Journal of the Physical Society of Japan
Vol. 76, No. 10, October, 2007, 104703#2007 The Physical Society of Japan

Magnetic and Structural Studies of the Quasi-Two-Dimensional
Spin-Gap System (CuCl)LaNb2 O7
Makoto Y OSHIDA, Nobuyuki OGATA, Masashi TAKIGAWAy,
Jun-ichi Y AMAURA, Masaki I CHIHARA, Taro K ITANO1 ,Hiroshi KAGEYAMA1 , Yoshitami A JIRO1 , and Kazuyoshi Y OSHIMURA1
1

Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581
Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502(Received June 21, 2007; accepted July 27, 2007; published September 25, 2007)

We report magnetization, nuclear magnetic resonance (NMR), nuclear quadrupole resonance (NQR),
and transmission electron microscopy (TEM) studies on the quasi-two-dimensional spin-gap system(CuCl)LaNb2 O7 , a possible candidate for the J1 –J2 model on a square lattice. A sharp single NQR line isobserved at the Cu and Cl sites, indicating that both Cu and Cl atoms occupy a unique site. However, theelectric ﬁeld gradient tensors at the Cu, Cl, and La sites do not have axial symmetry. This is incompatible
with the reported crystal structure. Thus the J1 –J2 model has to be modiﬁed. We propose alternative twodimensional dimer models based on the NMR, NQR, and TEM results. The value of the hyperﬁne
coupling constant at the Cu sites indicates that the spin density is mainly on the dð3z2  r 2 Þ orbital(z k c). At 1.5 K, Cu- and Nb-NMR signals disappear above the critical ﬁeld Bc1 ’ 10:3 T determinedfrom the onset of the magnetization, indicating a ﬁeld-induced magnetic phase transition at Bc1 .
KEYWORDS: NMR, NQR, TEM, (CuCl)LaNb2 O7 , spin-gap, quantum spin system
DOI: 10.1143/JPSJ.76.104703

1.

Introduction

Low-dimensional quantum spin systems with frustratinginteractions have recently been studied intensively both fromexperimental and theoretical aspects. The S ¼ 1=2 antiferromagnet on a square lattice with the nearest-neighbor andthe next-nearest-neighbor interactions (the J1 –J2 model) is awell known example. When the nearest neighbor interaction
J1 is antiferromagnetic (J1 > 0), the ground state has a Néelorder with the wave vector ð; Þ for J2 =J1 < 0:38 while acollinear order with the wave vector ð; 0Þ occurs for
J2 =J1 > 0:52.1–3) A spin liquid phase is proposed between
these phases near J2 =J1 ’ 0:5.1–3) A spin liquid phase is also
proposed for ferromagnetic J1 (J1 < 0) between the collinear
phase for J2 =J1 < 0:51 and the ferromagnetic phase forlarger J2 =J1 .3) The series of compounds (CuX)LaNb2 O7(X ¼ Cl, Br) is a candidate for the J1 –J2 model with mixed
ferro- and antiferromagnetic interactions.4–6) The structure
is reported to be tetragonal (space group P4=mmm) with
the CuX square lattice7,8) as shown in Fig. 1. In fact,(CuCl)LaNb2 O7 has a singlet ground state with a spin-gap4,5)
while (CuBr)LaNb2 O7 shows a collinear antiferromagnetic
order.6)
In (CuCl)LaNb2 O7 , the spin-gap is estimated to be 27 K
by ﬁtting the susceptibility data to the isolated dimer
model.4) The neutron inelastic scattering results also exhibit
magnetic excitations with the gap of 2.3 meV, although theresolution is limited.4) On the other hand, the high-ﬁeld
magnetization measurements revealed a sudden increase at
the critical ﬁeld Bc1 ¼ 10:3 T.5) The Zeeman energy at Bc1 ,gB Bc1 =kB ¼ 15 K, is apparently not suﬃcient to close thespin-gap at zero ﬁeld. In addition, the magnetization
saturates at Bc2 ¼ 30:1 T.5) The large interval between Bc1
and Bc2 indicates a large width of the triplet dispersion. ThisE-mail: yopida@issp.u-tokyo.ac.jp
E-mail: masashi@issp.u-tokyo.ac.jp

y

Cu
Cl
La

c

NbO6

b
a
Fig. 1. Schematic drawing of the crystal structure of (CuCl)LaNb2 O7 .7)

is inconsistent with the neutron inelastic scattering data
indicating that the triplet mode is almost dispersionless.4)
There are also open issues about the crystal structure. The
neutron diﬀraction study indicates that the Cl position
deviates from the ideal ð0; 0; 1=2Þ position with the C4 symmetry in the tetragonal space group P4=mmm.8) If thestructure deviates from the ideal square lattice, various ways
to form a spin-gap become possible.9) Unambiguous determination of the structure is crucial for good understanding ofa frustrated quantum spin system.
In this paper, we report magnetization, nuclear magnetic
resonance (NMR), nuclear quadrupole resonance (NQR),
and transmission electron microscopy (TEM) studies on(CuCl)LaNb2 O7 . Our results indicate that none of the Cu, Cl,
and La sites has the C4 -symmetry, incompatible with thereported tetragonal structure. Thus the J1 –J2 model for thesimple square lattice has to be modiﬁed. We propose two-

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M. YOSHIDA et al.

