Journal of the Physical Society of Japan
Vol. 71, No. 11, November, 2002, pp. 2637–2639#2002 The Physical Society of JapanLETTERSMagnetism of a New Spin-1 Material NaV(WO4 )2Takatsugu M ASUDA, Taiki S AKAGUCHI and Kunimitsu UCHINOKURA
Department of Advanced Materials Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656(Received June 28, 2002)

The magnetism of a new quantum-spin material NaV(WO4 )2 is studied. The crystal structure shows azig-zag S ¼ 1 spin chain along the c axis. The magnetic susceptibility shows that the material has a spin
gap. The exchange interaction and the energy gap are estimated to be J ¼ 180 K and E ¼ 26 K,
respectively. The possibility of a large next-nearest-neighbor interaction is discussed.
KEYWORDS: quantum spin systems, S ¼ 1 zig-zag chain
DOI: 10.1143/JPSJ.71.2637

Quantum spin systems are among the most interesting
physical models due to their simplicity. In some cases they
can be solved numerically or even analytically andexperimental results can reproduce theoretically predicted
results. One of the most famous and successful examples isthe Haldane gap1) which is observed in a one-dimensional
S ¼ 1 spin model. The Haldane conjecture, which predicted
the existence of a spin gap and the exponential decay of thespin correlation function, was justiﬁed by numericalcalculation2) and explained analytically by the use of an
approximate model, the valence bond solid model.3) Manyexperimental results also justiﬁed the conjecture.4,5)
Recently, S ¼ 1 spin chain with the next-nearest-neighborinteraction was studied theoretically.6–9) The rich phase
diagram of the ground state in the S ¼ 1 chain with a singleion anisotropy was obtained theoretically,9) but to date only
a few materials has been reported experimentally.10)
Candidate model compounds may be found among zig-zagchains. NaR3þ (WO4 )2 (R ¼ In, Sc11) S ¼ 0, Cr12) S ¼ 1=2or 3=2, and V13) S ¼ 0 or 1) are isostructural with each other.
The crystal structure is monoclinic and the space group is
P2=c. Figure 1 shows the crystal structure of NaIn(WO4 )2 ,11)which had been studied in the most detail among thematerials in NaR3þ (WO4 )2 family. The zig-zag chains of theedge-shared InO6 octahedra are extended along the c axis
and are separated by the zig-zag chains of NaO6 octahedra= In–In–In is 98.7 .
and large W6þ ions. The zig-zag angle Fig. 1. Crystal structure of NaIn(WO4 )2 which is isostructural withNaV(WO4 )2 . Zig-zag chains of InO6 and NaO6 octahedra are along the caxis. This ﬁgure is drawn according to the crystal data in ref. 11.

The lattice constants and the angle  are a ¼ 10:08 A,b ¼ 5:81 A, c ¼ 5:03 A, and  ¼ 90  0:5 . The magnetic
susceptibility in NaCr(WO4 )2 was reported12) and thequalitative behavior showed that the model Hamiltonian inthis material can be described by a low-dimensional spinmodel. The spin state V3þ (3d 2 ) is S ¼ 1 in the case of ahigh-spin state and S ¼ 0 in the case of a low-spin state.
Therefore, the S ¼ 1 low-dimensional spin model isexpected for NaV(WO4 )2 if the spin state of V3þ is thehigh-spin state. In this material, the lattice constants and theangle  are a ¼ 9:880 A, b ¼ 5:698 A, c ¼ 4:987 A, and ¼ 90:25 .13) A strong next-nearest-neighbor interaction is
expected based on the crystal structure. In this paper, wereport the magnetic susceptibility measurement inNaV(WO4 )2 .
A polycrystalline NaV(WO4 )2 sample was prepared in
two steps. The ﬁrst step was the solid-state reaction method.
The starting materials used were NaCO3 , V2 O3 , and WO3 . A
mixture of them placed in an evacuated quartz tube washeated in a furnace up to 800 C for 200 h. Intermediate
regrinding was required. The second step was the ﬂux
method. An appropriate mixture of NaV(WO4 )2 , which wasobtained in the ﬁrst step, and Na2 W2 O7 was heated to1000 C. The mixture was kept at this temperature for 24 h,cooled at the rate of 2 C/h to 650 C, and at 5 C/h to room
temperature. The solvent Na2 V2 O7 was removed in boilingwater. A dark brown needle-shaped single crystal wasobtained. The single crystals were too small for themeasurement of the magnetic susceptibility. We then groundthem and obtained a high-quality polycrystalline sample.
The magnetic susceptibility measurement was performed
using a commercial SQUID magneto-meter (MPMS,Quantum Design Co., Ltd.).
Figure 2(a) shows the magnetic susceptibility ofNaV(WO4 )2 . The magnetic susceptibility has a strong
temperature dependence, which means that the spin stateof V3þ ions is magnetic, i.e., a high-spin state, and S ¼ 1
spins are localized at the ions. A broad maximum, which isdue to antiferromagnetic ﬂuctuation, is observed atT  200 K and this means that the model Hamiltonian canbe described by a low-dimensional quantum spin model. Adecrease in the susceptibility at lower temperature isobserved, though the Curie-like behavior is observed at avery low temperature. The minimum value of the susceptibility (T  10 K) is about half the maximum value(T  200 K) in this material. The decrease of the suscept-E-mail: tmasuda@k.u-tokyo.ac.jp
2637

