PHYSICAL REVIEW B 74, 054418 共2006兲

Magnetic excitation in the spin-gap compound Cu2Sc2Ge4O13: Comparison to Cu2Fe2Ge4O13
T. Masuda1,* and G. J. Redhammer2
1International Graduate School of Arts and Sciences, Yokohama City University, 22-2, Seto, Kanazawa-ku, Yokohama City,Kanagawa 236-0027, Japan
Department of Material Science, Division of Mineralogy, University of Salzburg, Hellbrunnerstr. 34, Salzburg A-5020, Austria
共Received 27 April 2006; revised manuscript received 3 July 2006; published 16 August 2006兲

2The compound Cu2Sc2Ge4O13 is presented as a member of the family of weakly coupled spin chain anddimer compounds Cu2M 2Ge4O13. Magnetic susceptibility, heat capacity, and neutron inelastic-scattering measurements reveal that the compound has the same spin dimer component as Cu2Fe2Ge4O13. The observed
narrow-band excitation in bulk measurements is consistent with spin-gap behavior. The energy scale of theweakly coupled dimers in the Sc compound is perfectly coincident with that in the Fe compound.
DOI: 10.1103/PhysRevB.74.054418

PACS number共s兲: 75.10.Jm, 75.25.⫹z, 75.50.EeI. INTRODUCTION

In the last few decades, low-dimensional spin frameworks
have played key roles in condensed-matter science. Some of
the remarkable phenomena on such spin frameworks include
high critical temperature superconductivity in doped twodimensional antiferromagnets,1,2 exotic superconductivity inspin ladders,3,4 and multiferroics in frustrated compounds.5 A
fundamental topic from the point of magnetism underlying
these phenomena is the order or disorder in the ground state.
In some spin frameworks, the ground state is strongly disordered by quantum fluctuation and is characterized by associated spin-gap excitation. The spin liquid state, on the otherhand, is relatively robust with respect to external perturbation, and thus the spin correlation remains short-ranged evenat zero temperature. In conventional networks, such as chainsor planes with gapless excitation, the ordered states are induced at finite temperatures.
Bicomponent systems combining these distinct spinframeworks have recently been realized experimentally using
R2BaNiO5,6,7 Cu2Fe2Ge4O13,8 and Cu2CdB2O6.9 In the cooperative ordered state of such bicomponent systems, one component is strongly bound to a nonmagnetic singlet state,while the other maintains the usual ordered state. The weakly
coupled compound of Cu dimers and Fe chains,
Cu2Fe2Ge4O13, exhibits two spin excitations with separate
energy scales, clearly observable by neutron-scatteringexperiment.10 In the low-energy range below 10 meV, theexcitations are well explained by effectively coupled Fechains. The dimers behave as media that transfer exchange
coupling between Fe chains, and the intradimer interaction
can be included in effective interchain coupling. At higher
energy, the dispersionless excitation observed at ប␻⬃ 24 meV is qualitatively explained by the effect of Cudimers. The discovery of a member of the bicomponent compound family has been eagerly awaited in order to continue
systematic study of exotic types of ordering.
One of the present authors 共G.J.R.兲 recently identified theisostructural compound Cu2Sc2Ge4O13.11 The crystal structure is monoclinic, with structural parameters a= 12.336共2兲 Å, b = 8.7034共9兲 Å, c = 4.8883共8兲 Å, and ␤= 95.74共2兲, and space group P21 / m. A schematic drawing ofthe structure is shown in Fig. 1. The crankshaft chains ofFeO6 in Cu2Fe2Ge4O13 are replaced by nonmagnetic ScO61098-0121/2006/74共5兲/054418共4兲

chains, and the remnant Cu dimers are separated by GeO4
tetrahedra and ScO6 chains. All dimers are equivalent. On
the basis of this crystallography, Cu2Sc2Ge4O13 is a candidate for a monocomponent system with a single spin-gap
framework analogous to that of Cu2Fe2Ge4O13. In thepresent study, Cu2Sc2Ge4O13 is characterized by a combination of bulk measurements and thermal neutron-scatteringexperiment. Supplemental bulk measurements are also performed on the corresponding Fe compound in order to refine
the estimated exchange constants. It is demonstrated thatCu2Sc2Ge4O13 and Cu2Fe2Ge4O13 are ideal compounds forthe systematic study of bicomponent systems with spin-gap
and gapless frameworks.
II. EXPERIMENTAL DETAILSA polycrystalline sample of Cu2Sc2Ge4O13 was preparedby a solid-state reaction route.11 A high-quality sample wasobtained after several regrind and reheat procedures. As thecompound exhibits incongruent melting, a single crystal is
not available at present. For the Fe compound, a single crystal was obtained by the floating zone method, and 20 mg ofthe crystal was carefully cut from the rod-shaped bulk crystal
so as to ensure that the surface would be free of magnetic
impurities. The crystallographic c direction of these com-

FIG. 1. 共Color online兲 Crystal structure of isostructural compounds Cu2Sc2Ge4O13 and Cu2Fe2Ge4O13.

