PHYSICAL REVIEW B 78, 214410 共2008兲

Synthesis, structure, and magnetic properties of the two-dimensional quantum antiferromagnets(CuBr)A2B3O10 (A = Ca, Sr, Ba, Pb; B = Nb, Ta) with the 1/3 magnetization plateau
Y. Tsujimoto,1 H. Kageyama,1,* Y. Baba,1 A. Kitada,1 T. Yamamoto,1 Y. Narumi,2 K. Kindo,2 M. Nishi,2 J. P. Carlo,3A. A. Aczel,4 T. J. Williams,4 T. Goko,3,5 G. M. Luke,4 Y. J. Uemura,3 Y. Ueda,2 Y. Ajiro,1 and K. Yoshimura1
1

Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
2Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan
3Department of Physics, Columbia University, New York, New York 10027, USA
4
Department of Physics and Astronomy, McMaster University, Hamilton, Ontario, Canada L8S 4M1
5TRIUMF, Vancouver, British Columbia, Canada V6T 2A3
共Received 18 September 2008; revised manuscript received 28 October 2008; published 8 December 2008兲
A 1/3 magnetization plateau was recently observed in the layered perovskite 共CuBr兲Sr2Nb3O10 with S= 1 / 2 CuBr layers. In order to control the cell size and thus exchange parameters, we have prepared an
isostructural series of 共CuBr兲A2B3O10 共A = Ca, Sr, Ba, Pb; B = Nb, Ta兲 and investigated the magnetic properties.
We found that the stability of the 1/3 magnetization plateau is systematically tunable by the lattice parametera. A substantial role played by the superexchange pathway via BO6-BO6 in the magnetic properties is suggested in addition to that via Br. Specific heat and muon spin relaxation measurements show that the appearance of the plateau phase is accompanied by successive phase transitions in low fields—the first one is possibly
a structural transition and the second one is a magnetic transition. Frustration may induce the structural
distortion and stabilize the 1/3 plateau phase.
DOI: 10.1103/PhysRevB.78.214410

PACS number共s兲: 75.45.⫹j, 72.80.Ga, 75.30.Et, 75.50.Ee

I. INTRODUCTION

Over the past several decades, geometrically frustrated
antiferromagnets 共AF兲 with small spins have attracted considerable attention in condensed-matter physics because of
the emergence of novel quantum behaviors observed in mostcases at low temperatures.1,2 In particular, magnetic fields area useful tool to drive transitions into interesting phases best
featured by Bose-Einstein condensation 共BEC兲 of magnons
共triplets兲 and quantized magnetization plateaus.3 Experimentally, a 1/2 plateau was obtained in 关Ni2共Medpt兲2共␮-ox兲
共␮-N3兲兴ClO4 · 0.5H2O 关Medpt= methyl-bis共3-aminopropyl兲
amine兴,4 1/3 plateau in the diamond chain Cu3共CO3兲2共OH兲2
共Ref. 5兲 and the Kagomé-lattice Cu3共titmb兲2共OCOCH3兲6
关titmb= 1 , 3 , 5-tris共imidazol-1-ylmethyl兲-2,4,6
trimethylbenzene兴,6 1/3 and 2/3 plateaus in the distorted triangularlattice Cs2CuBr4,7 and 1/8, 1/4, and 1/3 plateaus in the
Shastry-Sutherland lattice SrCu2共BO3兲2.8 All the observed
plateaus seem to be in good agreement with Oshikawa etal.’s9 theory which predicts a topological condition for theappearance of plateaus, p共S − m兲 = integer, where p and m are
the period of the spin state and the magnetization per site,
respectively.
We recently reported that a triple-layered perovskite
共CuBr兲Sr2Nb3O10, obtained by an ion-exchange reaction, exhibits a quantized magnetization plateau at 1/3 of the fully
saturated magnetization, and successive transitions in the
low-field region 共Tc1 = 9.3 K and Tc2 = 7.5 K at zero field兲.10
As shown in Fig. 1, 共CuBr兲Sr2Nb3O10 is of tetragonal symmetry and CuBr4 squares edge share to form the S = 1 / 2
layer, which is widely separated by nonmagnetic triplelayered perovskite blocks 共c ⬃ 16 Å兲, making this compounda good two-dimensional quantum magnet. The observationof the 1/3 plateau is remarkable since it is naturally expectedin triangle-based lattices. 共CuBr兲Sr2Nb3O10 is characterized
1098-0121/2008/78共21兲/214410共10兲

by the square-based lattice. For the simple J1-J2 model,
where J1 and J2 denote nearest and next-nearest interactions,
respectively, and plateaus such as 1/2 are expected.11
A big advantage for ion-exchange reactions is the rational
preparation of desired structures, an ability that allows systematic tuning and understanding of the structural and physical properties. In the present case, the synthetic scheme toisgeneralized
into
yield
共CuBr兲Sr2Nb3O10
共CuX兲An−1BnO3n+1 共X = Cl, Br; A = La, Ca, Sr; B = Ti, Nb, Ta;n = 2, 3兲. This versatility has been successfully demonstrated
by magnetic studies of the double-layered 共n = 2兲 compounds
共c ⬃ 11 Å兲, revealing a spin-singlet ground state and BEC ofmagnons in 共CuCl兲LaNb2O7,12–14 collinear 共stripe兲 magnetic
order in 共CuBr兲LaNb2O7,15 and quantum phase separation in
共CuCl兲La共Nb1−xTax兲2O7.16
In this work, we have successfully synthesized a series of
triple-layered copper bromides 共CuBr兲A2B3O10 共A = Ca, Sr,
Pb, Ba; B = Nb, Ta兲, and investigated the relation between
structures and magnetic properties by means of x-ray diffraction 共XRD兲, magnetic susceptibility, specific heat, high-fieldmagnetization, and muon spin relaxation 共␮SR兲. Our main
motivations are to understand how the 1/3 plateau phase as
well as the low-field intermediate phase are influenced by theA- and B-site substitutions and obtain a general guide forsearching compounds with magnetization plateaus.
II. EXPERIMENTAL PROCEDURES
A. Synthesis

For A = 共Ca1−xSrx兲 共where x = 0, 0.25, 0.5, 0.75, and 1兲, theparent compounds of the Dion-Jacobson-type layered perovskites RbA2B3O10 共B = Nb, Ta兲 were synthesized by conventional high-temperature solid-state reactions as reported
in the literature.17 Starting reagents Rb2CO3 共⬎99.99%兲,214410-1©2008 The American Physical Society

PHYSICAL REVIEW B 78, 214410 共2008兲

TSUJIMOTO et al.

reactions between a corresponding parent phase and CuBr2,
as expressed by the following formula:A⬘A2B3O10 + CuBr2 → 共CuBr兲A2B3O10 + A⬘Br

BO6

关A⬘ = Rb, Cs; A = 共Ca, Sr兲, Ba, Pb; B = Nb, Ta兴.

