Journal of the Physical Society of Japan
Vol. 76, No. 6, June, 2007, 063711#2007 The Physical Society of JapanLETTERS

1/3 Magnetization Plateau in Spin-1/2 Square Lattice Antiferromagnet (CuBr)Sr2 Nb3 O10
Yoshihiro TSUJIMOTO1 , Yoichi B ABA1 , Noriaki O BA1 , Hiroshi KAGEYAMA1;2 y, Tomoya FUKUI2 ,Yasuo NARUMI2 , Koichi K INDO2 , Takashi S AITO3 , Mikio T AKANO3 ,Yoshitami A JIRO1;4 , and Kazuyoshi Y OSHIMURA1
1

Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502
2
Institute for Solid State Physics, The University of Tokyo, Kashiwa, Chiba 277-8581
3
Institute for Chemical Research, Kyoto University, Uji, Kyoto 611-0011
4
CREST, Japan Science and Technology Agency, Kawaguchi, Saitama 332-0012(Received April 11, 2007; accepted May 1, 2007; published June 11, 2007)

A new triple-layered perovskite (CuBr)Sr2 Nb3 O10 with the S ¼ 1=2 square lattice has been preparedthrough a chimie douce route. Presence of strong spin frustration is inferred from zero-ﬁeld speciﬁc heatmeasurements which exhibit successive phase transitions at 9.3 and 7.5 K. Application of magnetic ﬁelds
merges the transition temperatures at 3 T, suggesting that the intermediate phase is of magnetic origin
with ﬂuctuating spin–spin correlation. Despite the square geometry, magnetization curves have revealed
a metamagnetic transition to a novel phase characterized by a 1/3 plateau of the saturated magnetization.
KEYWORDS: (CuBr)Sr2 Nb3 O10 , square lattice, ion exchange, frustration, magnetization plateau, successive
phase transitions
DOI: 10.1143/JPSJ.76.063711

Historically, the study of geometrically frustration in spin
systems has been focused on the triangle-based models suchas triangular, kagomé and pyrochlore lattices.1) This is dueto the fact that they simply consist of single elements of
exchange constants, i.e., nearest-neighbor (NN) interactions(J1 ), and the abundance of experimental examples, allowing
the veriﬁcation and development of relevant theories. The
opposite holds true for the square-based models that involve
addition of next-nearest-neighbor (NNN) (J2 ) interactions.2)
In order to induce frustration into the latter systems, J1 andJ2 need to be of comparable strength but nature favors thedominance of the interactions for shorter bonds, resulting
in the well-known ð; Þ Néel ordered state.
However, the discovery of the experimental correspondences, Li2 VO(Si, Ge)O4 for the square lattice (termed as the
J1 –J2 model),3) CaV4 O9 for the 1/5-depleted square lattice,4)and SrCu2 (BO3 )2 for the Shastry-Sutherland lattice,5) has
activated research in this area. Recently, double-layered
perovskites (CuX)LaNb2 O7 (X = Cl, Br), synthesized by a
topotactic ion-exchange reaction,6) were added to the list of
the J1 –J2 model;7–11) For both compounds, strong competition is expected between the ferromagnetic (F) J1 andantiferromagnetic (AF) J2 . As a result, (CuBr)LaNb2 O7
establishes a ð; 0Þ collinear AF order (CAF) at 32 K witha reduced moment 0:6 B , while (CuCl)LaNb2 O7 has the
spin-singlet ground state, with a gap of 2.3 meV in the spin
excitation spectrum. Here, the choice of the halogen ion
seems to change the J2 =J1 ratio and hence determines theground state.
(CuX)LaNb2 O7 belongs to the Dion-Jacobson series
expressed as (CuX)An1 Bn O3nþ1 , where A is La3þ , Ca2þ ,Naþ , . . ., B is Nb5þ , Ta5þ , Ti4þ , n ¼ 2; 3; 4; . . ..6,10,11) The
rich diversity of the family brings a crucial advantage overexisting compounds, that is, a systematic control of themagnetic properties by varying parameters A, B, X, and n.
E-mail: yoshi@kuchem.kyoto-u.ac.jp
Permanent aﬃliation: Graduate School of Science, Kyoto University.
E-mail: kage@kuchem.kyoto-u.ac.jpyParticularly interesting is tuning n, by which one can control
the two-dimensionality (2D). In comparison with the n ¼ 2
compounds with a  4 Å, c  12 Å, the c-lattice constant for
the n ¼ 3 compounds is expanded by 4 Å (corresponding
to the one-perovskite unit), while remaining the a–lattice
constant nearly unchanged [see Fig. 1(a)], oﬀering a better
2D and enhanced quantum ﬂuctuations. Although severaln ¼ 3 compounds have been prepared so far,10,11) only little
is known about the magnetism. Here, we report the synthesis
and magnetic properties of a new n ¼ 3 compound(CuBr)Sr2 Nb3 O10 .
In a similar procedure as described in refs. 9 and 10,(CuBr)Sr2 Nb3 O10 forms from the ion-exchange reaction,
expressed as ‘‘RbSr2 Nb3 O10 + CuBr2 ! (CuBr)Sr2 Nb3 O10+ RbBr’’. The product was washed with distilled water toeliminate RbBr and unreacted CuBr2 , which allows us to
(a)