054418-1©2006 The American Physical Society

PHYSICAL REVIEW B 74, 054418 共2006兲

T. MASUDA AND G. J. REDHAMMER

FIG. 2. Magnetic susceptibility of Cu2Sc2Ge4O13. Dotted line
denotes theoretical calculation 共see text兲. Inset shows heat capacity
in zero field.

pounds is determined by the edge of a pair of cleavage
planes 兵1 1 0其. The magnetic susceptibility of both the Sc andFe compounds was measured under a 1000-Oe field using acommercial superconducting quantum interference device
magnetometer 共MPMS, Quantum Design Co. Ltd.兲. Heatcapacity measurements were performed using a commercial
calorimeter 共PPMS, Quantum Design Co. Ltd.兲. For theneutron-scattering experiment, 50 g of the Sc polycrystallinesample was placed in an Al can. The neutron inelasticscattering experiment was performed using the PONTA spectrometer installed by ISSP University of Tokyo at the 5G
beamline of JRR3 JAEA Tokai. Sollar collimation was employed in open-40⬘-40⬘-80⬘ configuration with E f= 13.5 meV, and a pyrolytic graphite filter was inserted after
the sample to eliminate contamination from higher harmonics. A closed-cycle helium refrigerator was used to achieve
low temperatures. Spurious peaks due to the Sc incoherent
scattering, which were accidentally observed in the case of2ki = 3k f , is subtracted from all constant-q scans. A vanadiumincoherent scan was performed to verify the calculations ofinstrumental resolution.
III. RESULTS

The magnetic susceptibility of Cu2Sc2Ge4O13 after Curie
term subtraction is shown in Fig. 2. A broad maximum at
170 K and a dramatic decrease at low temperature are observed. No phase transition was detected down to 2 K. This
thermally activated behavior suggests the existence of a spin
gap. The heat capacity in the zero field is shown in the inset.
The absence of a phase transition was consistently confirmedin these scans.
A series of constant-q scans at 5 K is shown in Fig. 3共a兲.
The scans are shown after linear background subtraction.
Well-defined peaks can be observed at energy transfer of
25 meV over all values of q. The peak width is close to thatof the calculated resolution function, and the peak energy ofthe present compound is coincident with that of the corresponding Fe compound.10 The constant-energy scan at ប␻FIG. 3. 共a兲 Constant-q scans at 5 K. Black solid lines denotesimple Gaussian fits, shaded areas represent instrumental resolution,and gray lines denote dimer excitation in the Fe compound fromRef. 10. 共b兲 Constant-energy scan at 5 K. Solid lines denote theoretical calculation 共see text兲.

= 25 meV is shown in Fig. 3共b兲 after background subtraction.
We used the constant-q scan at ប␻ = 20 meV as the background. The intensity exhibits a monotonic weakening withincreasing q. The temperature dependence of the energy scanat q = 3 Å−1 is shown in Fig. 4共a兲. Well-defined peaks withconstant width are observable up to 300 K. The temperaturedependence of the integrated intensity for the Sc compoundis summarized in Fig. 4共b兲.
The magnetic susceptibility of Cu2Fe2Ge4O13 is shown inFig. 5. While the behavior is qualitatively consistent withthat seen in the previous study on the Fe compound,8 theabsolute magnitude of the high-temperature susceptibility isapproximately 15% lower. As care was taken in the present
study to ensure that there would be no magnetic impurities
on the freshly cut bulk crystal surface, it is considered thatthe larger susceptibility results obtained previously were affected by a temperature-independent susceptibility component attributable to magnetic impurities on the surface of thebulk crystal.
Prior to obtaining the present data, the magnetic easy axis
was identified by measuring the angular dependence of themagnetization around the b axis 关Fig. 5共a兲兴. Enhanced modulation was observed in the a-c plane. The c and a* axes
approximately correspond to angles of 180° and 90°, respectively. The easy axis was identified by a minima in magnetization located approximately 45° from the c axis. This result is consistent with the magnetic structure analysis
conducted previously for the Fe compound.8
The magnetic susceptibility in the easy and hard directions is shown in Fig. 5共b兲. The marked decrease in susceptibility in the easy direction at ⱗ40 K is ascribed to the Néeltransition. The anisotropic behavior of typical antiferromag-054418-2

PHYSICAL REVIEW B 74, 054418 共2006兲

MAGNETIC EXCITATION IN THE SPIN-GAP¼FIG. 4. 共a兲 Temperature scans for Sc compound 共open circles兲
and Fe compound 共gray lines兲 共Ref. 8兲, obtained at q = 3 Å−1 andq = 2.3 Å−1, respectively. Solid lines denote Gaussian fits. 共b兲 Temperature dependence of integrated intensity for Cu2Sc2Ge4O13.
Solid line denotes theoretical calculation.

