Journal of the Physical Society of Japan
Vol. 77, No. 10, October, 2008, 104705#2008 The Physical Society of Japan

Antiferromagnetic Nuclear Resonancein the Quasi-Two-Dimensional (CuBr)LaNb2 O7
Makoto Y OSHIDA, Nobuyuki O GATA, Masashi T AKIGAWAy, 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 May 15, 2008; accepted July 29, 2008; published September 25, 2008)

We report nuclear magnetic resonance (NMR) studies in the antiferromagnetic state of the quasi-twodimensional (CuBr)LaNb2 O7 . The NMR spectra at zero magnetic ﬁeld and 4.2 K indicate a unique Cu
and Br sites with an internal ﬁeld of 5.7 T (at Cu) and 16.4 T (at Br), conﬁrming a magnetic order. For thelarge internal ﬁeld at the Br sites to be compatible with the collinear antiferromagnetic order observed byneutron diﬀraction experiments, the Br atoms must move signiﬁcantly oﬀ the center of the square of theCu sublattice so that the Br nuclei couple predominantly to two parallel Cu moments. While invalidating
the frustrated J1 –J2 model deﬁned on a C4 -symmetric square lattice, our results are compatible with thestructural model proposed for (CuCl)LaNb2 O7 by Yoshida et al.
KEYWORDS: NMR, (CuBr)LaNb2 O7 , quantum spin system, collinear order, structural distortion
DOI: 10.1143/JPSJ.77.104705

1.

Introduction

The recent successful synthesis of a new Dion–Jacobson
series of quasi-two-dimensional quantum spin systems(CuX)An1 Bn O3nþ1 (A ¼ La3þ , Ca2þ , Naþ , . . . , B ¼ Nb5þ ,Ta5þ , Ti4þ , X ¼ Cl, Br, n ¼ 2; 3; 4; . . .) by ion-exchange
reaction has enabled us to explore a wide variety of novel
quantum phenomena in a common structure of the CuX
magnetic layers, where Cu2þ ions (spin 1/2) form a squarelattice with X  ions located at the center of the square.1–7)
For example, (CuCl)LaNb2 O7 has a singlet ground state withan excitation gap of 2.3 meV2) and shows an intriguing
phase transition in magnetic ﬁelds.3,6,7) On the other hand,a collinear antiferromagnetic order at the wave vector
Q ¼ ð; 0; Þ occurs below TN ¼ 32 K in (CuBr)LaNb2 O7 .4)
Furthermore, (CuBr)Sr2 Nb3 O10 with a wider interlayer
separation exhibits a puzzling magnetization plateau at 1/3of the saturation.5)
Early structural studies on (CuX)LaNb2 O7 (X ¼ Cl or Br)
reported the tetragonal P4=mmm space group, where both
the Cu and the X sites have the C4 symmetry1,8) (Fig. 1).
Based on this, a Heisenberg spin model with the nearest
neighbor exchange J1 and the second nearest neighborexchange J2 (the so-called J1 –J2 model) was considered an
appropriate model. In fact, extensive theoretical work on thefrustrated J1 –J2 model predicts a collinear antiferromagnetic
order with the wave vector ð; 0Þ for J2  jJ1 j and a spinsinglet phase in the highly frustrated region J2 =jJ1 j  0:5
both for the positive (antiferromagnetic)9,10) and the negative(ferromagnetic)11) values of J1 . This appears to be corroborated nicely by the experimental observation of the collinear
order in (CuBr)LaNb2 O7 and the singlet ground state in(CuCl)LaNb2 O7 . The analysis of the susceptibility and themagnetization process indicated that J1 is ferromagnetic in(CuX)LaNb2 O7 .
E-mail: yopida@issp.u-tokyo.ac.jp
E-mail: masashi@issp.u-tokyo.ac.jp

y

Cu
X
La

c

NbO6

b
a
Fig. 1. Schematic crystal structure of (CuX)LaNb2 O7 (X ¼ Cl, Br).1)

