Journal of the Physical Society of Japan
Vol. 79, No. 1, January, 2010, 014709#2010 The Physical Society of Japan

Synthesis, Structural and Magnetic Propertiesof the Solid Solution (CuCl1 x Brx )LaNb2 O7 (0  x  1)
Yoshihiro T SUJIMOTO, Atsushi K ITADA, Hiroshi KAGEYAMAy,
Masakazu NISHI1 , Yasuo N ARUMI1;2 , Koichi K INDO1 ,Yoko KIUCHI1 , Yutaka U EDA1 , Yasutomo J. U EMURA3 ,Yoshitami A JIRO, and Kazuyoshi Y OSHIMURA
Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
Institute for Solid State Physics, University of Tokyo, 5-1-5 Kashiwanoha, Chiba 277-8581, Japan
2
Institute for Materials Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan3
Department of Physics, Columbia University, New York, NY 10027, U.S.A.
1(Received August 12, 2009; accepted October 7, 2009; published December 25, 2009)

The two-dimensional (2D) quantum spin system (CuCl)LaNb2 O7 has a spin-singlet ground state with agap of 2.3 meV, while the isostructural material (CuBr)LaNb2 O7 displays a collinear antiferromagnetic
order at TN ¼ 32 K. Here, we report on the synthesis of solid solution (CuCl1x Brx )LaNb2 O7(0  x  1), and its structural and magnetic properties investigated by magnetic susceptibility, high-ﬁeld
magnetization, and neutron diﬀraction measurements. The x dependences of cell parameters follow
Vegard’s law, verifying the uniform distribution of Cl and Br atoms at the halide site, although a more
complex structural evolution is inferred from an opposing correlation between the intra- and interlayer
cell distances (vs x). 5%-Br substitution is found to induce an antiferromagnetic order with TN ¼ 7 K,
consistent with recent SR results, and the magnetic structure is collinear, having a signiﬁcantly reduced
moment. Further Br substitution leads to a linear increase in TN up to x ¼ 1. These results indicate that
(CuCl)LaNb2 O7 is located in the vicinity of the quantum phase boundary.
KEYWORDS: quantum spin system, spin gap, (CuCl)LaNb2 O7 , (CuBr)LaNb2 O7 , susceptibility, magnetization,neutron diffraction
DOI: 10.1143/JPSJ.79.014709

1.

Introduction

Novel quantum phase transitions can be driven by tuning
various parameters such as magnetic ﬁeld and pressure,
not temperature. For a quantum spin system having a spinsinglet ground state with a ﬁnite gap, the application of an
external magnetic ﬁeld is known to induce the Bose–
Einstein condensation (BEC) of triplet magnons as observedin TlCuCl3 ,1–4) or the crystallization of triplet magnons toyield magnetization plateaus as observed in SrCu2 (BO3 )2 .5)
Cationic substitution is also a useful and versatileparameter for studying spin-singlet compounds, which isclassiﬁed into two types. One is substitution by (non)magnetic ions with diﬀerent spin multiplicities at themagnetic site. Magnetic order is induced by the substitutionof small amounts of Zn2þ (S ¼ 0) substitution for Cu2þ(S ¼ 1=2) in CuGeO3 6) and SrCu2 O3 ,7) and of Mg2þ (S ¼ 0)
substitution for Ni2þ (S ¼ 1) in PbNi2 V2 O8 .8) Of particularinterest is microscopic phase segregation in a doped onedimensional chain between spin-ordered and disorderedstates with a modulated staggered magnetization along thechain.9,10) The other type of cation substitution is conducted
for the countercations, which leads to chemical pressure
and/or bond randomness in the magnetic coupling constants.
A Bose-glass state has recently been suggested inTl1x Kx CuCl3 .11,12) By contrast, anionic substitution (e.g.,
O–S–Se and F–Cl–Br) has been rarely studied, mainly
owing to the large diﬀerences in anionic radius andelectronegativity, making it diﬃcult to prepare a homoge

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

y

La

Cu X
NbO6

c

b
a

Fig. 1. Crystal structure of (CuX)LaNb2 O7 (X ¼ Cl, Br).

neous solid solution. However, when magnetic ions arebridged by substitutable anions, we can control the superexchange coupling constants.
(CuX)LaNb2 O7 (X ¼ Cl, Br), as prepared by ion-exchange reactions, consists of CuX square-lattice layers with
S ¼ 1=2 separated by nonmagnetic perovskite blocks (seeFig. 1).13) (CuCl)LaNb2 O7 has a spin-singlet ground state
separated from the excited state by 2.3 meV,14) and magnetic
ﬁeld induces the Bose Einstein condensation (BEC) of triplet
magnons at 10.3 T.15,16) In contrast, the Br counterpart
undergoes a collinear antiferromagnetic (CAF) order at
32 K.17) (CuX)LaNb2 O7 were initially assumed as candidatesof the J1 –J2 model where the ferromagnetic (FM) nearest-

014709-1

J. Phys. Soc. Jpn., Vol. 79, No. 1

Y. TSUJIMOTO et al.

2.

