ARTICLE IN PRESS
Journal of Solid State Chemistry 182 (2009) 3275–3281

Contents lists available at ScienceDirect

Journal of Solid State Chemistryjournal homepage: www.elsevier.com/locate/jssc

Structural distortions in the spin-gap regime of the quantum antiferromagnet
SrCu2(BO3)2
C. Vecchini a,b,, O. Adamopoulos a,c, L.C. Chapon b, A. Lappas a,, H. Kageyama d, Y. Ueda e, A. Zorko faInstitute of Electronic Structure and Laser, Foundation for Research and Technology-Hellas, Vassilika Vouton, 711 10 Heraklion, Crete, Greece
ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire, OX11 0QX, United KingdomcDepartment of Chemistry, University of Crete, Voutes, 710 03 Heraklion, GreecedDepartment of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japane
Institute of Solid State Physics, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8581, Japanf
Institute Jožef Stefan, Jamova 39, 1000 Ljubljana, Sloveniab

a r t i c l e in fo

abstract

Article history:
Received 16 April 2009
Received in revised form
31 August 2009
Accepted 14 September 2009
Available online 19 September 2009

We report the ﬁrst crystallographic study within the low-temperature ( o 40 K) spin-gap region of thetwo-dimensional frustrated antiferromagnet SrCu2(BO3)2. The crystal system does not deviate from thetetragonal I-42m space group symmetry. However, our high-resolution neutron powder diffraction
measurements uncover subtle structural modiﬁcations below 34 K, concomitant to the formation of the
dimer singlet ground state. Intimate spin–lattice coupling leads to negative thermal expansion of thetetragonal structure, which reﬂects into particular local lattice adjustments. The extracted structuralparameters suggest the reduction of the buckling found in the copper–borate planes and thestrengthening of the leading, in-plane intra-dimer superexchange interaction. The observed contraction
along the c-axis, associated with the inter-dimer exchange in adjacent layers, indicates the involvementof weaker three-dimensional interactions in the magnetic properties. The rules posed by the crystal
symmetry do not preclude Dzyaloshinsky–Moriya interactions, which therefore remain as an importantsource of spin anisotropy necessary to rationalise the ground state behaviour.
& 2009 Elsevier Inc. All rights reserved.

Keywords:
Neutron diffraction
Frustrated system
Antiferromagnet
Two-dimensional system
Dimer
SrCu2(BO3)2
Spin-gap
Shastry–Sutherland
Strongly correlated systems

1. Introduction
Low-dimensional systems with a quantum-disordered singlet
ground state have attracted much attention in the past years, bothfrom the experimental as well as the theoretical point of view. The
Haldane (S =1, Y2BaNiO5) [1], spin-Peierls (S ¼ 12, CuGeO3) [2],ladder (S ¼ 12, SrCu2O3) [3] and plaquette (S ¼ 12, CaV4O9) [4]systems are members of the broader family, with a spin excitation
gap from the nonmagnetic singlet ground state to the ﬁrst excitedtriplet state. Quantum spin ﬂuctuations and/or magnetic anisotropy often play a decisive role in the determination of the natureof the ground state properties. A rich variety of phenomena havebeen observed and predicted in this type of materials; therefore,
the discovery of other examples of chemical compounds is worthy
as it can promote the understanding of fundamental processes
governing the spin-dynamics in the quantum critical regime.

 Corresponding author. Fax: +44 1235 44720.
 Also corresponding author. Fax: +30 2810 391305.

E-mail addresses: carlo.vecchini@stfc.ac.uk (C. Vecchini), lappas@iesl.forth.gr(A. Lappas).
0022-4596/$ - see front matter & 2009 Elsevier Inc. All rights reserved.
doi:10.1016/j.jssc.2009.09.017

More than twenty years ago, Shastry and Sutherland proposed
an interesting theoretical model [5]; they calculated the groundstate of an anisotropic quantum spin Heisenberg Hamiltonian
with next-neighbor interactions in two dimensions. SrCu2(BO3)2 isa Heisenberg system which displays a unique exchange topology.
This compound is indeed one of the ﬁrst experimental realizationsof the two-dimensional (2D) Shastry–Sutherland lattice [6,7], inwhich a rectangular network of spin-1/2 Cu2 + dimers is arranged
within a square-based structure with diagonal bonds, allowing fornearest- (J1, intra-dimer exchange pathway) and next-nearest(J2, inter-dimer exchange pathway) neighbor dimer interactions(Fig. 1). SrCu2(BO3)2 presents a dimerized nonmagnetic groundstate [8,9], with an energy gap of D =34(1) K [7,10] between the
singlet and the triplet states.
As the strong interplay between the crystal structure and themagnetic properties is a well-known aspect of low-dimensional
systems, in the recent years many theoretical works were
motivated from the phase diagram of the general Shastry–
Sutherland lattice type [11]. For the original 2D model, the exact
dimer ground state is realized for small x= |J2|/|J1|. Although there
are still open questions, there is reasonable consent that when theexchange interactions are tuned to a critical value xc, of about 0.7,