However, structural information obtained from subsequent experiments has raised serious doubt against thevalidity of the J1 –J2 model. The neutron diﬀraction experiments on (CuCl)LaNb2 O7 12) suggested signiﬁcant deviationof the Cl position from the center of the Cu square along the[100] direction. The Synchrotron X-ray diﬀraction on(FeCl)LaNb2 O7 13) and the transmission electron microscopy(TEM) measurements on (CuCl)LaNb2 O7 7) revealed asuperlattice reﬂections indicating an enlarged 2a  2b  cunit cell. The nuclear magnetic resonance (NMR) andthe nuclear quadrupole resonance (NQR) experiments in(CuCl)LaNb2 O7 7) demonstrated absence of the four-foldsymmetry around the c-axis at both the Cu and the Cl sites.
In particular, the principal axis of the electric ﬁeld gradient(EFG) tensor at the Cu sites with the largest principal value
was found to be perpendicular to the c-axis, providing
conclusive evidence for a drastic change of the local

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J. Phys. Soc. Jpn., Vol. 77, No. 10(a)M. YOSHIDA et al.

(b)

(c)

Fig. 2. (Color online) Possible structures of the CuCl plane proposed for (CuCl)LaNb2 O7 .7) The open and solid circles represent the Cu and Cl atoms,
respectively. In (a), the Cl atoms moves from the ideal ð0; 0; 1=2Þ position to ðx; y; 1=2Þ, ðx; y; 1=2Þ, ðx; y; 1=2Þ, or ðx; y; 1=2Þ and are still on thesame plane as the Cu atoms. In (b) and (c), a half of the Cl atoms moves up to ðx; 0; 1=2 þ Þ or ðx; 0; 1=2 þ Þ (black circles) and another half moves
down to ðx; 0; 1=2  Þ or ðx; 0; 1=2  Þ (grey circles). The enlarged unit cell is shown by the blue dashed lines. Note that both Cu and Cl occupy aunique crystallographic sites for all cases. The singlet dimer bonds are shown by the thick red lines.

structure from the tetragonal P4=mmm symmetry. Yetobservation of a single sharp NQR line for the Cu andthe Cl nuclei guarantees that they both occupy a unique
crystallographic site without signiﬁcant disorder. Yoshida
et al. has proposed possible structural models of the CuCl
planes in (CuCl)LaNb2 O7 , which are compatible with the
NMR, NQR, and TEM results7) (Fig. 2). In these models
with orthorhombic distortion, displacement of Cl atoms
generates diﬀerent exchange couplings among the nearest
neighbor Cu bonds, which were originally equivalent in theundistorted structure. The models shown in Fig. 2 where
the strongest antiferromagnetic bonds are shown by the red(thick) lines then naturally lead to a dimer singlet groud
state.
To obtain further insight into the structure and themagnetism in (CuX)LaNb2 O7 , we performed the NMR experiments in the collinear ordered phase of (CuBr)LaNb2 O7 .
The internal ﬁeld from ordered magnetic moments and the
EFG at the nuclear sites provide useful information on thelocal structure. We found a unique large internal ﬁeld at both
the Cu and the Br sites at 4.2 K, conforming a magnetic
order. However, if the Br nuclei coupled equally to the fourneighboring Cu spins, the internal ﬁelds from these spins
would have to be cancelled out to yield zero net ﬁeld
for the collinear AF structure. Thus our results provide
conclusive evidence for lower symmetry of the Br sites thatallows the Br nuclei to couple dominantly to only twoparallel Cu spins.
2.

Experimental Results

The powder sample of (CuBr)LaNb2 O7 was synthesized
by the following ion-exchange reaction as described inrefs. 2 and 4,
RbLaNb2 O7 þ CuBr2 ! (CuBr)LaNb2 O7 þ RbBr: ð1Þ
NMR spectra were obtained by recording the integrated
intensity of the spin–echo signal at discrete frequencies.
NMR spin–echo signal was observed at zero magnetic ﬁeld
and the temperature of 4.2 K in the frequency range 30 –260 MHz.
The obtained spectra are shown in Figs. 3(a) and 3(b)for the frequency ranges 80 – 260 and 30 –100 MHz, respectively. As shown in Fig. 3(a), sharp six resonance lines