Experimental Results and Discussion

The preparation of (CuCl1x Brx )LaNb2 O7 (x ¼ 0; 0:05;
0:33; 0:50; 0:66; 1) was performed by the following ionexchange reaction:
RbLaNb2 O7 þ (1  x)CuCl2 þ xCuBr2! (CuCl1x Brx )LaNb2 O7 þ (1  x)RbCl þ xRbBr: ð1Þ
The parent compound RbLaNb2 O7 was prepared by a hightemperature reaction using Rb2 CO3 (rare metallic, 99.9%),
La2 O3 (rare metallic, 99.99%), and Nb2 O5 (rare metallic,99.99%) following methods in the literature.22) Anhydrous
CuCl2 (Alfa, 99.999) and CuBr2 (Alfa, 99.999%) in
stoichiometric ratio, x, were mixed with RbLaNb2 O7 ,pressed into pellets inside an argon-ﬁlled glove box, sealedin evacuated (<103 Torr) Pyrex tubes, and heated at 320  C
for 7 days. To complete the desired reaction, a two-molar
excess of CuCl2 /CuBr2 relative to RbLaNb2 O7 was added.
The ﬁnal products were isolated by washing with warm
distilled water.
X-ray powder diﬀraction measurements were carried out
at room temperature with Cu K radiation on a M18XHF
diﬀractometer (Mac Science). Magnetic susceptibility measurements were performed using a superconducting quantum
interference device (SQUID) magnetometer (Quantum
Design MPMS) in the temperature range of 2 – 300 K at an
applied ﬁeld H ¼ 0:1 T. High-ﬁeld magnetization measurements were conducted using an induction method with amultilayer pulsed magnet installed at the Institute for Solid
State Physics, The University of Tokyo (ISSP). Magnetization data were collected at 1.3 K in magnetic ﬁelds up
to 60 T. Powder neutron diﬀraction measurements were
performed on the 5%-Br substituted sample using the
ISSP-PONTA triple-axis spectrometer (5G) installed at
JRR-3 of the Japan Atomic Energy Agency (JAEA), Tokai.
A polycrystalline sample of about 10 g mass was placed in a
vanadium cylinder. Neutrons with a wavelength of 2.3618 Å
were obtained by the (002) reﬂection of pyrolytic graphite(PG), and a collimation of open-400 -sample-800 -800 was

11.735

3.905

a axisc axisa axis (Å)

3.900

11.73011.725

3.895

11.7203.890
11.715
3.885

11.710

3.880
3.875

c axis (Å)

neighbor (J1 ) and antiferromagnetic (AFM) next-nearestneighbor (J2 ) interactions compete with each other.15,18)
However, nuclear magnetic resonance (NMR) and transmission electron microscopy measurements of the twocompounds demonstrated the absence of the C4 symmetry
at both Cu and X sites,19) inconsistent with the original
results of structural analysis.13) Several superstructures in the
CuX plane were proposed to explain the spin-singlet state for
X ¼ Cl19) and the CAF state for X ¼ Br.20) However, it is
not yet clear whether the proposed model can answer thequestions, for example, of why the ﬁeld-induced transition
occurs at a much lower ﬁeld than that expected from thezero-ﬁeld spin gap, and of how magnetic coupling diﬀers
between X ¼ Cl and Br.
In this study, we present the successful preparation of awhole solid solution (CuCl1x Brx )LaNb2 O7 (0  x  1) andits structural and magnetic characterizations by means of Xray diﬀraction, neutron diﬀraction, magnetic susceptibility
and high-ﬁeld magnetization. The motivation of the present
study is partly due to the recent observation of magnetic
order by muon spin relaxation (SR) for a 5%-Br substituted
sample (x ¼ 0:05).21)