(a)

(b)

Fig. 2. X-ray diﬀraction patterns of the (a) aligned and (b) unaligned
powder samples. The inset illustrates the method for preparing the aligned
sample.

dimensional dimer models which are consistent with our
NMR, NQR, and TEM results. Cu- and Nb-NMR signals
disappear above the critical ﬁeld Bc1 ’ 10:3 T at low
temperatures, indicating a ﬁeld-induced magnetic phasetransition at Bc1 .
2.

Experiment

The powder sample of (CuCl)LaNb2 O7 was synthesized
by the ion-exchange reaction of RbLaNb2 O7 with CuCl2 .4,7)
The magnetically aligned sample was prepared by rotating acylindrical tube ﬁlled with the (CuCl)LaNb2 O7 powder andepoxy (STYCAST1266) in a magnetic ﬁeld B ¼ 7 T. The
magnetic ﬁeld was applied perpendicular to the rotating axis
as shown in the inset of Fig. 2. In this conﬁguration, themagnetic hard axis tends to align along the rotating axis. The
X-ray diﬀraction pattern for the aligned sample was obtainedwith a MacScience M03X diﬀractometer using a monochromatic Cu K radiation as shown in Fig. 2(a). Here thealigned axis was kept perpendicular to the scattering wave
vector. Compared with the diﬀraction pattern for theunaligned powder shown in Fig. 2(b), the peaks corresponding to (00n) planes are strongly enhanced in the aligned
sample, where n is integer. This indicates that the c-axis is
the magnetic hard axis. The rocking curve for these peaks
with the half width of about 1.5 shows successful alignment. However, other peaks such as (102) or (110) are also
observed in the aligned sample, indicating that a certain
fraction of the sample remains unaligned.
The magnetic susceptibility  was measured for theunaligned powder sample with a SQUID magnetometer(Quantum Design MPMS). NQR measurements in zeromagnetic ﬁeld have been performed for the 63 Cu and 35 Cl
nuclei in the unaligned powder sample. Nuclear spin–lattice
relaxation rates were measured by the inversion recovery
method. NMR measurements in magnetic ﬁelds up to 11.7 T
have been performed on the aligned sample with themagnetic ﬁeld applied along the c-axis for 63;65 Cu, 35;37 Cl,
93
Nb, and 139 La nuclei. The TEM experiments were carriedout at room temperature using a JEM2010F system with an

Fig. 3. Temperature dependence of  measured for the unaligned powder
sample at 1 T. The solid circles represent the raw data. The open circles
represent  after subtracting the impurity contribution shown by thesolid line. The inset shows the magnetic ﬁeld (B) dependence of themagnetization at 2 K. The dashed line is the ﬁt to the form M ¼
NgSB BS ðxÞ þ AB.

operating voltage of 200 kV. The specimen was ﬁnely
ground in methanol and then placed on a Cu microgrid meshfor TEM observation.
3.

Results and Analysis

We ﬁrst analyze the temperature dependence of  in §3.1.
In §3.2, we show the NQR results, which demonstrate thatboth Cu and Cl atoms occupy a unique site and there is noapparent disorder. The electric ﬁeld gradient tensors at theCu, Cl, and La sites are investigated from the ﬁeld swept
NMR spectra in §3.3. These results indicate deviation of thecrystal structure from the reported one with a simple squarelattice. In §3.4, the temperature dependences of the magnetic
hyperﬁne shifts at the Cu and Cl sites are determined. Thenthe value of spin-gap is estimated. The hyperﬁne coupling
constants are also determined at the Cu, Cl, and Nb sites.
In §3.5, the high ﬁeld behavior above Bc1 is investigated at
the Cu and Nb sites. Finally, we show the TEM result inorder to provide additional information about the structure.
3.1 Magnetic susceptibility measurements
Figure 3 shows the temperature (T) dependence of 
measured at the ﬁeld of 1 T. The peak at 16 K and rapid
decrease at lower temperatures are quite consistent with theprevious report,4) indicating a singlet ground state. Below
4 K, however,  increases with decreasing temperatureprobably due to magnetic impurities. In order to investigate
the impurity contribution, we also measured magnetization
M up to 7 T. The inset of Fig. 3 shows the B-dependence of
M at 2 K. The data can be ﬁtted by the sum of a term
proportional to the Brillouin function BS ðxÞ and a B-linear
component M ¼ NgSBS ðxÞ þ AB (x ¼ gSB B=kB T). A good
agreement was obtained for the values S ¼ 1=2, N ¼
0:72%/Cu, and NA B A ¼ 3:0  103 emu/mol (NA is the
Avogadro constant) as shown by the dashed line in the inset
of Fig. 3. The ﬁrst term leads to the free spin contribution to, NA NgSB BS ðxÞ=B, due to isolated magnetic impurities(the solid line in Fig. 3). By subtracting this term from themeasured , we obtained the corrected  shown by theopen circles. The corrected  maintains a ﬁnite value(3  103 emu/mol) as T goes to 0. It is also detected in the104703-2

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Fig. 5. Inverse temperature dependence of 1=T1 at the 63 Cu and 35 Cl sites.
The solid lines show the ﬁt to an activation law 1=T1 / expðE=kB TÞ.