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C. Vecchini et al. / Journal of Solid State Chemistry 182 (2009) 3275–3281

the attempt to stabilise a long-range ordered antiferromagnetic(AFM) state, however, with no success so far.
The intriguing behaviour in SrCu2(BO3)2 is due to its magnetic
anisotropy that appears not well understood up till now. As the
crystal structure is anisotropic, with a rather large J1 exchange
coupling, the main contribution to spin anisotropy was shown[23] to be of Dzyaloshinsky–Moriya (DM) type, whose presenceobeys a number of rules posed by the crystal symmetry. Therefore
the knowledge of the low-temperature crystal structure is crucial
for the understanding of the magnetic properties of SrCu2(BO3)2.
While the crystal structure has been determined quite comprehensively by single crystal X-ray diffraction measurements down
to 100 K [24], no structural studies have been pursued up to now
at lower temperatures where novel quantum mechanical magnetic behaviour was found [6–10]. Since accurate knowledge ofthe lattice symmetry is necessary to rationalise the ground state
properties, here we report a detailed structural study for
SrCu2(BO3)2 at low-temperatures. We performed high-resolution
neutron powder diffraction (NPD) measurements between room
temperature (RT) and down to 2 K, with emphasis in the ‘‘spingap’’ regime (2oTo40 K) [25]. Our study demonstrates the onsetof subtle atomic displacements, concurrent with an unusual
negative thermal expansion in the dimerized state, all postulating
to delicate spin-lattice coupling effects for To40 K. This new
knowledge on the SrCu2(BO3)2 lattice, offers a valuable insight inview of future efforts aiming to understand how the ground stateenergy is minimized by lattice modiﬁcations pertaining to therearrangement of the magnetic interactions among the Cu dimers.

2. Experimental

Fig. 1. Low-temperature structure of SrCu2(BO3)2 projected: (a) along the ab-planeand (b) along the ac-plane. J1 and J2 the in-plane Cu–Cu intra-dimer and interdimer exchange integrals, respectively. J?1 and J?2 the out-of-plane Cu–Cu dimer
interactions.

a quantum phase transition [12] is expected to take place from adimer singlet to a plaquette singlet ground state [13]. Furthermore, the phase transition point between this intermediate,
frustration-induced phase and a gapless ordered state was also
estimated at xc2 ﬃ 0.86 [14], while the model reduces to a squarelattice Heisenberg antiferromagnet for some value of x b1. As
SrCu2(BO3)2 appears to be in the vicinity of a quantum criticalpoint that separates the dimer state from a gapless Ne el orderedstate, renders it a system of great interest. Among the various
choices of coupling constants, the optimal set shows a criticalratio xc ﬃ 0.635, with J1 (Cu1–Cu2 in Fig. 1) and J2 (Cu1–Cu3 inFig. 1) estimated to be 85 and 54 K, respectively [15]. These
parameters were shown to reproduce with accuracy both thetemperature dependence of the magnetic susceptibility as well asthat of the speciﬁc heat within the gap region.
Moreover, some authors have emphasized the importance of
the inter-layer coupling (J3), i.e. a Shastry–Sutherland lattice withthree-dimensional (3D) interactions, in order to properly model
the thermodynamic properties of this novel compound [15,16]. It
has been argued that such an inter-layer coupling (J3/J1 ﬃ0.09) caninﬂuence the excitation spectrum and shift the phase diagram
boundary from a gapped to a Ne el state [17]. Substitutions of
aliovalent cations, such as Na, Al, La, Y for Sr [18] that modify thechemical pressure on the Cu–O planes or dilution of the copper
sub-lattice with Zn or Mg ions [19–22] have also been reported inSingle crystals of SrCu2(11BO3)2 have been grown from a
Li11BO3-ﬂux as described elsewhere [26]. A 4 g polycrystalline
sample was produced from crashing the rods used for the single
crystal growth. Neutron powder diffraction experiments were
performed on the High-Resolution Powder Diffractometer (HRPD)
and on the General Material Diffractometer (GEM) at the neutron
spallation source ISIS (UK). The sample used for the present work
was inserted in a ﬂat rectangular sample holder (HRPD; 4 g
powder) and in a 6 mm Vanadium can (GEM; 1 g powder). HRPD
data were collected from room temperature to T= 2 K, withparticular interest in the low-temperature region. For To100 K,
temperature steps of 4 K were used, while for T4100 K, thetemperature was raised in steps of 50 K. Long counting time wasallowed for data collected at 2, 100 and 295 K. Measurements on
GEM were performed in the temperature range 2oTo40 K, on
warming with temperature intervals of 1 K and high statistics. In
both cases a standard ILL Orange cryostat was used. The collected
patterns were analyzed with the Rietveld method. Reﬁnements of
the nuclear structure were carried out with the GSAS program
suite [27].