11.705

0

0.2

0.4

0.6

0.8

1

11.700x
Fig. 2. Crystallographic unit-cell parameters as a function of Br concentration (x) in (CuCl1x Brx )LaNb2 O7 .

employed in combination with a PG ﬁlter placed before thesample to eliminate higher-order beam contamination.
Elemental analysis of the products, carried out by energy
dispersive spectroscopy (EDS) on a JSM-5600 scanningelectron microscope (JEOL), supported the nominal stoichiometry (CuCl1x Brx )LaNb2 O7 . X-ray diﬀraction proﬁlesof the whole solid solution (CuCl1x Brx )LaNb2 O7 wereindexed to the tetragonal symmetry as in the case of the end
members (x ¼ 0 and 1).13) The peak widths of the solid
solution were as sharp as those of the end members, and no
multiphase region was observed within the experimental
resolution. The uniform distributions of the Cl and Br atoms
at the X site were further supported by results of EDS on a
JEM-2010F transmission electron microscopy (TEM) with
an operating voltage of 200 kV at ISSP. The x dependences ofthe lattice parameters, as shown in Fig. 2, demonstrate thatboth a and c change in proportion to x, following Vegard’slaw, implying the successful preparations of the whole solid
solution. However, Br substitution cannot be simply understood as a negative chemical pressure, since the a-axis
increases and the c-axis decreases with increasing x, a ﬁnding
whose explanation remains unclear at the present stage.
However, this should be a common feature of this familyof ion-exchanged compounds, because (CuBr)LaTa2 O7 and(CuBr)La2 (Ti2 Nb)O10 also have shorter c-axes than their Cl
counterparts.23) The determination of the precise structure of(CuCl1x Brx )LaNb2 O7 is required in the future. For example,
a superstructure, as that found in (CuCl)LaNb2 O7 ,19) mightalso be observed in the (Cl, Br) solid solution.
Figure 3(a) shows the temperature dependence of themagnetic susceptibility ðTÞ for the solid solution in theregion below 50 K. The kink at 32 K for x ¼ 1 was ascribedto the onset of the CAF order.17) Likewise, kinks were foundat 17, 21, and 25 K for x ¼ 0:33, 0.5, and 0.67, respectively.
The linear decrease in the kink temperature [see Fig. 3(b)]strongly suggests that those kinks are due to magnetic orderas well. In Fig. 4, the magnetization curves for x  0:33
show a linear increase over a wide ﬁeld range. Although
the magnetizations do not saturate up to 60 T applied in thisstudy, one can say that the saturation ﬁeld would become
smaller with decreasing x, implying a weaker superexchange
constant for Cu–Cl–Cu than for Cu–Br–Cu.
On the other hand, as shown Figs. 3(a) and 4, both ðTÞand MðHÞ for x ¼ 0:05 are considerably diﬀerent from those

014709-2

J. Phys. Soc. Jpn., Vol. 79, No. 1(a) 800

15

I(3.5 K) -I(18 K) (cnt. /~6min)(a)Y. TSUJIMOTO et al.

10

5(CuCl0.95Br0.05)LaNb2O7(1/2 0 1/2)

16

19

600
400
200
0
-200
-400

17

18

20

2theta (deg)

0
0

10

20

30

40

I (10 cnt. /~6min)(b) 18.2

50

T N (K)

40
30

3

(b)
manetic susceptibility
neutron diffraction
heat capacity

20

0.2

0.4

x

0.6

0.8

1.0

Fig. 3. (a) Magnetic susceptibilities of (CuCl1x Brx )LaNb2 O7 measured
at H ¼ 0:1 T. Arrows indicate the kink temperatures. (b) x dependenceof TN ðxÞ, determined by magnetic susceptibility (solid circles), neutron
diﬀraction (open circles) and heat capacity (triangle) measurements.17)

x=0

1.0

x = 0.05

0.8

M/Msat

17.6
17.4
17.2
4

6

8

10

12

14

T (K)

0
0.0

x = 0.33
0.6

x = 1.0

0.4

x = 0.67
x = 0.50
M/M sat

0.8

0.2

0.6

x = 0.05

0.4

x=0

0.2
0.0
0

0

17.8

17.0

10

0.0

18.0

10

20

30

5

40

10

15

20

H (T)

50

25

30

60

H (T)
Fig. 4. Magnetization curves for (CuCl1x Brx )LaNb2 O7 measured at
1.3 K. The inset shows the magnetizations for x ¼ 0 and 0.05 below
H ¼ 30 T.

