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Competition between Helimagnetism and Commensurate Quantum Spin Correlationsin LiCu2 O2
T. Masuda,1 A. Zheludev,1 A. Bush,2 M. Markina,3 and A. Vasiliev3
1

Condensed Matter Sciences Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6393, USA
2
Moscow Institute of Radiotechnics, Electronics and Automation, Moscow 117464, Russia
3
Low Temperature Physics Department, Moscow State University, Moscow 119992, Russia(Received 6 October 2003; published 29 April 2004)
Neutron diffraction and bulk measurements are used to determine the nature of the low-temperatureordered state in LiCu2 O2 , a S  1=2 spin-chain compound with competing interactions. The spin
structure is found to be helimagnetic, with a propagation vector 0:5; ; 0,   0:174. The nearestneighbor exchange constant and frustration ratio are estimated to be J1  5:8 meV and J2 =J1  0:29,
respectively. For idealized quantum spin chains, these parameter values would signify a gapped spinliquid ground state with commensurate spin correlations. The observed temperature dependence of themagnetic propagation vector in LiCu2 O2 is attributed to a competition between incommensurate
helimagnetism in the classical spin model and commensurability in the quantum case. It is also
proposed that long-range ordering in LiCu2 O2 is facilitated by intrinsic nonstoichiometry.
DOI: 10.1103/PhysRevLett.92.177201

PACS numbers: 75.10.Pq, 75.25.+z, 75.30.Hx

A great deal of attention in magnetism has been recently given to systems with strong geometric frustration[1]. In classical magnets such competing interactions
often result in helimagnetic ground states with incommensurate long-range order [2]. For quantum systems, astrong frustration can destroy long-range order altogether,producing gapped spin-liquid phases and other exotic
states with only local spin correlations. Contrary to intuition, the periods and symmetries of such short-range
correlations are often totally different from those inclassical versions of the same models. Consider the simplest of frustrated magnets, namely, a spin chain withcompeting nearest-neighbor (NN) J1 and next-nearestneighbor (NNN) J2 antiferromagnetic (AF) interactions.
For a   J2 =J1 > 1=4, the classical model has a spinspiral structure with an incommensurate propagation vector q  arccos1=4. In contrast, for the frustration
parameter in the range c  0:24 <  < 0:5, the quantum S  1=2 model is a gapped spin liquid [3] with thecorrelation function peaked at a commensurate q [4]. 3D interactions in real quasi-1D materials tend to
suppress quantum spin fluctuations and restore semiclassical behavior. Frustrated quasi-1D systems thus becomestage to a unique competition between classical incommensurate and quantum commensurate correlations.
Until now, this phenomenon has not been addressed
experimentally, and the behavior of quasi-1D systems
with competing quantum and classical periodicities remains largely unknown. Only a handful of frustratedchain compounds have been identified, including SrCuO2[5], N2 H5 CuCl3 [6], and Cu[2-(2-aminomethyl)pyridine][7]. For the former two systems   1, while for thelatter   0:2 < c . The corresponding quantum andclassical models both have incommensurate or commensurate spin correlations, respectively, and the competition
phenomenon does not occur. Recent studies hint that the