3. Results and discussion
From the crystallographic point of view, SrCu2(BO3)2 shows asecond-order structural phase transition at TS = 395 K from spacegroup I4/mcm above TS to a non-centrosymmetric space group
I-42m below TS [24]. Below 395 K all our datasets could be reﬁned
with the proposed space group. Fig. 1 shows a representation of
the structure as derived after Rietveld reﬁnements of the room
temperature HRPD data. Our structural analysis shows that layers
extending in the ab-plane are formed by (BO3)3  groups and Cu2 +ðS ¼ 12Þ ions, while Sr2 + ions separate two adjacent layers along thec-axis. The coordination of copper by the rigid BO3 groups leads toARTICLE IN PRESS
C. Vecchini et al. / Journal of Solid State Chemistry 182 (2009) 3275–3281

Xs ðh k lÞ ¼ SHKL hH kK lL
2

HKL

with the term SHKL deﬁned for H +K +L= 4 (H,K,LZ0). For Lauesymmetries other than -1 (triclinic), the symmetry imposes
restrictions on the allowed SHKL terms. Since the Laue class ofthe structure for this compound is 4/mmm (tetragonal), only 4
independent coefﬁcients are allowed (i.e. for a tetragonal
symmetry: A= B, D= E= F= 0 and the corresponding anisotropic
strain parameters are S400 = S040, S202 = S022, S004, S220). The
reﬁnement with this model (including strain: w2 = 3.415, Bragg
R-factor= 4.5%, without strain: w2 = 12.97 and Bragg R-factor =10%
at T =2 K) showed large strain coefﬁcients, such as S004 1.77(4)and S202  3.13(3), while others like the S400 and S220 parameters
were found to be smaller (  2.28  10 1(5) and  1.24  10 1 (7),respectively). Based on this analysis, we also ﬁnd that the latticestrain does not seem to exhibit signiﬁcant temperature dependence within the T-range investigated. The enhanced SHKL
parameters are an indication of defects or disorder, which in thepresent case appears mainly along the c-direction, as the Stephens
coefﬁcients with non-zero L index are larger. This could be aneffect of the corrugation of the ab-planes below the high-T (TS)structural transition.
Importantly, the purpose of this study is to look for
spontaneous changes in the crystal system by means of Rietveld
reﬁnements as accurate knowledge of the lattice symmetry
determines the spin-anisotropies necessary to rationalise experimental observations, such as, forbidden singlet–triplet transitions
in high-ﬁeld ESR [29]. Along these lines it is worth noting that thedata collected on the HRPD diffractometer (Fig. 2a), have revealed
unusual negative thermal expansion of the lattice below T  40 K
(Fig. 2a, inset). We argue that this is primarily due to thein-plane expansion (0.02%; vide infra), which overcomes a slightcontraction along the c-direction. The quite unusual and puzzling
behaviour of SrCu2(BO3)2 around the T= 34 K region motivatedus to study the subtle lattice changes in more detail and theresults are discussed in the following paragraphs. Althoughthe HRPD data provide reliable information on the general
lattice modiﬁcations, the involved statistics do not allow for an
accurate determination of the T-dependence of crystallographic

3.0
Volume (Å3)

538.0

2.5

537.5

Intensity (arb. units)

537.0

2.0

536.5
536.0

1.5

0

50

100 150 200 250 300
T (K)