共1兲Each parent compound was thoroughly ground with twofold molar excess of CuBr2 共99.99%兲 in the argon-filled
glove box and was hand pressed into a pellet. The pellet wastransferred to a vacuum line without exposure to air, sealed
in an evacuated Pyrex tube 共⬍10−3 Torr兲, and then heatedfor 7 days at 350 ° C, the same temperature as employed tothe synthesis of 共CuBr兲LaNb2O7.15 The products were
washed with distilled water to eliminate the byproduct 共RbBr
or CsBr兲 and unreacted CuBr2, and dried overnight at
120 ° C. All final products are insulating and brown in color
such as 共CuBr兲LaNb2O7.

A

Br
Cu

B. CharacterizationscbaFIG. 1. Schematic crystal structure of 共CuBr兲A2B3O10 共A = Ca,
Sr, Ba, Pb; B = Nb, Ta兲. The arrow represents the superexchange
path via BO6-BO6.

CaCO3
共⬎99.99%兲,SrCO3
共⬎99.99%兲,Nb2O5
共⬎99.999%兲, and Ta2O5 共⬎99.999%兲 were weighed in an
appropriate stoichiometry for A and B and a 25% molar excess of Rb2CO3, and ground together with an agate mortar inan argon-filled glove box. Here, excess Rb2CO3 was added
to compensate the loss due to its volatilization. Then the
mixture was placed in an alumina crucible and heated in air
under ambient pressure at 850 ° C for 12 h. They were reground and heated to 1100 ° C for 24 h. Subsequently, all the
products were washed thoroughly with distilled water to remove the excess alkaline carbonate and dried overnight at
120 ° C. Because the Rb compounds could not be formed for
A = Pb and Ba,18,19 CsA2B3O10 was prepared in a similar
method as described above, using Cs2CO3 for A = Pb andCsNO3 for A = Ba as starting reagent. CsPb2Nb3O10 was prepared from stoichiometric quantities of PbO 共⬎99.99%兲 andNb2O5 with a 25% molar excess of Cs2CO3 共⬎99.99%兲, themixture of which was heated at 850 ° C for 12 h followed byadditional heating at 1000 ° C for 24 h with an intermediate
grinding. Note that CsPb2Ta3O10 could not be formed; instead of the desired phase, Pb3Ta4O13 was found as a main
phase together with a small amount of unidentified phases.
The Ba compounds, CsBa2B3O10 共B = Nb, Ta兲, were preparedfrom stoichiometric mixtures of Ba共NO3兲2 共⬎99.99%兲 andB2O5 with a 25% molar excess of CsNO3. The mixture washeated at 600 ° C for 6 h and then at 850 ° C for 3 h.
The syntheses of 共CuBr兲A2B3O10 共A = Ca, Sr, Pb, Ba; B= Nb, Ta兲 were performed by low-temperature ion-exchange

Powder XRD data of the samples before and after theion-exchange reactions were typically collected between 2␪
= 5° and 80° with a step of 0.02° and a 0.1 s count time usinga M18XHF diffractometer 共Mac Science兲 with a graphite
monochromator using Cu K␣ 共␭ = 1.5418 Å兲 radiation. The
impurity phases present in the products were identified using
the standards from the JCPDS database with the help of the
MXP software package equipped with the diffractometer. A
step of 0.01° and a 2 s count time were employed to collectthe data for the structural refinements. Rietveld refinements
were performed using the RIETAN2000 program.20 Profile refinements utilized the pseudo-Voigt function. The R factor
共R p兲, the weighted R factor 共Rwp兲, and S are defined as thefollowing profile: R p = 兺兩y io − y ic兩 / 兺yio, weighting profile
Rwp = 关兺wi共y io − y ic兲2 / 兺wiy 2io兴, and goodness of fit S= Rwp / Rexp. Rexp = 关共N − P兲 / 兺wiy 2io兴1/2, where y io and y ic are
the observed and calculated intensities, wi is the weighting
factor, N is the total number of y io data when the backgroundis refined, and P is the number of adjusted parameters.
Magnetic susceptibility measurements for 共CuBr兲A2B3O10
were performed on a powder sample using a superconducting quantum interference device 共SQUID兲 共Quantum Design,
MPMS-XL-HKD兲 magnetometer over the temperature range
T = 2 – 300 K in an applied magnetic field of H = 0.1 T in
both field-cooled 共FC兲 and zero-field-cooled 共ZFC兲 processes. High-field magnetization measurements were madeusing an induction method with a multilayer pulse magnet
installed at the Institute for Solid State Physics 共ISSP兲 at the
University of Tokyo. Magnetization data were collected at
4.2 and 1.3 K in magnetic fields of up to 60 T. Specific heatmeasurements were performed using a relaxation techniquewith a commercial physical property measurement system
共PPMS兲 共Quantum Design兲 from 2 to 40 K in zero magnetic
field. The hand-pressed pellet was mounted on an alumina
plate with grease for better thermal contact. ␮SR measurements were carried out for 共CuBr兲Sr2Nb3O10 and
共CuBr兲Ba2Ta3O10 on the M20 surface muon beamline at
TRIUMF. Spin-polarized positive muons were implanted in
the powder samples in zero-field 共ZF兲 ␮SR,21 and the time214410-2

PHYSICAL REVIEW B 78, 214410 共2008兲

SYNTHESIS, STRUCTURE, AND MAGNETIC PROPERTIES…

(a)histograms of the forward-backward asymmetry of the decay
positrons were recorded.

