Eur. Phys. J. B 19, 507–516 (2001)

THE EUROPEAN
PHYSICAL JOURNAL B
EDP Sciencesc Società Italiana di Fisica
Springer-Verlag 2001

Structural phase transition in the 2D spin dimer compound
SrCu2(BO3)2?
K. Sparta1 , G.J. Redhammer1 , P. Roussel1 , G. Heger1 , G. Roth1,a , P. Lemmens2 , A. Ionescu2 , M. Grove2 ,G. Güntherodt2 , F. Hüning3 , H. Lueken3 , H. Kageyama4, K. Onizuka4 , and Y. Ueda4
1

Institut für Kristallographie, RWTH Aachen, Jägerstr. 17-19, 52056 Aachen, Germany
Physikalisches Institut, RWTH Aachen, Sommerfeldstr., 52056 Aachen, Germany
3Institut für Anorgan. Chemie, Prof.-Pirlet-Str. 1, RWTH Aachen, 52056 Aachen, Germany
4
Institute for Solid State Physics, University of Tokyo, Roppongi 7-22-1, Tokyo 106-8666, Japan
2

Received 24 July 2000 and Received in final form 2 November 2000
Abstract. A displacive, 2nd order structural phase transition at Ts = 395 K from space group I 4 2 m below
Ts to I 4/m c m above Ts has been discovered in the two-dimensional spin dimer compound SrCu2 (BO3 )2 .
The temperature evolution of the structure in both phases has been studied by X-ray diffraction and Raman
scattering, supplemented by differential scanning calorimetry and SQUID magnetometry. The implicationsof this transition and of the observed phonon anomalies in Raman scattering for spin-phonon and interlayer
coupling in this quantum spin system will be discussed.
PACS. 75.10.jm Quantized spin models – 61.10.-i X-ray diffraction and scattering – 78.30.-j Infrared andRaman spectra

1 Introduction
Low dimensional quantum spin systems with a spin gap
and a quantum disordered singlet ground state are at thecenter of research on correlated electron systems. Thisis related to their interesting excitation spectra, divers
phase diagrams as well as a potential relevance for thedescription of superconductivity in weakly doped high-Tc
superconductors. With respect to spin topology, the existence of a singlet ground state in two-dimensional (2D)
spin systems is of special interest. This phenomenon isusually attributed to one-dimensional (1D) spin systems
like dimerized or frustrated Heisenberg spin chains andspin ladders. In 2D spin systems and in the absence ofspin anisotropies, an exotic exchange topology is requiredin order to favor a dimer phase with a spin gap insteadof a long-range magnetically ordered Néel-state. Recently,
the layered compound SrCu2 (BO3 )2 was identified as a
2D S = 1/2 Heisenberg system with a unique exchange
topology and a spin gap [1]. In this system Cu2+ ionsare arranged in the form of dimers that are orthogonallycoupled to each other. This peculiar arrangement leads
to spin frustration and very localized magnon excitations
that have a spin gap of ∆ = 34 K.
A strong interplay between crystal structure and magnetic properties is a well known and characteristic aspectof low dimensional spin systems. The spin-Peierls instabil?

Dedicated to Prof. Dr. Erwin Müller-Hartmann on the occasion of his 60th birthday.
ae-mail: roth@kristall.xtal.rwth-aachen.de

ity of a spin chain system is certainly one example [2]. Dueto a sufficiently strong spin-phonon coupling, a transition
from a homogeneous to a dimerized state with an spin gap
is induced. In addition, pronounced phonon anomalies areobserved depending on the energy of the mode with respect to the energy scale of the magnetic system [3–5].
On the other hand spin-phonon coupling renormalizes themagnetic excitation spectrum. Therefore, a careful analysis of the static and dynamic properties of these systems
is important.
We have performed structural, thermodynamic as well
as spectroscopic investigations on the 2D quantum spin
system SrCu2 (BO3 )2 and demonstrate, for the first time,the existence of a structural phase transition at Ts =395 K. For temperatures below Ts , an anharmonic temperature dependence of an optical phonon is observed.

2 The spin dimer compound SrCu2 (BO3 )2As shown in the original structure determination by Smith
and Keszler [6], SrCu2 (BO3 )2 forms, at room temperature, a tetragonal structure (s.g. I 4 2 m) with layers (inthe a-b-plane) of (BO3 )3− -groups and S = 1/2 Cu2+ ions, with the Sr2+ -ions separating these layers. Figure 1
shows the structure of SrCu2 (BO3 )2 projected along c.
The copper along with the oxygen atoms of the BO3 group form dimers of planar, edge sharing CuO4 -groups.
The spin dimers are connected orthogonally by triangularBO3 -groups.

508

The European Physical Journal B
F

E

D

Fig. 1. Structure of SrCu2 (BO3 )2 , single Cu-BO3 layer projected along c. Black: Cu, dark gray: B, light gray: O, white:
Sr (above / below the layer).