for x  0:33. However, their behaviors are similar to thosefor x ¼ 0.14,15) The ðTÞ for x ¼ 0:05 is characterized by abroad maximum at about 15 K and a substantial decrease inðTÞ below this temperature, and the concave behavior inMðHÞ at around 10 T (see the inset of Fig. 4) is reminiscentof the transition from the spin-singlet state to the ﬁeldinduced antiferromagnetic state. However, recent SR
experiments revealed the presence of a magnetic order inthis material.21) In fact, a very careful look at the ðTÞ data
revealed a tiny kink at around 7 K, suggesting the breakdownof the spin gap. Accordingly, in order to obtain insight into
the ground state of x ¼ 0:05, we performed neutron powder
diﬀraction measurements. Figure 5(a) shows the intensity
diﬀerence, I(3.5 K)–I(18 K), in the 2 range from 16 to 20 .
We observed a relatively weak magnetic peak corresponding

Fig. 5. (a) Diﬀerence plot of neutron scattering intensity for the x ¼ 0:05
sample, I(3.5 K)–I(18 K), corresponding to the ð1=2; 0; 1=2Þ magnetic
reﬂection. The solid curve is a single-component Gaussian ﬁt.
(b) Temperature dependence of the ð1=2; 0; 1=2Þ intensity. The solid line
is a guide to the eyes.

to the ð1=2; 0; 1=2Þ reﬂection, the peak width of which was
resolution limited. Hence, it is natural to assume that thismaterial has the same CAF order as (CuBr)LaNb2 O7(x ¼ 1).17) From the temperature dependence of this magnetic reﬂection [Fig. 5(b)], we estimated TN as 7 K, which
again agrees with the SR result. From the data at 3.5 K, themagnitude of the magnetic moment in the ordered state wasroughly estimated as 0.2(1) B , where the crystal structureof (CuCl)LaNb2 O7 determined by X-ray diﬀraction analysis
at room temperature13) and the magnetic structure withthe moments aligned parallel to the b-axis as found in(CuBr)LaNb2 O7 17) were assumed. The estimated orderedmoment is signiﬁcantly smaller than 0.6 B for x ¼ 1. It isalso evidenced from the SR measurements21) that themagnetic moment for x ¼ 0:05 is considerably smaller thanthat for 0:33  x  1. The observations of long-range
magnetic order induced by substituting only 5% Br andthe signiﬁcantly reduced magnetic moment for x ¼ 0:05
indicate that (CuCl)LaNb2 O7 is located in the vicinity of thequantum phase boundary adjacent to the ordered state.
Contrasting behavior has been observed in the Nb-site
substituted system (CuCl)La(Nb1y Tay )2 O7 ,21,24) in which
the spin-singlet state is robust against cationic substitution.
Substantial substitution on the order of y  0:4 is needed toinduce CAF magnetic order, but with the coexistence of theordered and disordered phases extending up to y ¼ 1. Notethat the eﬀect of chemical disorder in the magnetic layer
CuX is larger than that in the nonmagnetic layer LaB5þ 2 O7
[B5þ : Nb5þ or Ta5þ (d 0 )]. So far, there have been many
theoretical works on the rapid breaking of spin-singlet
dimers upon the addition of vacancies in a variety of spingapped models, a procedure which is considered relevant tocreating free spins. Some theories showed that staggered
spin-spin correlations are enhanced in the vicinity of spinvacancies,25–29) which accounts for the emergence of the014709-3

J. Phys. Soc. Jpn., Vol. 79, No. 1

Y. TSUJIMOTO et al.

ordered phase in the cationic-substituted 1D magnetic
materials CuGeO3 and SrCu2 O3 .9,10) In the 2D orthogonal
dimer SrCu2 (BO3 )2 , staggered magnetization develops
around the triplet excitation in the 1/8 plateau phase.5)
Thus, in spin-singlet compounds, independent of theirdimensionality, any local perturbations such as defects or
chemical randomness can potentially induce staggeredmagnetizations, leading to a magnetically ordered state. Byanalogy, the creation of magnetic order by a small amount of
Br substitution in (CuCl)LaNb2 O7 may be associated withstaggered correlations induced around Br ions. A rapid
depolarization of the SR signal observed in the 5%-Br
system21) may be related to the spatial variation of staggeredordered moment size. The SR spectra of CuGeO3 dopedwith Zn and Si exhibit fast relaxation owing to this eﬀect.9)
Further experiments are necessary to clarify the local state.
3.

