Low temperature magnetization of the S=1/2 kagome antiferromagnet ZnCu_3(OH)_6Cl_2
ABSTRACT The dc-magnetization of the unique S=1/2 kagome antiferromagnet Herbertsmithite has been measured down to 0.1K. No sign of spin freezing is observed in agreement with former muSR and ac-susceptibility results. The low temperature magnetic response is dominated by a defect contribution which exhibits a new energy scale $\simeq 1$ K, likely reflecting the coupling of the defects. The defect component is saturated at low temperature by H>8T applied magnetic fields which enables us to estimate an upper bound for the non saturated intrinsic kagome susceptibility at T=1.7K. Comment: to appear in PRB
arXiv:0710.0451v1 [cond-mat.str-el] 2 Oct 2007
Low temperature magnetization of the S=1/2 kagome antiferromagnet
F. Bert,1S. Nakamae,2F. Ladieu,2D. L’Hˆ ote,2P. Bonville,2F. Duc,3J.-C. Trombe,3and P. Mendels1
1Laboratoire de Physique des Solides, UMR CNRS 8502, Universit´ e Paris-Sud, 91405 Orsay, France
2Service de Physique de l’´Etat Condens´ e, DSM, CEA Saclay, 91191 Gif-sur-Yvette Cedex, France.
3Centre d’´Elaboration des Mat´ eriaux et d’´Etudes Structurales, CNRS UPR 8011, 31055 Toulouse, France
(Dated: February 2, 2008)
The dc-magnetization of the unique S=1/2 kagome antiferromagnet Herbertsmithite has been
measured down to 0.1 K. No sign of spin freezing is observed in agreement with former µSR and ac-
susceptibility results. The low temperature magnetic response is dominated by a defect contribution
which exhibits a new energy scale ≃ 1 K, likely reflecting the coupling of the defects. The defect
component is saturated at low temperature by H ? 8 T applied magnetic fields which enables us to
estimate an upper bound for the non saturated intrinsic kagome susceptibility at T = 1.7 K.
PACS numbers: 75.30.Cr, 75.30.Hx, 75.50.Lk
In triangular lattices, the frustration of antiferromag-
netic interactions associated to the enhancement of quan-
tum fluctuations for S=1/2 spins was acknowledged long
ago as a keypoint to stabilize novel ground states of mag-
netic matter1. Numerous theoretical studies have since
then emphasized the S=1/2 nearest-neighbor Heisenberg
antiferromagnet on the kagome lattice (KAH), a net-
work of corner sharing triangles.
approaches are complicated by the huge degeneracy of
the system, it is believed that the ground state could
be a unique realization of a disordered two dimensional
quantum liquid at T = 0, with a surprisingly small gap,
if any, to unconventional unconfined spinon excitations
and a gapless continuum of non magnetic excitations2,3,4.
Concurrently, growing efforts were made to identify a
model frustrated compound and find evidences for such
an exotic spin liquid ground state. Key features have
emerged from these experimental investigations like the
suppression of magnetic order at the energy scale of the
antiferromagnetic interaction, the persistence of spin dy-
namics at very low temperatures5,6or a large density
of low energy non magnetic states7. However, the frus-
trated compounds studied so far show strong deviations
from the ideal KAH (S> 1/2 spins, dilution of the mag-
netic lattice, anisotropic interactions). Besides, they of-
ten present marginal low T order or spin glass like be-
havior which forbid a close comparison to theoretical ex-
Only very recently, Herbersmithite, ZnCu3(OH)6Cl2,
a structurally perfect kagome antiferromagnet decorated
by Cu2+S=1/2 spins could be synthesized9. It belongs to
a large compound family ZnxCu4−x(OH)6Cl2where the
parent structure, clinoatacamite (x=0), is that of a dis-
torted S=1/2 pyrochlore. The substitution of Zn2+ions
preferentially on the less Jahn-Teller distorted Cu2+site
located in between the kagome planes restores the three
fold symmetry of the lattice for x > 1/3. Eventually the
Herbertsmithite compound (x = 1) presents decoupled
S=1/2 perfect kagome planes. Also, the magnetic order
which sets in clinoatacamite at 19 K gradually disappears
as x → 1 and for x = 1, muon spin resonance (µSR) in-
vestigation10has demonstrated the absence of any spin
freezing at least down to 50 mK, an energy scale 4000
times smaller than the main antiferromagnetic interac-
tion (J ≃ 190 K).