1.0
0.5
0.0
-0.5
1.0

0.8

1.2

1.4

1.6

1.8

2.0

2.2

2.0

2.3

d-spacing (Å)
0.20

0.15
Intensity (arb. units)a pronounced angular distortion (corrugation) of the CuO4 square
below TS, with important consequences on the effect of themagnetic anisotropy on the ground state properties. The nearestneighbor (nn) copper atoms form dimers of edge-sharing CuO4
groups, which are not co-planar at ToTS and as that the Cu-BO3
layer is not a mirror plane for the dimers, as it used to be above TS.
Each dimer is coordinated from both sides by the two symmetry
equivalent oxygens of the borate group. The dimers are orthogonally arranged with respect to each other in a topologicallyequivalent Shastry–Sutherland lattice arrangement.
In this lattice type each dimer becomes relatively strongly
coupled to the two neighboring orthogonal dimers (next-nearestneighbors=nnn) by super–superexchange interactions (J2) via
rigid BO3 groups. Our structural analysis ﬁnds that these BO3
groups do not show any appreciable temperature dependence in
the T range of interest. Indeed, the B–O1 and B–O2 distances
remain at values of 1.372(1) and 1.378(1) Å, respectively, while in
the low-T region. The corresponding angles are also rather
rigid, taking values of 122.90(5)1 for O1–B̂–O2 and 114.2(1)1 for
O2–B̂-O2 (Fig. 1). Rigidity in planar triboratre groups is frequently
met in metal-borate systems. For example, in LiB3O5, triborate
units composed of three inequivalent B–O bonds (1.349(5),1.367(1) and 1.396(1) Å) are connected with ﬂexible Li–O linkages
that are responsible for the anisotropic thermal expansion of thelattice [35]. In the present case, with the rigid BO3 interconnecting
the dimers, we will show that the different expansion tendency of
the CuO4 structural units allows in the SrCu2(BO3)2 subtle
modiﬁcations that could optimise interactions of different nature,such as the magnetic exchange coupling (vide infra).
Other crystal system changes, which were unveiled by the highresolution of the HRPD diffractometer, include a signiﬁcantbroadening of the Bragg reﬂections, inferring to distortions due
to microstrain. In order to properly take this into account, a modelwith anisotropic strain broadening based on Stephens formalism
has been incorporated in the Rietveld reﬁnements [28]. Within
this formalism, the spacing d between lattice planes for any
given reﬂection deﬁned by the Miller indexes hkl is 1/d2 =Ah2 + Bk2 + Cl2 + Dhk+ Ehl +Fhk, where the capital case letters represent metric parameters of the reciprocal lattice. Strain broadening
here is considered as a manifestation of the distribution of theseparameters. We can therefore write the contribution to thebroadening on a reﬂection hkl due to strain as s2(h k l). The
variance matrix for a Gaussian distribution of these parameters
can be expressed in the following way:

3277

0.10

0.05

0.00

0.8

1.0

1.3

1.5
1.8
d-spacing (Å)

Fig. 2. Rietveld plots for (a) T= 100 K diffraction pattern of SrCu2(BO3)2 collected on
the HRPD diffractometer. Inset: Full temperature evolution of the unit cell volume.
(b) T =2 K diffraction pattern of SrCu2(BO3)2 collected on the GEM diffractometer.
The black dots represent the data, red line is the calculated pattern ﬁtted to thedata, while the blue line at the bottom of the plot is the difference between
calculated and observed. The green vertical marks indicate the position of the
Bragg reﬂections. For interpretation of the references to colour in this ﬁgurelegend, the reader is referred to the web version of this article.

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C. Vecchini et al. / Journal of Solid State Chemistry 182 (2009) 3275–3281

parameters, such as bond lengths, bond angles and thermal
parameters, which can all reﬂect local lattice adjustments.
In order to derive precise crystallographic information andobserve structural deformations pertaining to the spin-gap region,
datasets were recorded on the GEM diffractometer (Fig. 2b) below
T= 40 K. We observe an expansion in the ab-plane and contractionin the c-axis (corresponds to volume expansion of 0.02%; Fig. 3), inagreement with the earlier HRPD work. Table 1 summarizes thelattice parameters and atomic positions from the T= 2 and 40 K
GEM datasets, respectively. Fig. 4a shows the temperaturedependence of the intra-dimer (Cu1–Ô1–Cu2) angle (Fig. 1). This
angle signiﬁcantly increases from about 98.02(7)1 at 40 K to about
98.49(7)1 at 2 K. At the same time, the intra-dimer Cu1–Cu2
distance (Fig. 1) expands, changing from 2.916(2) Å at 40 K to
2.930(2) Å at 2 K (Fig. 4b).
The increase of the Cu1–Cu2 distance is directly related to thelattice expansion in the ab-plane (Fig. 3a). This is partiallybalanced by a shortening of the Cu1–Cu3 inter-dimers distances(Fig. 4c). Very interestingly, we observed that the bending angle
between the CuO4 groups (Fig. 4d), deﬁned by the angle formed by
two adjacent CuO4 groups along the [11 0] direction, decreases
when the temperature is lowered and the planes become lesscorrugated at base temperature ( 2 K). This ‘‘ﬂattening’’ of the 2D
planes leads to an increase of the short inter-dimer distances(Cu3–Cu5; Fig. 5a) between adjacent layers, while the long inter-a (Å)

8.98508.98458.98408.9835c (Å)

6.64256.64206.64156.6410Vol (Å3)

536.15536.10536.05
0

10

20

30

40

Temperature (K)Fig. 3. Temperature evolution of the Rietveld reﬁned lattice parameters in the lowtemperature range (2r Tr 40 K; GEM diffractometer) of the SrCu2(BO3)2. (a) The
tetragonal a and b crystallographic directions; an unusual in-plane expansion is
resolved. (b) The c crystallographic direction; an out-of-plane contraction takes
place. (c) The unit cell volume; negative thermal expansion is uncovered within
the spin-gap region.

