A structurally perfect S = 1/2 Kagome antiferromagnet

Article abstract of DOI:10.1021/ja053891p

The syntheses and magnetic susceptibilities of a pure series of rare copper minerals from the atacamite family with general formula Zn_xCu_4-x(OH)₆Cl₂ (0 ≤ x ≤ 1) are reported. The structure of these compounds features a corner-sharing triangular kagome lattice of antiferromagnetically coupled Cu(II) ions. We correlate the onset of magnetic ordering with the mole fraction of paramagnetic Cu(II) ions located between kagome layers and demonstrate that the fully Zn-substituted compound shows no magnetic ordering down to 2 K, resulting in a highly spin-frustrated S = 1/2 lattice. Copyright

Full text of DOI:10.1021/ja053891p

Published on Web 09/09/2005
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A Structurally Perfect S ) /2 Kagome´ Antiferromagnet
Matthew P. Shores, Emily A. Nytko, Bart M. Bartlett, and Daniel G. Nocera*
Department of Chemistry, 6-335, Massachusetts Institute of Technology, 77 Massachusetts AVenue,
Cambridge, Massachusetts 02139-4307
Received June 13, 2005; E-mail: nocera@mit.edu
Nearly two decades ago, Anderson proposed that the resonating
valence bond (RVB) state may explain the scatterless hole transport
encountered in doped rare-earth cuprates.1 The quantum spin liquid
phase responsible for RVB is most likely to be found in low-
dimensional, low-spin, and geometrically frustrated systems.2
Accordingly, most theoretical investigations of RVB have concen-
1
trated on S )
/ antiferromagnets in kagome´ (corner-sharing
2
triangular) lattices due to the higher degree of geometric frustration.3
Materials featuring such lattices are predicted to display no long-
range magnetic order due to competing antiferromagnetic interac-
tions between nearest-neighbor spin centers. Though long sought,
1
“no perfect S ) /2 Kagome´ antiferromagnet has been up to now
synthesized”,4 and accordingly, most theoretical predictions of such
a lattice remain untested. Herein, we report the synthesis and
preliminary magnetic properties of a rare, phase-pure, copper
Figure 1. Crystal structure of Zn-paratacamite (1), Zn0.33Cu3.67(OH)6Cl2.
Left: local coordination environment of intralayer Cu3(OH)3 triangles and
interlayer Zn2+/Cu2+ ion; the projection is parallel to the crystallographic
c axis. Right: the {Cu3(OH)6} kagome´ lattice, projected perpendicular to
the c axis. The pure Zn2+-substituted compound 2 is isostructural to 1.
Selected interatomic distances (Å) and angles (deg) for 2: Zn-O, 2.101-
(5); Cu-O, 1.982(2); Cu-Cl, 2.7698(17); Zn‚‚‚Cu, 3.05967(16); O-Zn-
O, 76.21(18), 103.79(18), 180.00(19); O-Cu-O, 81.7(3), 98.3(3), 180.0;
O-Cu-Cl, 82.31(11), 97.68(11); Cl-Cu-Cl, 180.0; Cu-O-Cu, 119.1-
(2); Cu-O-Zn, 97.04(15).
1
hydroxide chloride mineral featuring structurally perfect S ) /2
kagome´ layers separated by diamagnetic Zn(II) cations.
We have employed a redox-based hydrothermal protocol to
prepare pure, single-crystal jarosite-based materials (AM3(OH)6-
(SO4)2, A ) alkali metal ion, M ) V, Cr, Fe).5 These compounds
feature kagome´ lattices composed of M3(OH)6 triangles; when M
) Fe(III), spins are antiferromagnetically coupled and frustrated.6
Substitution of the magnetic ion of Fe(III) (S ) 5/2) by Cu(II) (S )
1/2) was attempted, but charge imbalance on the kagome´ layers
appears to prevent the preparation of a Cu(II) jarosite. We therefore
turned our attention to developing hydrothermal methods for the
preparation of the topologically similar kagome´ series composed
of Cu(II) ionssthe atacamitessof general formula MCu3(OH)6Cl2
(M ) Co, Ni, Cu, Zn).7 Our initial attempts to prepare these rare
minerals in pure form began with the treatment of malachite
(Cu2(OH)2CO3) with NaCl and HBF4 under hydrothermal conditions
to form a blue microcrystalline compound whose powder X-ray
diffraction pattern is consistent with that of the mineral claringbullite
(PDF 86-0899),8 where Cu(II) ions occupy the interlayer M site
of MCu3(OH)6Cl2. Further hydrothermal treatment of this solid with
a large excess of ZnCl2 afforded a green powder interdispersed
with triangular plate crystals of MCu3(OH)6Cl2 possessing a mixed
and refinement are provided in the Supporting Information. Two
geometrically distinct metal sites are found. On the first site, a Cu-
(II) ion is surrounded by four equatorial hydroxide ligands and two
distant axial chloride ligands. The hydroxide ligands bridge copper
centers to form a kagome´ lattice composed of {Cu3(OH)6} triangles.
On the other site, a Zn(II) ion is ligated by six hydroxide ligands
in a trigonally compressed octahedral geometry. This site serves
to link the kagome´ layers into a dense three-dimensional structure.
Although it is difficult to differentiate Cu and Zn by standard X-ray
analysis, the two sites’ distinct coordination environments suggest
that the Jahn-Teller distorted Cu(II) ion should rest on the
tetragonally elongated intralayer site, whereas the d10 Zn(II) ion
should reside on the higher symmetry interlayer site. In support of
this contention, several refinements of the structure were carried
out in which either Zn or a Cu/Zn mixture was included on the
intralayer site; all resulted in a significant increase in refinement
residuals. Thus, Zn occupancy on the intralayer site is not
reasonable. Upon refinement of the interlayer site, however, it was
found that there was a slight but statistically significant preference11
for a Cu/Zn mixture rather than Zn alone, such that Zn site
occupancy refined to 33%. Best refinements of other crystals
harvested from batch reactions show that Zn occupancy varies from
crystal to crystal. These results highlight the difficulty of using
X-ray diffraction to determine Zn/Cu composition. All materials
used in these studies were therefore subject to chemical analysis
to ascertain the Zn/Cu stoichiometry.
M-site occupancy of Zn2+ and Cu2+
.
It is known that a solid solution exists for naturally occurring
ZnxCu4-x(OH)6Cl2 specimens, such that even macroscopically
“single” crystals may exhibit variable Cu/Zn composition at the
interlayer site.7 For x < 0.33, the crystal symmetry is monoclinic,
resulting in a distorted kagome´ lattice. At x ) 0.33, the crystal
symmetry increases to rhombohedral, and the Cu triangular
plaquettes become equilateral. This high symmetry phase of
intermediate Zn occupancy (0.33 e x < 1) is known as Zn-
paratacamite (1).10 The compositional end members are known as
clinoatacamite9 (x ) 0) and herbertsmithite (2) (x ) 1).10
The presence of Cu(II) ions in intra- and interlayer sites
contributes to the overall magnetic susceptibility. To unravel the
magnetic contributions of Cu(II) in the different sites, a series of
The single-crystal X-ray structure of the compound with 33%
Zn occupancy is shown in Figure 1. Details of the structure solution
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J. AM. CHEM. SOC. 2005, 127, 13462-13463
10.1021/ja053891p CCC: $30.25 © 2005 American Chemical Society