Conclusion

We succeeded in synthesizing the solid solution system(CuCl1x Brx )LaNb2 O7 (0  x  1) and investigated its
magnetic properties by means of susceptibility, magnetization, and powder neutron diﬀraction measurements. The
experimental results reveal that the switching of the spinsinglet state in (CuCl)LaNb2 O7 to a collinear-type magnetic
ordered state occurs by as little as 5% substitution of Br,
which is in stark contrast to the Ta-for-Nb substitution
systems. It is likely that the chemical disorder in themagnetic layer CuX has a stronger eﬀect on the magnetic
properties than that in the nonmagnetic layer LaB2 O7 .
The chemistry of the present material can yield a large
family of materials represented as (MX)An1 Bn O3nþ1 (M:divalent transition-metal, A: alkali, alkali-earth, and rareearth metals, n: integer),23) and these materials provide
a variety of magnetic states, depending on the tunable
parameters. For example, it was shown that substituting the
A-site in (CuBr)A2 Nb3 O10 controls the width of the 1/3
magnetization plateau.30) Here, we note that ion-exchange
reactions for yielding (MX)An1 Bn O3nþ1 rely on the stabilityof the byproduct alkali halides, in the present case RbCl
and RbBr, relative to transition-metal halides, so anionicsubstitution should be generally applied to the entire(MX)An1 Bn O3nþ1 systems. It would be interesting to see,e.g., how anionic substitution for (CuBr)Sr2 Nb3 O10 aﬀects
the 1/3 plateau phase.
Acknowledgements
This work was supported by a Grant-in-Aid for Science
Research on Priority Areas ‘‘Novel States of Matter Induced
by Frustration’’ (No. 19052004) from the Ministry of
Education, Culture, Sports, Science and Technology ofJapan, the Japan–U.S. Cooperative Science Program fromthe Japan Society for the Promotion of Science and NSF(No. 14508500001), and by the Global COE program
International Center for Integrated Research and Advanced
Education in Materials Science, Kyoto University, Japan.
This work was also supported by Murata Science Foundation(No. A71115). The work at Columbia University was
supported by US NSF grants DMR-05-02706 and DMR-0806846. One of the authors (Y.T.) was supported by the Japan
Society for the Promotion of Science for Young Scientists.