Table 1
Atomic positions obtained from full proﬁle Rietveld reﬁnements of the GEM
powder diffraction data of SrCu2(BO3)2.
AtomWyckoff pos

x/a

y/b

Z/c

Occ.

Biso

(a)
Sr
Cu
B
O1
O2

4c
8i
8i
8i
16j

0
0.11535(7)0.29499(8)0.40081(9)0.32811(7)1/20.11535(7)0.29499(8)0.40081(9)0.14604(8)00.2895(2)0.2386(2)0.1973(2)0.2591(2)

1.0
1.0
1.0
1.0
1.0

0.07(2)0.05(2)0.02(2)0.12(2)0.10(2)

(b)
Sr
Cu
B
O1
O2

4c
8i
8i
8i
16j

0
0.11482(7)0.29463(8)0.40049(9)0.32780(8)1/20.11482(7)0.29463(8)0.40049(9)0.14578(8)00.2894(2)0.2380(2)0.1964(2)0.2586(2)

1.0
1.0
1.0
1.0
1.0

0.10(3)0.09(3)0.02(2)0.13(3)0.14(2)(a) T= 2 K: Lattice parameters: a= 8.98493(6) Å, c= 6.64117(8) Å, V= 536.135(8) Å3.
Weighted proﬁle Rwp (%) = 3.95, Proﬁle Rp (%) =3.70, Bragg R-factor (%)= 4.47,
w2 = 13.99. (b) T= 40 K. Lattice parameters: a= 8.98354(6) Å, c = 6.64229(8) Å,
V= 536.059(8) Å3. Weighted proﬁle Rwp (%)= 3.92, Proﬁle Rp (%) =3.76, Bragg
R-factor (%) = 4.3, w2 = 14.71. Estimated standard errors at the last signiﬁcant digit
are given in parenthesis.

dimer distances (Cu2–Cu4; Fig. 5b) do not change signiﬁcantly inthe spin-gap region. Planar CuO4 groups are common in 2D
cuprates such as the Bi2CuO4 system [36]. In this long-range
antiferromagnetically ordered system, where superexchangeinteractions play a major role, Cu–Cu distances are about
2.899(3) Å (namely slightly shorter than in SrCu2(BO3)2), while^
the O–Cu–O
angles are much closer to 901 (i.e. 89.89(3)1) withrespect to those (i.e. 81.28(7)1) measured in SrCu2(BO3)2. The
geometry of the staggered CuO4 groups in Bi2CuO4 does notsupport cation–anion–cation exchange interactions, but super–
superexchange interactions involving two oxygen atoms. Suchinteractions have been invoked as being responsible for shortrange order along the chains. These short-range correlations
determine the observed antiferromagnetic behaviour that relates
Cu atoms belonging to different chains.
Let us now consider the effect of inter- and intra-dimer
exchange interactions on the lattice and the distortions therefore
observed in SrCu2(BO3)2. Below 34 K, the leading interaction thatmodiﬁes the nuclear structure of SrCu2(BO3)2 is the isotropic
magnetic exchange. Indeed, the opening of the Cu1–Ô1–Cu2 angle(Fig. 4a) and the increase of the Cu1–Cu2 dimer distances(Fig. 4b), while BO3 side groups remain unmodiﬁed at low-T (videinfra), suggest a strengthening of the intra-dimer superexchange(J1). If we assume AFM spin arrangement of the Cu moments
within each dimer, the application of Goodenough–Kanamori–
Anderson (G–K–A) rules [30] would suggest enhanced nn (J1)exchange integrals (Fig. 1). Interestingly, in SrCu2(BO3), the interdimer exchange path (which contains the rigid BO3 groups)
shrinks (Fig. 4c), showing an opposite trend compared to theintra-dimer one that elongates (Fig. 4b). All the lattice changes
occur while crossing-over into the spin-gap regime. We therefore
assume that at low enough temperature signiﬁcant spin-latticecoupling is established when the concentration of triplets
increases (with increasing T). This will tend to minimize theintra-dimer exchange; hence the shrinkage of the lattice (due to a
reduction of the Cu–Ô–Cu angle) with increasing temperature,
before the natural thermal expansion takes over. Consequently,
the enhanced spin–lattice coupling leads to the observed negative
thermal expansion of 0.02% in the ab-plane (Fig. 3).
In support to this behaviour comes a recent synchrotron X-ray
diffraction study where lattice contraction in SrCu2(BO3)2 hasbeen also observed when the strength of an intense appliedmagnetic ﬁeld is raised at low-temperatures (1.5 K). This tuneable

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98.6

2.932

98.5

2.930
Cu-Cu intra-dimer (Å)

Cu-O1-Cu (deg)

3279

98.4
98.3
98.2
98.1

2.928
2.926
2.924
2.922
2.920
2.918
2.916

Cu1-O1-Cu2

98.0

Cu1-Cu2

2.914
0

10

20
Temperature (K)

30

40

0

20

30

40

30

40

Temperature (K)