Fig. 4. NQR spectra (a) at the 63 Cu sites (T ¼ 1:9 K) and (b) at the 35 Cl
sites (T ¼ 2:9 K).

magnetization curve as the B-linear component. This ismuch larger than the typical value of the Van Vleck
susceptibility of Cu2þ (105 –104 emu/mol). The NMR
shifts at all sites do not show such large residual values at
low temperatures as we discuss later. Hence the large
residual susceptibility at low T is considered to be extrinsic,
e.g. due to a secondary phase.
3.2 NQR spectra and relaxation rates
Figure 4 shows the NQR spectra at zero ﬁeld for the 63 Cu
and 35 Cl sites, both having the nuclear spin I ¼ 3=2. A sharp
single NQR line is observed for each nuclei. This shows thatboth Cu and Cl atoms occupy a unique site and there is no
substantial disorder for the Cu and Cl positions. The NQR
frequencies NQR are determined to be 29.68 MHz for 63 Cu
and 14.88 MHz for 35 Cl. The values of NQR and thespectrum shape show no temperature dependence from 10 to
1.5 K, indicating that the structure is unchanged at low
temperatures.
Figure 5 shows the inverse temperature dependenceof 1=T1 at the 63 Cu and 35 Cl sites at zero ﬁeld. At
both sites, 1=T1 is well ﬁtted by an activation law 1=T1 /expðE=kB TÞ. The activation energy is obtained as
E=kB ¼ 23  2 K for Cu and E=kB ¼ 21  1 K for Cl.
Below 4 K, 1=T1 deviates from the activation law andbecome independent of temperature below 3 K. The originof the constant relaxation rate at low temperatures is likely
to be impurities.
3.3 Field swept NMR spectra and EFG tensors
In the inset of Fig. 6, we show a typical ﬁeld swept CuNMR spectrum for the aligned sample with the magnetic
ﬁeld B applied parallel to the c-axis. The spectrum has four
sharp peaks assigned to the 63 Cu- and 65 Cu-NMR lines fromthe aligned part of the sample. The spectrum also shows aFig. 6. Frequency–ﬁeld diagram at 3 K at the 63 Cu sites in the appliedmagnetic ﬁelds B parallel to the c-axis. The dotted lines represent theresonance modes for the case of axially symmetric EFG around thec-axis. The solid lines are the ﬁt to the results obtained from the
Hamiltonian (2). The inset shows the Cu-NMR spectrum at 43 MHz.

broad tail spreading to higher ﬁeld. This tail probably comesfrom the unaligned portion of the sample. The resonanceﬁelds are determined precisely from the peak positions.
The frequency–ﬁeld ( f –B) diagram can be constructed byplotting the resonance ﬁelds for various NMR frequencies
between 26 and 55 MHz as shown in Fig. 6.
The resonance frequency is generally determined from thefollowing Hamiltonian including the magnetic hyperﬁneinteraction and the electric quadrupole interaction,10)
H ¼ hðB  I þ I  K^  BÞ


X
eQ
3
V ðI I þ I I Þ   I 2 ;þ
6Ið2I  1Þ ;
2

ð1Þ

where h is the Planck’s constant, Q is the nuclear quadrupole
moment,  is the gyromagnetic ratio, K^ is the magnetic
hyperﬁne shift tensor,  is 0 ( 6¼ ) or 1 ( ¼ ), andV ¼ @2 V=@@ (;  ¼ x, y, or z) is the component of theelectric ﬁeld gradient (EFG) tensor. If the Cu sites have theC4 -symmetry around the c-axis in the tetragonal crystal
structure, V is axially symmetric, that is, V ¼ 0 for  6¼
 and Vzz ¼ 2Vxx (Vxx ¼ Vyy ; z k c). If the magnetic ﬁeld isapplied parallel to the symmetric c-axis, three resonance104703-3

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Fig. 7. Frequency–ﬁeld diagram at 3 K at the 35 Cl sites in the appliedmagnetic ﬁelds B parallel to the c-axis. The solid lines show the ﬁtobtained from the Hamiltonian (2). The inset shows the Cl-NMR
spectrum at 31 MHz.