Once Herbertsmithite is acknowledged to be the first
good candidate for the realization of the KAH model,
the magnetic susceptibility and heat capacity are the first
quantities of interest as they straightforwardly probe the
nature of the ground state, either magnetic or not, and
the excitation spectrum. At low T, these thermodynamic
quantities show respectively a Curie-like tail11,12and a
Schottky-type11,13anomaly. It was soon recognized that
Dzyaloshinsky-Moriya interactions, which are allowed in
Herbertsmithite structure, can yield such a drastic in-
crease of the low T susceptibility14. However magnetic
defects could also account for these features, a scenario
sustained by recent NMR data15and neutron diffraction
refinements of the structure13,16. Despite a poor sensitiv-
ity, these latter point at a large (6 − 10%) Cu/Zn inter-
site mixing. This chemical disorder would likely reflect
the finite energy of the Jahn-Teller process that selects
the Zn substitution site. Both the resulting dilution of
the kagome magnetic network and the interplane Cu2+
ions may contribute to the defect component. In this pa-
per, we report on a detailed investigation of the Herbert-
smithite magnetization at low temperature (T > 0.1 K)
and up to moderately high fields (H < 14 T). Both sets of
data are consistently analyzed in terms of a large defect
contribution. We show that the low T intrinsic suscepti-
bility can be nonetheless estimated.
A ZnCu3(OH)6Cl2powder sample was prepared by the
hydrothermal method described in Ref.9,10. Low tem-
perature dc-magnetization (0.1 K< T < 3 K) was mea-
sured in a home made SQUID magnetometer for fixed
external magnetic fields up to 0.7 T. For T > 0.3 K,
each data point was obtained by extracting the sample
through the pick-up coils. To avoid heating effect, for
0.1 K< T < 0.4 K, the sample was kept at a fixed po-
sition in the pick-up coils and we measured the SQUID
temperature in 0.1 T external field on a log-log plot. The
local susceptibility measured by35Cl NMR line shift falls in
the shaded area15. The dashed line is a Curie Weiss fit for
1.5 K< T < 3 K (see text). Inset: T-dependence of the in-
verse of the susceptibility at low temperature.
Molar dc-susceptibility of Herbertsmithite versus
voltage variation as a result of the T-dependent sample
magnetization.Besides, dc-magnetization curves were
recordered versus field (0 < H < 14 T) at constant tem-
perature in a commercial vibrating sample magnetome-
ter (VSM). Standard SQUID data up to 5 T and for
T >1.8 K were also used to complement and calibrate
the low T data.
The temperature dependence of the dc magnetic sus-
ceptibility χ of Herbertsmithite measured in a 0.1 T ap-
plied field is presented on Fig. 1 in the whole studied
temperature range (0.1 K< T < 300 K). At high tem-
perature T ?150 K), the susceptibility shows a Curie-
Weiss behavior which yields the exchange constant J ≃
190 K11,17. At lower temperature, the susceptibility in-
creases much more rapidly down to ≃ 0.5 K where it
eventually flattens. Down to the lowest temperature of
the experiment T = 0.1 K, there is no sign of a mag-
netic transition in agreement with former µSR10and ac-
susceptibility11measurements. The T-dependence of the
total dc-magnetization M has been also measured be-
tween 0.1 K and 3 K for fixed applied fields H in the
range 0.05 - 0.7 T. Characteristic plots of M/H versus
T are presented in Fig. 2. At low temperature, satura-
tion effects are evidenced by the decrease of M/H with
increasing fields. More precisely, the field dependence of
the magnetization measured at 0.2 K is plotted in the
inset of fig. 2. At this temperature, the data are well
described by the linear M = χ(0.2 K)H relation for low
fields H ≤ 0.1 T while saturation effects are clearly ob-
served for H ≥ 0.2 T. Therefore, the flattening at low
temperature of M/H ≃ χ measured for H = 0.1 T in
Fig.1 can not be ascribed to a field effect.
The NMR lineshift of chlorine in Herbertsmithite was
measured recently15. This local probe investigation is
FIG. 2: (Color online) M/H as a function of temperature for
different H. Inset: M normalized by the saturated magneti-
zation of one mole of S=1/2 spins (Cu2+) Msat = 5583 emu,
at 0.2 K as a function of H. The data are extracted from the
temperature scans of the main panel. The straight line is a
plot of χ(0.2 K)H.
thought to give the intrinsic susceptibility χi which is
found to strongly deviate from the macroscopic SQUID
data χ for T ? 50 K. Indeed, despite large error bars due
to the broadening of the NMR line, χi shows a broad
maximum or at least a saturation below ≃ 50 K. One
can then put an upper limit to the intrinsic susceptibil-
ity χi < 1.5 × 10−3cm3/mol Cu as represented by the
shaded area in Fig. 1. The maximum of χilikely reflects
a moderate enhancement of the short range AF correla-
tions as in the well studied kagome bilayer case18,19,20.