5.135

11.35
Cu1-Cu3

CuO4-CuO4

11.30
Bending Angle (deg)5.134
Cu-Cu inter-dimer (Å)

10

5.133
5.132
5.131

11.25
11.20
11.15
11.10
11.05
11.00
10.95
10.90
10.85

5.130

10.80
0

10

20
Temperature (K)

30

40

0

10

20
Temperature (K)Fig. 4. Temperature dependence of: (a) intra-dimer exchange pathway angle Cu1–Ô1–Cu2. (b) The intra-dimer Cu1–Cu2 distances. (c) The inter-dimer Cu1–Cu3 distances,(d) the layer corrugation, deﬁned as the angle between neighboring CuO4 groups within each layer in SrCu2(BO3)2. The vertical dashed line in each one of the plots marks
the entering into the spin-gap region.

parameter also increases the population of triplets as does thetemperature increase [34] and the authors reported the observation of a close relationship between the lattice constants andmagnetization. They found a variation of the in-plane lattice
constant with an applied ﬁeld, Bi, of the order of  Da/a= [a(B0) a(Bi)]/a(B0)  0.5  10  4 at 30 T, 1 10  4 at 35 T. Very interestingly,
their ﬁndings are in agreement with our structural measurements
for the temperature dependence of the basal plane lattice
parameters, which result in changes (  Da/a =[a(T= 2 K)  a(T)]/a(T= 2 K)) of the same order of magnitude, namely, 0.5  10  4 at
7 K, 1 10  4 at 10 K and 1.2  10  4 at 35 K.
Together with the effect of the frustrated, isotropic superexchange interactions (J1, J2) on the lattice, it is worth considering
the inﬂuence of two possible weaker interactions to the spin gap,
namely the inter-layer coupling J3 and the magnetic anisotropy.
The latter involves the antisymmetric Dzyaloshinsky–Moriya
interaction D  (Si  Sj), where Si, Sj represent the spins atneighboring sites [23], that justiﬁes the ﬁne structure of theexcited triplet state and its unusual magnetic ﬁeld dependence[31,32]. In the SrCu2(BO3)2 structure, a center of inversion at the
middle of the dimer bond forbids the intra-dimer DM interaction(T4TS), and instead the inter-dimer out-of-plane DM interaction
evolves as the dominant one. When we lower the temperature, theinversion center of symmetry is lost at the I4/mcm to I-42m
structural transition [11,24] and another DM component may playa role. Namely the nn intra-dimer DM interaction can become
important, which has been suggested as a pathway to account forforbidden singlet–triplet transitions in high-ﬁeld ESR [29,33].
From the analysis of the present NPD data (ToTS), we ﬁndthat the lattice symmetry does not preclude nn (Cu1–Cu2) DMinteractions. When we enter the spin-gap region (o 34 K), the inplane structure becomes more rigid due to the strengthening of
intra-dimer interactions (vide supra). Such a modiﬁcation of thecrystal lattice leads to a decrease of the observed planar buckling,
but the mirror plane lost below TS is not recovered, meaning that
nn DM interactions are still a feasible mechanism.
Furthermore, we realize that weak three-dimensional exchange interactions can also develop in the system through theﬂattening of the ab-plane (o34 K), as evidenced by the increase of
the Cu3–Cu5 ion distances (Fig. 5a) that correspond to the shortinter-dimer separation between the layers. On the contrary, thelong inter-dimer distances (Cu2–Cu4; Fig. 5b) remain almost
unaltered below T= 34 K. The two types of inter-layer couplings(J?1, J?2; Fig. 1b) that are established herein, have been estimatedto range from J?/J1 0.094 to 0.21 [15,16]). As they are relatively
weaker with respect to the corresponding in-plane exchange

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C. Vecchini et al. / Journal of Solid State Chemistry 182 (2009) 3275–3281

Cu-Cu Inter-layer (short) (Å)

3.482
3.480
3.478
3.476
3.474
3.472
Cu3-Cu5
3.470
0

10

20

30

40

Temperature (K)dimer system and the concurrent widening of the angle connecting nearest-neighbour Cu sites, suggests the strengthening of theintra-dimer antiferromagnetic interactions. We ﬁnd that theincrease in the intra-dimer separation changes quite signiﬁcantly
the structure. The novel orthogonal arrangement of the dimers
leads to a net expansion in the ab-plane and a reduction to the inplane inter-dimer distances. These lattice distortions that takeplace at low enough temperatures (o34 K) are not exclusive to inplane modiﬁcations. Importantly, the buckling of the copper–
borate planes is also modiﬁed. The structural analysis suggeststhat the out-of-plane coupling strengthen somehow, due to theshrinkage along the c-direction. It reﬂects a more three-dimensional type of behaviour for the SrCu2(BO3)2 lattice within the
spin-gap temperature region. At low-temperatures ( o34 K),
the rules posed by the crystal symmetry (I-42m) on the Cu
dimers allow for Dzyaloshinsky–Moriya (DM) coupling of themagnetic moments. Our analysis suggests that DM interactions
remain a crucial spin anisotropy for understanding the intriguing
SrCu2(BO3)2 magnetic behaviour.

