T. Masuda et al- Cooperative Ordering of Gapped and Gapless Spin Networks in Cu2Fe2Ge4O13

8/3/2019 T. Masuda et al- Cooperative Ordering of Gapped and Gapless Spin Networks in Cu2Fe2Ge4O13

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Cooperative Ordering of Gapped and Gapless Spin Networks in Cu2Fe2Ge4O13

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, USA2CEA-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, Japan4NIST 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 Cu2Fe2Ge4O13are studied using bulk methods, neutron diffraction, and inelastic neutron scattering. It is shown thatthis material can be described in terms of two low-dimensional quantum spin subsystems, one gappedand t he 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 fluctua-tions are often potent enough to completely destroylong-range order even at zero temperature. Quantum dis-

order in systems with a spin gap, also known as quan-tum spin liquids, is particularly robust. These systemsresist spin freezing, i.e., forming a magnetically or-dered state, even in the presence of weak 3-dimensional(3D) interactions or magnetic anisotropy. In contrast,gapless low-dimensional magnets have a quantum-critical g round state and, being extremely sensitive toany external perturbations, can be forced to order moreeasily. Either way, when quasi-low-dimensional magnetsdo order, it typically involves some interesting and exoticphysics. For example, spin freezing may be induced bynonmagnetic [1,2] or magnetic [3] impurities, or by aBose-condensation of magnons induced by an external

magnetic field [46].An alternative ordering mechanism can be envisioned

in a complex material that incorporates two intercalatedlow-dimensional subsystems. Particularly interesting arecases involving a mixture of gapless and gapped entities.If these two spin networks were totally isolated from oneanother, they would remain disordered at any T > 0, dueto their reduced dimensionality [7]. However, arbitraryweak interactions between the two subsystems can dras-tically change this outcome. Divergent one- or two-dimensional correlations in the gapless subsystem, com-bined with short-range correlations in t he thi rd directionpropagated by the subsystem with a gap, will ultimatelycoalesce into a 3D ordered phase at a finite temperature.Provided that interactions between the two subsystemsare relatively weak, this new cooperative ordered statecan be expected to possess some rather unique character-istics. Among these are a strong quantum suppression ofordered moments in the nominally gapped subsystem, acoexistence of conventional spin waves and remanent gapmodes, interactions, and anticrossing between suchexcitations, etc. In the present Letter we report an experi-

mental realization a nd study of this novel cooperativeordering mechanism in the quantum ferrimagnetCu2Fe2Ge4O13.

The crystal structure of Cu2Fe2Ge4O13 [8] can beviewed as a modification of that of the famous spin-Peierls compound CuGeO3 [9]. It consists of t hree d istinctcomponents: crankshaf t-shaped chai ns of edge sharingFeO6 octahedra, Cu-O-Cu dimers, and oligomers of fourGeO4 tetrahedra [8]. The mutual arrangement of thesestructu ral elements is visuali zed in Fig. 1(a) and 1(b). Thespace group is monoclinic, P21=m, with lattice parame-ters 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. Theyare lin ked by GeO4 tetrahedra in c direction and by Cu

2

dimers in the a direction. A plausible network of super-exchange pathways is shown i n Fig. 1(c). The key piece ofinformation required to understand the magnetism ofCu2Fe2Ge4O13 is the hierarchy of the corresponding ex-change constants. Knowing this hierarchy will allow usto formulate the model in terms of spin chains,planes, and dimers.

Single crystals of Cu2Fe2Ge4O13 were grown in O2atmosphere by floating zone method and were character-ized using bulk magnetic susceptibility and heat capacitymeasurements. The T curves measured using a com-mercial SQUID magnetometer in a n H 1000 Oe mag-netic field applied perpendicular and parallel to f110gplane are plotted in open symbols in Fig. 2(a). T hesedata are characteristic of a quasi-low-dimensional anti-ferromagnet: the development of broad maximum at T100 K is followed by an antiferromagnetic phase transi-tion at TN 39 K. This transition is also manifest in theheat capacity data shown in Fig. 2(b) and is the onlyprominent feature in our temperature range.