are observed in the frequency range 100 – 260 MHz, which
can be grouped into three pairs. The peak frequencies
are determined by ﬁtting each line to a Lorentzian andthe results are shown in Table I. A natural interpretation
for such a spectrum is the superposition of resonance fromtwo kinds of spin 3/2 nuclei, both having the dominantmagnetic Zeeman interaction split by the subdominant
electric quadrupole interaction. On the other hand, rather
broad lines with only ﬁve visible peaks are observed in
the frequency range 30 –100 MHz, as shown in Fig. 3(b).
However, we have succeeded in decomposing the observed
spectrum into three pairs of Lorentzian as shown by the reddashed lines. Thus the spectrum below 100 MHz can beinterpreted again by two types of spin 3/2 nuclei withdominant magnetic Zeeman interaction and subdominantquadrupole interaction. The peak frequencies in this frequency range are also listed in Table I. There are indeed
four spin 3/2 nuclear species contained in (CuBr)LaNb2 O7 ,which are 63 Cu, 65 Cu, 79 Br, and 81 Br. The values of their
nuclear gyromagnetic ratio ( ) and the isotopic ratios of thenuclear magnetic moments and the nuclear quadrupole
moments ( Q) are listed in Table II, where  stands for themass number.
3.

Analysis I

We ﬁrst assign the resonance lines in Figs. 3(a) and 3(b)to the four nuclear species. The NMR resonance frequencies
for a spin I nucleus in zero magnetic ﬁeld is generally
determined by the following Hamiltonian,14,15)
H ¼ Hm þ Hq ;ð2Þ
Hm ¼ h I  Bint


hQ
1
Hq ¼
3Iz2  I 2 þ ðIþ2 þ I2 Þ
2
6
with
Q ¼

3e Q
Vzz ;
2Ið2I  1Þh

ð3Þ

where Hm (Hq ) describes the magnetic Zeeman (electric
quadrupole) interaction, h is the Planck’s constant, Bint is theinternal (hyperﬁne) magnetic ﬁeld at the nuclear sites
produced by the electronic magnetic moments, and Vzz ¼@2 V=@z2 is the z-component of the EFG tensor at the nucleus.

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J. Phys. Soc. Jpn., Vol. 77, No. 10

M. YOSHIDA et al.

79

(a)

Br
81

Br

Spin echo intensity

Cu

80

100

120

140

160

180

200

220

240

260

Frequency (MHz)
(b)

63

(c)

Cu
65

Cu

z

79

θ

Br

Bint

y
x
30

40

50

60

70

80

90

100

ϕ

110

Frequency (MHz)Fig. 3. (Color online) The NMR spectra obtained at zero magnetic ﬁeld and 4.2 K (open circles) for the frequency ranges (a) 80 – 260 and (b) 30 –110 MHz.
The black solid lines show the ﬁtting to the sum of six Lorentz functions and the red dashed lines represent the decomposition into each line.
(c) Deﬁnition of the polar and the azimuthal angles specifying the direction of the internal ﬁeld with respect to the principal axes of the electric ﬁeld
gradient (EFG).

Table I. Peak frequencies of the NMR spectra in Fig. 3.
sl
(MHz)

c
(MHz)

sh
(MHz)

63

Cu

36:6

0:3

64:5

0:3

92:7

0:5

65

Cu

43:0

0:5

69:0

0:5

95:0

1:0

79

Br

102:440:1

185:980:05

247:36

0:2

81

Br

127:34

0:1

195:56

0:1

249:9

0:2

Table II.
63

Cu

 (MHz/T)

65

11.2893
79

Br

Values and isotopic ratios of nuclear moments.17Þ (MHz/T)
10.667181

 (MHz)/T65

=63 

12.0932

1.0712

 (MHz)/T

81

11.4984

1.0779

79

= 

65

Q=63 Q

0.9252
81

Q=79 Q

0.8354

Here x, y, and z denote the principal axes of the EFG tensor
satisfying the relation jVxx j  jVyy j  jVzz j and the asymmetry parameter of the EFG is deﬁned as  ¼ ðVxx  Vyy Þ=Vzz(0    1, note that Vxx þ Vyy þ Vzz ¼ 0). If the quadrupole
interaction is absent, the 2I þ 1 nuclear spin levels areequally split by the Zeeman interaction, giving rise to asingle resonance frequency
0 ¼  Bint :lines depend on the orientation of the internal magnetic ﬁeld
relative to the principal axes of the EFG. We deﬁne the polar
and the azimuthal angles  and specifying the direction ofBint with respect to the principal axes of the EFG as shown in
Fig. 3(c).
When the magnetic Zeeman interaction is dominant overthe quadrupole interaction,  Bint  Q , which indeed turns
out to be case for the NMR spectra in Fig. 3, the resonancefrequencies can be calculated by the perturbation theory up
to second order with reasonably good accuracy. For the caseof I ¼ 3=2, there are three resonance lines; the central line,
the high frequency satellite and the low frequency satellite
lines, whose frequencies are denoted by c , hs , and ls . The
perturbation theory gives the following expression,c ¼ 0 þ ð2Þ
ð5aÞ
c
ð1Þ
ð2Þ
hs ¼ 0 þ  þ s
ð5bÞ
ð1Þ
ð2Þ
ls ¼ 0   þ s :ð5cÞ
The ﬁrst order shift ð1Þ and the second order shifts ð2Þ
c and
16)
ð2Þ
s are expressed as