(b)

NbO6
Sr
Cu Br

b
a

(c)

c b

b

a

a

Fig. 1. (a) Structure of (CuBr)Sr2 Nb3 O10 . Small and large open circles,
and solid circles denote, respectively, Sr, Br and Cu atoms, and octahedra
are NbO6 . The magnetic [CuBr]þ layer is sandwiched by the nonmagnetic [Sr2 Nb3 O10 ] slabs. (b), (c) Possible magnetic structures at
the 1/3 plateau, where magnetic unit cells are represented in grey.

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J. Phys. Soc. Jpn., Vol. 76, No. 6

LETTERS

carry out quantitative analysis of the magnetic properties.
The powder x-ray diﬀraction data collected on an M18XHF
diﬀractometer (Mac Science) were readily indexed on
the tetragonal symmetry. The lattice parameters a ¼
3:91069ð4Þ Å, c ¼ 16:0207ð3Þ Å are similar to those of aknown (CuCl)Ca2 Nb3 O10 (a ¼ 3:8496 Å, c ¼ 15:6593 Å).10)
The a axis is slightly longer than that of (CuBr)LaNb2 O7(a ¼ 3:9025 Å), reﬂecting the diﬀerence in the ionic radii ofthe A sites (rSr ¼ 1:58 Å, rLa ¼ 1:50 Å). No trace of impurity
phase was found within the experimental resolution of
the present experiment. Static magnetization measurements
were performed on a powder sample with a SQUID
magnetometer (Quantum Design, MPMS) over the temperature range T ¼ 2 { 300 K at magnetic ﬁelds H up to 5 T.
High-ﬁeld magnetization measurements up to 30 T weremade using an induction method with a multilayer pulse
magnet installed at Institute for Solid State Physics (ISSP),The University of Tokyo. Speciﬁc heat capacity measurements were performed from 2 to 40 K in magnetic ﬁelds
up to 9 T by the heat-relaxation method using a QD-PPMS
at Institute for Chemical Research.
Figure 2(a) shows the T dependence of magnetic susceptibility  of (CuBr)Sr2 Nb3 O10 measured at 0.1 T. The ﬁt
to the Curie–Weiss law plus a T-independent term, ðTÞ ¼
C=ðT  Þ þ 0 , for 100 < T < 300 K gives the Weisstemperature  ¼ 20:9ð3Þ K, Curie constant C ¼ 0:408ð1Þ
emu K/(mol Cu), and 0 ¼ 1:36ð3Þ  104 emu/(mol Cu).
The obtained value of C agrees well with that expected for
1 mol of Cu2þ ions, meaning completion of the ion-exchange
reaction. The positive  implies that the F J1 has a greater

Fig. 2. (a) ðTÞ and ðTÞ1 for (CuBr)Sr2 Nb3 O10 measured at 0.1 T.
The dotted line is the Curie–Weiss ﬁt. (b) MðTÞ=H and dðMðTÞ=HÞ=dT
at 0.1, 0.5 T. (c) MðTÞ=H at 2, 3, 4 T.