new quasi-one-dimensional charge-ordered material
LiCu2 O2 [8–12] contains S  1=2 spin chains with  inthe range c <  < 0:5, and thus may be an ideal model
system for this investigation. The compound seems topossess characteristics of a spin-liquid state, including a
gap   6 meV in the magnetic excitation spectrum [11],and yet undergoes at least one magnetic ordering transition at Tc  22 K [8,11,12]. To complicate matters, muon
spin resonance studies indicate a precursor transition at
T1  24 K, and recent bulk measurements [11] point toyet another magnetic phase transition at T   9 K. In thepresent work, we use neutron diffraction and additionalbulk measurements to make sense of this complex behavior. We find concrete evidence of competing quantum andclassical periodicities in LiCu2 O2 , and also discuss theimportant role of intrinsic chemical disorder.
As discussed in detail in Refs. [11,12], LiCu2 O2 contains an equal number of Cu and Cu2 ions in distinct
nonequivalent crystallographic positions. The magnetic
Cu2 ions carry S  1=2 and form ‘‘triangular’’ two-leg
ladders (Fig. 1), which can also be viewed as zigzag chainswith competing NN and NNN interactions, JNN and
JNNN , respectively. These chains run along the b axis of
the orthorhombic crystal structure, and are well separated
from each other by double chains of nonmagnetic Li
ions and layers of nonmagnetic Cu sites. One key element of the present work was the preparation of samples
with a thoroughly controlled chemical composition.
Single crystals of LiCu2 O2 were grown in an alundum
crucible in air atmosphere using the self-flux method. The
lattice parameters a  5:7301, b  2:86064, and c  were verified by powder x-ray diffraction,
12:4172 A
which also confirmed the absence of any appreciable
amounts of crystalline impurity phases. All crystals
were found to be microscopically twinned with respect
to the [1,1,0] plane, so that a  2b [12].

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FIG. 1 (color). Crystallographic unit cell of LiCu2 O2 showing
the magnetic Cu2 sites (green balls) and the planar helimagnetic spin structure (arrows) determined in this work.

Unexpectedly, a thermogravimetric analysis revealed
that the samples had lower content of Cu ions thanfollows from the stoichiometric formula Li1  Cu2 
O2 . The density was determined to be   5:12 g=cm3
at room temperature, which corresponds to an actual
composition Li1:16 Cu1:84 O2:01 . Chemical disorder and a
Cu deficiency by as much as x  16% are thus inherently
present. The ‘‘surplus’’ Li ions in Li1:16 Cu1:84 O2:01 occupy Cu2 sites, due to a good match of ionic radii.
Charge compensation requires that the introduction of
16% nonmagnetic Li ions into the double chains isaccompanied by a transfer of 16% of the S 
1=2-carrying Cu2 ions onto the Cu interchain sites.
Thus, our Li1:16 Cu1:84 O2:01 crystals (referred to as simply
LiCu2 O2 throughout the rest of the paper) have appreciable concentrations of both nonmagnetic Li impurities
in the zigzag chains, and magnetic Cu2 impurities positioned in between chains.
The single-crystal samples were characterized using
bulk techniques. T data were taken in a commercial
SQUID magnetometer in the temperature range 5–350 K
and a magnetic field H  100 Oe applied parallel (k ) or
perpendicular (? ) to the a; b cleavage plane (Fig. 2).
The main feature is a broad maximum at T  36 K
characteristic of a quasi-one-dimensional magnet, whichsignifies the formation of short-range correlations within
the chains. Taking the temperature derivative of the magnetic susceptibility (Fig. 2, inset) reveals a sharp anomaly
at Tc  22 K, which we attribute to the onset of longrange magnetic order. The high-temperature part of theT curve is expected to be representative of isolated
zigzag chains. The data taken above T  50 K were therefore analyzed in the framework of the quantum S  1=2
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FIG. 2. Temperature dependence of magnetic susceptibility of
LiCu2 O2 measured in a magnetic field H  100 Oe (symbols).
The solid line is a fit based on the frustrated S  1=2 chain
model, as described in the text. Taking a numerical derivative(inset) reveals a phase transition Tc  22 K (arrow).

