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Cooperative Ordering of Gapped and Gapless Spin Networks in Cu2 Fe2 Ge4 O13
T. Masuda,1,* A. Zheludev,1 B. Grenier,2 S. Imai,3,† K. Uchinokura,3,‡ E. Ressouche,2 and S. Park4
1Condensed Matter Science Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee, 37831-6393, USA
2CEA-Grenoble, DRFMC / SPSMS / MDN, 17 rue des Martyrs, 38054 Grenoble, Cedex, France
3Department of Advanced Materials Science, University of Tokyo, 5-1-5, Kashiwa-no-ha, Kashiwa, 277-8581, Japan
4
NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, Maryland, 20899, USA(Received 20 April 2004; published 9 August 2004)
The unusual magnetic properties of a novel low-dimensional quantum ferrimagnet Cu2 Fe2 Ge4 O13
are studied using bulk methods, neutron diffraction, and inelastic neutron scattering. It is shown that
this material can be described in terms of two low-dimensional quantum spin subsystems, one gapped
and the other gapless, characterized by two distinct energy scales. Long-range magnetic orderingobserved at low temperatures is a cooperative phenomenon caused by weak coupling of these two spinnetworks.
DOI: 10.1103/PhysRevLett.93.077202

PACS numbers: 75.10.Jm, 75.25.+z, 75.50.Ee

In low-dimensional magnets, quantum spin fluctuations are often potent enough to completely destroy
long-range order even at zero temperature. Quantum disorder in systems with a spin gap, also known as ‘‘quantum spin liquids,’’ is particularly robust. These systems
resist ‘‘spin freezing,’’ i.e., forming a magnetically ordered state, even in the presence of weak 3-dimensional(3D) interactions or magnetic anisotropy. In contrast,
gapless low-dimensional magnets have a quantumcritical ground state and, being extremely sensitive toany external perturbations, can be forced to order moreeasily. Either way, when quasi-low-dimensional magnets
do order, it typically involves some interesting and exotic
physics. For example, spin freezing may be induced bynonmagnetic [1,2] or magnetic [3] impurities, or by a
Bose-condensation of magnons induced by an external
magnetic field [4 –6].
An alternative ordering mechanism can be envisioned
in a complex material that incorporates two intercalated
low-dimensional subsystems. Particularly interesting arecases involving a mixture of gapless and gapped entities.
If these two spin networks were totally isolated from one
another, they would remain disordered at any T > 0, due
to their reduced dimensionality [7]. However, arbitrary
weak interactions between the two subsystems can drastically change this outcome. Divergent one- or twodimensional correlations in the gapless subsystem, combined with short-range correlations in the third direction
propagated by the subsystem with a gap, will ultimately
coalesce into a 3D ordered phase at a finite temperature.
Provided that interactions between the two subsystems
are relatively weak, this new cooperative ordered state
can be expected to possess some rather unique characteristics. Among these are a strong quantum suppression ofordered moments in the nominally gapped subsystem, acoexistence of conventional spin waves and remanent gap
modes, interactions, and ‘‘anticrossing’’ between such
excitations, etc. In the present Letter we report an experi-mental realization and study of this novel cooperative
ordering mechanism in the quantum ferrimagnet
Cu2 Fe2 Ge4 O13 .
The crystal structure of Cu2 Fe2 Ge4 O13 [8] can beviewed as a modification of that of the famous spinPeierls compound CuGeO3 [9]. It consists of three distinct
components: ‘‘crankshaft’’-shaped chains of edge sharing
FeO6 octahedra, Cu-O-Cu dimers, and oligomers of four
GeO4 tetrahedra [8]. The mutual arrangement of thesestructural elements is visualized in Fig. 1(a) and 1(b). Thespace group is monoclinic, P21 =m, with lattice parameters a  12:101, b  8:497, c  4:869, and  96:131 .
Fe3 and Cu2 carry S  5=2 and S  1=2, respectively.
The crankshaft FeO6 chains run along the b axis. They
are linked by GeO4 tetrahedra in c direction and by Cu2
dimers in the a direction. A plausible network of superexchange pathways is shown in Fig. 1(c). The key piece of
information required to understand the magnetism of
Cu2 Fe2 Ge4 O13 is the hierarchy of the corresponding exchange constants. Knowing this hierarchy will allow usto formulate the model in terms of spin ‘‘chains,’’‘‘planes,’’ and ‘‘dimers.’’
Single crystals of Cu2 Fe2 Ge4 O13 were grown in O2
atmosphere by floating zone method and were characterized using bulk magnetic susceptibility and heat capacity
measurements. The T curves measured using a commercial SQUID magnetometer in an H  1000 Oe magnetic field applied perpendicular and parallel to f110g
plane are plotted in open symbols in Fig. 2(a). These
data are characteristic of a quasi-low-dimensional antiferromagnet: the development of broad maximum at T 
100 K is followed by an antiferromagnetic phase transition at TN  39 K. This transition is also manifest in theheat capacity data shown in Fig. 2(b) and is the only
prominent feature in our temperature range.
As a ‘‘zeroth approximation,’’ the measured susceptibility was fit to a sum of two contributions calculated for
isolated S  5=2 chains [10] and S  1=2 dimers. The

