PRL 96, 047210 (2006)

PHYSICAL REVIEW LETTERS

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Dynamics of Composite Haldane Spin Chains in IPA-CuCl3
T. Masuda,1,* A. Zheludev,1,† H. Manaka,2 L.-P. Regnault,3 J.-H. Chung,4,‡ and Y. Qiu4,‡1

Condensed Matter Science Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6393, USA
Graduate School of Science and Engineering, Kagoshima University, Korimoto, Kagoshima 890-0065, Japan
3
CEA-Grenoble, DRFMC-SPSMS-MDN, 17 rue des Martyrs, 38054 Grenoble Cedex 9, France
4
NCNR, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA(Received 5 November 2005; published 2 February 2006)

2

Magnetic excitations in the quasi-one-dimensional antiferromagnet IPA-CuCl3 are studied by cold
neutron inelastic scattering. Strongly dispersive gap excitations are observed. Contrary to previously
proposed models, the system is best described as an asymmetric quantum spin ladder. The observed
spectrum is interpreted in terms of composite Haldane spin chains. The key difference from actual S  1chains is a sharp cutoff of the single-magnon spectrum at a certain critical wave vector.
DOI: 10.1103/PhysRevLett.96.047210

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

Antiferromagnetic 2-leg spin (S  1=2) ladders and theclosely related S  1 Haldane spin chains [1,2] are an
example of quantum disorder and mass generation in extended spin networks. In these quantum spin liquids, themagnetism is suppressed due to collective zero-point fluctuations and the unique topology of one dimension (1D),rather than to finite system size. Spin ladders play a keyrole in the dynamics of stripe phases in high-temperature
superconductors [3] and under certain conditions canthemselves support exotic types of superconductivity [4].
On a more fundamental level they are ideal models forstudying the collective spin dynamics in 1D, quantum
critical points and phase transitions in external magnetic
fields, and the effects of quenched disorder.
Despite the wealth of relevant theoretical results, experimental studies are lagging behind because of a shortage of suitable model compounds. In the best known
ladder examples Sr14 Cu24 O41 [5] and SrCu2 O3 [6] the large
energy scales of magnetic interactions limit spectroscopic studies, especially at high fields. A typical problem with many known Haldane-gap systems [7,8] is a large
single-ion magnetic anisotropy that is often associated withS  1 spins, and qualitatively affects the dynamics andfield behavior [9]. Moreover, a Haldane spin chain intrinsically has a smaller Hilbert space than S  1=2 spin ladders, and therefore lacks certain very interesting spectralfeatures [10]. In this Letter we report the discovery of
an isotropic ladder spin network in the S  1=2 compound CH3 2 CHNH3 CuCl3 (IPA-CuCl3 ), that was previously thought to be a prototypical ferromagneticantiferromagnetic (F-AF) spin chain [11]. We use inelastic
neutron scattering to study its magnetic excitation spectrum. The experiments reveal a spectacular truncation of
the magnon branch at certain critical wave vectors that we
attributed to peculiarities of magnon interactions.
IPA-CuCl3 crystallizes in a triclinic space group P1 with
 b  9:705 A, c  6:083 A,   97:62 ,a  7:766 A,  101:05 , and   67:28 [11]. The key features ofthe structure are shown in Fig. 1. The magnetism is due to0031-9007=06=96(4)=047210(4)$23.00

S  1=2-carrying Cu2 ions arranged in sheets parallel tothe a; c crystallographic plane. These sheets are well
separated by nonmagnetic organic layers. A spin gap of  1:5 meV in IPA-CuCl3 was first discovered by
Manaka et al. [11] in T measurements. This value isconsistent with the critical field Hc  11 T that induces anordered antiferromagnetic phase at low temperatures [12].
The gap was attributed to a singlet ground state of bondalternating Cu2 chains running along the crystallographic
c axis, as shown by the dotted line in Fig. 1. Indeed, thismodel consistently explained all magnetization curves and
ESR experiments, with a quantitative agreement obtained
assuming alternating F-AF bonds [11]. An F coupling
between nearest-neighbor Cu2 sites J1 < 0 [13] is consistent with the relevant Cu-Cl-Cu bond angles in the
crystal structure of IPA-CuCl3 .
At the center of the present work are inelastic neutron
scattering experiments on deuterated IPA-CuCl3 samples,
prepared by crystallization from solution [11]. The T

FIG. 1 (color). Layers of magnetic Cu2 (red) and the bridging
Cl ions (cyan) in IPA-CuCl3 . Previously proposed alternating
Cu chains (dotted line) run along the c axis. Actual asymmetricspin ladders (shaded) are parallel to the a direction. The ladderrungs are defined by the vector d.