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J. Phys. Soc. Jpn., Vol. 71, No. 11, November, 2002

2.0LETTERS(a)χ (10 emu/mol)

1.5-3

1.00.5H = 1000 Oe

0.00

100

200
300
Temperature (K)2.0400(b)χ (10 emu/mol)

1.5Experiment
Fittedcurve
CurieExponential

-3

1.0
0.5
0.0
020

4060
Temperature (K)

80

100

2.0(c)
χ (10 emu/mol)

1.9-3

1.8
1.7
1.6200Experiment
Fittedcurve
250

300
350
Temperature (K)400Fig. 2. (a) The magnetic susceptibility in NaV(WO4 )2 . (b) The ﬁt to thedata below 75 K by Curie and exponential decay curves. (c) The ﬁt to thedata at 250 K . T by high-temperature expansion.

ibility is more signiﬁcant than that in a gapless onedimensional quantum spin model. In the case of the S ¼ 1=2
spin system, for example, the ratio of the minimum to themaximum value of the susceptibility is about 0.7.14) No
anomaly due to a phase transition is observed down to 2 K.
Therefore, we concluded that this material has a spin gap.
In Fig. 2(b), we ﬁt the data to,

CE
¼
þ Aexp :
ð1Þ
T kB T
The obtained energy gap and Curie constant areE ¼ 26:4 K and C ¼ 10:0 103 emu K/mol, respectively. The eﬀective number of impurity spins, x, wasestimated from the Curie constant and x ¼ 1:0% under theassumption that S ¼ 1 and g ¼ 2. The V3þ ion is easily
oxidized and the valence number easily changes, which may
be the reason for the spin impurity. The V4þ ion, forexample, would induce a free S ¼ 1=2 spin.
The spin interaction, assuming the Heisenberg model, isestimated by high-temperature expansion.15) The ﬁtting
equation is22 þ 0:0194 TJ þ 0:777 TJ
2B g2 N¼
 : ð2Þ
kB T 3 þ 4:346 J þ 3:232 J 2 þ5:834 J 3
TTTThe ﬁt to the experimental data is shown in Fig. 2(c). g ¼