ð4Þ

A ﬁnite value of the quadrupole coupling Q causes theresonance to split into 2I lines. The frequencies of the split
104705-3ð1Þ ¼ ðQ =2Þj3 cos2   1 þ  cos 2 sin2 j

ð6aÞ

2
2
2
ð2Þ
c ¼ ðQ =120 Þfð9=4Þ sin ð9 cos   1Þ22

þ ð3=2Þ cos 2 sin ð9 cos  þ 1Þ

þ 2 ½2 þ 3 cos2  þ ð9=4Þ cos2 2 sin4  g
2
2
2
ð2Þ
s ¼ ðQ =120 Þ sin ½18 cos   12 cos 2222

þ 2 ð1  cos 2 sin Þ :

ð6bÞ

2

cos 
ð6cÞ

J. Phys. Soc. Jpn., Vol. 77, No. 10

M. YOSHIDA et al.

In general, the n-th order shifts ðnÞc,hs,ls for the threeðnÞresonance lines satisfy the relations, ðnÞc ¼ 0 and hs ¼
ðnÞ
ðnÞ
ðnÞ
ls for odd n and hs ¼ ls for even n.
From eqs. (3), (5b), (5c), and (6a), one ﬁnds that the
separation between the two satellite lines is proportional to
the nuclear quadrupole moment,hs  ls ¼ 2ð1Þ /  Q:

ð7ÞThis means that the ratio of this separation for the two
isotopes on the same chemical and magnetic environment isequal to the ratio of their nuclear quadrupole moments. The
NMR spectra in the two panels of Fig. 3 both show two setsof quadrupole split three lines. The ratio of the diﬀerence
between the highest and the lowest frequencies obtained
from the data in Table I is 0.8457 for the spectrum in (a) and
0.9269 for the spectrum in (b). These values are indeed very
close to the isotopic ratio of the nuclear quadrupole moments
for Br (0.8354) and Cu (0.9251) shown in the Table II,
allowing us to assign the resonance lines as indicated inFig. 3 and Table I. The ﬁrst order quadrupole shifts are
obtained as(8a)
28:1 ð26:0Þ MHz
for 63 Cu (65 Cu)
ð1Þ
 ¼
79
81
(8b)
72:46 ð61:28Þ MHz for Br ( Br):
These values are much smaller than the Zeeman frequencies,
which is approximately equal to the center line frequency
shown in Table I. Therefore, our use of the perturbation
theory is justiﬁed.
If we neglect the second order quadrupole shift, themagnitude of the internal ﬁeld Bint can be crudely estimatedfrom the center line frequency as Bint 5:7 T for the Cusites and Bint 17 T for the Br sites. More accurate
determination is described in the next section. The existenceof such large internal ﬁelds at zero magnetic ﬁeld is the
direct evidence for a magnetically ordered state withspontaneous magnetic moments, consistent with the neutron
diﬀraction experiments.4)

that nearly a unique set of parameters can be obtained
already by the perturbation analysis. For the case of Cu
showing rather broad spectrum, however, we were not able
to determine the parameters completely.
4.1 Br sites
We ﬁrst determine each term in the perturbation expression from the observed resonance frequencies for the two Br
isotopes. From eqs. (4) and (6a)–(6c), the values of eachterm in the perturbation expression for the two isotopes canbe related as81
0 ¼ ð81 =79 Þ79 0 ¼ 1:0779  79 0
ð9aÞ
81 ð1Þ
81
79
79 ð1Þ
79 ð1Þ
 ¼ ð Q= QÞ  ¼ 0:8354  
ð9bÞ
81
79
2
ð Q= QÞ 79 ð2Þ
81 ð2Þ
c,s ¼ 81 79
c,s ¼ 0:6474  79 ð2Þ
c,s : ð9cÞ
ð = Þ
From the observed values of 79 c and 81 c (Table I), we
obtain 79 0 and 79 ð2Þ
c , using eqs. (5a), (9a), and (9c),79
79