Y. TSUJIMOTO et al.

magnitude than the AF J2 , in contrast to the negative  forthe n ¼ 2 cases [ ¼ 5:1 K for (CuBr)LaNb2 O7 and9:6 K for (CuCl)LaNb2 O7 ].7,9) The deviation from theCurie–Weiss behavior appreciable below 100 K is attributable to development of short-range magnetic ordering.
Instead of a broad maximum in ðTÞ typically seen for
low-dimensional spin systems, however, we observed arather smooth growth of ðTÞ with reducing T which
continues until it ﬂattens out below 5 K. At this point, it ishard to judge whether or not a magnetic transition exists andif it does at which temperature it occurs, but the absence ofthe so-called Curie-tail originated from magnetic impurities
and defects assures again a good quality of the sample.
No broad maximum would be characteristic of a system
where F dominates AF.
Speciﬁc heat is a technique that can probe phasetransitions with higher sensitivity. The Cp vs T plot at 0 T
clearly (Fig. 3) demonstrates two peaks at 9.3 K (Tc1 ) and7.5 K (Tc2 ), suggesting successive phase transitions. Nondiscontinuous character and the absence of T hysteresis in
Cp ðTÞ as well as ðTÞ indicate the transitions to be of second
order. Successive phase transitions are known as characteristic features of low-dimensional spin systems with geometrical frustration, as experimentally observed in triangularlattices such as CsCoCl3 and CsNiCl3 .12) It would be thus
natural to consider that the geometrical frustration in(CuBr)Sr2 Nb3 O10 plays a crucial role in this phenomena as
well. Namely, observed transitions might be those from theparamagnetic state (P) to the intermediate magnetic state(M1 ) at Tc1 and ﬁnally to a diﬀerent and probably moreordered magnetic state (M2 ) at Tc2 . If the M1 phase isassociated with a magnetic ordering of some kind, Tc1 andTc2 should be aﬀected by the magnetic ﬁeld. In fact, theapplication of magnetic ﬁelds decreases Tc1 while it
increases Tc2 and ﬁnally merges two transitions together ataround 3 T. Subsequently, the transition temperature Tc
determined by Cp ðTÞ draws a dome shaped boundary
peaking at 5 T on the T–H phase diagram, as shown in
Fig. 4. It is likely that a magnetic state below the boundary ismost stabilized around 5 T, as will be discussed later.
The gradual increase in Cp ðTÞ above 12 K in the P regionis nearly insensitive to H. Since there exist no isomorphic
compounds used as a nonmagnetic reference to derive
the lattice contribution T 3 , we roughly assumed as ¼ 0:97ð2Þ  103 J/(K4 mol). Subtracting T 3 from theraw data at 0 T, one obtains magnetic speciﬁc heat Cm , andthe subsequent T-integration of Cm =T gives the magnetic
entropy Sm , both of which are shown in the inset of Fig. 3.
The measured entropies at Tc2 and Tc1 , respectively, are at
most 20 and 30% of the total entropy (R ln 2), indicating thatthe present spin system is eﬀectively correlated over muchhigher temperatures but nevertheless, cannot readily show along-range order at such temperatures due to enhanced 2D(by increased n) along with competing in-plane interactions.
Stimulated by the observation of successive phasetransitions in low magnetic ﬁelds, we conducted themeasurements of the T dependence of magnetization at
ﬁxed magnetic ﬁelds (H < 5 T). As shown in the inset of
Fig. 2(c), a distinct inﬂection appears in the M=H vs T
curves at H ¼ 2, 3 and 4 T. The temperature at which thisinﬂection occurs gradually increases with H and agrees well

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J. Phys. Soc. Jpn., Vol. 76, No. 6

Y. TSUJIMOTO et al.

Fig. 3. Cp vs T of (CuBr)Sr2 Nb3 O10 measured at 0, 1, 2, 3, 5, and 9 T.
The solid line represents the phonon term. Inset: Cm =T (open circles)
and Sm (solid line) for H ¼ 0 T. The broken line is the linear ﬁt in the
low-T region.

Fig. 5. Normalized (bottom) and diﬀerential (top) magnetizations for(CuBr)Sr2 Nb3 O10 measured in pulsed ﬁelds. The static magnetization isshown in the inset, where a small hysteresis is seen. The dotted line
corresponds to the 1/3 magnetization.