T. MASUDA et al.

2:3 and J ¼ 180 K are obtained. To estimate the exact valueof J, we should consider anisotropy, interchain interaction,and next-nearest-neighbor interaction. However, ﬁtting
equation which includes all of them has not been reported
and we adopted the ﬁtting equation based on the simplest
Heisenberg Hamiltonian here.
In the 1D S ¼ 1 Heisenberg model, the relation between
the energy gap and the exchange interaction is 0:41J.16,17) Generally the Haldane gap is deﬁned as
E ¼
the gap at the antiferromagnetic zone center, but in thefollowing discussion, we deﬁne E as the spin gap in theglobal reciprocal lattice. The reason is that we estimated Efrom the magnetic susceptibility measurement. InNaV(WO4 )2 , the relation is E ¼ 0:15J and the energygap is signiﬁcantly suppressed. There are three possible
causes for the suppression of the energy gap, i.e., the singleion anisotropy D, the interchain interaction Jinter , and thenext-nearest-neighbor interaction JNNN . In the quasi-1D
antiferromagnets reported so far, the next-nearest-neighborinteraction was neglected because the spin chain is almost
linear. The relation between the energy gap and the singleion anisotropy was reported in refs. 16 and 17, and the Jinter –D phase diagram and experimental results are summarized inFig. 1 in ref. 18. NENP has a relatively large D in the S ¼ 1
quasi-1D antiferromagnet; it has the largest D in Fig. 1 inref. 18. Even in NENP, the relation between E and J isE ¼ 0:22J.4) Here E is the minimum energy gap
between singlet ground state and the lowest excited statein the global reciprocal lattice. The discrepancy in therelation is larger for NaV(WO4 )2 .
In NaV(WO4 )2 , the spins form a zig-zag chain and astrong next-nearest-neighbor interaction is expected. If thenext-nearest-neighbor interaction is antiferromagnetic,NaV(WO4 )2 would be a model for a frustrated S ¼ 1 chain.
In this case the relation, E ¼ 0:15J, does not havequalitative meaning because we adopted the ﬁtting equation
based on the simplest Heisenberg model. The antiferromagnetic NNN interaction suppresses the antiferromagnetic
short-range order and broad maximum in the magnetic
susceptibility shifts to a low temperature with the increase ofJNNN . In CuGeO3 , for example, J ¼ 88 K based on thesimple Heisenberg model19) and J ¼ 150 K based on theNNN interaction model.20) We can say that J ¼ 180 K isunderestimated by use of eq. (2) and the coeﬃcient 0.15 in
the relation between J and E is smaller if we consider theNNN interaction.
The ground state of the S ¼ 1 spin chain with NNN
interaction has been studied theoretically.6–9,21) If theexchange interaction is isotropic and the single ion
anisotropy is absent the energy gap increases ﬁrst, and then,decrease with increasing next-nearest-neighbor interaction
strength.21) At  JNNN =J ¼ 0:74 the ground state changesto ‘‘double Haldane phase.’’ If the exchange interaction isXXZ model-like7,8) or the exchange interaction is anisotropic Heisenberg model and a single-ion anisotropy ispresent,9) the existence of ‘‘gapped and gapless chiralphases’’ is proposed. The phase is novel in that the orderparameter is a chirality, l ¼ Sxl Sylþ1  Syl Sxlþ1 . Because of theexistence of the novel phase, the spin gap in the quasi-1D
antiferromagnet with the next-nearest-neighbor interaction
and with the single-ion anisotropy will be suppressed.

J. Phys. Soc. Jpn., Vol. 71, No. 11, November, 2002

LETTERSThe relation between E and J in NaV(WO4 )2 indicatesthe suppression of the Haldane gap. The suppression of thespin gap might be explained only by the interchaininteraction or the single-ion anisotropy, but the crystal
structure indicates the existence of the next-nearest-neighborinteraction. Therefore, another possible explanation for thesuppression of the Haldane gap in NaV(WO4 )2 is that thetheoretically predicted gapped and gapless chiral phases ordouble Haldane phase exist and the ground state of thismaterial is close to these phases.
We found a new spin-gap material, NaV(WO4 )2 . The spin
chain is zig-zag and the possibility of a frustrated S ¼ 1
chain in this material is discussed. The estimation of D bymagnetization measurement will be necessary in the future.
The experiments on materials of the NaV(WO4 )2 family
may lead to the discovery of gapped and gapless chiralphases or double Haldane phase.
The authors thank A. Zheludev for fruitful discussion.
This work was supported in part by a Grant-in-Aid for COE
Research, and one of the authors (T.M.) was also supportedby a Grant-in-Aid for Scientiﬁc Research on Priority Area
from the Ministry of Education, Culture, Sports, Science,and Technology.
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