Å(CuBr)A2B3O10

III. RESULTS

B=
B=

A. Synthesis and lattice parametersB=
B=

A´A2B3O10

Å

(b)

3

(c)
Å

The XRD patterns for all the parent compounds
A⬘A2B3O10 obtained in this study were readily indexed on
the tetragonal cell with approximate lengths of 4 and 16 Å
for the a and c axes, respectively. No trace of impurity
phases was found in the profiles of the Ca-, Sr-, and Pbbased parent compounds within the experimental resolutionof the present experimental conditions. On the other hand,
the Ba-based parent compounds, CsBa2Nb3O10 and
CsBa2Ta3O10, were yielded together with a small amount of
nonmagnetic impurity Ba5Nb4O15 共6%兲 and Ba5Ta4O15
共4%兲, as also reported in the literature.18 Here, the ratio of
the main-to-impurity phase was roughly estimated from therelative intensity of XRD patterns. Attempts to yield purephases by changing, e.g., reaction temperature and time did
not improve the results.
The XRD patterns for 共CuBr兲A2B3O10 were also indexable by the tetragonal symmetry without any extinction conditions. The lattice parameters are similar to those of reandportedcompounds
共CuCl兲Ca2Nb3O10
共CuCl兲La2Ti2NbO10.22 It is therefore natural to assume thatthe structures of all the ion-exchanged compounds obtainedin the present study are identical with 共CuCl兲Ca2Nb3O10 having the P4 / mmm space group. No impurity phase was foundin 共CuBr兲Ca2Ta3O10 and 共CuBr兲Sr2Ta3O10 within experimental resolution. The Ba-based compounds were successfully formed but together with Ba5Nb4O15 共Ba5Ta4O15兲
which was already present after the high-temperature synthesis of CsBa2Nb3O10 共CsBa2Ta3O10兲. For the synthesis of
共CuBr兲Pb2Nb3O10, PbO2, to which CsPb2Nb3O10 decomposed during the ion-exchange reaction, was yielded together
with the main phase. These impurities could not be separated
from the main product but the nonmagnetic nature of the
impurity phases would not prevent us from capturing theessential magnetic features of 共CuBr兲A2B3O10 at least from aqualitative point of view. Very weak unidentified peaks weredetected in the XRD data of 共CuBr兲Ca2Nb3O10,
共CuBr兲Sr2Nb3O10, 共CuBr兲Pb2Nb3O10, and 共CuBr兲Ba2B3O10.
Figures 2共a兲 and 2共b兲 show the lattice parameters for
共CuBr兲A2B3O10 共and corresponding precursors for comparison兲 plotted against the ionic radius of rA2+, where rCa2+= 1.34 Å, rSr2+ = 1.44 Å, rPb2+ = 1.49 Å, and rBa2+ = 1.61 Å in
the 12-fold coordination were used.23 The lattice parameters
were determined by least-squares calculations of selectedpeaks in the XRD profile. The average ionic radius of thesolid solution between Sr and Ca is defined as that weighted
for the relative molar ratio. It is recognized that the a lattice
parameter slightly increases upon the ion-exchange reaction
共1兲, which reflects the formation of a fairly rigid network
consisting of corner-shared BO6 octahedra. On the contrary,
the expansion along the c axis relative to the parent compound is more prominent 共0.7– 0.8 Å兲, which is a consequence of the insertion of copper-bromine arrays in between

Å

FIG. 2. Plots of the a and c lattice parameters and the cellvolumes for 共squares兲 A⬘A2B3O10 共A⬘ = Rb, Cs; A = Ca, Sr, Ba, Pb;
B = Nb, Ta兲 and 共circles兲 共CuBr兲A2B3O10.

perovskite blocks. The same trends have been observed in
the known compounds.22,24
In the case of A = alkali earth metal, both cell parameters
exhibit a linear increase with rA2+, as also observed for theparent compounds. In other words, both lattice parameters
are insensitive to B. This observation is naturally understoodconsidering the same ionic radius of ⬃0.64 Å for Nb5+ andTa5+ in the sixfold coordination.23 A notable feature has been
observed when A is lead, i.e., 共CuBr兲Pb2Nb3O10, where bothlattice parameters show a slight deviation from the linear
relation in Figs. 2共a兲 and 2共b兲 with the c lattice parameter
being shorter than expected, whereas the a lattice parameter
is longer. Note that a smaller difference in the c axis between
daughter and mother compounds 共⬃0.5 Å兲 for A = Pb would
not be attributed to the incomplete ion-exchange reaction but
to the steric effect of the 6s2 lone pair in Pb as observed in

214410-3

PHYSICAL REVIEW B 78, 214410 共2008兲

TSUJIMOTO et al.

(a)

(b)

(CuBr)Ca2Nb3O10(CuBr)Ca2Ta3O10
a = 3.86926(4)c = 15.6866(2)a = 3.85456(2)c = 15.6189(1)Rwp = 7.85%
Rp = 5.80%
S = 2.38

Rwp = 5.67%
Rp = 4.17%
S = 2.36

10

20

30

40

50

(c)

60

70

80

10

20

30

40

50

(d)

(CuBr)Sr2Nb3O10

30

40

50

60

70

80

80

a = 3.90722(3)c = 16.0280(2)Rwp = 7.93%
Rp = 6.03%
S = 2.18

Rwp = 9.25%
Rp = 7.16%
S = 2.42

20

70(CuBr)Sr2Ta3O10

a = 3.90997(3)c = 16.0197(2)

10

60

10

20

30

40

50

60

70

80

FIG. 3. Rietveld structure refinements for 共a兲 共CuBr兲Ca2Nb3O10, 共b兲 共CuBr兲Ca2Ta3O10, 共c兲 共CuBr兲Sr2Nb3O10, and 共d兲 共CuBr兲Sr2Ta3O10,
showing the calculated 共top, solid line兲 and observed 共top, dotted line兲 XRD patterns. The difference is indicated by a solid line at the bottom.
共CuBr兲A2B3O10 adapts to the space group P4 / mmm similar to 共CuCl兲Ca2Nb3O10.

other oxides such as PbVO3.25 What is interesting in relation
to this is that the cell volume of 共CuBr兲A2B3O10 关Fig. 2共c兲兴
exhibits linear behavior for the entire A site series including
lead. The steric expansion in the cell volume ofCsPb2Nb3O10 originally induced by the lone pair in lead islikely released by the ion-exchange reaction.
Now we are in possession of compounds with variable
lattice parameters governed by rA2+ 共apart from a small deviation seen in A = Pb兲, allowing systematic investigation of
the magnetism. Since the distance between the CuBr layers
共i.e., the c lattice parameter兲 is much longer, the magnetic
properties presented in Sec. III C would be mostly influenced
by the a lattice parameter.
B. Structural refinements