modes appear at the frequencies R and jNQR  R j, whereR ¼ ð1 þ Kcc ÞB and NQR ¼ 3eQVzz =2Ið2I  1Þh, provided that all the components of K^ are much smaller than one.
These results shown by the straight dotted lines in Fig. 6 areapparently in contradiction with the nonlinear behavior of
the experimental data. This gives the direct evidence that theCu sites do not have axial symmetry around the c-axis.
In the following, we assume that the c-axis is one of theprincipal axes of the EFG tensor at the Cu sites. This is thecase, for example, when the Cu–Cl planes have the mirror
symmetry. Although this assumption may not be strictly
valid in the real structure, it is not possible to determine V
from the available data without any assumption. The nuclear
Hamiltonian (1) is rewritten for the magnetic ﬁeld parallelto the c-axis (z-axis) as
H ¼ hBð1 þ KÞIzð2Þh
þ ðx Ix2 þ y Iy2 þ z Iz2 Þ;3where K is the magnetic hyperﬁne shift along the c-axisand  ¼ ½3eQ=2Ið2I  1ÞhV .10) Although eq. (2) contains four parameters (z , x , y , and K), the number of
independent parameters can be reduced to two (K and z )fromthe relations x þ y þ z ¼ 0 and NQR ¼
ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃp2z þ ðx  y Þ2 =3, where the NQR frequency NQR is
determined to be 29.68 MHz in §3.1. Four eigenvalues ofthis Hamiltonian can be calculated analytically in the caseof I ¼ 3=2, resulting in six resonance modes. As shownin Fig. 6, the experimental data are well ﬁtted by the solidlines obtained from eq. (2) with z ¼ 16:26  0:02 MHz,x ¼ 13:37  0:02 MHz, y ¼ 29:64  0:02 MHz, and
K ¼ 0:44  0:02%.
Figure 7 shows the f –B diagram at the 35 Cl sites obtained
from the ﬁeld swept NMR spectra of the aligned sample. A
typical spectrum is shown in the inset of Fig. 7. The appliedmagnetic ﬁeld B was parallel to the aligned direction(c-axis). The spectrum also shows the 139 La-NMR lines.
The negative intensity is due to improper rf-pulse
conditions, which were optimized for Cl signal. The f –B
diagram can be ﬁtted by solving the Hamiltonian (2) in thesame way as has been done for the Cu sites. In Fig. 7, thesolid lines show the results calculated for the parameter

Fig. 8. Field swept NMR spectrum at the 139 La sites at 6 K and 31 MHz in
the magnetic ﬁeld parallel to the c-axis. The inset shows the =0 versus
1=20 plot at 115 K.

values z ¼ 14:17  0:02 MHz, x ¼ 3:13  0:02 MHz,y ¼ 11:04  0:02 MHz, and K ¼ 0:04  0:02%.
Figure 8 shows the ﬁeld swept 139 La-NMR spectrum at
6 K and 31 MHz in the magnetic ﬁeld parallel to the c-axis.
The seven peaks split by the quadrupole interaction for I ¼
7=2 are clearly observed. Since the quadrupole interaction at
the La sites is much smaller than that at the Cu and Cl sites,
the second order perturbation theory is suﬃcient to extract
the values of  and K. We assume the c-axis to be one ofthe principal axes for EFG. The resonance frequency
between the states jmi and jm  1i is obtained from the
Hamiltonian (2) as1m$m1 ¼ 0 ð1 þ KÞ  m 
z
2
ð3Þ


ðx  y Þ219;mðm  1Þ 
4
120
where 0 ¼ B.11) If we deﬁne the frequency shiftm m$m1  0 , the frequency shift of the central line
1=2 obeys the relation,
1=2
5 ðx  y Þ2
¼Kþ
:
12
0
20

ð4Þ

Therefore, 1=2 =0 plotted against 1=20 should yield astraight line with the slope ð5=12Þðx  y Þ2 and the intercept
K at 1=20 ¼ 0. The inset of Fig. 8 shows the =0 versus
1=20 plot at 115 K. We ﬁnd that K at the La sites is almost
zero (8  103  2  103 %) and jx  y j ¼ 1:57 MHz.
The value of z is determined from the frequency shift forthe satellite lines as z ¼ jm$m1  mþ1$m j=ð2m  1Þ.
The values of z , x , and y are determined to be 2:23  0:02,
0:33  0:02, and 1:90  0:02 MHz, respectively.
The values of  determined by NMR are listed in Table I
for the Cu, Cl, and La sites. It should be noted that the values

Table I.

Principal values of EFG tensors at the Cu, Cl, and La sites.
Cu

Cl

La

z (MHz)x (MHz)

16:26  0:02
13:37  0:02

14:17  0:02
3:13  0:02

2:23  0:02
0:33  0:02

y (MHz)29:64  0:02

11:04  0:02

1:90  0:02

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Fig. 9. Temperature dependence of K at the 63 Cu sites for the magnetic
ﬁeld parallel to the c-axis. The dashed and dotted lines show thecalculated results for the isolated dimer model and the two dimensional
coupled dimer model, respectively.