Once these correlations have developed, it is doubtful
that there will be a subsequent rise of the susceptibil-
ity at lower temperature and we assume that the above
upper limit for χi also stands down to 0 K. The low
temperature dc-susceptibility which is the subject of this
report is therefore mainly dominated by a defect contri-
bution. In the following we will make the simplest as-
sumption that the intrinsic and defect contributions are
uncorrelated and therefore χ = χd+χiwith χi/χd< 0.1
for T < 2 K. As previously mentioned, one can antici-
pate two types of defects in the structure which can both
show a paramagnetic-like behavior and which both con-
tribute to χdin our analysis. First some Cu2+ions could
lie on the interplane site. Their coupling to the kagome
planes is likely very weak, maybe slightly ferromagnetic,
as discussed in Ref.9. Second, the dilution of the kagome
magnetic lattice by Zn2+ions is believed to locally stabi-
lize dimers and to induce a weak staggered magnetization
on further neighboring sites21. This non trivial extended
response of the system around a spin vacancy constitutes
the second magnetic defect. In the closely related cop-
per based anisotropic kagome structure of Volborthite22,
the controlled magnetic dilution by Zn/Cu substitution
indeed yields a Curie-like tail that scales with the Zn
We first consider the intermediate temperature range
1.5 K –10 K. As shown in the inset of Fig.1, 1/χ ≃ 1/χd
does not extrapolate to 0 when T → 0 as would be ex-
pected for free spins following a Curie law. Instead χd
rather shows a Curie-Weiss behavior χd= Cd/(T + θd).
A proper fit of the low T data requires an accurate knowl-
edge of χi(T). In the absence of such data, we fit with
a constant χi in the two extreme cases; χi = 0 which
yields θd= 0.85 K and Cd= 0.040 cm3/mol Cu/K (fit
range 1.5 K< T < 3 K) and χi = 1.5 × 10−3cm3/mol
Cu which yields θd= 0.80 K and Cd= 0.0345 cm3/mol
Cu/K (fit range 2 K< T < 10 K). A fit of the high tem-
perature (T > 150 K) data gives a Curie-Weiss constant
CCW ≃ 0.5 cm3/mol Cu. If one assumes that the mag-
netic defects behave as S=1/2 spins, their contribution
corresponds to ∽ 7% of weakly coupled S=1/2 spins out
of the total Cu2+contribution. This number is remark-
ably similar to the estimated number of two level systems
which contribute to the Schottky anomaly in heat ca-
pacity measurements13and also of misplaced Cu2+from
neutron diffraction refinement13,16. This latter finding
suggests that the main contribution to χd comes from
the interplane Cu2+(S=1/2 defects) whereas the inte-
grated staggered magnetization around a Zn2+amounts
to a rather small moment.
More puzzling is the behavior below 1 K where a subse-
quent enhancement of the susceptibility appears (Fig. 1,
inset). The above described Curie-Weiss regime accounts
then only qualitatively for the flattening of χ(T) (see
dashed line in main panel and inset). At 0.1 K the rise of
χ with respect to the extrapolated Curie-Weiss behavior
is about 1.3 × 10−2cm3/mol Cu, i.e. one order of mag-
nitude larger than the upper limit of χi. This enhance-
ment is therefore also related to the defect contribution
χd. No Field Cooling-Zero Field Cooling opening could
be detected below 1 K. Moreover χ does not show any
peak or divergence that would signal long range order-
ing. Thus, the rise of χ for T ≃ θd, probably reflects
a strengthening of some ferromagnetic-like correlations
between the magnetic defects rather than some kind of
ordering. It is noticeable that a slight slowing down of
the electronic spin fluctuation is detected at this same
temperature T ≃ θdin µSR experiments. This nicely cor-
roborates the correlation strengthening picture. θdis also
close to the temperature of the maximum of the Schot-
tky anomaly in zero field heat capacity data. Therefore,
kBθdappears as a new energy scale for Herbertsmithite,
most likely related to the magnetic defect system.
The magnetic response of the defects strongly domi-
nates the total susceptibility at low temperature and it
is difficult to extract any information on the KAH con-
tribution.However, one can expect different field de-
pendences for the two contributions. Namely, the weakly
coupled magnetic defects should be more easily saturated
than the Cu2+spins belonging to the perfect kagome
network with the stronger J ≃ 190 K coupling. To fur-
ther investigate the field dependence of the magnetiza-
tion we measured M(H) curves in a vibrating sample
magnetometer up to 14 T for constant temperatures in
FIG. 3: (Color online) Normalized magnetization (Msat =
5583 emu) measured versus field in a VSM for 3 character-
istic temperatures. The magnetization data at 0.2 K are
also reported from the inset of Fig. 2.
the same temperatures, M − χiH versus H/(T + θ) with
χi = 1.25 × 10−3cm3/mol Cu and θ = 1.3 K.