The initial inspection of the XRD data of 共CuBr兲A2B3O10
suggested that they adopt the same structure as
共CuCl兲Ca2Nb3O10 with a tetragonal symmetry 共space group
P4 / mmm兲.22 Starting from this space group and atomic coordinates for 共CuCl兲Ca2Nb3O10, we performed Rietveld refinement of the XRD profile of 共CuBr兲Sr2Nb3O10. The isotropic displacement parameters Uiso of the oxygen andniobium atoms were independently constrained to the samevalue during refinement. The fit converged reasonably, providing Rwp = 9.25% and R p = 7.16. The experimental and theoretical profiles and the difference are presented in Fig. 3共a兲.
The refined structural parameters are shown in Table I. The
fractional atomic positions do not differ largely from those of
共CuCl兲Ca2Nb3O10. However, the Uiso for the bromine site,
0.097共2兲 Å2, is extraordinarily large. This implies that thebromine ions in 共CuBr兲Sr2Nb3O10 move off the 1d Wyckoffsite 共 21 , 21 , 21 兲, which was also proposed in the course of therefinement of 共CuX兲LaB2O7 共X = Cl, Br; B = Nb, Ta兲 and
共CuCl兲Ca2Nb3O10.22,24 Accordingly, the disorder model thatplaced the bromine on the 4m 共x, 0, 21 兲 with a fixed site
occupancy factor 共sof兲 of 25% was examined, which resulted
in x = 0.439共3兲, and the Uiso for Br dropped to reasonablevalues 关0.020共3兲兴. R factors Rwp and R p were reduced to
9.15% and 7.07%. Refining the sof of the fourfold brominesite did not improve the results. We also tried to place bromine atoms at more general positions 8q 共x, y, 21 兲 with afixed sof of 0.125 but the fit ended up with x ⬃ 0.
Subsequently, we refined the crystal structures of
共CuBr兲Ca2Nb3O10, 共CuBr兲Ca2Ta3O10, and 共CuBr兲Sr2Ta3O10
in the same way as 共CuBr兲Sr2Nb3O10 but for simplicity without taking into account any disorder of the bromine atoms.
The refinement converged reasonably, providing Rwp= 5.21% and R p = 3.88 for 共CuBr兲Ca2Nb3O10, Rwp = 7.85%
and R p = 5.80 for 共CuBr兲Ca2Ta3O10, and Rwp = 7.93% andR p = 6.03 for 共CuBr兲Sr2Ta3O10. The profile fits and the structural parameters are represented in Figs. 3共b兲–3共d兲 and Table
I. As expected, the Uiso at the bromine site is large, suggesting the displacement of bromine atoms off the ideal position.
The structures of the Ba- and Pb-containing compounds
could not be refined because of the presence of the unidentified impurities.
C. Magnetic properties
1. Magnetic susceptibility

In Fig. 4, we present the temperature dependence of themagnetic susceptibilities ␹ 共⬅M / H兲 of 共CuBr兲A2B3O10 关A

214410-4

PHYSICAL REVIEW B 78, 214410 共2008兲

SYNTHESIS, STRUCTURE, AND MAGNETIC PROPERTIES…

TABLE I. The crystallographic data for 共CuBr兲A2B3O10 共A = Ca, Sr; B = Nb, Ta兲.
Atom

Site

共A , B兲 = 共Ca, Nb兲
Cu
1b
Br
1d
Ca
2h
Nb1
1a
Nb2
2g
O1
2f
O2
2g
O3
4i
O4
2g
共A , B兲 = 共Ca, Ta兲
Cu
1b
Br
1d
Ca
2h
Ta1
1a
Ta2
2g
O1
2f
O2
2g
O3
4i
O4
2g
共A , B兲 = 共Sr, Nb兲
Cu
1b
Br
1d
Sr
2h
Nb1
1a
Nb2
2g
O1
2f
O2
2g
O3
4i
O4
2g
共A , B兲 = 共Sr, Ta兲
Cu
1b
Br
1d
Sr
2h
Ta1
1a
Ta2
2g
O1
2f
O2
2g
O3
4i
O4
2g

x

y

z

ga

100Uiso 共Å2兲b

0
0.5
0.5
0
0
0
0
0
0

0
0.5
0.5
0
0
0.5
0
0.5
0

0.5
0.5
0.1431共3兲
00.2668共1兲
00.122共1兲
0.2441共9兲
0.365共1兲

1.00共2兲
1.05共2兲
1
1
1
1
1
1
1

4.0共3兲
7.8共4兲
1.27共17兲
0.5共1兲
0.5
4.0共2兲
4
4
4

0
0.5
0.5
0
0
0
0
0
0

0
0.5
0.5
0
0
0.5
0
0.5
0

0.5
0.5
0.1427共2兲
00.269 69共7兲00.1213共8兲
0.2444共6兲
0.3739共9兲

1.011共8兲
1.049共7兲
1
1
1
1
1
1
1

2.3共2兲
9.7共2兲
0.86共12兲
0.058共14兲
0.05
3.98共17兲
3.9
3.9
3.9

0
0.5
0.5
0
0
0
0
0
0

0
0.5
0.5
0
0
0.5
0
0.5
0

0.5
0.5
0.1389共1兲
00.272 77共9兲
00.1218共5兲
0.2481共3兲
0.3807共6兲

0.959共7兲
0.976共6兲
1
1
1
1
1
1
1

1.7共2兲
4.41共19兲
0.84共5兲
0.04共3兲
0.04
1.19共13兲
1.1
1.1
1.1

0
0.5
0.5
0
0
0
0
0
0

0
0.5
0.5
0
0
0.5
0
0.5
0

0.5
0.5
0.139 30共13兲
00.27284共7兲
00.1252共7兲
0.2462共5兲
0.3900共7兲

0.948共9兲
1.048共7兲
1
1
1
1
1
1
1

0.8共2兲
5.8共2兲
0.12共6兲
0.55共2兲
0.55
0.30共14兲
0.3
0.3
0.3

ag is the site occupancy.
b

The isotropic displacement parameters Uiso of oxygen, niobium, and tantalum are independently constrained
to the same values while in the refinement.

= Ca (Fig. 4共a兲), Sr (Fig. 4共b兲), Pb (Fig.4共c兲), and Ba (Fig.
4共d兲)兴 measured in zero-field cooling mode. No differences
are seen between ZF and field coolings. The reciprocal susceptibilities exhibit concave curves in the high-temperature
region, pointing to a sizable contribution of diamagnetism
from core electrons and/or aforementioned nonmagnetic im-purities. Thus, fitting to the Curie-Weiss law plus a
T-independent term, ␹共T兲 = C / 共T − ␪兲 + ␹0, where C and ␪
represent the Curie constant and the Weiss temperature, respectively, was performed in the temperature range T= 100– 300 K. The obtained parameters are listed in Table II.
The values of C agree well with that expected for 1 mol of214410-5

PHYSICAL REVIEW B 78, 214410 共2008兲

TSUJIMOTO et al.