(CuBr)Sr2Nb3O10

Fig. 4. The T–H phase diagram for (CuBr)Sr2 Nb3 O10 , determined by
Cp ðTÞ (open circles), dMðTÞ=dT (open squares), MðTÞ (open circles), andMðHÞ (crosses).

with Tc2 determined by the Cp ðTÞ experiment. It is worth
noting that Tc2 at 0 T and 0.5 T coincides with the temperature at which dðM=HÞ=dT takes a minimum value[Fig. 2(b)], so it may be the measure of Tc2 in a low-H
region below 1 T. In contrast, the T dependence of magnetization has no apparent anomaly at Tc1 even in the presenceof H. A plausible explanation is that the M1 state may be anordered but partially disordered state with considerable
ﬂuctuations, which smears out a long-range-order featurein MðTÞ.
Figure 5 shows the pulsed-ﬁeld magnetizations divided by
the saturated magnetization MðHÞ=Ms and diﬀerential
magnetizations dMðHÞ=dH. The most prominent aspect ofthe present paper is the appearance of a plateau corresponding to the 1/3 of the full magnetization. The plateau
becomes obscured with increasing T and vanishes at 9 K, inagreement with the phase boundary determined by Cp ðTÞand MðTÞ. Since the magnetization curves at 4.2 K and thatat 1.3 K (not shown) are nearly identical, non-ﬂat plateau is
not due to thermal eﬀects but due to the use of powder
sample, the magnetization of which should be averaged byanisotropic g factors. Additionally, some anisotropic terms
such as Dzyaloshinski–Moriya interaction and staggered
g tensor may also play a role in making the plateau oblique
as in SrCu2 (BO3 )2 .13)
The 1/3 magnetization plateau has been theoretically
predicted for various triangle-based lattices,14) as experimentally veriﬁed by, e.g., Cs2 CuBr4 and a copper complex.15,16) However, for commensurability reasons calculations of the frustrated square lattice predict plateaus such as
1/2 and 1/4.17) An exception is seen in SrCu2 (BO3 )2 having
the 1/3, 1/4, and 1/8 plateaus, for which oblique magnetic
unit cells are suggested due to the orthogonal arrangementof dimers.5) By analogy, we may have to take deviations
from the ideal square lattice into considerations, among
which are the site disorder of the Br ions from the ideal 1bsite as suggested in (CuCl)LaNb2 O7 and the orbital orderof the Cu ions, making otherwise equivalent J1 (J2 ) bonds
inequivalent.
Although a clear physical picture of the 1/3 plateau in(CuBr)Sr2 Nb3 O10 has yet to be revealed, one can derive
possible magnetic structures following the theory by
Oshikawa et al. who proposed the quantization conditionon the magnetization at a plateau of Heisenberg spin system,pðS  mÞ ¼ integer, where p and m are the period of the spinstate, the magnetization per site, respectively.18) For S ¼
1=2, the minimal necessary condition of the 1/3 plateau(m ¼ 1=6) is p ¼ 3. Since (CuBr)Sr2 Nb3 O10 has one Cu2þion in its chemical unit cell (p ¼ 1), the breaking oftranslational symmetry is needed to satisfy the quantization
conditions. We present in Figs. 1(b) and 1(c) two possible
magnetic structures of the collinear type, where the F chainsalign as up-up-down in the layer with a propagation vectorof k ¼ ð2=3; 0Þ and ð=3; 2=3Þ. They are analogous to063711-3