frustrated-chain model for which only the high-temperature expansions valid at T * J have been calculated todate [13]. The gyromagnetic ratios gk  2:04 and g? 
2:23 were measured in a separate electron spin resonanceexperiment. The frustration ratio was fixed at the value  0:29, as determined from neutron scattering experiments (see below). With these assumptions excellent fits
are obtained with J1  5:81 meV, as shown in solidlines in Fig. 2.
The anomaly at Tc is also manifest in the specific heatdata measured using a ‘‘Termis’’ quasiadiabatic microcalorimeter and plotted in Fig. 3. The peak observed at
T  Tc is well defined, but, as indicated by arrows in the
blowup plot, actually has a characteristic flattop that
extends between Tc  22 and T1  24 K, in agreementwith the results of Ref. [12]. The solid line in Fig. 3
represents a crude estimate for the phonon contribution.
The temperature dependence of magnetic entropy is plotted in the lower right inset of Fig. 3. Characteristic of alow-dimensional system, a large fraction of the entropy isreleased above the ordering temperature. The sharp 9 K
anomaly reported in Ref. [11] is totally absent in our Tand CT data. We suspect that this feature is due to an
impurity phase, most likely Li2 CuO2 , which is known togo through an AF transition at 9 K [14].
The nature of the magnetically ordered state wasdetermined in a neutron diffraction experiment using
a single-crystal sample prepared with a naturally occurring Li isotope mixture and cut to a thin-plate 0:9 1515 mm3 parallel to the a; b plane. The measurements were performed at the HB1 and HB1A 3-axis
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FIG. 3. The measured temperature dependence of specificheat in LiCu2 O2 (open symbols) indicates a phase transition
at Tc  22 K and a possible precursor at T1  24 K (arrows).
Subtracting the phonon contribution (solid line) allows one to
extract the temperature dependence of magnetic entropy (lower
right inset).

spectrometers installed at the High Flux Isotope Reactor
at ORNL. Integrated Bragg intensities were collected in
2-axis mode, with a well-collimated incident neutron
beam of a fixed energy Ei  14:7 meV produced by apyrolitic graphite PG(002) monochromator. Absorption
corrections were applied assuming a thin-plate geometry.
Additional high-resolution measurements of the magnetic propagation vector were performed in 3-axis
mode, with a PG(002) analyzer and 480 400 400
2400 collimators.
The main finding of this work is that below Tc  22 K
LiCu2 O2 acquires incommensurate magnetic long-rangeorder. The phase transition leads to the appearance of new
Bragg reflections that can be indexed as f2n 
1=2; k  ; lg, n; k; l integer,   0:174. Such peaks
were observed in both crystallographic twins. The peakwidths were found to be resolution limited along all three
crystallographic directions at all temperatures below Tc .
A typical scan across the (0.5, 0.826, 0) reflection taken at
T  2 K is shown in the inset of Fig. 4(a). The corresponding peak intensity is plotted as a function of temperature in Fig. 4(a). A simple power law fit to the datataken above T  15 K yields Tc  22:36 K and  
0:250:07. The residual intensity seen in Fig. 4(a) at T >Tc is due to critical scattering and is not a sharp peak inq space.
Interestingly, the magnetic propagation vector in
LiCu2 O2 is temperature dependent, as was deduced
from Gaussian fits to k scans across the (0.5, 0.826, 0)
peak [Fig. 4(b), symbols]. Below T  17 K, the incommensurability parameter shows little variation andappears to have a strictly incommensurate value  
0:17382. However, as Tc is approached from below,
 progressively decreases as indicated by the arrow in
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FIG. 4. (a) Measured temperature dependence of the (0.5,0.826, 0) magnetic peak intensity in LiCu2 O2 (symbols). The
solid line is a power law fit to the data. Inset: k scan across thisreflection measured at T  2 K. (b) Measured incommensurability parameter  plotted as a function of temperature. The
solid line is a guide for the eye. The arrow indicates the strong
variation of  near Tc .