(a)
A = CaχTmax

A = CaA = SrT c2(b)

A = SrT c1

B = Nb

B = NbHc1

B = Taχ

T c Tmax

(a)

Tmax

B = Ta(b)

B = Nb

B = TaχTmax

A = Pb

B = TaHc2

B = Nbχ(c)

A = BaA = Pb(d)

A = BaB = Nb

B = Nb

Hc1

Tc2

Hc2

Tc1

B = TaHc1

B = NbHc2

B = Nb(d) B = Ta

(c)

(f)

(e)

(A, B)

FIG. 4. The magnetic susceptibilities of 共CuBr兲A2B3O10 measured in a field of 0.1 T after cooling in zero field.

(Sr, Ta)(Ca, Nb)

Cu2+ ions 共0.375 emu K / mol兲 and g = 2, supporting the designated compositions. Common to the 共CuBr兲A2B3O10 family, ␪ is positive, indicating that the ferromagnetic 共FM兲 interaction is dominant in contrast to the double-layered
system 共CuX兲LaNb2O7 共X = Cl, Br兲 having negative ␪. From
the A site dependence of the a lattice parameter in
共CuBr兲A2B3O10, it is intuitively expected that ␪ changes linearly as a function of rA2+. In practice, however, ␪ depends
on both A- and B-site ions despite the structural closenessbetween Nb and Ta compounds for a given A. This may
indicate complex superexchange pathways as will be discussed later.
The ␹-T curves of the A = Ca case, 共CuBr兲Ca2Nb3O10 and
共CuBr兲Ca2Ta3O10, exhibit a broad maximum, a characteristic
behavior of low-dimensional quantum antiferromagnets, but␹,the temperature at which ␹ takes a maximum value, Tmax␹␹differs between Nb 共Tmax = 15 K兲 and Ta 共Tmax = 22 K兲. A
Curie tail at lower temperatures would be due to a small
amount of defects in the CuBr layer and/or residual impuriTABLE II. The parameters obtained by Curie-Weiss fit to thesusceptibilities of 共CuBr兲A2B3O10. C, ␪, and ␹0 represent Curie
constant, Weiss temperature, and T-independent term, respectively.

CompoundC
共emu K/mol兲␪共K兲

␹0 ⫻ 104
共emu/mol兲

共CuBr兲Ca2Nb3O10
共CuBr兲Ca2Ta3O10
共CuBr兲Sr2Nb3O10
共CuBr兲Sr2Ta3O10
共CuBr兲Ba2Nb3O10
共CuBr兲Ba2Ta3O10
共CuBr兲Pb2Nb3O10

0.3985共6兲
0.383共1兲
0.408共1兲
0.423共2兲
0.399共2兲
0.404共1兲
0.4366共9兲

4.6共1兲
3.2共2兲
20.9共3兲
13.2共4兲
14.9共6兲
14.7共3兲
17.4共2兲

−3.08共1兲
−0.71共2兲
−1.36共3兲
−3.85共5兲
−4.79共6兲
−4.21共3兲
−5.27共2兲

(Ca, Ta)

Hc1
Hc2

A = Ca1−xSrx/ T χmax (T/K)

FIG. 5. 共Color online兲 共a兲-共e兲 Magnetization curves measured at
1.3 or 4.2 K for 共CuBr兲A2B3O10. 共f兲 Magnetization curves of
共CuBr兲Ca2B3O10 and 共CuBr兲Sr2Ta3O10 scaled by the temperatureof the maximum susceptibility T␹max. For clarity, the magnetization
of 共CuBr兲Sr2Ta3O10 is shifted by 0.2.
␹
ties. For A = Sr, the ␹ of 共CuBr兲Sr2Ta3O10 共Tmax= 12 K兲 issimilar to those of the Ca systems. By marked contrast,
共CuBr兲Sr2Nb3O10 apparently has a featureless curve with amonotonic increase and finally flattens out at lower temperatures. Our previous specific-heat experiments, however, revealed successive phase transitions at 9.3 K 共=Tc1兲 and
7.5 K 共=Tc2兲, which was discussed in terms of the competition 共or frustration兲 between mixed 共FM- and AF-兲 interactions in the CuBr layer.10 For A = Pb, the ␹-T curve increases
monotonically with decreasing temperatures but a kink implying a magnetic transition was observed at around 6 K. For
A = Ba, 共CuBr兲Ba2Nb3O10 shows a drastic drop at 5 K, suggestinganantiferromagnetictransition,
while
共CuBr兲Ba2Ta3O10 shows a featureless temperature dependence similar to that of 共CuBr兲Sr2Nb3O10.

2. Magnetization curves

Figure 5 depicts the magnetizations M共H兲 of
共CuBr兲A2B3O10 关A = Ca (Fig. 5共a兲), Sr (Fig. 5共b兲), Pb (Fig.
5共c兲), and Ba (Fig. 5共d兲)兴 normalized by the saturation magnetizations M s at 1.3 or 4.2 K. Let us first discuss the resultsof the B = Nb system. As previously reported,10
共CuBr兲Sr2Nb3O10 exhibits a 1/3 magnetization plateau be214410-6

PHYSICAL REVIEW B 78, 214410 共2008兲

SYNTHESIS, STRUCTURE, AND MAGNETIC PROPERTIES…

(a)(CuBr)A2B3O10
B = Nb

Hc2−Hc1

B = Ta1/3 plateau

1/3 plateau

ionic radii (Å)
FIG. 6. 共Color online兲 The compositional dependence of theplateau width Hc2 − Hc1 in 共CuBr兲A2B3O10 as a function of the ionicradius of the A site. The lines are drawn as guides for the eyes.