The copper dimer is coordinated from both sides by
two symmetry equivalent oxygens (O2) belonging to thesame BO3 -group in the form of a “chelate”, the bridging oxygens between the two coppers are formed by theremaining third oxygen atom (O1) of the BO3 -group.
The coordination of copper by the rigid BO3 -groups withthreefold symmetry leads to a pronounced angular distortion of the CuO4 square which is rather unusual for a
Cu2+ -containing oxo-cuprate.
The distance between nearest and next-nearest Cu
neighbors in the same layer is 2.9 Å and 5.1 Å, shortest
interlayer distances are 3.5 Å and 4.35 Å at 100 K. The
strength of the resulting antiferromagnetic intradimer andinterdimer exchange coupling within the layer has been
estimated to be J1 = 100 K and J2 = 68 K with theratio x = J2 /J1 = 0.68 [7]. Due to the orthogonal arrangement of the Cu-Cu dimers in the a-b-plane of thecompound, a 2D, strongly frustrated quantum spin system is formed with an interesting exchange topology andexceptional magnetic properties: SrCu2 (BO3 )2 is the first
known representative of the so-called Shastry-Sutherland
lattice with an exact dimer ground state and a large spin
gap [7,8]. Furthermore, SrCu2 (BO3 )2 is very close to aquantum critical point separating the dimer state from agapless Néel-ordered state [7,9,10]. This magnetic ordering is expected for large interdimer coupling J2 where thecritical ratio x = J2 /J1 exceeds x = 0.7. The exchange
topology corresponding to large x is a 2D square latticeof spins as realized, e.g. in the CuO2 -planes of high temperature superconductors.
Recently, the importance of interlayer coupling J⊥ forthe thermodynamic properties at larger temperatures has
been highlighted [11,12]. However, it is also probable that
this coupling renormalizes the excitation spectrum andshifts the quantum critical point. The interlayer coupling
along the c-axis exists despite a similar orthogonal arrangement of dimers with respect to two layers as forthe coupling between dimers within one layer. From mag-netic susceptibility measurements, an appreciable interlayer coupling of x⊥ = J⊥ /J1 = 0.094−0.21 has been
estimated [11,12].
The magnetic susceptibility χ(T ) furthermore supports the existence of a nonmagnetic singlet ground state
and a spin gap. Its temperature dependence shows amaximum at Tmax = 15 K and a rapid decrease toward lower temperatures [1] (Fig. 4). A rather complex
low temperature magnetic excitation spectrum has beenfound using neutron scattering, ESR and Raman scattering [13–15]. It consists of a very flat and only weakly
dispersing triplet branch with a spin gap ∆ = 34 K to
the singlet ground state and an additional second triplet
branch ∆0 = 55 K with a larger dispersion. The second
branch is interpreted as a triplet bound state excitationof two elementary triplets. The binding energy is given
by EB = 2∆ − ∆0 = 13 K. In addition, Raman scattering shows the existence of four well-defined magnetic
modes with energies in the range of 1... 3∆ not identicalwith the neutron scattering results. These Raman modes
show no splitting in an applied magnetic field and are
therefore attributed to collective singlet bound states of
two and three elementary triplets [15]. Similar effects havealso been observed in the quantum spin systems CuGeO3and NaV2 O5 [16–18]. The existence of magnetic boundstates with a finite binding energy is always connectedwith magnon-magnon interaction that is especially strong
in SrCu2 (BO3 )2 due to the frustrating interdimer interaction J2 [11,12,19,20].

3 Experimental
Crystals of SrCu2 (BO3 )2 have been grown from a
LiBO3 -flux as described elsewhere [21]. Single crystal
X-ray diffraction data were collected on an imaging
plate diffractometer (STOE-IPDS, MoKα -radiation, pyrolytic graphite monochromator). The diffractometer was
equipped with a Cryostream liquid N2 -cryostat (100 K...
300 K, accuracy 0.1 K) and a hot gas stream heating stage
mounted on a goniometer head (300 K... 623 K, accuracy
2 K). A total of 22 complete single crystal diffraction data
sets at different temperatures have been collected [22].
Programs X-SHAPE [23] for numerical absorption correction and SHELXL93 [24] for structure refinement were
employed.
Powder X-ray diffraction experiments (Siemens
D500, flat sample, Bragg-Brentano geometry, Gemonochromator, CuKα1 -radiation, furnace with Ptheating element) were performed (T = 298 K... 500 K)
to determine the lattice parameters. To improve the accuracy, silicon was used as an internal standard and lattice
parameters were obtained from full pattern Rietveld refinements. The temperature dependence of the intensityof selected reflections was measured on a 4-circle diffractometer (MoKα -radiation, T = 298 K... 400 K, accuracy
0.5 K).
Raman scattering experiments have been performedin quasi-backscattering geometry with the polarization of

K. Sparta et al.: Structural phase transition in SrCu2 (BO3 )2




F DD FFPFP
FP DD .

 DD .




FPFPFP





.



.



.



.





.
.
.

7HPSHUDWXUH . 









.

































FP,QWHQVLW\ DUEXQLWV ,QWHQVLW\ DUEXQLWV 





.