Fig. 10. Temperature dependence of the ﬁeld swept spectrum at the Nbsites at 75 MHz for the applied magnetic ﬁelds B parallel to the c-axis.

in Table I are determined on the assumption that the c-axis is
one of the principal axes of EFG. The EFG tensor is notaxially symmetric around the c-axis for all sites. That is,none of these sites has the C4 -symmetry, which is incompatible with the reported tetragonal structure. Thus the J1 –J2model for the simple square lattice has to be modiﬁed forproper description of this system. We discuss modiﬁed
models in §4.3.
3.4 Hyperﬁne shift and coupling constant
By repeating the above analysis for diﬀerent temperatures, we obtained the temperature dependence of K.
Figure 9 shows the temperature dependence of K at the Cusites in the magnetic ﬁeld parallel to the c-axis. The shiftconsists of the contributions from the spin and Van Vleck
susceptibility at the Cu sites, K ¼ Ks þ KVV . Each term isrelated to the spin and the Van Vleck susceptibility as
Ks ¼ ðAhf =NA B Þs , KVV ¼ ðAorb =NA B ÞVV . The chemical
shift is expected to be negligibly small compared with thespin and orbital shifts due to d-electrons of Cu2þ . As shownin Fig. 9, K decreases with decreasing T and is extrapolated
to zero at T ¼ 0. This means Ks and Ahf are positive. Since
KVV is always positive, we can conclude that KVV is nearlyzero and Ks approaches zero at T ¼ 0. It should be noted thatwhile  contains impurity contribution, K is free from
impurities, and thus provides direct evidence for a spin-gap.
We estimate the spin-gap in two diﬀerent models. The
dashed line in Fig. 9 is the ﬁt to the isolated dimer model 0 1C
1EK ¼ KVV þ
1 þ exp
;
ð5Þ
T
3
kB T
from which we obtained E0 =kB ¼ 21:8 K and KVV ¼
0:02  0:02%. Note that the shift was determined in
the range of magnetic ﬁeld from 1 to 5 T. Considering the
reduction of the gap by the average ﬁeld gB hBi=kB ’ 4 K(hBi ¼ 3 T), the gap at zero ﬁeld is estimated to be 26 K.
This value is rather close to the gap ( 27 K) estimatedfrom the neutron inelastic scattering and the susceptibility
measurements.4,5) However, the isolated dimer model
ignores the dispersion of the triplet excitations. In the
opposite limit, where the triplets have large dispersion

Fig. 11. K– plot for the Cu, Cl, and Nb sites.

þ cq2 , the spin susceptibility is determined by
the excitationnear the bottom of the dispersion Ks /R
ð1=TÞ Dð Þnð Þ d / expðE00 =KB TÞ, where Dð Þ is thedensity of state, which is constant for
E00 in two
dimension, and nð Þ is the Bose factor. The dotted line in
Fig. 9 shows the ﬁt to this model with E00 =kB ¼ 15 K.
Therefore, the gap is estimated to be 19 K at zero ﬁeld. The
gap values obtained in this study are compared with thereported results in §4.1.
Figure 10 shows the temperature dependence of the ﬁeld
swept NMR spectrum at the Nb sites. The nine peaks for
I ¼ 9=2 is observed at 1.5 K and the central line is indicatedby the arrow. The central and the eight satellite lines shift tolower ﬁelds with increasing temperature, indicating sizable
hyperﬁne coupling at the Nb sites to spin magnetization of
Cu ions. In addition, we observed another peak marked by
the solid square in Fig. 10. This peak does not shift withtemperature, indicating no hyperﬁne coupling to the Cu
spins. In fact, 1=T1 for this peak is 10 times smaller than thatfor the intrinsic signal at low temperatures. Therefore, we
conclude that this signal comes from extrinsic nonmagnetic
phases. Imperfection of the ion-exchange reaction is apossible origin of such nonmagnetic impurely phases.
Figure 11 shows the K– plot for various sites obtained
for the temperature range 1.5 – 20 K. Here, a Curie term due
q ¼ E

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Table II. Hyperﬁne coupling constants for B k c.

Ahf (T/B )

Cu

Cl

Nb

13:8  0:3

6:9  0:5

2:84  0:08

Fig. 13. Frequency dependence of the ﬁeld swept NMR spectrum at theNb sites at 1.5 K in the applied magnetic ﬁelds B parallel to the c-axis.
The inset shows the Bcenter -dependence of the integrate intensity. The
dotted lines show the critical ﬁeld Bc1 .

Fig. 12. Frequency dependence of the ﬁeld swept NMR spectrum at theCu sites at 1.5 K in the applied magnetic ﬁelds B parallel to the c-axis.
The dotted lines show the critical ﬁeld Bc1 .

to magnetic impurities was removed from the  data as
described in §3.1. The hyperﬁne coupling constants Ahf
for B k c are determined to be 13:8  0:3, 6:9  0:5, and2:84  0:08 T/B for the Cu, Cl, and Nb sites, respectively(Table II). Although the NMR shifts at all sites approachnear zero as T ! 0,  maintains a ﬁnite value (3  103
emu/mol) as mentioned in §3.1. Note that the impurity termfrom free spins has been already subtracted. The residual at low temperatures, which corresponds to the B-linear
magnetization in the inset of Fig. 3, does not couple toany nuclei observed by NMR. Hence we conclude that it has
as extrinsic origin.
3.5 High magnetic ﬁeld region
Figure 12 shows the ﬁeld swept NMR spectrum at 1.5 K
for the Cu sites at diﬀerent frequencies in the higher
magnetic ﬁeld region above Bc1 ’ 10:3 T. The very sharp
peaks are due to the NMR-coil made from Cu. The 63;65 CuNMR lines from the aligned sample are indicated by thearrows. Their intensity decreases with increasing B and thepeaks from the aligned sample disappear slightly below
Bc1 ¼ 10:3 T. This is because the spin–spin relaxation time
T2 is getting shorter when the ﬁeld approaches Bc1 . Thereremains a broad signal near Bc1 , observed in the spectrumat 130 MHz. Since this signal has much longer T2 , it isprobably due to some impurity phases.
Figure 13 shows the frequency dependence of the ﬁeld
swept spectrum at the Nb sites. The quadruple split peaks
for 93 Nb (I ¼ 9=2) are observed at 90 MHz. The intensity ofthe split peaks decreases with increasing B and the signal
disappears slightly below Bc1 in a similar way as has been
observed for the Cu signals. Above Bc1 , the spectrum with
one central peak and broadened quadrupole satellites isobserved (115 MHz). This signal probably has the same
origin as the unshifted signal observed at 75 MHz at hightemperatures (Fig. 10). In the inset of Fig. 13, the integrated