As a zeroth approximation, the measured suscepti-bility was fit to a sum of two contributions calculated forisolated S 5=2 chains [10] and S 1=2 dimers. The

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best fit is obtained assuming the Cu-Cu and Fe-Fe ex-change 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 by

room-temperature ESR measurements. T he result of thefit is shown in a solid line in Fig. 2, with the dashed anddotted lines representing the Fe chain and Cu dimercomponents, 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 experi-ments on t he CRG-D23 li fting-counter diffractometerat Institute of Laue Langevin. 338 nuclear and 222magnetic independent reflections were collected at T 1:5 K using a 0.3 g sample. The results unambiguouslyindicate an almost antiparallel and slightly cantedspin structure with all spins predominantly in a; ccrystallographic plane, as shown in Fig. 1(c). The propa-gation vector is (0, 0, 0.5). The most important resultpertains to the magnitudes of the ordered moments:mCu 0:384B and mFe 3:623B. The momentsorientations in the standard Cartesian coordinatesystem linked to the crystallographic unit cell were foundto be mCu 0:227; 0:035; 0:301B and mFe 2:163; 0:121; 2:892B, respectively. The temperature

dependence of the magnetic structure was deduced fromthe behavior of 2 1 0:5, 0 2 0:5, 1 1 0:5, and2 1 1:5 Bragg reflections. The evolution of sublatticemoments for Fe3 and Cu2 are shown i n 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 forCu2Fe2Ge4O13 are antiferromagnetic (Fig. 1). Our mainfinding, however, is the drastic suppression of t he orderedmoments on t he Cu2 sites, as compared to their classicalexpectation value of 1B. To explain this behavior wehave to assume that the Cu dimers are effectively isolatedfrom the rest of the system and become only partiallypolarized by the long-range order on the Fe sites. In otherwords, JCu JCuFe, and the Cu

2 moments are reduceddue to strong local quantum spin fluctuations within thedimers. The suppression of the Fe3 moment is less pro-nounced. Th is 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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FIG. 2. (a) Magnetic susceptibility of Cu2Fe2Ge4O13 mea-sured in field applied perpendicular and parallel to cleavedplane (symbols). Solid, dashed and dotted lines are explainedin the text. (b) Heat capacity of Cu2Fe2Ge4O13 in zero field.

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Fe

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FIG. 1 (color). (a) and (b) Crystal structure ofCu2Fe2Ge4O13projected onto a; b and a; c crystallographic planes.(c) Magnetic structure and possible exchange pathways inCu2Fe2Ge4O13.


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structure can be attributed to Dzyaloshinskii-Moriyainteractions and other insignificant anisotropy effects.

The strongly dimerized nature of the Cu2 spins hasone interesting consequence. At the Mean Field level, ifeach dimer is treated as single inseparable entitiy, theordered moment on the Cu sites is seen as being inducedby a n effective external staggered exchange field. It isdetermined by the staggered magnetization functionMH; T for an isolated dimer. Excluding directinterdimer interactions, the exchange field H is propor-tional to the ordered moment on the Fe subsystem,regardless of the internal network of the latter. Assum-

ing that kBT JCu , MH; T MH; 0 M0H. This establishes a unique relation betweenmCu and mFe:

mCu M0mFe; (1)

where JCuFe is the effective Mean Field couplingconstant. For Cu2Fe2Ge4O13, this relation indeed holdsvery well, as shown in the inset of Fig. 3. Here the solidline is a best fit of Eq. (1) to the experimental dataobtained with JCuFe=JCu 0:11.

While the Cu subsystem appears to be well describedas a collection of dimers, the network of Fe3 spins isconsiderably more complicated, with several possibleinteraction pathways i n the b; c plane. To better under-stand these interactions, we performed a series of inelas-tic neutron scattering experiments that probed the low-energy spin excitation spectrum. The data were collectedfor energy t ransfers of up to 10 meV using the SPINS cold3-axis spectrometer installed at the National Institute ofStandards and Technology and the HB1 thermal 3-axisspectrometer at the High Flux Isotope Reactor at OakRidge National Laboratory. Two coaligned single crystal

samples had a total mass of 3.5 g. Several configurationswere exploited, with final neutron energies of 5 meV,3 meV, or 13.5 meV, with several settings of the samplerelative 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 en-ergy width were observed at all wave vectors, as illus-