QQ





509

 ED .

 ED .             
5DPDQVKLIW FP

























5DPDQVKLIW FP 

Fig. 2. Raman spectra of SrCu2 (BO3 )2 in (aa) (upper panel)and (ba) scattering geometry (lower panel) at T = 413 K(above Ts ) and T = 293 K (below Ts ). Arrows point at lines
which vanish upon transition into the high-temperature phase.

Fig. 3. Frequency of the phonon mode with A1 symmetry at
60 cm−1 (at low temperatures) as a function of temperature
between 15 K and 524 K. Inset: Frequency of the mode, normalized to the frequency at T = 15 K.

incident and scattered light in the a-b-plane of the single
crystals. The spectra were recorded with a 488-nm excitation line of an Ar-laser, a Dilor-XY triple-spectrometerand a back-illuminated, liquid-N2 cooled CCD detector.
Magnetic susceptibility between room temperatureand 4.3 K was measured with a SQUID magnetometer.
Differential scanning calorimetry (DSC) measurements
were carried out on a Mac Science DSC3200S analyzer
in the 280–467 K temperature region in air at the same
warming or/and cooling rate of 10 K/min. Approximately
20 mg of finely ground sample was placed in an aluminum
capsule. Calcined alpha-Al2 O3 was used as internal reference standard in air.

shown in the inset of Figure 3 the frequency of this mode
decreases further for higher temperatures. Noteworthy isalso the pronounced increase of the linewidth with temperature (Fig. 3). Upon approaching Ts , this line vanishes
into the “foot” of a quasi-elastic scattering contribution.
For T > Ts the mode and the quasi-elastic scattering are
no longer observable. This behavior points to its possible origin as a soft mode of the transition. From symmetry considerations for temperature T < Ts a mode with
A1 symmetry and for T > Ts a mode with B2u mode is
expected. The latter is not Raman-active and can therefore not be investigated in our experiments. The temperature interval with non-negligible phonon frequency shiftis unusually large in magnitude. These observations point
to an anomalous anharmonicity of the lattice properties.
Our single crystal X-ray diffraction experiments show similar effects in the temperature dependence of the c-axis
lattice parameter and in the z-components of anisotropic
displacement parameters (see below).

4 Raman scattering results
Raman scattering experiments have been performed in thetemperature range from 5–550 K. In Figure 2 measurements for temperatures above and below Ts = 395 K reflect the symmetry change in the disappearance of somemodes for T > Ts (see arrows in Fig. 2). The observed excitations of phonon origin extend from 32 to 1400 cm −1 ,with two-phonon density of states at highest frequencies.
For T < Ts the experimentally observed modes (in the
a-b-plane) divide up into 13 excitations with the symmetries Γab = 8A1 + 2B1 + 3B2 . A symmetry analysis basedon the space group I 4 2 m leads to a number of 24 modes
that are allowed with Γab = 9A1 + 6B1 + 9B2 . The hightemperature structure with the space group I 4/m c mleads to a number of 16 modes that are allowed in Raman
scattering with Γab = 5A1g + 5B1g + 6B2g . A detailed
analysis of the spectra will be presented elsewhere [25].
A pronounced phonon anomaly is observed as function of temperature in the low frequency range, see Figure 3. A mode with A1 symmetry shows a softening in frequency from 62 cm−1 at T = 15 K to 32 cm−1 at RT. As

5 Magnetic and thermodynamic results
SQUID magnetometry (Fig. 4) shows, besides the lowtemperature features already discussed, a small but significant drop of the magnetic susceptibility just below 395 K(see inset in Fig. 4). The step is, as we shall show, theresponse of the magnetic system to a structural phasetransition and reflects the modification of the interlayer
exchange interaction for temperatures below Ts . The magnitude of the step normalized to the maximum of the susceptibility is ∆χ(T )/χmax = 4 × 10−3 . A further discussion of this effect and the interlayer coupling follows in
Section 6.2.
DSC-experiments (differential scanning calorimetry,Fig. 5) are compatible with a second order phase transition close to 395 K with no latent heat associated with it.

510

The European Physical Journal BFPRO PPRO OLQ%*




PRO





F   P PRO


























7 .















7 .





Fig. 4. Molar magnetic susceptibility between 4.3 K and
440 K. Inset: Susceptibility close to Ts after subtraction of alinear background.
Fig. 6. Temperature dependence of reflections (013) and (004).
The continuous line is a fit to the data points for I(013) using
I(T ) = const. × (T − Ts )2β with β = 0.34(1).

Fig. 5. DSC-measurement of SrCu2 (BO3 )2 upon heating.