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3.0
62.0

3.0

χ (10-2Ge 42.0
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H = 1000 Oe
H ⊥ {1,1,0}
H // {1,1,0}

TN1.0(c)
0.0
0

20

4060

50

100

150

200

0.0

3+0250300

T(K)Cu-Fe2+(b)

400

300
80

-1-1C (Jmol K )

Cu

FeFe

200

60
40100

FIG. 1 (color). (a) and (b) Crystal structure of Cu2 Fe2 Ge4 O13
projected onto a; b and a; c crystallographic planes.
(c) Magnetic structure and possible exchange pathways inCu2 Fe2 Ge4 O13 .

best fit is obtained assuming the Cu-Cu and Fe-Fe exchange constants to be JCu  25 MeV and JFe 
1:7 MeV, respectively. The average gyromagnetic ratioof Cu2 and Fe3 is determined to be g  2:04 byroom-temperature ESR measurements. The result of thefit is shown in a solid line in Fig. 2, with the dashed anddotted lines representing the Fe chain and Cu dimer
components, correspondingly. Though rather crude, thissimple analysis gives us a rough idea of the magnitude ofthe relevant exchange constants.
The spin arrangement in the magnetically orderedstate was determined by neutron diffraction experiments on the CRG-D23 lifting-counter diffractometerat Institute of Laue Langevin. 338 nuclear and 222
magnetic independent reflections were collected at T 
1:5 K using a 0.3 g sample. The results unambiguously
indicate an almost antiparallel and slightly canted
spin structure with all spins predominantly in a; ccrystallographic plane, as shown in Fig. 1(c). The propagation vector is (0, 0, 0.5). The most important result
pertains to the magnitudes of the ordered moments:mCu  0:384B and mFe  3:623B . The moment’s
orientations in the standard Cartesian coordinate
system linked to the crystallographic unit cell were foundto be mCu   0:227; 0:035; 0:301B and mFe 2:163; 0:121; 2:892B , respectively. The temperature
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100

150

200

250

300

T (K)

FIG. 2. (a) Magnetic susceptibility of Cu2 Fe2 Ge4 O13 measured in field applied perpendicular and parallel to cleaved
plane (symbols). Solid, dashed and dotted lines are explainedin the text. (b) Heat capacity of Cu2 Fe2 Ge4 O13 in zero field.

dependence of the magnetic structure was deduced fromthe behavior of 2 10:5, 0 2 0:5,  1 1 0:5, and 2 1 1:5 Bragg reflections. The evolution of sublattice
moments for Fe3 and Cu2 are shown in the main panelof Fig. 3. They were determined under the assumption thatall spin orientations are T-independent.
The observed antiparallel spin arrangement indicatesthat all the exchange constants in our model forCu2 Fe2 Ge4 O13 are antiferromagnetic (Fig. 1). Our main
finding, however, is the drastic suppression of the orderedmoments on the Cu2 sites, as compared to their classicalexpectation value of 1B . To explain this behavior wehave to assume that the Cu dimers are effectively isolated
from the rest of the system and become only partiallypolarized by the long-range order on the Fe sites. In other
JCu Fe , and the Cu2 moments are reduced
words, JCu
due to strong local quantum spin fluctuations within thedimers. The suppression of the Fe3 moment is less pronounced. This is undoubtedly due to the large value of theFe3 spin and allows us to regard the Fe subsystem as asemiclassical one. The observed small canting of the spin
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Fe moment
Cu moment
3.0

