicates ferromagnetic
ities χd based on the isolated dimer modelJ1 bonds and the signiﬁcant frustration
with ∆ = 26.5 K and 70 K. The enlarged
due to sizable AFM J2 bonds. It meansplot is presented in the inset.
that the observed spin-liquid phase is essentially diﬀerent from that expected for the antiferromagnetic exchanges between
the Néel order and collinear phases. Shannon et al. theoretically suggest that
there should also be a spin-liquid phase occurring for J2 /J1 ∼ −0.5 between the
ferromagnetic and collinear ordered phases.18) We ﬁtted our χs data using the hightemperature series expansion developed by Rosner et al.,19) where J1 + J2 was ﬁxed
to be 10 K. However, as one can see from Fig. 10, the best ﬁt was obtained when J1 isclose to zero, where the long-range ordered state should be stabilized. The deviationof the J1 -J2 model might suggest possible additional contribution of distant neighborexchanges such as J3 and J4 . As an alternative scenario, the eﬀect of disorder ofchlorines within the CuCl plane as suggested by the neutron diﬀraction patterns atroom temperature20) might be seriously taken into account.
Summary

To summarize, we synthesized through the topochemical ion-exchange routea series of magnetic compounds with the general formula (CuX)An−1 Bn O3n+1 inwhich S = 1/2 copper ions form the square lattice, separated well by the nonmagnetic
perovskite slabs. All compounds show the magnetic behaviors characteristic of lowdimensional antiferromagnets. It should be emphasized that the magnetic properties

46

H. Kageyama et al.
800
12

600
χ (x10-3 emu/mol)

χ-1 (mol/emu)

400

0.1 T

200

(CuCl)LaNb 2 O 7
0

J1 + J2 = 10 K

10

0

50

100

150

200

250

J1 = 10.5 K
J1 = 5.0 K
J1 = 0.5 K
J1 = −5.0 K
J1 = −10.0 K

8
6
4
2

H = 0.1 T(CuCl)LaNb2O7

0

300

T (K)
Fig. 9. Reciprocal susceptibilities, 1/χs and1/χd .

10

T (K)

100

Fig. 10. Comparison between χs and those
based on the high-temperature series expansion.19)

can be tunable with varying A, B, X and n, thus oﬀering the opportunities to study
the phase diagram of J1 -J2 model. In particular, (CuCl)LaNb2 O7 has the spinsinglet ground state with the energy gap of 26.7 K, which should arise from thestrong geometrical frustration and quantum ﬂuctuations that destabilize the classicalordering.
Acknowledgements
This work has been partly supported by 21st Century COE Program, Kyoto
University Alliance for Chemistry.
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