trated by typical scans shown in Fig. 4(b). At least twoseparate excitation branches are present. Their dispersionalong the a direction was undetectable in our experi-ments. In contrast, the dispersion along the b and c

reciprocal-space axes is quite pronounced. The measureddispersion curves are plotted in symbols in Fig. 4(a).These low-energy data can be explained by conventionalspin wave theory for a 2-dimensional network that in-cudes 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 of

particular values of the 3D magnetic unit cell structurefactors, only two modes produce strong contributions at atime for each of the scans shown. An excellent fit to thedata is obtained assuming JFe 1:602 meV and J

0Fe

0:121 meV, and assuming a small empirical anisotropygap 2:0240 meV. The result of the fit is shown insolid lines in Fig. 4(a). T he obtained value of JFe isconsistent with our previous estimate based on simple-minded fits to magnetic susceptibility data. We concludethat the Fe layers a re indeed to be viewed as chainsrunning along the b crystallographic axis, with onlyweak interchain coupled a long 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 Cu2Fe2Ge4O13. The keypoint is that JFeCu, JFe JCu. As previously explainedin Ref. [3] for the case of R2BaNiO5 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 acous-tic fluctuations of t he Fe3 spins. However, the couplingbetween the two subsystems can not be ignored: it isessential for completing a 3D network of magnetic inter-actions and enabling long-range magnetic ordering at afinite temperature. At low frequencies t he dimers can beintegrated out and replaced by an effective interaction Jeffbetween Fe3 spins along the a axis. Since the staggeredsusceptibility of each Cu dimer is proportional t o 1=JCu,we can estimate Jeff / J

2FeCu=JCu. The absence of spin

wave dispersion along the a axis can thus be explainedeither by the weakness of JFeCu that couples the twosubsystems, or by the large value of JCu.

To summarize, our experiments reveal the unconven-tional cooperative ordering of the low-dimensional quan-

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


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tum spin subsystems of Cu2Fe2Ge4O13 and the persis-tence of quantum spin fluctuations even in the 3D-orderedphase. A very interesting remaining issue is that ofCu2-centered excitations in this material, expected tooccur at higher energy transfers: what happens to thetriplet dimer modes when long-range order sets in? Inthe context of separation of energy scales, they may beexpected 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 formulaCun2Fe2GenO3n1[8]. In these species, the Fe layers

alternate with layers of Cu oligomers of length n 2.Cooperative ordering can be expected in all these mate-rials, but should be qualitatively different in even-n andodd-n members, where the Cu subsystem is either gappedand gapless, respectively.

We than k Dr. Chakoumakos for crystal structure analy-sis 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 t he NSF through Grants No. DMR- 0086210and No. DMR-9986442. Work in Japan was supported inpart by a Grant-in-Aid for COE Research SCP CoupledSystem from the Ministry of Education, Science, Sportsand Culture of Japan.

*Electronic address: [email protected] address: Optical Device Dept. R & D Divisions,The Furukawa Electronic Co., Ltd. 2-4-3, Okano, Nishi-ku, Yokohama, Kanagawa, 220-0073, Japan

Present address: The Institute of Physical and ChemicalResearch (RIKEN ), Wako, Saitama 351-0198, Japan

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[10] M. E. Fisher, A m. J. Phys. 32, 343 (1964).[11] Because of a small a lternation in bond length, t he cou-

pling constant JFe may actually slightly alternate fromone bond to the next. This alternation is apparently tooweak to affect the dispersion relations measured in

this work, and was thus not included in the spin wavecalculation.

[12] A.W. Saenz, Phys. Rev. 125, 1940 (1962).

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FIG. 4. (a) Typical constant-q sca ns col le ct ed i nCu2Fe2Ge4O13 at T 1:4 K for different wave vectors.Shaded Gaussian curves represent the experimental energyresolution. Solid lines are Gaussian fits to the data.(b) Measured dispersion of low-energy spin waves inCu2Fe2Ge4O13 (symbols). Lines represent spin wave theoryfits to the data as described in the text.


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T. Masuda et al- Cooperative Ordering of Gapped and Gapless Spin Networks in Cu2Fe2Ge4O13