1) T. Nikuni, M. Oshikawa, A. Oosawa, and H. Tanaka: Phys. Rev. Lett.
84 (2000) 5868.
2) S. E. Sebastian, N. Harrison, C. D. Batista, L. Balicas, M. Jaime, P. A.
Sharma, N. Kawashima, and I. R. Fisher: Nature 441 (2006) 617.
3) T. Waki, Y. Morimoto, C. Michioka, M. Kato, H. Kageyama, K.
Yoshimura, S. Nakatsuji, O. Sakai, Y. Maeno, H. Mitamura, and T.
Goto: J. Phys. Soc. Jpn. 73 (2004) 3435.
4) N. Tsujii, O. Suzuki, H. Suzuki, H. Kitazawa, and G. Kido: Phys. Rev.
B 72 (2005) 104402.
5) K. Kodama, M. Takigawa, M. Horvatic, C. Berthier, H. Kageyama,
Y. Ueda, S. Miyahara, F. Becca, and F. Mila: Science 298 (2002)
395.
6) T. Masuda, A. Fujioka, Y. Uchiyama, I. Tsukada, and K. Uchinokura:Phys. Rev. Lett. 80 (1998) 4566.
7) M. Azuma, M. Takano, and R. S. Eccleston: J. Phys. Soc. Jpn. 67(1998) 740.
8) Y. Uchiyama, Y. Sasago, I. Tsukada, K. Uchinokura, A. Zheludev, T.
Hayashi, N. Miura, and P. Böni: Phys. Rev. Lett. 83 (1999) 632.
9) K. M. Kojima, Y. Fudamoto, M. Larkin, G. M. Luke, J. Merrin, B.
Nachumi, Y. J. Uemura, M. Hase, Y. Sasago, K. Uchinokura, Y. Ajiro,
A. Revcolevschi, and J.-P. Renard: Phys. Rev. Lett. 79 (1997) 503.
10) S. Ohsugi, Y. Tokunaga, K. Ishida, Y. Kitaoka, M. Azuma, Y.
Fujishiro, and M. Takano: Phys. Rev. B 60 (1999) 4181.
11) M. P. A. Fisher, P. B. Weichman, G. Grinstein, and D. S. Fisher: Phys.
Rev. B 40 (1989) 546.
12) Y. Shindo and H. Tanaka: J. Phys. Soc. Jpn. 73 (2004) 2642.
13) T. A. Kodenkandath, J. N. Lalena, W. L. Zhou, E. E. Carpenter, C.
Sangregorio, A. U. Falster, W. B. Simmons, Jr., Charles J. O’Connor,
and J. B. Wiley: J. Am. Chem. Soc. 121 (1999) 10743.
14) H. Kageyama, T. Kitano, N. Oba, M. Nishi, S. Nagai, K. Hirota,
L. Viciu, J. B. Wiley, J. Yasuda, Y. Baba, Y. Ajiro, and K. Yoshimura:
J. Phys. Soc. Jpn. 74 (2005) 1702.
15) H. Kageyama, J. Yasuda, T. Kitano, K. Totsuka, Y. Narumi, M.
Hagiwara, K. Kindo, Y. Baba, N. Oba, Y. Ajiro, and K. Yoshimura:
J. Phys. Soc. Jpn. 74 (2005) 1702.
16) A. Kitada, Z. Hiroi, Y. Tsujimoto, T. Kitano, H. Kageyama, Y. Ajiro,
and K. Yoshimura: J. Phys. Soc. Jpn. 76 (2007) 093706.
17) N. Oba, H. Kageyama, T. Kitano, J. Yasuda, Y. Baba, M. Nishi, K.
Hirota, Y. Narumi, M. Hagiwara, K. Kindo, T. Saito, Y. Ajiro, andK. Yoshimura: J. Phys. Soc. Jpn. 75 (2006) 113601.
18) N. Shannon, B. Schmidt, K. Penc, and P. Thalmeier: Eur. Phys. J. B 38
(2004) 599.
19) M. Yoshida, N. Ogata, M. Takigawa, J. Yamaura, M. Ichihara, T.
Kitano, H. Kageyama, Y. Ajiro, and K. Yoshimura: J. Phys. Soc. Jpn.
76 (2007) 104703.
20) M. Yoshida, N. Ogata, M. Takigawa, T. Kitano, H. Kageyama, Y.
Ajiro, and K. Yoshimura: J. Phys. Soc. Jpn. 77 (2008) 104705.
21) Y. J. Uemura, A. A. Aczel, Y. Ajiro, J. P. Carlo, T. Goko, D. A.
Goldfeld, A. Kitada, G. M. Luke, G. J. MacDougall, I. G. Mihailescu,
J. A. Rodriguez, P. L. Russo, Y. Tsujimoto, C. R. Wiebe, T. J.
Williams, T. Yamamoto, K. Yoshimura, and H. Kageyama: Phys. Rev.
B 80 (2009) 174408.
22) J. Goparakrishman, V. Bhat, and B. Raveau: Mater. Res. Bull. 22(1987) 413.
23) T. A. Kodenkandath, A. S. Kumbhar, W. L. Zhou, and J. B. Wiley:
Inorg. Chem. 40 (2001) 710.
24) A. Kitada, Y. Tsujimoto, H. Kageyama, Y. Ajiro, M. Nishi, Y.
Narumi, K. Kindo, M. Ichihara, Y. Ueda, Y. J. Uemura, and K.
Yoshimura: Phys. Rev. B 80 (2009) 174409.
25) P. M. Hansen, J. A. Riera, A. Delia, and E. Dagotto: Phys. Rev. B 58
(1998) 6258.
26) T. K. Ng: Phys. Rev. B 54 (1996) 11921.
27) T. Miyazaki, M. Troyer, M. Ogata, K. Ueda, and D. Yoshioka: J. Phys.
Soc. Jpn. 66 (1997) 2580.
28) N. Nagaosa, A. Furusaki, M. Sigrist, and H. Fukuyama: J. Phys. Soc.
Jpn. 65 (1996) 3724.
29) Y. Motome, N. Katoh, N. Furukawa, and M. Imada: J. Phys. Soc. Jpn.
65 (1996) 1949.
30) Y. Tsujimoto, H. Kageyama, Y. Baba, A. Kitada, T. Yamamoto, Y.
Narumi, K. Kindo, M. Nishi, J. P. Carlo, A. A. Aczel, T. J. Williams,
T. Goko, G. M. Luke, Y. J. Uemrua, Y. Ueda, Y. Ajiro, and K.
Yoshimura: Phys. Rev. B 78 (2008) 214410.

014709-4