6 Single crystal X-ray diffraction
6.1 Symmetry and phase transition
SrCu2 (BO3 )2 undergoes a second order phase transitionat 395 K. This transition is characterized by the disappearance of reflections of type 0kl: k and l both odd for
T > Ts . The symmetry of the low temperature phase (I 4
2 m, No. 121) implies the extinction rule 0kl: k + l odd.
The systematic extinctions in the high-temperature phaseare compatible with the centro-symmetric space group I
4/m c m (No. 140) and its non-centrosymmetric subgroups
I 4 c m (No. 108) and I 4 c 2 (No. 120). Currently, no
macroscopic measurements are available which could help
in deciding about the space group of the high temperaturephase. However, structure refinements (see below) in all
three space groups – properly taking into account possible twins for the non-centrosymmetric space groups – giveno reason to choose one of the non-centrosymmetric spacegroups: The R-values do not improve significantly upon
reducing the symmetry and the pronounced anisotropyof the displacement parameters of Cu, O and B is also
not reduced. The identification of inversion twins in the
low temperature phase also clearly points to a centrosymmetric high temperature phase. Furthermore, the disappearance of certain Raman modes (see Fig. 2) is also inline with this symmetry assignment. We therefore conclude that the space group of the high-temperature phaseof SrCu2 (BO3 )2 is I 4/m c m. It is worth noting that the
space group of the low-temperature phase (I 4 2 m) is
a maximal non-isomorphic subgroup of the space groupof the high-temperature phase (I 4/m c m) but not of
the alternative space groups I 4 c m and I 4 c 2. This
group-subgroup relation is one of the prerequisites for theapplication of the Landau-theory for 2nd order phase transitions. As the transition occurs without a change of thecrystal system, the symmetry reduction is accompaniedby the formation of merohedral twins (inversion twins).
The continuous character of the phase transition at
395 K in SrCu2 (BO3 )2 can directly be seen in Figure 6:
Plotted is the intensity of reflection (013) of type 0kl: kand l odd and of an “ordinary” reflection (004) as a function of temperature. The continuous line in Figure 6 is a
fit of the intensity of the (013)-reflection by a power lawof the form I(T ) = const. × (T − Ts )2β . The exponent βamounts to 0.34(1) in accordance (within one standard deviation) with the expected value of 0.33 for a 3-D second
order structural phase transition. Other reflections of type(0kl) with both k and l odd behave similarly, while most of
the “ordinary” reflections gain some intensity upon heating to the transition temperature (Fig. 6). This apparent
transfer of intensity from reflections 0kl with k and l odd
reflects the continuous evolution of the structural distortion (described below) over a broad temperature range
within the low temperature structure. At Ts , the distortion vanishes, as does the intensity transfer and the intensity of the (004)-reflection decreases according to theincrease of the thermal displacements with increasing temperature, leading to the observed “cusp” in Figure 6. The
absence of any significant hysteresis in these experiments

K. Sparta et al.: Structural phase transition in SrCu2 (BO3 )2

















F





F>c@

D





]FRRUGLQDWH

D>c@
























] %






] 2






] &X







511

] 2





7HPSHUDWXUH>.@













7HPSHUDWXUH>.@Fig. 8. Fractional coordinates z of Cu, O2, B, O1 as a functionof the temperature.

(a)





&HOO9ROXPH>c @


























7HPSHUDWXUH>.@(b)
Fig. 7. Lattice parameters a and c (a) and unit cell volume V(b) as a function of temperature from powder X-ray diffraction.

(not shown) is also in line with the assumption of a 2ndorder phase transition.
Figure 7a shows the lattice parameters a and c andFigure 7b the unit cell volume V as a function of temperature. Again in accordance with a second order phase transition, there is no discontinuous change of these quantities
at Ts . Instead, only the slopes δa/δT , δc/δT and δV /δT
are discontinuous at Ts . Notably, the unit cell volume goespractically unaffected through the transition with only avery small change of slope at Ts (Fig. 7b).
The “strange” temperature dependence of the lattice
parameters deserves some additional comments: Above Ts ,the temperature dependence of a and c is dominated by
the linear thermal expansion originating from the anharmonicity of the thermal displacements. We assume thatthe large displacement amplitudes of atoms Cu, O1, O2
and B along c directly correspond to a high degree ofanharmonicity and therefore to the rather large observed
linear expansion coefficient of SrCu2 (BO3 )2 along c ((1/c)∆c/∆T ≈ 2.6×10−5 K−1 ) above Ts . The much smaller linear expansion coefficient along a above Ts (it averages, infact, to almost zero within the limited temperature range
and accuracy of the experiment) would then reflect thesmaller displacement amplitudes and therefore the almost
harmonic character of the vibrations in the a-b-plane (seediscussion of displacement parameters below). These conclusions agree very well with the anomalous properties of
the 60 cm−1 -phonon discussed above.
Below Ts , the anisotropy of the expansion is distinctly
changed: Large expansion coefficient along a, almost zero
expansion along c. We believe this to be due to an
additional contribution to the apparent thermal expansion caused by the continuous internal structural change,
namely the temperature dependent reduction of the corrugation of the Cu-BO3 -layers with increasing T : This effectalone would result in an additional positive contribution
to a as T increases (the layer becomes progressively flatter and a increases as T approaches Ts ) and a negative
contribution to the length of the c-axis (a flat layer takes
less space along c than a corrugated layer). This qualitatively describes the large nonlinear expansion along a
below Ts with its upward curvature close to Ts (due tothe critical behavior of the corrugation angle) as well as
the temperature dependence of the c-lattice parameter,
which is almost constant with a slight drop close to Ts :As the apparent expansion along c is essentially the difference between the “ordinary” positive linear expansion
and the anomalous nonlinear shrinkage along c, the temperature of this drop has no special meaning but is justthe temperature, where the critically increasing negative
contribution overcomes the linear expansion term.
The phase transition can also be discussed in termsof internal structural parameters: In the low temperature
structure – stable from Ts = 395 K down to at least 100 K,
the lowest temperature used in our X-ray diffraction experiments – the Cu-B-O-network is buckled, corresponding to the absence of centrosymmetry (s.g. I 4 2 m). However, the z-coordinates of Cu, B, O1 and O2 are all not
far away from the special value of 0.25. Upon approaching the transition temperature from below, these atoms
move towards the special position on the mirror plane atz = 0.25, which is situated at z = 0 in the space group