Fig. 4(b). The minimum value of  observed in our
experiments is about 0.172. Intensity being the limiting
factor, we were unable to locate any magnetic Braggreflections in the narrow temperature range Tc < T <T1 , though several reciprocal-space planes were thoroughly searched.
The spin arrangement in the ordered state was deduced
from the analysis of 23 nonequivalent magnetic Bragg
peaks with 0  h  3:5, 0  k  1:5, and 0  l  8. A
representational analysis of the crystallographic spacegroup with the observed propagation vector [15] showsthat, assuming all the magnetic Cu2 sites carry thesame moment (no spin-density wave), the symmetrycompatible magnetic structures are composed of uniform
planar spin helixes propagating along the double zigzag
chains. The fixed relative rotation angle between consecutive spins is   1 . Any spins related by a translation along the c axis and a axes are parallel andantiparallel to each other, respectively. The orientationof the spin-rotation plane and an overall intensity scaling
factor were refined using a combined reverse Monte Carloand least squares algorithm to best fit the experimental
data. An excellent fit is obtained with all spins confined tothe a; b crystallographic plane, as visualized in Fig. 1.
The relative phases of the spin spirals in the two zigzag chains in each crystallographic unit cell cannot be
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determined due to the presence of q domains. Apart from
that, the determination of the magnetic structure is unambiguous, as are our estimates for the coupling parameters of the proposed model. In an alternative model
recently discussed in Ref. [16], frustration occurs within
individual (rather then double) chains, which can, in
principle, also produce the observed magnetic structure.
However, the estimated coupling constants are incompatible with the observed magnetic propagation vector, andimply an unlikely dominance of NNN Cu-Cu interactions
 distances.
that span over large 5:7 A
In LiCu2 O2 , the competition between commensuratequantum spin fluctuations and the classical tendency toform an incommensurate helimagnetic state is rather
severe. In the ordered phase,  is determined by thebalance of exchange energies, which enables us to directly
estimate the frustration ratio   1=4 cos   0:29.
As previously mentioned, an isolated zigzag chain withsuch  is gapped and has the nonuniform susceptibilityq peaking at the commensurate AF position q 
2 =b. Magnetic ordering of weakly interacting gappedspin chains is commonly described by the chain-mean
field (chain-MF) model. For LiCu2 O2 , one could expect
this approach to work particularly well, as our dataclearly show the dominance of 1D interactions in thismaterial. However, in the chain-MF framework the projection of the magnetic propagation vector onto the chain
axis corresponds to the maximum of bare chain susceptibility, i.e., to   0. Such behavior is in stark contrast to
the one actually observed in LiCu2 O2 , where helimagnetism ultimately wins at low temperatures and  > 0.
A competition between commensurate and incommensurate ground states may be behind the observed T dependence of , which increases as one goes deeper into
the ordered phase. This temperature variation may, inturn, be responsible for one or more ‘‘devil’s staircase’’lock-in transitions, occurring in the narrow range Tc <T < T1 . A series of such transitions, smeared out by
pinning and quenched disorder, and resulting in glassy
states with short-range order, could very well account for
the unusual phase found in this T range and characterized
by a plateau in the measured CT curve.
An important point to emphasize is that interchaininteractions, which are ultimately responsible for longrange ordering in LiCu2 O2 , should be strongly influenced
by the chemical disorder inherently present in our
samples. In particular, they may be mediated by theestimated 16% of magnetic Cu2 impurities positioned
in between the chains. A similar model is realized inRx Y1 x 2 BaNiO5 rare earth nickelates, where classicalR3 ions bridge the Ni-based gapped spin chains [17].
Despite the gap in isolated chains, long-range order occurs for an arbitrary small concentration of impurities[18], and involves ordering of both the impurity spins andthe chain spins. At the present stage, it is difficult to177201-4

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speculate about the implications of such a mechanism
for LiCu2 O2 . Further work is also needed to understandthe effect of a reduced correlation length in the chainsthemselves, due to nonmagnetic Li2 impurities.
By mapping out the spin excitation spectrum, future
inelastic neutron experiments will undoubtedly explain
the apparent failure of the chain-MF approach in
LiCu2 O2 and further our understanding of this uniqueborderline quantum/classical frustrated and disordered
antiferromagnet.
This work was partially supported by RFBR Grants
No. 02-02-17798 and No. 03-02-16108. Work at ORNL
was carried out under DOE Contract No. DE-AC0500OR22725.

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