4.372

Cu-Cu Interlayer (long) (Å)

Acknowledgements

4.370
We would like to thank R.M. Ibberson for help with theexperiments. AL acknowledges partial support from the European
Commission (‘‘Construction of New Infrastructures’’, ISIS Target
Station II, contract no. 011723), and the EU access to research
infrastructures program of ISIS (Project Reference: HPRI-CT-200100116). This work was partially supported by Grants-in-Aid for
Science Research on Priority Areas ‘‘Novel States of Matter
Induced by Frustration’’ (No. 19052004) from the Ministry of
Education, Culture, Sports, Science and Technology of Japan.

4.368
4.366
4.364
4.362
Cu1-Cu4

Appendix. Supporting Information

4.360
0

10

20
Temperature (K)30

40Fig. 5. Temperature evolution of: (a) the short inter-layer distances, between Cu3–
Cu5 sites and (b) the long inter-layer distances, between Cu1–Cu4 sites in adjacent
Cu–BO3 planes of the SrCu2(BO3)2. The vertical dashed line in each one of the plots
marks the entering into the spin-gap region.

integrals, they are expected to play a minor role in the observed
structural distortions.
The current NPD data analysis ﬁnds small crystal systemchanges that do not violate restrictions posed by the tetragonal
I-42m lattice symmetry of SrCu2(BO3)2. A comprehensive theoretical study, based on the structural modiﬁcations described in thiswork is desirable. We expect that it will improve the understanding of the temperature evolution of the exchange coupling
integrals and the role of magnetic anisotropy within the spin-gap
region.

4. Conclusions
We performed extensive high-resolution, high-statistics neutron powder diffraction measurements on the two-dimensional
quantum antiferromagnet SrCu2(BO3)2, between room temperature and down to 2 K. Subtle spin–lattice coupling was unveiled in
the low-temperature region (o34 K), where the spin-singlet state
populates and characterises the ground state properties. The
Rietveld analysis of the NPD data revealed an unusual negative
thermal expansion of the lattice, which reﬂects upon subtle latticeadjustments without space group symmetry (I-42m) change. The
dimerization of the Cu–Cu ions, mapping onto an orthogonal spin-

Supplementary data associated with this article can be foundin the online version at doi:10.1016/j.jssc.2009.09.017.

References[1] J. Darriet, J.P. Regnault, Solid State Commun. 86 (1993) 409.
[2] M. Hase, I. Terasaki, K. Uchinokura, Phys. Rev. Lett. 70 (1993) 3651.
[3] M. Azuma, Z. Hiroi, M. Takano, K. Ishida, Y. Kitaoka, Phys. Rev. Lett. 73 (1994)
3463.
[4] S. Taniguchi, T. Nishikawa, Y. Yasui, Y. Kobayashi, M. Sato, T. Nishioka,
M. Kontani, K. Sano, J. Phys. Soc. Jpn. 64 (1995) 2758.
[5] B.S. Shastry, B. Sutherland, Physica B 108 (1981) 1069.
[6] H. Kageyama, K. Yoshimura, R. Stern, N.V. Mushnikov, K. Onizuka, M. Kato,
K. Kosuge, C.P. Slichter, T. Goto, Y. Ueda, Phys. Rev. Lett. 82 (1999) 3168.
[7] K. Kodama, M. Takigawa, M. Horvatic, C. Berthier, H. Kageyama, Y. Ueda,
S. Miyahara, F. Becca, F. Mila, Science 298 (2002) 395.
[8] H. Nojiri, H. Kageyama, K. Onizuka, Y. Ueda, M. Motokawa, J. Phys. Soc. Jpn. 68(1999) 2906.
[9] H. Kageyama, M. Nishi, N. Aso, K. Onizuka, T. Yosihama, K. Nukui, K. Kodama,
K. Kakurai, Y. Ueda, Phys. Rev. Lett. 84 (2000) 5876.
[10] H. Kageyama, K. Onizuka, T. Yamauchi, Y. Ueda, S. Hane, H. Mitamura, T. Goto,
K. Yoshimura, K. Kosuge, J. Phys. Soc. Jpn. 68 (1999) 1821.
[11] S. Miyahara, K. Ueda, J. Phys.: Condens. Matter 15 (2003) R327.
[12] S. Miyahara, K. Ueda, Phys. Rev. Lett. 82 (1999) 3701.
[13] Z. Weihong, J. Oitmaa, C.J. Hamer, Phys. Rev. B 60 (1999) 6608;
E. Müller-Hartmann, R.R.P. Singh, C. Knetter, G.S. Uhrig, Phys. Rev. Lett. 84(2000) 1808.
[14] A. Koga, N. Kawakami, Phys. Rev. Lett. 84 (2000) 4461.
[15] S. Miyahara, K. Ueda, J. Phys. Soc. Jpn. (Suppl.) B 69 (2000) 72.
[16] C. Knetter, A. Buhler, E. Müller-Hartmann, G.S. Uhrig, Phys. Rev. Lett. 85(2000) 3958.
[17] A. Koga, J. Phys. Soc. Jpn. 69 (2000) 3509.
[18] G.T. Liu, J.L. Luo, N.L. Wang, X.N. Jing, D. Jin, T. Xiang, Z.H. Wu, Phys. Rev. B 71
(2005) 014441.
[19] G.T. Liu, J.L. Luo, Y.Q. Guo, S.K. Su, P. Zheng, N.L. Wang, D. Jin, T. Xiang, Phys.
Rev. B 73 (2006) 014414.