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0.0
0.0

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ExperimentDimer

mCu (µB)

m (µB)

0.4

0

1.0

10

2.0
mFe (µB)

3.0

4.0

20
T (K)

30

40

FIG. 3. Measured temperature dependence of the Fe3 - andCu2 -ordered moments (main panel). Inset: ordered moment on
the Cu2 sites plotted vs. that on Fe3 . The solid line is a fit tothe staggered magnetization curve for an isolated dimer.

structure can be attributed to Dzyaloshinskii-Moriya
interactions and other insignificant anisotropy effects.
The strongly dimerized nature of the Cu2 spins has
one interesting consequence. At the Mean Field level, if
each dimer is treated as single inseparable entitiy, theordered moment on the Cu sites is seen as being induced
by an effective external staggered exchange field. It isdetermined by the staggered magnetization functionM H ; T for an isolated dimer. Excluding directinterdimer interactions, the exchange field H is proportional to the ordered moment on the Fe subsystem,
regardless of the internal network of the latter. Assuming that kB T
JCu , M H ; T M H ; 00M H . This establishes a unique relation between
mCu and mFe :0mFe ;mCu  M(1)

where   JCu Fe is the effective Mean Field coupling
constant. For Cu2 Fe2 Ge4 O13 , this relation indeed holds
very well, as shown in the inset of Fig. 3. Here the solidline is a best fit of Eq. (1) to the experimental dataobtained with JCu Fe =JCu  0:11.
While the Cu subsystem appears to be well described
as a collection of dimers, the network of Fe3 spins is
considerably more complicated, with several possible
interaction pathways in the b; c plane. To better understand these interactions, we performed a series of inelastic neutron scattering experiments that probed the lowenergy spin excitation spectrum. The data were collectedfor energy transfers of up to 10 meV using the SPINS cold
3-axis spectrometer installed at the National Institute ofStandards and Technology and the HB1 thermal 3-axis
spectrometer at the High Flux Isotope Reactor at Oak
Ridge National Laboratory. Two coaligned single crystal
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samples had a total mass of 3.5 g. Several configurations
were exploited, with final neutron energies of 5 meV,
3 meV, or 13.5 meV, with several settings of the sample
relative to the scattering plane. A detailed report of thesemeasurements will be published elsewhere, and only themain results will be summarized here.
Sharp spin wave excitations of resolution-limited energy width were observed at all wave vectors, as illustrated by typical scans shown in Fig. 4(b). At least two
separate excitation branches are present. Their dispersion
along the a direction was undetectable in our experiments. In contrast, the dispersion along the b and c
reciprocal-space axes is quite pronounced. The measured
dispersion curves are plotted in symbols in Fig. 4(a).
These low-energy data can be explained by conventional
spin wave theory for a 2-dimensional network that incudes only the Fe3 spins, and direct Fe-Fe exchangeinteractions shown in Fig. 1 [11]. Dispersion curves forthis model were calculated as explained in Ref. [12]. Witheight Fe3 ions per magnetic unit cell there are actuallyfour two-fold degenerate spin wave branches. Because ofparticular values of the 3D magnetic unit cell structure
factors, only two modes produce strong contributions at atime for each of the scans shown. An excellent fit to the0 data is obtained assuming JFe  1:602 meV and JFe
0:121 meV, and assuming a small empirical anisotropy
gap   2:0240 meV. The result of the fit is shown insolid lines in Fig. 4(a). The obtained value of JFe isconsistent with our previous estimate based on simpleminded fits to magnetic susceptibility data. We conclude
that the Fe layers are indeed to be viewed as chainsrunning along the b crystallographic axis, with only
weak interchain coupled along the c direction.
The fact that the low-energy excitations are entirely
due to the Fe3 moments confirms the main idea behindour ‘‘two-subsystem’’ model for Cu2 Fe2 Ge4 O13 . The key
point is that JFe Cu , JFe
JCu . As previously explainedin Ref. [3] for the case of R2 BaNiO5 nickelates, such ahierarchy of exchange constants leads to a separation ofenergy scales of magnetic excitations. The Cu centered(dimer) excitations are confined to high frequencies,
while low frequencies are entirely dominated by ‘‘acoustic’’ fluctuations of the Fe3 spins. However, the coupling
between the two subsystems can not be ignored: it isessential for completing a 3D network of magnetic interactions and enabling long-range magnetic ordering at afinite temperature. At low frequencies the dimers can beintegrated out and replaced by an effective interaction Jeff
between Fe3 spins along the a axis. Since the staggered
susceptibility of each Cu dimer is proportional to 1=JCu ,2
we can estimate Jeff / JFe
Cu =JCu . The absence of spinwave dispersion along the a axis can thus be explained
either by the weakness of JFe Cu that couples the twosubsystems, or by the large value of JCu .
To summarize, our experiments reveal the unconventional cooperative ordering of the low-dimensional quan077202-3