512

The European Physical Journal B

D

D

D

2

2

  c    

2

%

D

2
    c    
&X

%

&X

2

2

  c22  %  c2  &X    
&X

%

2

%

2

  c
2

2

2

(c)

(a)
F

F

>C@>C@2

2    c  c22  c

%

2

&X

2

&X

2

%

2

%

2

&X

2

&X

2

2

(b)

(d)

Fig. 9. Projection of the Cu2 (BO3 )2 plaquette: a) along c at 100 K, b) along [110] at 100 K, c) along c at 433 K, d) along [110]at T = 433 K. Inscribed: Selected distances and angles, standard deviations in parentheses.

of the high temperature phase I 4/m c m. Figure 8 shows
this approach to the special position for atoms Cu, B, O1
and O2.
In Figure 9, the central structural element of
SrCu2 (BO3 )2 , the pair of edge sharing CuO4 -groups with
their terminal BO3 -groups, is depicted in two projections
along c (top) and along [110] (bottom) both below (left)
and above (right) Ts . The major difference between thetwo phases is the buckling of the Cu-BO3 -layers which
continuously goes to zero as T approaches Ts . As the corrugation of the Cu-BO3 -network vanishes at the phasetransition, the angle between the normal onto the planes
through the oxygen atoms belonging to the two neighboring CuO4 -“squares” (the “bending angle” of the plaquettes) should be an appropriate internal structural orderparameter. It varies from about 11 ◦ at T = 100 K to 0◦
at Ts = 395 K and also shows a critical exponent close to
0.33 (Fig. 10). On the other hand, the angle between thenormals onto the CuO4 -and the BO3 -plane is almost independent of temperature (Fig. 10) with only a small effectclose to Ts . This observation suggests, that the bending
angle of the neighboring CuO4 -“squares” indeed constitutes the dominant contribution to the observed temperature dependence of the intensities of (0kl)-reflections withboth k and l odd and can serve as an internal order parameter, which vanishes at Ts .
As to the phenomenological classification of the transition it should be noted, that this is very clearly a displacive transition, as opposed to an order-disorder-type ofphase transition: The very shallow potential minimum of
atoms Cu, B, O1 and O2 along c (leading to the large andpresumably anharmonic displacements) which is centeredat the mirror plane above Ts shifts off this special position at and below Ts and becomes steeper as T decreases.

Fig. 10. Angles between the normals onto neighboring molecular planes: CuO4 -CuO4 -bending angle and CuO4 -BO3 -angle
as a function of temperature.

Obviously, the two deformation variants of the Cu-BO3 layer in SrCu2 (BO3 )2 , which are related by a center ofsymmetry, cannot coexist locally (that is, within the coherence volume of the diffraction experiment). Instead, thetwo possible deformation patterns correspond to the twoorientation states of the twin domains which form uponcooling through Ts .
6.2 Low-temperature phase
The results of the original work by Smith and Keszler [6]are confirmed by this study, the quality of the refinement,
however, has been improved by performing an elaborate
numerical absorption correction and by properly taking

K. Sparta et al.: Structural phase transition in SrCu2 (BO3 )2513

Table 1a. Atomic coordinates in the low temperature space group I42m (100 K). Cell parameters: a = 8.982(2) Å, c =6.643(2) Å.
AtomMultiplicity

Wyckoff
letterSitesymmetry

x

y

z

Sr
Cu
B
O1
O2

4
8
8
8
16

c
i
i
i
j

222
m
m
m
1

0
0.11456(5)0.2947(4)0.4003(3)0.3279(3)0.5
0.11456(5)0.2947(4)0.4003(3)0.1453(3)00.2884(1)0.240(1)0.2000(6)0.2568(5)Table 1b. Atomic coordinates in the high temperature space group I4/mcm (433 K). Cell parameters: a = 9.0005(2) Å,c = 6.6546(2) Å.
AtomMultiplicity