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PHYSICAL REVIEW LETTERS

and ESR data for the deuterated samples agree well withthose for the nondeuterated ones. Twenty single crystals
with total mass of 3.5 g were coaligned to a mosaic spreadof 4. The data were collected using cold-neutron 3-axis
spectrometers NG5-SPINS in NIST and IN12 in ILL, andat the Disc Chopper time-of-flight spectrometer (DCS) at
NIST [14]. The sample was mounted with the a; c crystallographic plane parallel to the scattering plane of the
instruments and maintained at or below T  1:5 K. On
SPINS we utilized (guide)—80’—80’—(open) collimations and a BeO filter after the sample for a fixed-final
neutron energy Ef  3:7 meV, selected by a flat pyrolitic
graphite analyzer. On IN-12 a Soller collimator of 60’ wasused only at presample position. A Be filter was positioned
after the sample. Neutrons of fixed-incident Ei  4:7 meVor fixed-final Ef  3:5 meV energies were used in conjunction with a horizontally focusing pyrolitic graphite
analyzer. A constant background (typically 1:5 counts=
min , depending on configuration) was subtracted fromall 3-axis data sets. On the DCS instrument the data weretaken with Ei  6:7 meV neutrons, the incident beam
forming an angle of 60 with the a direction. The background was directly measured by removing the sample
from the cryostat.
A series of constant-E and constant-q scans revealed
well-defined long-lived magnetic gap excitations in a largepart of the Brillouin zone in IPA-CuCl3 . Typical data areshown in Fig. 2. Our measurements unambiguously showthat the magnetic strong-coupling direction in IPA-CuCl3
is along the crystallographic a axis. The global dispersion
minimum is at q  2n1
2 ; 0; 0 with n integer [Fig. 3(a)],and also corresponds to a maximum of observed inelastic
intensity. In contrast, the dispersion along the c axis israther weak, with an energy minimum at l  0 in Fig. 3(b).
The originally proposed model of bond-alternating F-AF
chains running along the crystallographic c axis is thus

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totally inconsistent with our results. Nevertheless, themeasured gap energy   1:2 meV is in agreement withthat deduced from bulk measurements.
In the wave vector range 0:2 h 0:8 and 1:2 h
1:8, where sharp magnon peaks were observed, the 3-axis
data were analyzed using a model single-mode (SM) crosssection, with an empirical spin-gap dispersion relation[15], slightly modified to accommodate a transverse dispersion:Sq; ! / SSM q!  !q ;(1)!2q  !20 cos2 h  2  4b20 sin2 l sin2 h
 c20 sin2 2h;(2)where q  ha  kb  lc . The gap is equal to  at l 
0, and is allowed to slightly oscillate along c with atransverse bandwidth b0 . The boundary energy corresponds to !0 . The cross section was numerically convoluted with the spectrometer resolution function calculated
in the Popovici approximation [16] and fit to the experimental data. The magnetic form factor for Cu2 ions wasbuilt into the fits. Separate coefficients SSM q were used
for each constant-q scan to determine the 3-dimensional
structure factor in the most model-independent manner
possible. The parameters of the dispersion relation in
Eq. (2) were treated as global for all the collected scans.
The fitting procedure yielded !0  4:089 meV,  
1:171 meV, b0  0:671 meV, and c0  2:159 meV.
Scans simulated using these parameter values are shown as
shaded areas in Figs. 2(b)–2(d). The dispersion relations
are plotted in solid lines in Fig. 3. Symbols in these plots
were obtained in fits to individual scans, as opposed to
global fits to the measured data. Figure 4(a) shows the ldependence of the single-mode component of the dynamic
structure factor SSM q measured at h  0:5. The h depen-

FIG. 2 (color). Time-of-flight (a) and 3-axis (b), (c), (d) inelastic neutron data measured in IPA-CuCl3 at T  1:5 K. The
suppression of inelastic intensity at h 0:5 in (a) is due to a large l (momentum transfer along c ) and the FM-dimer structure
factor for the magnon branch (see text). For h > 0:5, l is small at all times: jlj < 0:2. In (b), (c), (d) the shaded areas are calculated peak
shapes due to resolution.