ARTICLE IN PRESS
C. Vecchini et al. / Journal of Solid State Chemistry 182 (2009) 3275–3281[20] A. Fukaya, Y. Fudamoto, I.M. Gat, T. Ito, M.I. Larkin, A.T. Savici, Y.J. Uemura,
P.P. Kyriakou, G.M. Luke, M.T. Rovers, H. Kageyama, Y. Ueda, Physica B 326(2003) 446.
[21] S. Haravifard, S.R. Dunsiger, S.E. Shawish, B.D. Gaulin, H.A. Dabkowska,
M.T.F. Telling, T.G. Perring, J. Bonca, Phys. Rev. Lett. 97 (2006) 247206.
[22] A. Lappas, A. Schenck, K. Prassides, Physica B 326 (2003) 431.
[23] O. Ce pas, K. Kakurai, L.P. Regnault, T. Ziman, J.P. Boucher, N. Aso, M. Nishi,
H. Kageyama, Y. Ueda, Phys. Rev. Lett. 87 (2001) 167205.
[24] K. Sparta, G.J. Redhammer, P. Roussel, G. Heger, G. Roth, P. Lemmens,
A. Ionescu, M. Grove, G. Guntherodt, F. Hüning, H. Lueken, H. Kageyama,
K. Onizuka, Y. Ueda, Eur. Phys. J. B 19 (2001) 507.
[25] For clarity in the discussion we deﬁne the region below T =34 K as the ‘‘spin
gap’’ regime to address the structural and magnetic changes that occur as aconsequence of the modiﬁcation in population of the singlet and triplet
states. We therefore use this terminology throughout the manuscript.
[26] H. Kageyama, K. Onizuka, T. Yamauchi, Y. Ueda, J. Crystal Growth 206 (1999)
65.

3281

[27] A.C. Larson, R.B.V. Dreele, General Structure Analysis System (GSAS), Los
Alamos National Laboratory Report LAUR 86-748, 1994.
[28] P.W. Stephens, J. Appl. Crystallogr. 32 (1999) 281.
[29] H. Nojiri, H. Kageyama, Y. Ueda, M. Motokawa, J. Phys. Soc. Jpn. 72 (2003) 3243.
[30] J. Goodenough, A. Wold, R.J. Arnott, N. Menyuk, Phys. Rev. 124 (1961) 373.
[31] A. Zorko, D. Arcon, H. van Tol, L.C. Brunel, H. Kageyama, Phys. Rev. B 69 (2004)
174420.
[32] A. Zorko, D. Arcon, H. Kageyama, A. Lappas, Appl. Magn. Reson. 27 (2004) 267.
[33] G.A. Jorge, R. Stern, M. Jaime, N.H. nd J. Bonca, S.E. Shawish, C.D. Batista,
H.A. Dabkowska, B.D. Gaulin, Phys. Rev. B 71 (2005) 092403.
[34] Y. Narumi, N. Terada, Y. Tanaka, M. Iwaki, K. Katsumata, K. Kindo,
H. Kageyama, Y. Ueda, H. Toyokawa, T. Ishikawa, H. Kitamura, J. Phys. Soc.
Jpn. 78 (2009) 043702.
[35] Yu.F. Shepelev, R.S. Bubnova, S.K. Filatov, N.A. Sennova, N.A. Pilneva, J. Solid
State Chem. 178 (2005) 2987.
[36] J.L. Garcia-Munoz, J. Rodriguez-Carvajal, F. Sapina, M.J. Sanchis, R. Ibanex,
D. Beltran-Porter, J. Phys.: Condens. Matter 2 (1990) 2205.