In the inset, for
FIG. 4: (Color online) Full squares : normalized magnetiza-
tion of Herbertsmithite measured at 1.7 K versus field. The
solid line is a linear fit of the data for H > 10 T which likely
reflects the non saturated intrinsic susceptibility χi. Open
squares : the defect contribution obtained by subtracting the
above linear contribution from the full square magnetization
curve. Dashed line : Brillouin function for 7.7% of free S=1/2
spins. Inset: the shaded area on the SQUID χ(T) plot repre-
sents the possible values of χi from this study.
the range 1.7 K–25 K. Characteristic results are shown
in Fig. 3.At 1.7 K, a strong saturation effect is ob-
served above ∼2 T and up to ∼8 T where M(H) reaches
a linear regime. At higher temperature, the saturation
effect gradually disappears and at 10 K a nearly linear
dependence is recovered. This behavior is compatible
with a simple decomposition of the magnetization into a
defect and an intrinsic contribution M = Md+ Mi. One
then assumes that for moderately high fields (H < 14 T)
with respect to the coupling energy scale J, the linear
Mi(H,T) = χi(T)H relation holds and that the defect
magnetization Mdfollows a Brillouin like saturation. In
this scenario, at 1.7 K, the regime for H > 10 T where the
magnetization is a linear function of H, is explained by
the complete saturation of the magnetic defects and the
slope of M(H) is a direct measure of the intrinsic suscep-
tibility χi(1.7 K). In Fig. 4 the straight line corresponds
to χi(1.7 K) = 1.5 × 10−3cm3/mol Cu. It is the largest
possible value for the intrinsic susceptibility so that the
remaining defect magnetization extracted from our data
(open squares) does not decrease at high fields.
noticeable that the fully saturated defect magnetization
amounts then to ∼ 8% of the saturated magnetization
of one Cu2+mole, in perfect agreement with the ∼ 7%
estimate given by the low T Curie-Weiss behavior of the
defect susceptibility. However, one cannot exclude that
the complex magnetic defects at play in Herbertsmithite
are not completely saturated even at the lowest temper-
ature and highest field of this study. Part of or the whole
linear regime could then be ascribed to the defect con-
tribution. The extracted χi value is therefore only the
upper limit of the kagome susceptibility at low tempera-
ture. The possible values of χifor T ? 1.7 K from this
analysis are represented by the shaded area in the inset
of Fig. 4.
As shown by the dashed line in Fig. 4, a simple S=1/2
Brillouin function fails to capture the field dependence
of the defect magnetization Md = M − χiH.
ble reasons for this are that 1) the magnetic defects are
complex objects involving the point defect itself, likely
a misplaced Zn/Cu atom, and the local screening of the
defect by the neighboring spins, so that one does not
expect a simple S=1/2 effective spin value, 2) the mag-
netic defects are slightly antiferromagnetically coupled
which tends to reduce the field effect with respect to the
H/T dependence of free spins. Note that unconstraining
the spin value of the Brillouin function does not give
either a good fit of the H and T dependence of Md.
As shown in the inset of Fig. 3, the Md(T,H) data for
1.7 K< T < 10 K merge on a same curve if one uses the
scaling variable H/(T+θ) which accounts phenomenolog-
ically for the AF coupling. Good scaling is obtained for
χi= 0.00125±0.00025 cm3/mol Cu and θ = 1.1±0.2 K
in agreement with θCW extracted from the low T Curie
Weiss fit of the susceptibility. It is noticeable that be-
low 1 K, deviations from this scaling appear gradually.
Eventually, the 0.2 K curve can not be made to fall on
the T > 1 K ones, even with different χi and θ values.
It suggests that the effective defect moment does change
below 1 K which corroborates the enhanced correlations
scenario drawn from the analysis of the T dependence of
In summary, from a detailed study of the temperature
and field dependence of the magnetization at low T , we
can draw a coherent picture of the Herbertsmithite mag-
netic behavior. The Curie-like tail in the susceptibility
can be safely attributed to a defect contribution. The
magnetic defects, probably of two kinds, behave in aver-
age as weakly coupled spins (S ?= 1/2). Signature of the
coupling energy ≃ 1 K are found ubiquitously in thermo-
dynamics measurements as well as in the spin dynamics.