Wyckoff
letterSite
Symmetry

x

y

z

Sr
Cu
B
O1
O2

4
8
8
8
16

a
h
h
h
k

422
m2m
m2m
m2m
m

0
0.38597(7)0.2952(7)0.4015(5)0.1728(4)0−0.11403(7)0.2048(7)0.0985(5)−0.1462(4)

0.25
0
0
0
0

Values in parentheses are estimated standard deviations in the last digit [22].

merohedral twinning into account [24]. Also, the temperature dependence of internal (coordinates etc.) as well
as external structural parameters (lattice constants) has
been closely followed by a large number of independentmeasurements and refinements. The volume fraction of themerohedral twins refined to a value of 0.50(0.02), not significantly different from equipartition. Although the deviation from centrosymmetry is rather small, the introduction of twinning does improve the already very good
R-value significantly (weighted R-value for F 2 : 5.77% reduced to 3.97% for the room temperature data set). The
small deviation from centrosymmetry in the low temperature phase and the accompanied presumably small excessenergy in the domain walls is consistent with (incoherent)
microtwinning with a volume fraction close to 0.5.
Table 1 summarizes the structural parameters for thelow- together with those of the high-temperature phase fortwo example temperatures [22]. Within the experimental
error, the BO3 -groups remain planar in the whole temperature range studied. The two symmetry independent
B-O-bond lengths remain very similar to each other andchange very little with temperature. After correction forlibrational shortening, a small apparent shrinkage of thebond lengths still persists (see Fig. 9a and c). The angulardistortion within the BO3 -plane is significant (Fig. 9) but
also virtually temperature independent.
The same applies to the intralayer Cu-O and Cu-Cudistances and to the Cu-O-Cu angle, which is relevant
for the magnetic exchange interaction. Again, a small decrease of the bond lengths with increasing temperature remains even after librational shortening correction. There isa small but significant deviation of the Cu-atom from theFig. 11. Shortest interlayer Cu-Cu distances as a function oftemperature.

plane of its coordinating oxygen atoms: The copper moves
by about 0.05(1)Å to the convex side of the Cu-BO3 plaquette (see Fig. 9). This shift is almost independentof the temperature except very close to the phase transition, where the deviations become larger but also, owing
to the pronounced pseudosymmetry (the extra reflectionsof type (0kl), k and l odd are rather weak close to the transition) increasingly insignificant. Above Ts , the CuO4 - andBO3 -groups are flat and coplanar by symmetry.
The symmetry change at Ts is most clearly seen in
the temperature dependence of the two shortest interlayer
Cu-Cu-distances plotted in Figure 11. Figure 12 shows
the corresponding geometry of the Cu-Cu-arrangement at
100 K. As the corrugation of the Cu-BO3 -layer reduces

514

The European Physical Journal B

%W


%W

%W





%W







%W














%W

%W





E

%W





F
D

















%W


%W




%W

%W



(a)



Fig. 12. Local Cu-Cu-arrangement with corresponding distances (in Å) at 100 K. The distances plotted in Figure 11
are represented as black and white sticks, intra-layer distances: light gray, intermediate inter-layer distances: thin“bond sticks”. Arrows indicate, how the Cu-atoms shift upontransition to the high temperature phase.

upon heating, the shortest interlayer Cu-Cu-distances approach each other and become degenerate in the high temperature phase. It should be noted that these distances
are much shorter than the second shortest Cu-Cu distancein the layer and should therefore also influence the magnetic properties. Indeed, interlayer coupling is now discussed as a relevant parameter of this unusual quantum
spin system. The interlayer exchange coupling constantx⊥ = J⊥ /J1 estimated from an analysis of χ(T ) ranges
from 0.094 to 0.21 [11,12]. To a first approximation, thiscoupling simply reduces the magnetic susceptibility. The
sudden change of the crystal structure for T < Ts , i.e.
the shift of Cu-Cu-distances, allows to test this effect. For
the high temperature phase the equidistance of the layers
should in first order compensate the frustrated interlayer
coupling. In the low temperature phase, however, the coupling between the layers is dominated by the shortest CuCu distance and compensation is cancelled. This is dueto the strong nonlinearity of the exchange coupling withrespect to atomic distances. The decrease of the susceptibility ∆χ(T )/χmax = 4 × 10−3 at T = Ts shown in theinset of Figure 4 directly corresponds to the rapid development of splitting Cu-Cu-distances shown in Figure 11.
Calculations from reference [11] using a frustrated doublelayer model can be used to estimate the sign and an upperboundary for the expected effect on the susceptibility. In
qualitative agreement with our observation a decrease of
the susceptibility ∆χ(T )/χmax = 0.03 is expected if an interlayer interaction of x⊥ = 0.094 is completely switched
off.
Another interesting observation is the fact, that the
pronounced anisotropy of the displacement parameters of(b)Fig. 13. Principal components of the displacement tensors of(a) Cu and (b) O1 along c (U33 ) and a (U11 ).