0:17 MHz:

ð10Þ

79

ð1Þ ¼ 72:46

0:14 MHz;

79

ð2Þ
s ¼ 0:33

0:14 MHz:

ð11Þ

We now use the above results to ﬁnd the possible range ofparameter values in the nuclear Hamiltonian. Note that thesecond order shift for the satellite lines 79 ð2Þ
s [eq. (11)] isvery small compared with that for the central line 79 ð2Þ
c[eq. (10)]. This puts strong constraints as we see below.
First, by noting that the upper limit of the right-handside of eq. (6a) is set by Q , we obtain 79 ð1Þ  79 Q . The
experimental value of 79 ð1Þ in eq. (11) then sets a lower
limit for 79 Q , 79 Q 72:46 MHz. Next, putting this lower
limit and the experimental value of 79 0 in eq. (10) intoeq. (6c), we obtain

Analysis II

In this section, we try to determine the internal ﬁeld,
the EFG, and their relative orientation from the NMR
frequencies for both the Br and the Cu sites. The nuclear
Hamiltonian eq. (2) is speciﬁed by ﬁve parameters, Bint , Q ,, , and . Their values are independent of isotopes except
for Q , which is proportional to the nuclear quadrupole
moment [eq. (3)]. Although the second order perturbation
expression, eqs. (5a)–(5c) with eqs. (6a)–(6c), gives reasonably accurate resonance frequencies, it contains only fourð2Þ
independent parameters, 0 , ð1Þ , ð2Þc , and s . Therefore, wemust examine the higher order terms to determine all theparameters of the Hamiltonian. In what follows, we ﬁrst use
the perturbation expression to ﬁnd an appropriate range ofthe parameter values. We then diagonalize the Hamiltoninan
eq. (2) numerically to calculate the resonance frequencies
exactly and seek the P
best parameter values which minimizes
2
 cal 2  2
 obs
deﬁned as 2 ¼ ;k ½ð obsk  k Þ = k , where k cal( k ) is the observed (calculated) resonance frequency of
the k-th line (k ¼ c, hs, or ls) for the isotope  and  k is theexperimental uncertainty listed in Table I.
For the case of Br spectrum showing sharp lines, thefrequencies can be determined quite accurately. We found

0:14 MHz;ð2Þ
c ¼ 11:41

Then from the observed values of 79 ls and 79 hs andeqs. (5b) and (5c), we obtain794.

0 ¼ 174:57

ð2Þ
s

2:506ð1  Þ½ð18  12 þ 22 2 Þ
þ 22 ð1  2 Þ ;

ð12Þ

2

where we deﬁned¼ cos  and  ¼ cos 2 . Note thatthe minimum of the right-hand side of eq. (12) is locatedat  ¼ 1 and  ¼ 1 within the deﬁned range 0    1,
1    1 for any value of . Therefore,
79

ð2Þ
s

20:05 ð1  Þ:

ð13Þ

Then the small experimental value of 79 ð2Þ
s ¼ 0:33 MHz
restricts the possible range of either near zero (  0:017,
 82 ) or near one (0:983,   7:4 ). If’1( ’ 0), 79 Q ’ 79 ð1Þ ¼ 72:46 MHz from eqs. (6a) and2(11). Then from eq. (6b), 79 ð2Þ
c ’ 2:506 (MHz). However, this is clearly incompatible with the experimental valueof 11.41 MHz [eq. (10)]. Therefore, possible solutions mustsatisfy ’ 0 ( ’ 90 ).
The possible ranges of parameter values are determined asfollows. We ﬁrst ﬁx the value of . Then 79 Q is expressedby  and  using eq. (6a) and the experimental value of79 ð1Þ
 . By putting this expression into eqs. (6b) and (6c), thevalues of  and  are determined by solving these equa79 ð2Þ
tions using the experimental values of 79 ð2Þ
s .
c and
We found that solutions exist only for 0   0:0024

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J. Phys. Soc. Jpn., Vol. 77, No. 10

M. YOSHIDA et al.

Table III. Calculated Br NMR frequencies. The numbers in parentheses
indicate the diﬀerence from the experimental values shown in Table I.
c
(MHz)

sh
(MHz)

103
102

79

Br

102.53 (0.09)

185.97 (0.01)

247.38 (0.02)

81Br

127.31 (0:03)