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FIG. 4. (a) Typical constant-q scans collected inCu2 Fe2 Ge4 O13 at T  1:4 K for different wave vectors.
Shaded Gaussian curves represent the experimental energy
resolution. Solid lines are Gaussian fits to the data.
(b) Measured dispersion of low-energy spin waves in
Cu2 Fe2 Ge4 O13 (symbols). Lines represent spin wave theory
fits to the data as described in the text.

tum spin subsystems of Cu2 Fe2 Ge4 O13 and the persistence of quantum spin fluctuations even in the 3D-orderedphase. A very interesting remaining issue is that of
Cu2 -centered excitations in this material, expected tooccur at higher energy transfers: what happens to thetriplet dimer modes when long-range order sets in? In
the context of separation of energy scales, they may be
expected to survive in the ordered state. In this case, atleast one member of the triplet will have longitudinalpolarization, and therefore be totally incompatible withconvectional spin wave theory. Another exciting avenue
for future studies are other members of the hypotheticalfamily of compounds with the general formulaCun 2 Fe2 Gen O3n1 [8]. In these species, the Fe layers

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alternate with layers of Cu oligomers of length n 2.
Cooperative ordering can be expected in all these materials, but should be qualitatively different in even-n andodd-n members, where the Cu subsystem is either gappedand gapless, respectively.
We thank Dr. Chakoumakos for crystal structure analysis in the early stage of this study. Work at ORNL wascarried out under Contract No. DE-AC05-00OR22725,
U.S. Department of Energy. Experiments at NIST weresupported by the NSF through Grants No. DMR-0086210
and No. DMR-9986442. Work in Japan was supported inpart by a Grant-in-Aid for COE Research ‘‘SCP Coupled
System’’ from the Ministry of Education, Science, Sports
and Culture of Japan.

*Electronic address: masudat@ornl.gov†
Present address: Optical Device Dept. R & D Divisions,
The Furukawa Electronic Co., Ltd. 2-4-3, Okano, Nishiku, Yokohama, Kanagawa, 220-0073, Japan‡Present address: The Institute of Physical and Chemical
Research (RIKEN), Wako, Saitama 351-0198, Japan[1] M. Hase, I. Terasaki, Y. Sasago, K. Uchinokura, andH. Obara, Phys. Rev. Lett. 71, 4059 (1993).
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A. Zheludev, T. Hayashi, N. Miura, and P. Böni, Phys.
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[4] Z. Honda, H. Asakawa, and K. Katsumata, Phys. Rev.
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[6] Y. Chen, Z. Honda, A. Zheludev, C. Broholm,
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[8] T. Masuda, B. C. Chakoumakos, C. L. Nygren, S. Imai,and K. Uchinokura, J. Solid State Chem. 176, 175 (2003).
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[11] Because of a small alternation in bond length, the coupling constant JFe may actually slightly alternate fromone bond to the next. This alternation is apparently too
weak to affect the dispersion relations measured inthis work, and was thus not included in the spin wave
calculation.
[12] A.W. Sáenz, Phys. Rev. 125, 1940 (1962).

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