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PHYSICAL REVIEW LETTERS

FIG. 3 (color online). Magnon dispersion measured in
IPA-CuCl3 along the a (a) and c (b) directions (symbols).
Heavy solid lines are fits, as described in the text. In (a) thelabeled shaded areas (green online) indicate the domain of the 2magnon continuum. Solid arrows show the positions of scans in
Figs. 2(c) and 2(d). Dashed arrows show the critical wave
vectors.

dence of this structure factor for l  0 is shown in
Fig. 4(b).
The measured c-axis modulation of the magnon intensity is exactly explained by a ferromagnetic dimer with aparticular spin separation d in the crystal structure (Fig. 1):d  0:0854; 0:1316; 0:4432. The data on the h 2n1
reciprocal-space rods are very well reproduced by2
assuming SSM q / cos2 hdx  ldz =!q , as shown by
the solid line in Fig. 4(a). To a good approximation one canthus describe IPA-CuCl3 in terms of uniform chains madeup of these ferromagnetically correlated spin pairs. The
chains run along the crystallographic a axis and are composed of effective S  1 spins. Since the single-mode[Fig. 4(b)], theintensity has its maximum at h  2n12correlations between the nearest-neighbor effective S  1
spins are predominantly antiferromagnetic. If one assumes
that near the magnetic zone center a dominant fraction of
the total spectral weight is contained in the single-mode
excitations, one can reproduce the measured h dependence
of intensity with only nearest-neighbor AF interactions in
the S  1 chains. For this model Sh / sin2 h=!h ,which is in good agreement with experiment [solid line
in Fig. 4(b)]. We conclude that the singlet ground state in
IPA-CuCl3 and the gap excitations are due to composite
S  1 Haldane spin chains that run perpendicular to theoriginally proposed bond-alternating chains directions.
As shown in Fig. 1 the crystal structure of IPA-CuCl3
presents a number of possible AF superexchange routes

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FIG. 4 (color online). Measured l (a) and h dependencies (b)of single-magnon excitation intensities in IPA-CuCl3 (symbols).
Solid lines are simulations, as described in the text.

between Cu2 spins along the a axis. In the most generalcase, the appropriate model for IPA-CuCl3 is a spin ladderwith F rung interactions J1 , a leg coupling constant J2 , anda diagonal exchange interaction of magnitude J3 (presumably also AF). If this interaction were infinitely strong, themapping onto a Haldane spin chain would be exact. In fact,
the measured dispersion differs from that for an ideal S 
1 chain. In the latter, the ratio of the spin wave velocity v
to the gap energy  is v=  6 [17]. In contrast, in
IPA-CuCl3 v=  3:1, about twice as small. The analogy
with Haldane spin chains is thus only qualitative, and thejJ1 j is probably of the same order of magnitude as J2 andJ3 . Without a direct comparison with first-principle calculations, the exact values of the exchange constants can not
be deduced from the measured dispersion and intensity
modulation of the single-magnon excitations. The observed small dispersion of magnetic excitations along thec direction indicates a weak coupling J4 between individual ladders (Fig. 1). From the position of the dispersion
minimum we conclude that J4 < 0.
A remarkable feature of the measured spectrum is theabrupt disappearance of the magnon branch at a certain
critical wave vector qc . This phenomenon is well illustrated by the time-of-flight data of Fig. 2(a). The sharp gap
excitation extends to h  12  hc  0:8, where hc  0:3,
and then vanishes abruptly, rather than persisting to thezone boundary at h  1. Constant-q 3-axis data reveal
similar behavior at the equivalent wave vector h 32  hc  1:2. The well-defined resolution-limited peakseen at h  1:2 [Fig. 2(c)] is weakened and broadened ath  1:15 [Fig. 2(d), where the shaded area is the simulated

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PHYSICAL REVIEW LETTERS

profile for a resolution-limited peak], and is totally absent
at h  1:1 (not shown).
Such a dramatic spectrum termination phenomenon has
been recently discovered and investigated in the quasi-2Dmaterial PHCC [18]. To our knowledge, IPA-CuCl3 is the
only other known spin-gap material with a similar feature.
The effect can be explained by a coupling between singlemagnon and multimagnon states [18–20]. The domain of
the two-magnon continuum in IPA-CuCl3 , though invisible
in our experiments due to low intensity and a very tightenergy resolution, can be calculated using the measured
one-magnon dispersion. As represented by the labeled(green online) shaded areas in Fig. 3(a), the continuum
has a gap of 2. Note that the single-magnon branchcrosses into the 2-magnon continuum at exactly h 2n1
hc . Energy and momentum conservation laws for2
bid any single-magnon excitation outside the domain to
decay into bunches of multiple magnons. For 2n1
2  hc <2n1
h < 2  hc the magnons in IPA-CuCl3 are thus stable.
Their contribution to the dynamic structure factor are sharp
-function peaks. This restriction is removed for magnons
inside the continuum: they are rendered unstable throughdecaying into pairs of lower-energy magnons. Their energy
width (inverse lifetime) is dramatically increased. In
IPA-CuCl3 this effect is particularly strong, and for 2n1
2 