195.64 (0.08)

249.85 (0:05)(90    87:2 ). For this range of , other parameters takethe values, 0:85    1 (74   90 ), 0:31 
0:28, and 114:7  79 Q  115:1 MHz. The magnitude of theinternal ﬁeld is obtained as Bint ¼ 79 0 =79  ¼ 16:37 T. Thus
the second order perturbation analysis signiﬁcantly narrows
down the possible range of the parameters.
We have further reﬁned the parameter values obtained
above by numerical diagonalization of the nuclear
Hamiltonian to calculate 2 and by seeking the minimumof 2 . We have changed the value of each parameter
successively within an appropriate range to ﬁnd the global
minimum of 2 by iteration. Then the ﬁnal adjustment of theparameter values was done by using parabolic expansion of2
with respect to the parameters to calculate the precise
location of the minimum and to estimate uncertainties of theparameter values. The ﬁnal results are the following:
Bint ¼ 16:40

0:01 ðTÞ;79

0:4 ðMHzÞ;Q ¼ 112:5

 ¼ 0:330 0:005;
 ¼ 89:5 1:0 ðdegÞ;¼ 87:8

4:9 ðdegÞ;

0.5

0.9

χ2

sl
(MHz)

η = 0.1

104

ð14Þ

2

with
¼ 1:8. The resonance frequencies calculated fromthese parameter values are compared with the experimental
data in Table III. The ﬁnite value of  indicates lack of
C4 -symmetry at the Br sites, similarly to the Cl sites in(CuCl)LaNb2 O7 where  ¼ 0:56,7) again ruling out the
tetragonal P4=mmm space group.
4.2 Cu sites
Applying the same perturbation analysis to the Cu data,
we obtain the following values of the Zeeman frequency,
the ﬁrst and the second order quadrupolar shifts for the63
Cu nuclei, 63 0 ¼ 64:2 2:0 MHz (Bint ¼ 5:7 T), 63 ð1Þ ¼
28:05 0:29 MHz, 63 ð2Þ
2:1 MHz, 63 ð2Þ
c ¼ 0:3s ¼ 0:5
2:1 MHz. The rather large uncertainties of these values,
however, prevent us from narrowing the range of parametervalues eﬃciently.
In fact, the experimental Cu resonance frequencies can be
reproduced quite well by numerical diagonalization of thenuclear Hamiltonian for any value of  between 0 and 1 asshown in Fig. 4, where 2 is plotted against  for several
values of  with other parameter values ﬁxed to minimize 2 .
The 2 always shows a single deep minimum well below one
at a small value of ,   7 , except when  is very close toone. For  ¼ 1, there are two minima in 2 at  ¼ 6 and at
 ¼ 83 . The optimized values of Bint and 63 Q minimizing
2
depend only slightly on : Bint ¼ 5:72 T and 63 Q ¼ 28:3
MHz for  ¼ 0 change to Bint ¼ 5:67 T and 63 Q ¼ 29:4
MHz for  ¼ 1. The optimized value of stays at 90 when
 0:3. When  is small ( ’ 0:1), cannot be determinedsince the Hamiltonian itself depends only weakly on .

10

1

10

0

10

1.0

-1

0

10

20

30

40

50

θ (degree)

60

70

80

90

Fig. 4. (Color online) The -dependence of 2 of the Cu NMR spectrum
for various values of . Values of other parameters are chosen tominimize 2 : Bint ¼ 5:716 T, 63 Q ¼ 28:31 MHz, ¼ 1:3 for  ¼ 0:1,
Bint ¼ 5:705 T, 63 Q ¼ 28:45 MHz, ¼ 89:8 for  ¼ 0:5, Bint ¼ 5:680 T,
63
Q ¼ 29:03 MHz, ¼ 90 for  ¼ 0:9 and Bint ¼ 5:670 T, 63 Q ¼ 29:38
MHz, ¼ 88:7 for  ¼ 1:0. Note that 2 always takes one deep
minimum at a small value of  (  6 ) except when  is very close toone.