tween 2.0 T 共=Hc1兲 and 8.1 T 共=Hc2兲, and there is a small
hysteresis below 3 T. Substitution chemistry revealed that the
1/3 plateau is indeed robust. As seen in Fig. 5共c兲, the magnetization of 共CuBr兲Pb2Nb3O10 also exhibits a 1/3 plateau
between Hc1 = 1.7 T and Hc2 = 5.8 T along with a small hysteresis below 2.5 T. The width of the plateau, Hc2 − Hc1, is 4.1
T, which is narrower than 6.1 T in 共CuBr兲Sr2Nb3O10, indicating that the A-site replacement by the larger cation destabilizes the plateau phase. Further increasing of the size of the
A-site cation leads to the disappearance of the plateau; noplateau was observed in 共CuBr兲Ba2Nb3O10 关Fig. 5共d兲兴. Decreasing the size of the A site 共vs Sr兲 also results in the sameoutcome; no plateau was observed in 共CuBr兲Ca2Nb3O10 关Fig.
5共a兲兴. Instead, the magnetization increases linearly in the
low-field region, followed by nonlinear growth until it saturates. The nonlinear growth is possibly associated with quantum effects as reported for the double-layered system
共CuBr兲LaNb2O7.15 Magnetization measurements were also
conducted for the solid solution 共CuBr兲共Ca1−xSrx兲2Nb3O10
共x = 0.25, 0.50, and 0.75兲, as shown in Fig. 5共e兲. We observed
a 1/3 plateau only for x = 0.75. As shown in Fig. 6, the Hc2− Hc1 vs rA2+ plot clearly demonstrates an intimate correlation between rA2+ 共or more specifically, the a lattice parameter兲 and the stability of the plateau phase.
The 1/3 plateau phase can be tuned not only by the A site
but also by the B site. In the case of B = Ta, only
共CuBr兲Ba2Ta3O10 showed a 1/3 plateau 共Hc1 = 1.0 T and
Hc2 = 4.0 T兲. It is interesting that there exists a converse relation: no plateau for 共A , B兲 = 共Sr, Ta兲 and 共Ba, Nb兲, andplateaus for 共Ba, Ta兲 and 共Sr, Nb兲. Although the data available are limited, it is anticipated that, in analogy to the Nbcase, the plateau-stabilizing region is shifted to the right in
Fig. 6. Conditions for the appearance of the plateau would
come from a subtle balance between the magnetic interactions mediated by Br and those mediated by BO6-BO6 共seeFig. 1兲.
3. Heat capacity

Figure 7 shows the temperature dependence of the totalheat capacity C p in zero magnetic field for

(b)

(c)

FIG. 7. The temperature variation in the heat capacity on
共CuBr兲Ca2Ta3O10, 共CuBr兲Sr2Nb3O10, and 共CuBr兲Ba2Ta3O10. The
C p / T is shown in the inset to emphasize the anomaly at the transition temperature.

共CuBr兲Ca2Ta3O10, 共CuBr兲Sr2Nb3O10, and 共CuBr兲Ba2Ta3O10.
共CuBr兲Ca2Ta3O10 exhibits a tiny anomaly at 16.6 K. This␹so that it is attributed totemperature is slightly below Tmax
the onset of long-range magnetic order. As reported
previously,10 共CuBr兲Sr2Nb3O10 undergoes successive
second-order-like phase transitions at Tc1 = 9.3 K and Tc2= 7.5 K. Interestingly, 共CuBr兲Ba2Ta3O10 undergoes succes-

214410-7

PHYSICAL REVIEW B 78, 214410 共2008兲

TSUJIMOTO et al.
8

(a)

0.20

7
6

0.15

0.10

A共t兲 = A3 exp共− ␭fastt兲 + A4 exp共− ␭slowt兲.

5
4

λfast
λslow

3

λ0

2

σ

0.05

1

(CuBr)Sr2Nb3O10
0.00

0

1

2

3
4
Time (µ s)

5

0

6

0

2

4

6
8
T (K)

10

12

4

0.20

(c)

(d)

10 K
7K
5K
2K

λfast

3
Relaxation rate (µs−1 )0.15

Corrected Asymmetry

namical field. A1,2 are the fractional site population of themuons. The ␮SR spectra below Tc2 were analyzed using thesum of two exponential functions,

(b)

10 K
8K
7.5 K
6K
2K

Relaxation rate (µs−1 )Corrected Asymmetry

0.25

0.10

λslow
λ1
2

1

0.05

(CuBr)Ba2Ta3O10
0.00

0

1

2

3
4
Time (µ s)

5

6

0

0

2

4

6
T (K)

8

10

FIG. 8. 共a兲,共c兲 The time evolution of ␮SR asymmetry and 共b兲,共d兲
the temperature dependence of estimated relaxation rate in zero
field for 共CuBr兲Sr2Nb3O10 and 共CuBr兲Ba2Ta3O10. The solid lines
are guides for the eyes.

sive phase transitions as well at Tc1 = 9.0 K and Tc2 = 5.0 K.
Therefore, successive phase transitions should be common tomaterials with a 1/3 plateau in their magnetizations.
4. Muon spin relaxation

To obtain more insight into the nature of successive phaseandtransitions
observed
in
共CuBr兲Sr2Nb3O10
共CuBr兲Ba2Ta3O10, we have performed ␮SR measurements,
which offer a unique opportunity in detecting a static magnetic order at high sensitivity. Figure 8共a兲 shows the
spectrafor
temperature-dependent
ZF-␮SR
共CuBr兲Sr2Nb3O10. At high temperatures above Tc1, the corrected asymmetry A共t兲 shows a Gaussian-like decay, in consistency with a paramagnetic state. However, such aGaussian-like decay continues even below Tc1, meaning thatthe intermediate state for Tc2 ⬍ T ⬍ Tc1 is paramagnetic, indisagreement with the previous interpretation that the transition at Tc1 is magnetic in nature.10 The spectrum shapechanges drastically from Gaussian to exponential below Tc2,
confirming that long-range magnetic order onsets at Tc2.
The time spectra above Tc2 were best fitted by the following formula:
A共t兲 = A1 exp关− 共␴t兲2兴 + A2 exp共− ␭0t兲.