h
there
are
no
detectablesingle-magnon
hc < h < 2n1c2states.
What drives the decay process is interactions between
magnons. Interestingly, in an ideal symmetric spin ladderthe matrix elements between single-magnon and 2-magnon
states are exactly zero, so the single mode survives inside
the 2-magnon continuum [19,20]. In particular, in an isotropic Haldane spin chain stable magnons are expected topersist all the way to the zone-boundary. We can speculatethat the abrupt disappearance of the magnon branch in
IPA-CuCl3 , which distinguishes these composite Haldane
spin chains from actual ones, is due to a symmetrybreaking diagonal interaction J3 .
Contrary to what was previously thought, IPA-CuCl3 isa beautiful asymmetric spin ladder system, that for many
purposes can be seen as a ‘‘composite’’ Haldane spin
chain. Unlike an ideal Haldane spin chain, though, itfeatures a spectacular end-of-spectrum effect at a certain
critical wave vector. Future neutron work will focus on a
direct observation of excitation continua, effects of highmagnetic field, and Br-dilution.
We thank M. Stone, I. Zaliznyak, and M. Zhitomirsky
for insightful discussions. S. Raymond is appreciated for
his experimental support at ILL. Work at ORNL wascarried out under Contract No. DE-AC05-00OR22725,
US Department of Energy. T. M. was partially supportedby the US - Japan Cooperative Research Program on
Neutron Scattering between the US DOE and Japanese
MEXT. The work at NIST is supported by the National

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Science Foundation under Agreements No. DMR9986442, No. DMR-0086210, and No. DMR-0454672.

*Electronic address: tmasuda@yokohama-cu.ac.jp
Present address: International Graduate School of Arts andSciences, Yokohama City University, 22-2, Seto,
Kanazawa-ku, Yokohama city, Kanagawa, 236-0027,
Japan.
†
Electronic address: zheludevai@ornl.gov
Present address: Department of Materials Science andEngineering, University of Maryland, College Park, MD,
20742, USA.
‡
Present address: Department of Materials Science andEngineering, University of Maryland, College Park, MD,
20742, USA.
[1] F. D. M. Haldane, Phys. Lett. 93A, 464 (1983); Phys. Rev.
Lett. 50, 1153 (1983).
[2] S. R. White, Phys. Rev. B 53, 52 (1996).
[3] J. M. Tranquada, H. Woo, T. G. Perring, H. Goka, G. D.
Gu, M. Fujita, and K. Yamada, Nature (London) 429, 534(2004).
[4] M. Uehara, T. Nagata, J. Akimitsu, H. Takahashi, N. Môri,
and K. Kinoshita, J. Phys. Soc. Jpn. 65, 2764 (1996).
[5] M. Matsuda, K. Katsumata, H. Eisaki, N. Motoyama,
S. Uchida, S. M. Shapiro, and G. Shirane, Phys. Rev. B
54, 12 199 (1996).
[6] M. Azuma, Z. Hiroi, M. Takano, K. Ishida, and Y. Kitaoka,
Phys. Rev. Lett. 73, 3463 (1994).
[7] L. P. Regnault, I. Zaliznyak, J. P. Renard, and C. Vettier,Phys. Rev. B 50, 9174 (1994).
[8] A. Zheludev, Y. Chen, C. L. Broholm, Z. Honda, and
K. Katsumata, Phys. Rev. B 63, 104410 (2001).
[9] A. Zheludev et al., Phys. Rev. Lett. 88, 077206 (2002);
Phys. Rev. B 68, 134438 (2003); 69, 054414 (2004).
[10] O. P. Sushkov and V. N. Kotov, Phys. Rev. Lett. 81, 1941
(1998).
[11] H. Manaka, I. Yamada, and K. Yamaguchi, J. Phys.
Soc. Jpn. 66, 564 (1997).
[12] H. Manaka, I. Yamada, Z. Honda, H. A. Katori, and
K. Katsumata, J. Phys. Soc. Jpn. 67, 3913 (1998).
[13] In our definition J > 0 corresponds to AF interactions.
The 2-spin Hamiltonian is written as JS1 S2 . Note that
Refs. [11,12] use a different convention: J > 0 corresponds to ferromagnetism and the exchange term isJS1 S2 .
[14] J. R. D. Copley and J. C. Cook, Chem. Phys. 292, 477(2003).
[15] T. Barnes and J. Riera, Phys. Rev. B 50, 6817 (1994).
[16] M. Popovici, Acta Crystallogr. Sect. A A31, 507 (1975);
M. Popovici, D. Stoica, and I. ionita, J. Appl. Crystallogr.
20, 90 (1987).
[17] E. S. Sørensen and I. Affleck, Phys. Rev. B 49, 15 771(1994).
[18] M. B. Stone, I. A. Zaliznyak, T. Hong, C. L. Broholm, andD. H. Reich, cond-mat/0511266.
[19] M. E. Zhitomirsky (private communication).
[20] A. Kolezhuk and S. Sachdev, cond-mat/0511353.

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