Let us compare these results with those obtained forthe non-magnetic (CuCl)LaNb2 O7 by Cu NMR experiments
at various magnetic ﬁelds.7) By assuming that the c-axis
is one of the principal axes of the EFG, it was found thatthe z-axis with the largest principal value of EFG in(CuCl)LaNb2 O7 lie in the ab-plane, 63 Q ¼ 29:64 MHz and ¼ 0:098.7) We notice that the values of 63 Q are almost
identical for the two materials, indicating the similar local
structure. We also expect that they have similar values of .
Therefore, it is very unlikely that  in (CuBr)LaNb2 O7
is close to one. Then we conclude from the above resultsthat  is very small (  6 ) in (CuBr)LaNb2 O7 . The
analysis of the Cu spectrum in (CuBr)LaNb2 O7 demonstrates that the Cu-NMR spectrum can be well reproduced by the EFG parameters which are nearly equal tothose for (CuCl)LaNb2 O7 and the internal ﬁeld of about
5.7 T must be directed nearly parallel to the z-axis of the
EFG tensor, which corresponds to the largest principal valueof EFG.
5.

Discussion

Summarizing the analysis in the previous sections, wefound the following: (1) There is an internal ﬁeld of 5.7 T at
the Cu sites directed along the z-axis of the EFG. (2) There isan internal ﬁeld of 16.4 T at the Br sites directed perpendicular to the z-axis of the EFG.
Let us ﬁrst discuss the results on the Cu sites. Since thevalue of Q at the Cu site is nearly the same for the Br and Cl
compounds, we expect the two compound to have the samez-axis of the EFG, which was found to be in the ab-plane in(CuCl)LaNb2 O7 .7) The internal ﬁeld directed along thez-axis in (CuBr)LaNb2 O7 is then consistent with the neutron
results reporting the ordered moment parallel to the b-axis.4)
The internal ﬁeld at the Cu nuclei is mainly due to themagnetic moment on the same Cu ion being observed (theon-site hyperﬁne ﬁeld), which is anisotropic reﬂecting theanisotropic shape of the Cu-3d orbital. It is concluded fromthe anisotropy of the Cu NMR shift in (CuCl)LaNb2 O7 that104705-5

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the Cu spin is mainly on the dð3y2  r 2 Þ orbital, where y isparallel to the crystalline c-axis.7) The internal ﬁeld of 5.7 Tthen corresponds to the magnetic moment of 0:5 0:1 B in
the ab-plane from the hyperﬁne coupling constant Ahf? ¼
11 2 T/ B .7) This value is consistent with the orderedmoment of 0.6 B observed by neutron diﬀraction.4)
We next discuss the results on the Br sites. In contrast
to the Cu sites, the internal ﬁeld at the Br sites is due tothe transferred hyperﬁne interaction, which is the coupling
between the magnetic moments and the ligand nuclei
through the covalency eﬀects. If the structure were thetetragonal P4=mmm,1) the Br nuclei would couple equallyto the four nearest neighbor Cu moments. Then the totalinternal ﬁeld would have to be cancelled out to zero for thecollinear AF order with the wave vector ð; 0; Þ, which wasobserved by neutron diﬀraction experiments.4) The ﬁnite
internal ﬁeld at the Br sites, therefore, gives direct evidence
for structural distortion breaking the four-fold symmetry at
the Br sites. The ﬁnite value of , the asymmetry parameterof EFG, at the Br sites is another independent piece ofevidence for such structural distortion. Yet, the sharp six
peaks in the Br-NMR spectrum ensure a unique crystallographic site without appreciable disorder.
These features of the local symmetry at the Br sites
are exactly what were found for the Cl sites in (CuCl)LaNb2 O7 ,7) which have led Yoshida et al. to propose
possible structural models with orthorhombic distortion
shown in Fig. 2. We now examine if the same models
provide consistent account for the results on (CuBr)LaNb2 O7 as well. In (CuCl)LaNb2 O7 , the z-axis of the
EFG at the Cl sites is parallel to the c-axis. This is likely tohold also for the Br sites in (CuBr)LaNb2 O7 , since theinternal ﬁeld at the Br sites should be parallel to the Cu
moments, which lie in the ab-plane, and  ¼ 90 . Thisprefers the model (a) rather than (b) and (c) shown in Fig. 2,
since the Cl (or Br) sites are then on the mirror plane,
therefore, the c-axis can be a principal axis. Yoshida et al.
have argued that the displacement of Cl atoms makes theexchange coupling shown by the red lines in Fig. 2 muchstronger than the other bonds, leading to local dimer singlet
formation in (CuCl)LaNb2 O7 .
If this bond remains strong and antiferromagnetic in(CuBr)LaNb2 O7 , the collinear AF order shown in Fig. 5(a)should appear. In this structure, however, Br nuclei couple
dominantly to two antiparallel moments, therefore, theinternal ﬁeld can never be as large as 16.4 T. In fact, the