O1, O2, B and Cu in the high temperature phase is not
spontaneously reduced upon transition to the low temperature phase. Instead, it gradually decreases with decreasing temperature over a very broad temperature range.
The Sr-displacement parameters, on the other hand, areisotropic and stay so over the whole temperature range
studied, in the high- as well as in the low-temperature
structure. The plot of the principal components of thedisplacement tensors of atoms Cu and O1 as a functionof temperature looks rather unusual. Figure 13 shows U11(along a) and U33 (along c) of Cu and O1. The anisotropy
U33 /U11 increases from 3:1 at low temperatures to about
15:1 well above Ts . The components U33 along the c-axis
vary nonlinearly with T below Ts . This suggests, thateither anharmonicities or a continuous evolution of thelocal potential close to Ts (or both) play a role. Given
the high absorption coefficient of the title compound
even for MoKα -radiation, a detailed discussion seems inappropriate at this stage. The question of anharmonic

K. Sparta et al.: Structural phase transition in SrCu2 (BO3 )2

displacement parameters will be addressed in a forthcoming paper on the basis of single crystal neutron diffractiondata.
6.3 High-temperature phase
Considerable effort was spent on the various possible alternative descriptions of the high temperature phase, assuming that I 4/m c m would only be a pseudo-symmetry: Ourfinal model in I 4/m c m with its pronounced anisotropic
displacement parameters was compared to a split isotropic
model in which atoms Cu, O1, O2 and B were split alongc according to the mirror plane perpendicular to c andrefined with isotropic displacement parameters. The maximum split amounts to about 0.52(4) Å for z(O1) at 100 K.
This description resulted in practically no improvementof the R-values as compared to the non-split anisotropic
model but has the disadvantage of the physically dubious
occurrence of half atoms with unphysically short distances
and is therefore not considered to be useful.
The description of the structure of the high temperature phase in the two non-centrosymmetric space groups
I 4 c m and I 4 c 2, which are as well compatible with theobserved extinction rules, was also considered: Refinementwith anisotropic displacement parameters and the corresponding twins lead again to no improvement of the Rvalues with respect to the I 4/m c m model. Also, strong
correlations between various parameters and large standard deviations of the twinning ratio indicate that this description as a pseudo-symmetry problem is not adequate.
Moreover, such a description does not significantly reduce
the anisotropic displacement parameters. Finally, nothingis gained also by a description with split isotropic atoms
in space groups I 4 c m and I 4 c 2 and the corresponding
twins.
This leads to the conclusion that there is no reason whatsoever to choose a space group other than I
4/m c m for describing the high temperature phase of
SrCu2 (BO3 )2 . Due to the mirror plane perpendicular tothe c-axis in space group I 4/m c m, both the BO3 - groupas well as the pair of edge sharing CuO4 -groups are required by symmetry to be flat and coplanar. In-plane B-O
and Cu-O distances are again essentially temperature independent (see Fig. 9 for the respective values at 433 K).
All out of plane distances are of course dominated by the
steep increase of the c-lattice parameter above Ts .
Within the CuO4 -groups, the displacement parametersof the atoms increase from O2, the outer edge, shared with
the BO3 -group, through Cu to O1, the common edge ofthe two neighboring CuO4 -groups (Fig. 9). This suggests a
rigid-body bending motion of this group with the O2-O2edge as a libration axis and increasing displacement amplitudes with increasing distance from that axis: Smaller
displacements along c for O2, intermediate displacements
for Cu and the largest displacements for O1. We believethat this is directly related to the structural instabilityof the high temperature phase that subsequently leads tothe second order phase transition to the low temperaturephase at 395 K.

515

7 Conclusions
We have discovered and characterized a structural phasetransition in the spin-dimer compound SrCu2 (BO3 )2 at
Ts = 395 K by single crystal and powder X-ray diffraction,
by Raman scattering and also by magnetometry and DSC.
The low temperature structure has been re-determined
and refined at several different temperatures between Ts =395 K and 100 K taking merohedral twinning into account.
The high temperature phase of SrCu2 (BO3 )2 has been
described for the first time. The continuous, 2nd order,
displacive structural phase transition is characterized by atemperature dependent tilt of the two neighboring CuO4 squares sharing a common edge. The tilt vanishes at andabove Ts .
The relevance of this transition also for the low temperature properties of SrCu2 (BO3 )2 is twofold: Firstly, thecontinuous structural changes connected with the transition extend over a very large temperature range in thestability field of the low temperature phase. We therefore
consider it important to know the temperature evolutionof the structure in detail. Only this allows to accurately
describe the structural foundations of the low temperaturemagnetic properties of SrCu2 (BO3 )2 . This is even more so,
because the magnetic properties of SrCu2 (BO3 )2 are dominated by competing exchange interactions, a situation inwhich symmetry plays an important role and even small
structural distortions could drastically alter the magnetic
ground state. We whish to emphasize that the main distortions we are discussing in this paper are corrugationsof the Cu-BO3 -layer. As these are not distortions within
the a-b-plane they presumably do not influence the intralayer exchange or its ratio x. However, they shouldhave a stronger impact on the interlayer interaction. In
fact, this interaction along c is most strongly influenced
by the phase transition described here, as is clearly shownby the step in the magnetic susceptibility. Comparing thiseffect with recent calculations [11], a reasonable agreement
is found in sign and magnitude of the step, which further
corroborates our interpretation. Secondly, as a further important consequence of the symmetry change at the phasetransition, the merohedral twinning needs to be taken into
account in the interpretation of any measurement that issensitive to such spatially coexisting orientation states.
The presence of the resulting internal boundaries – presumably in high concentrations – also needs to be kept inmind in interpreting defect sensitive solid state properties.
We acknowledge fruitful discussions with G.S. Uhrig and C.
Gros and financial support by the Deutsche Forschungsgemeinschaft (DFG) within SFB 341. The work in Tokyo was supported by a Grant-in-Aid for Encouragement Young Scientists
from The Ministry of Education, Science, Sports and Culture.
K.S. acknowledges financial support within the joint programof the Deutsche DFG on “Quantum effects in electronically
low-dimensional transition metal compounds” under grant HE
3034/2-1. G.J.R. gratefully acknowledges the financial supportof the Humboldt-Foundation.