intensity of the whole spectrum is plotted against the ﬁeld of
the central line (Bcenter ). The intensity normalized by thevalue at 7.2 T decreases with increasing Bcenter and vanishes
at 9.5 T, slightly below Bc1 , except for the contribution from
impurity phases, indicating that a ﬁeld-induced magnetic
phase transition occurs around Bc1 . The ﬁeld-induced
transition is also indicated by the recent speciﬁc heatmeasurements in magnetic ﬁelds.12)
3.6 TEM result
In order to obtain further information about the crystal
structure, we performed TEM measurements at room
temperature. Shown in Figs. 14(a) and 14(b) are the [001]zone lattice images that demonstrate contrasts with a special
period of about 4 Å along h100i, consistent with the

(a)

40Å

b
a

(b)

(c)

b*
010

[001]

100

a*

20Å
Fig. 14. (a) High-resolution TEM image of (CuCl)LaNb2 O7 at room
temperature along the [001]-zone axis and (b) its enlarged view. (c)Corresponding electron diﬀraction pattern, where indices are given basedon the tetragonal unit cell of the P4=mmm structure.7)

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M. YOSHIDA et al.

lattice parameter. However, the corresponding electron
diﬀraction [Fig. 14(c)] has revealed weak reﬂections suchas ð1=2; 0; 0Þ or ð0; 1=2; 0Þ, in addition to strong fundamental
reﬂections relevant to the reported crystal structure. The
weak reﬂections are commensurate and indicate the doubling of the lattice period of both a- and b-axes, i.e., the sizeof the unit cell is given by 2a  2b. Such a superstructure
has not been detected even by high q-resolution synchrotron
X-ray diﬀraction,13) presumably due to tiny modulationof the atoms and/or small domain size. Note that thesuperstructure reﬂection at ð1=2; 1=2; 0Þ was observed in(FeCl)LaNb2 O7 .13)
4.

(a)

dε

(b)

d(yz), d(z x)

dε

d(xy)
d(yz), d(z x)

d(xy)
Δ1

dγ

Δ0

Δ2

d(3z2-r2)d(x2-y2)dγd(x2-y2)d(3z2-r2)

Fig. 15. Orbital energy levels for Cu2þ in a tetragonal crystal ﬁeld. The
ground state wave function is dðx2  y2 Þ in (a) or dð3z2  r 2 Þ in (b).

Discussion

4.1 Spin-gap
The gap value in (CuCl)LaNb2 O7 is still controversial,while it has been investigated by several experimental
methods. The most direct method is the inelastic neutron
scattering, which shows the magnetic excitation with the gap
energy of 2.3 meV (26.7 K).4) Although it is possible that thelimited energy resolution masks ﬁne structure of the neutron
spectrum and the true gap may be somewhat smaller, thelarge discrepancy between this value and the gap derived
from the critical magnetic ﬁeld, gB Bc1 =kB ¼ 15 K, cannot
be explained by such an eﬀect.
From the susceptibility measurements, the gap is estimated to be 27 K by using the isolated dimer model.4)
The magnetic hyperﬁne shift determined by NMR is freefrom impurity contribution and provides more reliable spin
susceptibility. Using the isolated dimer model, the gap value
is determined to be 26 K, consistent with the susceptibility
results. We have also examined a two-dimensional coupleddimer model with a large width of the triplet dispersion andobtained the gap value of 19 K. Since these two models
correspond to the opposite limits of zero and inﬁnite widthof the dispersion, the values 26 and 19 K set the upper andthe lower bounds for the true gap. From the NQR relaxation
rate 1=T1 at the Cu and Cl sites, the gap value is determined
to be 23  2 and 21  1 K, respectively, consistent withthe above range. This range is still signiﬁcantly larger thangB Bc1 =kB (¼ 15 K).
To reconcile the discrepancy between the gap estimated at
low magnetic ﬁelds and Bc1 , Kageyama et al. proposed
formation of two-triplet bound states with S ¼ 2.5) If twotriplet bound states are stabilized due to frustration, the gap
can close before B reaches =gB and a nematic order may
be realized above Bc1 .14) The Cu- and Nb-NMR signals wereundetectable above Bc1 at 1.5 K due to divergence of 1=T2
as mentioned before (Figs. 12 and 13). To investigate themagnetic structure above Bc1 , we need measurements at
higher ﬁelds and lower temperatures.
4.2 d-orbital
The experimental determination of Ahf and KVV at the Cusites provides information about the Cu d-orbital. In thissection, we compare the experimental results of Ahf and KVVwith the calculated values. Figure 15 shows the orbitalenergy levels for Cu2þ in tetragonal crystal ﬁelds. The Cu2þ
ions have one d-hole with either dðx2  y2 Þ or dð3z2  r 2 Þwave function. The hyperﬁne coupling constants Ahf
k (forB k z) and Ahf? (for B ? z) are expressed as0 B 3
hr i
Ahf
k ¼