(a)

(b)

Fig. 5. (Color online) Possible spin conﬁgurations of the collinear orderon the distorted lattice. Only the pattern (b) is compatible with the large
internal ﬁeld observed at the Br sites.

observed internal ﬁeld is nearly equal to those reported for(CH3 NH3 )2 Cu(Cl1x Brx )4 (15.8 and 15.2 T),18) which is atypical example of strong transferred hyperﬁne interaction
via the -bond between Cu-dðx2  y2 Þ orbital and the Br-p
orbital. The transferred hyperﬁne interaction should be
weaker for a Br-Cu pair in (CuBr)LaNb2 O7 , where the spin
density is mainly on the dð3y2  r 2 Þ orbital. Thus the large
internal ﬁeld of 16.4 T is possible only if the hyperﬁne ﬁelds
from two Cu spins add. In other words, the Br nuclei mustcouple dominantly to two parallel moments as shown in
Fig. 5(b).
The same hybridization process involved in the transferred hyperﬁne interaction also causes the superexchangeinteractions. The strong asymmetry in the transferred hyperﬁne interaction, then induces inequivalent exchange interactions. The models shown in Fig. 2(a), for example, include
ﬁve distinct exchange interactions. It is known that thesuperexchange interaction through the path Cu–X–Cu isvery sensitive to small structural variation and often changes
sign.19) Therefore, it is conceivable that dominant exchange
coupling changes from antiferromagnetic in (CuCl)LaNb2 O7
to ferromagnetic in (CuBr)LaNb2 O7 by small diﬀerence in
the ionic position, even if the both compounds show thesame type of structural distortion.
From the susceptibility and the magnetization data,
however, it is unlikely that single ferromagnetic interaction
dominate over other iteractions in (CuBr)LaNb2 O7 . The
Weiss temperature W , deﬁned by the Curie–Weiss law of
the susceptibility ¼ C=ðT þ W Þ, changes from 9.6 K in
(CuCl)LaNb2 O7 2) to 5.1 K in (CuBr)LaNb2 O7 .13) The positive value of W indicates that averaged interaction is still
antiferromagnetic in (CuBr)LaNb2 O7 , even though it is lessso compared with (CuCl)LaNb2 O7 . The saturation ﬁeld Bcof the magnetization curve gives a measure of stabilityof the antiferromagnetic state. The increase of Bc from30 T in (CuCl)LaNb2 O7 3) to 70 T in (CuBr)LaNb2 O7 13)
points to higher stability of the antiferromagnetic state in(CuBr)LaNb2 O7 , presumably due to overall increase of
exchange interaction in Br compounds. It appears that thediﬀerent ground states in the Cl and Br compounds is theresults of subtle balance among several inequivalent frustrating interactions. Precise theoretical studies are desired torelate our structural model to the magnetic ground state.
6.

Summary

We have presented the Cu and Br NMR spectra in thecollinear antiferromagnetic state in (CuBr)LaNb2 O7 at zeromagnetic ﬁeld and T ¼ 4:2 K and determined the values of
the internal ﬁeld, EFG tensor and their relative orientation.
The results at the Cu sites conﬁrmed an AF order of about
0:5 0:1 B /Cu in the ab-plane. In order for the large
internal ﬁeld at the Br sites to be compatible with thecollinear AF order observed by neutrons, the Br sites must
be displaced from the center of the Cu square lattice tocouple strongly to only two parallel Cu spins. Our resultsin (CuBr)LaNb2 O7 can be explained consistently by the
structural model proposed for (CuCl)LaNb2 O7 , provided
that the pairs of Cu spins, which form singlet dimes in the Cl
compound, are aligned parallel in the Br compounds due tomodiﬁed exchange interactions brought by small diﬀerencein the ionic displacement.

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Acknowledgment
This work was supported by Grants-in-Aid for ScientiﬁcResearch (Nos. 18740202 and 17684018) and Grants-inAid on Priority Areas ‘‘Invention of Anomalous Quantum
Materials’’ (Nos. 16076204 and 16076210) and ‘‘Novel Stateof Matter Induced by Frustration’’ (No. 19052004) from the
Ministry of Education, Culture, Sports, Science and Technology, Japan.

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