共2兲

The first term is the Kubo-Toyabe function that describes
nuclear dipole relaxations. The second term takes into consideration the development of two-dimensional magnetic
correlations among S = 1 / 2 spins of Cu2+, providing a dy-

共3兲

The calculated relaxation rates are given in Fig. 8共b兲. They
rapidly increase at Tc2 and saturate toward T → 0. The twocomponents of the relaxation rates may originate either fromtwo crystallographically inequivalent muon sites or from astructurally unique but magnetically inequivalent site.
Figure 8共c兲 shows the ZF-␮SR spectra forThe
spectraexhibit,like
共CuBr兲Ba2Ta3O10.
共CuBr兲Sr2Nb3O10, slow relaxation for T ⬎ Tc2 and fast relaxation for T ⬍ Tc2. The damping of the A共t兲 becomes fasterbelow 5 K 共=Tc2兲 owing to the slowing down of fluctuationsof Cu2+ spins. This demonstrates that the successive phasetransitions derive from the same mechanism, whatever it is.
Unlike 共CuBr兲Sr2Nb3O10, however, A共t兲 above Tc2 could be
fitted by a single exponential equation with relaxation rate ␭1
while the relaxation rate below Tc2 was obtained by fitting
the asymmetry curves to Eq. 共3兲. Similar behavior was foundin the paramagnetic state of a quasi-one-dimensional chain
Ca3Co2O6.26,27
IV. DISCUSSION

In the early stages of the magnetic study on these ionexchanged materials, it was simply assumed that the perovskite blocks An−1BnO3n+1 were magnetically inert and that
only the superexchange pathway through Cu-X-Cu determined the magnetic properties.12 However, the susceptibilities and magnetizations in the present study show
B-dependent behavior, indicating that in-plane superexchange interactions of Cu-BO6-BO6-Cu provide a significant
contribution, in addition to those of Cu-Br-Cu. In general,
one takes it for granted that the superexchange interaction
through a nonmagnetic polyhedron such as SO4, PO4, andBO3 is negligibly small in comparison with that through asingle anion such as O, Cl, and Br, yet the former becomes insome cases dominant over the latter. A representative example is found in 共VO兲2P2O7, which was once thought as aspin ladder system from the naive argument of the chemical
structure28,29 but then turned out to be a one-dimensional
alternating chain system with the strongest exchange givenby the V-PO4-V pathway.30 From the NMR study of
共CuCl兲LaNb2O7, the dz2 orbital along the c axis 共thus pointing to the neighboring BO6 octahedra兲 is assigned as theorbital to accommodate an unpaired electron.31 It is highly
possible that 共CuBr兲A2B3O10 employs the same electronic
configurations which facilitate the hybridization between dz2
orbitals and BO6 octahedra.32
How are the magnetic interactions of 共CuBr兲A2B3O10 affected by chemical substitution? 共CuBr兲Ca2Nb3O10,
共CuBr兲Ca2Ta3O10, and 共CuBr兲Sr2Ta3O10 show a broad maxi␹= 15, 22, and 12 K, respecmum in the susceptibility at Tmax␹tively. In accordance with Tmax, the saturation magnetic fieldchanges: Hs = 25.1, 39.8, and 22.7 T. As shown in Fig. 5共f兲,␹, demonstrating
the magnetization curves are scaled by Tmax
that the magnitude of the magnetic interactions is tuned by

214410-8

SYNTHESIS, STRUCTURE, AND MAGNETIC PROPERTIES…

PHYSICAL REVIEW B 78, 214410 共2008兲

the A-site as well as B-site substitutions. Comparison between 共CuBr兲Ca2Ta3O10 and 共CuBr兲Sr2Ta3O10 suggests thatmagnetic interactions become stronger by decreasing the alattice parameter. However, the situation is not so simple
since the appearance condition of the 1/3 plateau should belinked to the ratio of magnetic interactions. The implicationof the domelike structure of the plateau width 共Fig. 6兲 is thatthe a lattice parameter influences not only the magnitude but
also the relative ratio. Here, we wish to recall that
共CuBr兲Sr2Nb3O10 with the largest ␪ 共⬎0兲 showed the widest
plateau. Thus, increased ferromagnetic interactions 共vs antiferromagnetic interaction兲 will result in stabilizing the 1/3
plateau phase.
It would be difficult to explain the experimentally observed 1/3 plateau in the framework of the J1-J2 model. Recently, Shannon and Momoi33 theoretically investigated the
J1-J2-J3 model and showed the 1/3 plateau in a certain parameter range. However, we would like to stress the fact thatthe 1/3 plateau in the high-field magnetization curve is accompanied by successive phase transitions at low field. Applying the quantization condition p共S − m兲 = integer 共S = 1 / 2,
m = 1 / 6兲 to the present case, one obtains p = 3 共or 6, 9,…兲.
Therefore, the structural transition at Tc1 involves a breakingof the translational symmetry that triples the unit cell of thecrystal structure. In relation to this, the coupled dimer system
NH4CuCl3 shows a structural phase transition involving adoubling of the unit cell in zero field, which is crucial for theappearance of the 1/4 and 3/4 magnetization plateaus.34 It
would be possible in our compounds that the structural transition at Tc1 triggers the 1/3 plateau: it may change the symmetry and make some magnetic interactions nonequivalent.
Further structural studies at low temperatures, in particular,
synchrotron XRD and TEM, are highly desired. Singlecrystal growth is also in progress.

tions with CuBr2 of A⬘A2B3O10 共A⬘ = Rb, Cs; A = Ca, Sr, Ba,
Pb; B = Nb, Ta兲. The Rietveld refinements for the powder
XRD patterns have revealed that 共CuBr兲A2B3O10 共A = Ca, Sr;
B = Nb, Ta兲 are isostructural with 共CuCl兲Ca2Nb3O10 with thespace group of P4 / mmm although rather large thermal parameters of the bromine ion suggest statistically disordered
distribution into more general sites. The lattice parameters
predominantly change with the size of the A site ion, apartfrom a small deviation for A = Pb. The stability of the 1/3
magnetization plateau is controlled systematically by the alattice parameter. Furthermore, the successive phase transitions were observed at zero field and assigned as the structural one at Tc1 and the magnetic one at Tc2. It is consideredthat the former is derived from the rearrangement in the
CuBr layer, leading to stabilization of the 1/3 plateau phasein high fields. Further experimental efforts and theoreticalsupport are needed for full understanding of the relation between the structural and magnetic properties in
共CuBr兲A2B3O10.

V. CONCLUSIONS

We have synthesized a series of layered compounds containing two-dimensional CuBr layers by ion-exchange reac-

ACKNOWLEDGMENTS

This work was supported by Grants-in-Aid for Science
Research on Priority Areas “Novel States of Matter Induced
by Frustration” 共No. 19052004兲 and “Invention of Anomalous Quantum Materials” 共No. 16076210兲 from the Ministryof Education, Culture, Sports, Science and Technology ofJapan, and by the Global COE program International Center
for Integrated Research and Advanced Education in Material
Science, Kyoto University, Japan. The ␮SR work was supported by JSPS and NSF under the Japan-U.S. Cooperative
Science Program “Phase separation near quantum criticalpoint in low-dimensional quantum spin systems” 共Contract
No. 14508500001兲. The work at Columbia University was
supported by U.S. NSF Grants No. DMR-05-02706 and No.
DMR-08-06846.