4

0 B 3
hr i 
Ahf? ¼40 B 3
hr
¼
i

Ahf
k
4

0 B 3
Ahf
hr
¼
i

?
4


4 6
8
 þ

7 7 1 0

2 11
þ þ
for dðx2  y2 Þ
7
7 1

4 6
þ þ
7 7 2
2 45
 for dð3z2  r 2 Þ;
7
7 2
ð6Þ

where 0 is the permeability of vacuum,is the corepolarization coeﬃcient, is the spin–orbit coupling parameter, and i (i ¼ 0; 1; 2) is the energy between the groundstate and the excited sate shown in Fig. 15.15,16) The valuesof , , and hr 3 i for Cu2þ ions are common to all insulating
materials within 10 – 20%, typically given as ¼ 0:28,¼ 8:8  102 eV, and hr 3 i ¼ 4:26  1031 m3 .15,16) idepends on materials but should be of the order of a few eV.
We take i ¼ 2:0 eV.15,16) By using these values, Ahfk2
and Ahf? are estimated to be 24:1 and 2.71 T/B for dðx 
y2 Þ and 10.2 and 12:2 T/B for dð3z2  r 2 Þ, respectively.
Compared with the experimental values, Ahf (¼ 13:8 T/B ),
2
2
hf
2
2
Ahf
k for dðx  y Þ and A? for dð3z  r Þ can be excluded
because they lead to large negative shifts. Note that themagnetic ﬁeld is parallel to the c-axis in the experiment,
and we consider the cases where the z-axis of the orbital
is either parallel or perpendicular to the c-axis. Among22
the other two cases, Ahf
k for dð3z  r Þ is by far thefavorable.
The vanishing Van Vleck susceptibility KVV ’ 0 for B k
c also supports the dð3z2  r 2 Þ orbital. For B k z, theVan Vleck susceptibility VV (emu/mol) is calculated as
X jh n jLz j 0 ij2
VV ¼ NA 2B
;
ð7Þ
n 0
n6¼0
where 0 is the grand state with the energy 0 and n is theexcited state with the energy n . For the dð3z2  r 2 Þ orbital,
VV is zero. On the other hand, VV for dðz2  x2 Þ is
calculated to be NA 2B =1 ’ 1:6  105 emu/mol, leading
to KVV ¼ 2hr 3 iVV =NA ¼ 0:23%. This is clearly incompatible with the experimental observation. Therefore, we
conclude that the Cu spins are on the d-orbital consisting
mainly of dð3z2  r 2 Þ. This is natural because the Cu–O
bonding (1.84 Å) is much shorter than the Cu–Cl bonding in
the ab plane (3.14 or 2.40 Å).8) Such structure and thediﬀerence of the ionic valence (O2 vs Cl ) make the104703-7