J. Phys. Soc. Jpn., Vol. 76, No. 6

LETTERSCAF in (CuBr)LaNb2 O7 , where the F chains align but ina sequence of up-down. It is conceived that the stabilityof the up-up-down conﬁguration in the layer is rationalized
by the presence of H and the dominance of F interactions
deduced from positive . Intuitively, one may also consider
the case where the F layers stack along the c axis as up-updown, based on the competition between NN and NNNinterlayer interactions, which may then be mapped on the
ANNNI (axial NNN Ising) model. However, we can discard
the scenario since it would be impossible to attribute thefairly large saturation ﬁeld (Hs ¼ 14:4 T) and plateau width(2:4 < H < 8:2 T) to the NN and NNN interlayer couplings
having distances of 16 and 32 Å, respectively. In order todetermine the magnetic structure, neutron diﬀraction and
NMR under magnetic ﬁelds are necessary, which is inprogress.
Finally, we will point to the nature of the M2 phase. The
abrupt increase in MðHÞ at 1.6 T until reaching to the 1/3
plateau region is interpreted as a metamagnetic transition to
the 1/3-plateau state, although T and H dependence ofspeciﬁc heat measurements could not detect any anomaly
associated with the transition. The metamagnetic-transition
ﬁeld determined by the peak of dM=dH is nearly independent of T. From the absence of spontaneous magnetizationand the positive value of , one may assume that CAF isrelevant magnetic order for the M2 phase. Then, on thebasis of J1 –J2 model, the obtained  and Hs values yield
J1 =kB ¼ 51:5 K and J2 =kB ¼ 30:6 K. It is interesting topoint out that the ratio J2 =J1 ¼ 0:59 locates the system
to a far more frustrated region than J2 =J1 ¼ 1:1 for(CuBr)LaNb2 O7 (J1 =kB ¼ 35:6 K and J2 =kB ¼ 41:3 K).19)
Here, the size of A cations which modiﬁes the in-plane
constant should be eﬀective in controlling J1 and J2 .
Vicinity to the most frustrated point J2 =J1 ¼ 0:50 might
be a key for the appearance of the 1/3 plateau.
In general, the speciﬁc heat has universal behavior
characterized by CðTÞ / T d= , where d and  denote thespatial dimensionality and the exponent of magnon dispersion in the long wave limit (where ! / k ). For conventional spin systems (d ¼ 3), the critical exponent d= below
Tc is 1.5 and 3, for F and AF cases, respectively. As
expected, a cubic exponent is observed for (CuBr)LaNb2 O7
well below Tc .9) However, what has been observed in(CuBr)Sr2 Nb3 O10 is diﬀerent from either of them; as shownin Fig. 3, Cm in the present compound has a T 2 dependence
below 5 K (<Tc2 ), a characteristic feature for 2D AF spinwaves. The measured quadratic critical exponent in(CuBr)Sr2 Nb3 O10 implies the existence of 2D spin–spin
correlation. The distinct low-energy mode that appears notfor (CuBr)LaNb2 O7 but for (CuBr)Sr2 Nb3 O10 is likely to bea consequence of increased n. In 2D triangular-based
compounds SrCr8 Ga4 O19 and NiGa2 S4 in which a large
ground state degeneracy is suggested, the quadratic trend
remains even down to dilution temperatures.1,20) The present
Cp ðTÞ experiment was performed only down to 2 K. It isinteresting to check whether the quadratic feature continues
at lower T which may be associated with highly disorderedground state or ﬁnally shifts to the cubic dependence. Notethat the linear extrapolation curve of Cm =T runs throughthe origin, which may be in favor of the former scenario.
To summarize, we have demonstrated that a new

Y. TSUJIMOTO et al.

compound (CuBr)Sr2 Nb3 O10 , designed using the ion-exchange reaction, has unique magnetic features such as
successive phase transitions and T 2 dependence in Cm ,which are not seen in (CuCl)LaNb2 O7 and (CuBr)LaNb2 O7 .
Most remarkably, we have observed the quantized plateau
at 1/3 of the saturation magnetization, presumably due toenhanced 2D and competing in-plane interactions. It issurprising that choice of parameters (A, B, X, n) resulted incompletely diﬀerent magnetic properties. Further studies on
the whole family (CuX)An1 Bn O3nþ1 will provide global
understanding of the nature of the square lattice antiferromagnets.
The authors thank fruitful discussion with M. Nishi and K.
Totsuka. This work has been supported by Grants-in-Aid forYoung Scientists (A) (No. 17684018) and Science Research
on Priority Area (No. 16076210 and No. 451) from the
Ministry of Education, Culture, Sports, Science and Technology of Japan. A part of this work has been done while
HK worked as a visiting professor at ISSP, The Universityof Tokyo.
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