The complex nature of the defects challenges both chem-
istry to achieve a better control of Zn/Cu site occupation
and theory to describe their magnetic behavior. Remark-
ably, such a large quantity of defects does not seem to
alter the underlying KAH physics. Besides, although the
effect of the ≃ 10 T external fields used in this study
is not clearly known, our results are compatible with a
finite kagome susceptibility at T ≃ J/100 and thus ques-
tion the ground state nature and the presence of a gap.
Although we showed in this study that the low T up
turn of the macroscopic susceptibility can be explained
in a defect scenario without Dzyaloshinsky-Moriya per-
turbation terms contrary to the initial proposal of Ref.14,
they could nonetheless impact the low T intrinsic proper-
ties and possibly increase the polarisability of the ground
state of this unique realization of a S=1/2 kagome sys-
1P. Anderson, Mater. Res. Bull. 8, 153 (1973).
2P. Lecheminant, B. Bernu, C. Lhuillier, L. Pierre, and
P. Sindzingre, Phys. Rev. B 56, 2521 (1997).
3C. Waldtmann, H.-U. Everts, B. Bernu, C. Lhuillier,
P. Sindzingre, P. Lecheminant, and L. Pierre, Eur. Phys.
J. B 2, 501 (1998).
4G. Misguich and C. Lhuillier,
Dimensional Quantum Antiferromagnets (World Scien-
tific, 2005), cond-mat/0310405.
5Y. Uemura, A. Keren, K. Kojima, L. Le, G. Luke, W. Wu,
Y. Ajiro, T. Asano, Y. Kuriyama, M. Mekata, et al., Phys.
Rev. Lett. 73, 3306 (1994).
6D. Bono, P. Mendels, G. Collin, N. Blanchard, F. Bert,
A. Amato, C. Baines, and A. D. Hillier, Phys. Rev. Lett.
93, 187201 (2004).
7A. P. Ramirez, B. Hessen, and M. Winklemann, Phys. Rev.
Lett. 84, 2957 (2000).
Frustration in Two-
8F. Bert, D. Bono, P. Mendels, F. Ladieu, F. Duc, J.-C.
Trombe, and P. Millet, Phys. Rev. Lett. 95, 087203 (2005).
9M. Shores, E. Nytko, B. Bartlett, and D. Nocera, J. Am.
Chem. Soc. 127, 13462 (2005).
10P. Mendels, F. Bert, M. A. de Vries, A. Olariu, A. Harrison,
F. Duc, J. C. Trombe, J. S. Lord, A. Amato, and C. Baines,
Phys. Rev. Lett. 98, 077204 (2007).
11J. S. Helton, K. Matan, M. P. Shores, E. A. Nytko, B. M.
Bartlett, Y. Yoshida, Y. Takano, A. Suslov, Y. Qiu, J.-H.
Chung, et al., Phys. Rev. Lett. 98, 107204 (2007).
12O. Ofer, A. Keren, E. A. Nytko, M. Shores, B. Bartlett,
D. Nocera, C. Baines, and A. Amato, cond-mat/0610540
13M. Vries, K.V.Kamenev, W.A.Kockelmann, J.Sanchez-
Benitez, and A.Harrison, arXiv:0705.0654 (2007).
14M. Rigol and R. P. Singh, Phys. Rev. Lett. 98, 207204
15T. Imai, E. A. Nytko, B. Bartlett, M. Shores, and D. G.
Nocera, cond-mat/0703141 (2007).
16S.-H. Lee, H. Kikuchi, Y. Qiu, B. Lake, Q. Huang,
17G. Misguich and P. Sindzingre arXiv:0704.1017 (2007).
18P. Mendels, A. Keren, L. Limot, M. Mekata, G. Collin,
and M. Horvati´ c, Phys. Rev. Lett. 85, 3496 (2000).
19C. Mondelli, K. Andersen, H. Mutka, C. Payen, and
B. Frick, Physica B 267–268, 139 (1999).
20D. Bono, P. Mendels, G. Collin, and N. Blanchard, Phys.
Rev. Lett. 92, 217202 (2004).
21S. Dommange, M. Mambrini, B. Normand, and F. Mila,
Phys. Rev. B 68, 224416 (2003).
22Z. Hiroi, M. Hanawa, N. Kobayashi, M. Nohara, H. Takagi,
Y. Kato, and M. Takigawa, J. Phys. Soc. Jpn. 70, 3377
23F. Bert, D. Bono, P. Mendels, J.-C. Trombe, P. Millet,
A. Amato, C. Baines, and A. Hillier, J. Phys.: Condens.
Matter 16, S829 (2004).