J. Phys. Soc. Jpn., Vol. 76, No. 10

M. YOSHIDA et al.

dð3z2  r 2 Þ orbital favorable for the d-hole. It should be
noted that broken axial symmetry revealed by our NMR data
should allow slight mixing of other components such asdðx2  y2 Þ. The large hyperﬁne ﬁeld at the Nb sites can thenbe understood as due to the transferred hyperﬁne interaction
through the dð3z2  r 2 Þ orbital. We suspect that the interplane exchange interaction through the path Cu–O–Nb–O–
Nb–O–Cu and the nearest-neighbor exchange interaction
through the path Cu–O–O–O–Cu may not be completely
negligible.
4.3 Possible model
Precise structural information of the CuCl plane is crucial
to understand the origin of the spin-gap in this compound.
Our NQR results show that both Cu and Cl have only one
site and there is no apparent disorder. This means that
periodic superstructure should be realized, even though thedomain size of the superstructure may be very small.
Although Caruntu et al. proposed disorder in the Cl position
based on their neutron diﬀraction experiments,8) their results
are not necessarily incompatible with the NQR results
because possibility of a superstructure was not considered in
the analysis of the neutron data. In addition to the NQR
results, the EFG tensor does not have axial symmetry at theCu, Cl, and La sites and the TEM result shows that the unit
cell is doubled along both the a- and the b-axes from theoriginal square lattice. Therefore, J1 –J2 model for the simple
square lattice has to be modiﬁed. Whangbo and Dai
proposed models of ring clusters with even number of spinsbased on the neutron results to account for the spin-gap.
They lead, however, to several inequivalent Cu and Cl sites,inconsistent with our NQR results.
The rather large spin-gap suggests that the real structure
has such a feature that allows natural formation of Cu
dimers. Figures 16(a), 16(b), 16(e), and 16(f) show examples of such structures, where we assume that Cu maintains
the ideal position for the square lattice ð1=2; 1=2; 1=2Þ. The
structure in Fig. 16(a) is simplest and leads to a twodimensional dimer system as shown in Fig. 16(c). Here,dimers are formed by the dominant exchange path J1 , andconnected with each other by J10 , J100 , and J2 . If J1 isantiferromagnetic, a spin-gap is naturally formed. This
structure has only one Cu and Cl site. The neutron
diﬀraction study suggests that Cl moves oﬀ the ideal
ð0; 0; 1=2Þ position to one of the ðx; 0; 1=2Þ, ðx; 0; 1=2Þ,ð0; x; 1=2Þ, and ð0; x; 1=2Þ positions in a random manner.8)
The structure in (a) is an ordered version of the structure
proposed from the neutron experiments.8) However, theunit vectors a^  b^ of the structure (a) leads to the superstructure reﬂection at ð1=2; 1=2; 0Þ but cannot account for theobserved TEM reﬂections such as ð1=2; 0; 0Þ and ð0; 1=2; 0Þ.
Therefore, Cl should take more general positions. We
propose three models (b), (e), and (f), which are consistent
with both the NQR and TEM results. In the structure (b), Cl
moves oﬀ the ideal ð0; 0; 1=2Þ position to a position,
ðx; y; 1=2Þ, ðx; y; 1=2Þ, ðx; y; 1=2Þ, or ðx; y; 1=2Þ, still
maintaining only one site. The dominant exchange path J1
makes the dimers, which are connected by other exchange
paths J10 , J100 , J2 , and J20 as shown in Fig. 16(d). In the
structures (e) and (f), Cl moves oﬀ to ðx; 0; 1=2 þ Þ,
ðx; 0; 1=2  Þ, ðx; 0; 1=2 þ Þ, or ðx; 0; 1=2  Þ. The

Fig. 16. Possible structures for the CuCl plane. The open and solid circles
represent the Cu and Cl ions, respectively. The dashed lines in (a), (b),(e), and (f) indicate the unit cell for the superstructure. In the structure (e)and (f), the solid and gray spheres represent the Cl atoms above andbelow the Cu plane, respectively.

solid and gray spheres represent the Cl atoms above andbelow the Cu plane, respectively. In both (e) and (f), theexchange paths are the same as the structure (a) that isshown in Fig. 16(c). Both models (c) and (d) generate
frustration.
A useful insight is obtained by comparing the magnetic
ground state of (CuCl)LaNb2 O7 and (CuBr)LaNb2 O7 , whichshows a collinear antiferromagnetic order.6) We haveobserved a large internal ﬁeld of 16 T at the 79;81 Br sites in(CuBr)LaNb2 O7 by zero ﬁeld NMR. The details will be
published in a separate paper. If J1 is antiferromagnetic in(CuBr)LaNb2 O7 , the internal ﬁeld at the Br sites should becanceled out for the structures (a), (e), and (f). Therefore, if
the two materials have the same structure, (b) is the only
possibility. However, the exchange interaction through Cl or
Br is very sensitive to small structural variation and oftenchanges from ferromagnetic to antiferromagnetic.17) Therefore, J1 for (CuBr)LaNb2 O7 may be ferromagnetic, even
if J1 for (CuCl)LaNb2 O7 is antiferromagnetic. If J1 isferromagnetic in the structures (a), (e), and (f), a large
internal ﬁeld of the ordered moment survives. Therefore,both models (c) and (d) are possible. It seems that theseexamples exhaust possible structures within the condition of
the uniqueness of the Cu and Cl sites and the doubled
periodicity along the a- and b-axes, although we are not able
to prove rigorously.

104703-8

J. Phys. Soc. Jpn., Vol. 76, No. 10

5.

M. YOSHIDA et al.

Summary

NMR, NQR, and TEM results of (CuCl)LaNb2 O7 havebeen reported. A sharp single NQR line observed at each Cu
and Cl site indicates that both Cu and Cl atoms occupy aunique site. The electric ﬁeld gradient tensor shows that
there is no axial symmetry around the c-axis at the Cu, Cl,
and La sites. These results indicate that the J1 –J2 model forthe simple square lattice has to be modiﬁed. We propose a
two-dimensional dimer model for this compound. Cu- and
Nb-NMR signals disappear above the critical ﬁeld Bc1 ’
10 T at low temperatures, indicating a ﬁeld-induced magnetic phase transition occurs at Bc1 .
Acknowledgment
We would like to thank T. Momoi, N. Shannon, H. Nojiri,
and K.-Y. Choi for valuable discussions. This work was
supported by Grants-in-Aid for Scientiﬁc Research (Nos.
18740202 and 17684018) and Grants-in-Aid on Priority
Areas ‘‘Invention of Anomalous Quantum Materials’’ (Nos.
16076204 and 16076210) from the Ministry of Education,
Culture, Sports, Science and Technology of Japan.

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