516

The European Physical Journal B

References
1. 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, 3168 (1999) and H. Kageyama,
J. Phys. Soc. Jpn 69, 65 (2000).
2. J.W. Bray, L.V. Iterrante, I.S. Jacobs, J.C. Bonner, The
Spin-Peierls Transition, in Extended Linear Chain Compounds, Chap. 7, edited by J.S. Miller (Plenum Press, NewYork 1983), pp. 353–415.
3. G. Uhrig, Phys. Rev. B 57, 14004 (1998).
4. C. Gros, R. Werner, Phys. Rev. B 58, 14677 (1998).
5. M. Grove, P. Lemmens, G. Güntherodt, B.C. Sales, F.
Büllesfeld, W. Assmus, Phys. Rev. B 61, 6126 (2000).
6. R.W. Smith, D.A. Keszler, J. Solid State Chem. 93, 430(1991).
7. S. Miyahara, K. Ueda, Phys. Rev. Lett. 82, 3701 (1999).
8. B.S. Shastry, B. Sutherland, Physica B 108, 1069 (1981).
9. Z. Weihong, C.J. Hamer, J. Oitmaa, Phys. Rev. B 60, 6608
(1999).
10. E. Müller-Hartmann, R.R.P. Singh, Ch. Knetter, G.S.
Uhrig, Phys. Rev. Lett. 84, 1808 (2000).
11. Sh. Miyahara, K. Ueda, submitted to J. Phys. Soc. Jpn,
cond-mat/0004260.
12. Ch. Knetter, A. Bühler, E. Müller-Hartmann, G.S. Uhrig,
Phys. Rev. Lett. 85, 3958 (2000).
13. H. Kageyama, M. Nishi, N. Aso, K. Onizuka, T.
Yoshihama, K. Nukui, K. Kodama, K. Kakurai, Y. Ueda,
Phys. Rev. Lett. 84, 5876 (2000).
14. H. Nojiri, H. Kageyama, K. Oniduka, Y. Ueda,

M. Motokawa, J. Phys. Soc. Jpn 68, 2906 (1999).
15. P. Lemmens, M. Grove, M. Fischer, G. Güntherodt, V.N.
Kotov, H. Kageyama, K. Onizuka, Y. Ueda, Phys. Rev.
Lett. 85, 2605 (2000).
16. G. Els, P.H.M.v. Loosdrecht, P. Lemmens, H. Vonberg,
G. Güntherodt, G.S. Uhrig, O. Fujita, J. Akimitsu, G.
Dhalenne, A. Revcolevschi, Phys. Rev. Lett. 79, 5138
(1997).
17. P. Lemmens, M. Fischer, G. Els, G. Güntherodt, A.S.
Mishchenko, M. Weiden, R. Hauptmann, C. Geibel, F.
Steglich, Phys. Rev. B 58, 14159-62 (1998).
18. P. Lemmens, M. Fischer, G. Els, G. Güntherodt, M.
Weiden, C. Geibel, F. Steglich, Physica B 259-261, 1050
(1999).
19. G.S. Uhrig, H.J. Schulz, Phys. Rev. B 54, 9624 (1996).
20. G. Bouzerar, A.P. Kampf, G.I. Japaridze, Phys. Rev. B
58, 3117 (1998).
21. H. Kageyama, K. Onizuka, T. Yamauchi, Y. Ueda, J.
Crystal Growth 206, 65 (1999).
22. The complete data for all temperatures is available fromthe correspondence author upon request. Data will also bedeposited in the ICSD crystallographic data base.
23. X-SHAPE and X-RED: Programs for the optimization of
the crystal shape (w.r.t. the merging R-value) and numerical absorption correction, Stoe & Cie, 1996.
24. SHELXL93, Program package for structure refinement,
G.M. Sheldrick, Göttingen 1993.
25. K.-Y. Choi, P. Lemmens, G. Güntherodt, Y. Pashkevich,
K. Sparta, G. Roth, H. Kageyama, K. Onizuka, Y. Ueda,
in preparation.