T. Goto J. Phys. Soc. Jpn. 69, 1016 共2000兲.

*Author to whom correspondence should be addressed;
kage@kuchem.kyoto-u.ac.jp
1 A. P. Ramirez, Annu. Rev. Mater. Sci. 24, 453 共1994兲.
2 M. F. Collins and O. A. Petrenko, Can. J. Phys. 75, 605 共1997兲.
3 T. M. Rice, Science 298, 760 共2002兲.
4
Y. Narumi, M. Hagiwara, R. Sato, K. Kindo, H. Nakano, and M.
Takahashi, Physica B 246-247, 509 共1998兲.
5 H. Kikuchi, Y. Fujii, M. Chiba, S. Mitsudo, T. Idehara, T. Tonegawa, K. Okamoto, T. Sakai, T. Kuwai, and H. Ohta, Phys. Rev.
Lett. 94, 227201 共2005兲.
6 Y. Narumi, K. Katsumata, Z. Honda, J. C. Domenge, P. Sindzingre, C. Lhuillier, Y. Shimaoka, T. C. Kobayashi, and K. Kindo,
Europhys. Lett. 65, 705 共2004兲.
7 T. Ono, H. Tanaka, O. Kolomiyets, H. Mitamura, T. Goto, K.
Nakajima, A. Oosawa, Y. Koike, K. Kakurai, J. Klenke, P. Smeibidle, and M. Meißner, J. Phys.: Condens. Matter 16, S773
共2004兲.
8 K. Onizuka, H. Kageyama, Y. Narumi, K. Kindo, Y. Ueda, and

9 M. Oshikawa, M. Yamanaka, and I. Affleck, Phys. Rev. Lett. 78,

1984 共1997兲.
Tsujimoto, Y. Baba, N. Oba, H. Kageyama, T. Fukui, Y.
Narumi, K. Kindo, T. Saito, M. Takano, Y. Ajiro, and K.
Yoshimura, J. Phys. Soc. Jpn. 76, 063711 共2007兲.
11 A. Honecker, Can. J. Phys. 79, 1557 共2001兲.
12 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, 1702 共2005兲.
13 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, 1702 共2005兲.
14 A. Kitada, Z. Hiroi, Y. Tsujimoto, T. Kitano, H. Kageyama, Y.
Ajiro, and K. Yoshimura, J. Phys. Soc. Jpn. 76, 093706 共2007兲.
15 N. Oba, H. Kageyama, T. Kitano, J. Yasuda, Y. Baba, M. Nishi,
K. Hirota, Y. Narumi, M. Hagiwara, K. Kindo, T. Saito, Y. Ajiro,
and K. Yoshimura, J. Phys. Soc. Jpn. 75, 113601 共2006兲.
10 Y.

214410-9

PHYSICAL REVIEW B 78, 214410 共2008兲

TSUJIMOTO et al.
16

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, K. Yoshimura, and H. Kageyama,
arXiv:0806.2021 共unpublished兲.
17
H. Kageyama, T. Kitano, R. Nakanishi, J. Yasuda, N. Oba, Y.
Baba, M. Nishi, Y. Ueda, Y. Ajiro, and K. Yoshimura, Prog.
Theor. Phys. Suppl. 159, 共Suppl.兲, 39 共2005兲.
18 V. Thangadurai, P. S. Beurmann, and W. Weppner, J. Solid State
Chem. 158, 279 共2001兲.
19 M. A. Subramanian, J. Goparakrishnan, and A. W. Sleight,
Mater. Res. Bull. 23, 837 共1988兲.
20
F. Izumi and T. Ikeda, Mater. Sci. Forum. 198, 321 共2000兲.
21 R. S. Hayano, Y. J. Uemura, J. Imazato, N. Nishida, T.
Yamazaki, and R. Kubo, Phys. Rev. B 20, 850 共1979兲.
22
T. A. Kodenkandath, A. S. Kumbhar, W. L. Zhou, and J. B.
Wiley, Inorg. Chem. 40, 710 共2001兲.
23
R. D. Shannon, Acta Crystallogr. A 32, 751 共1976兲.
24
T. A. Kodenkandath, J. N. Lalena, W. L. Zhou, E. E. Carpenter,
C. Sangregorio, A. U. Falster, W. B. Simmons, Jr., C. J.
O’Connor, and J. B. Wiley, J. Am. Chem. Soc. 121, 10743
共1999兲.

25

A. A. Belik, M. Azuma, T. Saito, Y. Shimakawa, and M. Takano,
Chem. Mater. 17, 269 共2005兲.
26
J. Sugiyama, H. Nozaki, J. H. Brewer, E. J. Ansaldo, T. Takami,
H. Ikuta, and U. Mizutani, Phys. Rev. B 72, 064418 共2005兲.
27 S. Takeshita, J. Arai, T. Goko, K. Nishiyama, and K. Nagamine,
J. Phys. Soc. Jpn. 75, 034712 共2006兲.
28
D. C. Johnston, J. W. Johnson, D. P. Goshorn, and A. J. Jacobson, Phys. Rev. B 35, 219 共1987兲.
29 T. Barnes and J. Riera, Phys. Rev. B 50, 6817 共1994兲.
30 A. W. Garrett, S. E. Nagler, D. A. Tennant, B. C. Sales, and T.
Barnes, Phys. Rev. Lett. 79, 745 共1997兲.
31
M. Yoshida, N. Ogata, M. Takigawa, J. Yamaura, M. Ichihara, T.
Kitano, H. Kageyama, Y. Ajiro, and K. Yoshimura, J. Phys. Soc.
Jpn. 76, 104703 共2007兲.
32 M. Yoshida, N. Ogata, M. Takigawa, J. Yamaura, M. Ichihara, T.
Kitano, H. Kageyama, Y. Ajiro, and K. Yoshimura, J. Phys. Soc.
Jpn. 77, 104705 共2008兲.
33
N. Shannon and T. Momoi 共private communication兲.
34
Ch. Rüegg, M. Oettli, J. Schefer, O. Zaharko, A. Furrer, H.
Tanaka, K. W. Krämer, H.-U. Güdel, P. Vorderwisch, K. Habicht, T. Polinski, and M. Meissner, Phys. Rev. Lett. 93, 037207
共2004兲.

214410-10