FIG. 5. 共a兲 Angular dependence of magnetization in
Cu2Fe2Ge4O13 共180° is roughly coincident with crystallographic caxis兲. 共b兲 Magnetic susceptibility of Cu2Fe2Ge4O13 in field oriented
parallel to the magnetic easy and hard axes. Solid, dashed, anddotted lines denote theoretical calculations 共see text兲.

nets is clearly observed in the hard direction. The existenceof a single anomaly over the entire temperature region meansthat the transition is a cooperative ordering in the bicomponent system. In the high-temperature region, enhancement ofshort-range antiferromagnetic correlation is indicated by thebroad maximum around 100 K. As discussed below, the totalsusceptibility can be explained by the sum of Fe coupledchain and Cu dimer components.

1d 2␴
sin qd ␦共ប␻ − JCu兲.
⬀ A共T兲兩f共q兲兩2 1 −d⍀d␻qd

IV. ANALYSIS AND DISCUSSION

Consistent with the crystallography, a spin dimer model isemployed to describe the magnetic susceptibility of the Sc
compound, as given by␹cu =Ng2␮B2.
kBT共eJCu/kBT + 3兲

共1兲

Here N is the number of Cu ions, g is gyromagnetic ratio,and JCu is the intradimer interaction. The fit to the data isquite reasonable 共dashed line, Fig. 2兲 with parameters of g= 2.02 and JCu = 25.共4兲 meV.14 The dimer energy is close tothat of the Cu mode observed in Cu2Fe2Ge4O13 in the previous neutron-scattering study.8 The spin framework ofCu2Sc2Ge4O13 is thus equivalent to the Cu dimers inCu2Fe2Ge4O13. The neutron cross section for spin dimers12 isgiven by冉冊共2兲

The powder average is included in the above formula. An
intradimer distance 共d兲 of 3.01 Å is adopted here consistent
with the crystallography 共Fig. 1兲. Here, f共q兲 is the magnetic
form factor of Cu2+ ions and A共T兲 is a temperature scaling
factor proportional to the thermal distribution of the singlet
ground state, 1 / 关1 + 3 exp共−JCu / kBT兲兴.
The dispersionless excitations observed in the series ofconstant-q scans 关Fig. 3共a兲兴 is consistent with the descriptionof Eq. 共2兲, and the equation affords a JCu value of24.共5兲 meV in agreement with the susceptibility measurements. The monotonic decrease and slight shoulder structure
seen in the constant-energy scan is also reproduced well by
this formula 关Fig. 3共b兲兴. The temperature dependence of integrated intensity 关Fig. 4共b兲兴 is further consistent with thecalculation using this value of JCu = 24.共5兲 meV. As the energy width in the constant-q scans appears to be greater than
the instrumental resolution 关Fig. 3共a兲兴, the dimers are weakly
coupled. Interdimer interaction is included by replacing thedelta function in Eq. 共2兲 with Gaussian and Lorentzian peakfunctions. The fitting is reasonable for both cases, affording
an estimated intrinsic width of 3.0– 5.0 meV. This range represents the bandwidth for Cu dimer excitation inCu2Sc2Ge4O13.

054418-3

PHYSICAL REVIEW B 74, 054418 共2006兲

T. MASUDA AND G. J. REDHAMMERIn Cu2Fe2Ge4O13 the energy scales of Fe and Cu spinframeworks are well separated.10 The magnetic susceptibilityin such a case can thus be described by the sum of individualcontributions. In the lower energy range, the chain meanfield RPA 共Ref. 13兲 theory is employed for effectivelycoupled Fe spin chains. Here, Cu dimers between Fe chainsare included in the effective interchain coupling. It is assumed that Fe chains on the b axis are isotropically coupledwith a coordination number z of 4. The uniform magnetic
susceptibility is then given by

␹Fe =

␹0
⬘ ␹0
1 − zJFe

共3兲

where JFe and JFe⬘ are inchain and interchain interactions and␹0 is the susceptibility of isolated classical spin chains.15 Inthe high-energy range, the Cu dimer framework dominates
the excitation. The interdimer interaction is small as suggested by the dispersionless excitation.8 It is therefore assumed that the susceptibility can be expressed by the sum ofEqs. 共3兲 and 共1兲.
Fitting of the model to the Fe compound was performedby fixing the Cu dimer parameters to that of the Sc compound. An excellent fit to the data was thus obtained 关Fig.
5共b兲兴, yielding parameters of JFe = 1.6共8兲 meV and JFe⬘
= 0.17共1兲 meV. These values are consistent with the previous
neutron results.10 The data and associated fitting results showthat Cu2Fe2Ge4O13 is a bicomponent system, and that
Cu2Sc2Ge4O13 has the same dimer component as the Fecompound.
The obtained exchange parameters are summarized inTable I. The perfect coincidence between JCu of the Sc andFe compounds shows that the Sc compound has the samespin dimer framework as the Fe compound. The remarkabledifference between Cu modes in cooperative ordering andthe spin liquid can also be observed from the respective temperature dependences. The peak observed for the Fe compound becomes substantially broader with increasing tem-*Previous address: Condensed Matter Science Division, Oak Ridge
National Laboratory, Oak Ridge, TN 37831-6393, USA. Electronic address: tmasuda@yokohama-cu.ac.jp
1 J. G. Bednorz and K. A. Müller, Z. Phys. B: Condens. Matter 64,
189 共1986兲.
2 Y. Tokura, H. Takagi, and S. Uchida, Nature 共London兲 337, 345
共1989兲.
3
E. Dagotto, J. Riera, and D. Scalapino, Phys. Rev. B 45, 5744
共1992兲.
4
M. Uehara, T. Nagata, J. Akimitsu, H. Takahashi, N. Môri, and K.
Kinoshita, J. Phys. Soc. Jpn. 65, 12199 共1996兲.
5G. Lawes, A. B. Harris, T. Kimura, N. Rogado, R. J. Cava, A.
Aharony, O. Entin-Wohlman, T. Yildrim, M. Kenzelmann, C.
Broholm et al., Phys. Rev. Lett. 95, 087205 共2005兲.
6
A. Zheludev, E. Ressouche, S. Maslov, T. Yokoo, S. Raymond,and J. Akimitsu, Phys. Rev. Lett. 80, 3630 共1998兲.
7
A. Zheludev, J. P. Hill, and D. J. Buttrey, Phys. Rev. B 54, 7216

TABLE I. Exchange parameters for Cu2Sc2Ge4O13 andCu2Fe2Ge4O13.

Sc 共bulk兲
Sc 共neutron兲
Fe 共bulk兲
Fe 共neutron, Ref. 8兲

JCuJFeJFe⬘

25.共4兲 meV
24.共5兲 meV
25.共4兲 meV
24.共2兲 meV

1.6共8兲 meV
1.60共2兲 meV

0.17共1兲 meV
0.12共1兲 meV

perature 关Fig. 4共a兲兴. This mode appears to be influenced by
the magnetic ordering at 40 K.
V. CONCLUSION

In summary, a combination of bulk measurements andneutron-scattering experiment revealed that Cu2Sc2Ge4O13 isa monocomponent compound of Cu2Fe2Ge4O13. All data
were consistently explained by a weakly coupled dimermodel. The perfect coincidence in the values of JCu demonstrates that Cu2M 2Ge4O13 共M = Fe and Sc兲 is a rare experimental realization of cooperative ordering and an associatedspin-liquid state.
ACKNOWLEDGMENTS

The authors express their great appreciation to R. Jin andB. C. Sales for heat-capacity measurements, and A. Zheludev
for fruitful discussion in the early stage of this study. The
technical help of M. Matsuura, S. Watanabe, and K. Hirota inneutron-scattering experiment is also gratefully acknowledged. This work was supported by a grant under the 2005
Strategic Research Project 共Grant No. W17003 and Grant
No. K17028兲 of Yokohama City University, Japan, and by agrant to G.J.R. from the Fond zur Foerderung der wissenschaftlichen Forschung 共FWF兲, Austria 共Grant No. R33N10兲. This work was also partially supported by Oak Ridge
National Laboratory 共ORNL兲 funding under Contract No.
DEAC05-00OR22725 共U. S. Department of Energy兲.

共1996兲.
T. Masuda, A. Zheludev, B. Grenier, S. Imai, K. Uchinokura, E.
Ressouche, and S. Park, Phys. Rev. Lett. 93, 077202 共2004兲.
9M. Hase, M. Kohno, H. Kitazawa, O. Suzuki, K. Ozawa, G. Kido,
M. Imai, and X. Hu, Phys. Rev. B 72, 172412 共2005兲.
10T. Masuda, A. Zheludev, B. Sales, S. Imai, K. Uchinokura, and S.
Park, Phys. Rev. B 72, 094434 共2005兲.
11G. J. Redhammer and G. Roth, J. Solid State Chem. 177, 2714
共2004兲.
12 A. Furrer and H. U. Gudel, J. Magn. Magn. Mater. 14, 256
共1979兲.
13 D. J. Scalapino, Y. Imry, and P. Pincus, Phys. Rev. B 11, 2042
共1975兲.
14 In this paper the exchange constants J’s are defined by H
= J兺iSi · Si+1.
15 M. E. Fisher, Am. J. Phys. 32, 343 共1964兲.
8054418-4