C O M M U N I C A T I O N S
O-Cuintra ) 119.1° is expected to give rise to strong antiferro-
magnetic exchange,13 as observed for all compounds. The absence
of an ordering temperature in 2 is a clear indication of strong spin
frustration, which inhibits the tendency for spins to order and hence
suppresses TC relative to ΘCW. For 2, spin frustration is sufficiently
pronounced that no ordering is observed to the temperature limit
of the SQUID susceptometer, despite the value of ΘCW ) -314
K! With the introduction of Cu(II) ions into the interlayer site, a
ferromagnetic exchange interaction is engendered owing to the
introduction of an additional Cuintra-O-Cuinter superexchange
pathway; a Cuintra-O-Cuintra ) 97.0° is expected to give rise to
a weak ferromagnetic exchange interaction.13 With spin frustration
suppressing antiferromagnetic ordering within the kagome´ layers,
the ferromagnetic ordering event involving the interlayer Cu(II)
ions is readily observed (see Figure 2a). Moreover, the increase in
|ΘCW| as the paramagnetic occupancy of the interlayer site decreases
(Figure 2b) is consistent with the contribution of the ferromagnetic
exchange interaction becoming less prevalent as x f 1.
Ramirez has provided a measure for spin frustration by defining
f ) |ΘCW|/TC, with values of f > 10 signifying a strong effect.2 As
is evident from f > 157, the pure phase of ZnCu3(OH)6Cl2 (2) is
one of the most frustrated spin systems discovered to date. Of
consequence to RVB, this spin frustration occurs in a layered
1
kagome´ S ) /2 spin system. The foregoing results show that this
long-sought spin lattice is achieved when the interstitial sites of
kagome´ layers composed of Cu3(OH)6 triangles are solely occupied
by diamagnetic Zn(II) ions. Characterization of Zn[Cu3(OH)6Cl2]
by neutron scattering is underway.
Acknowledgment. We thank NSF for providing B.M.B. and
E.A.N. with predoctoral fellowships, DuPont for providing B.M.B.
with a Graduate Fellowship Award, Mr. K. Matan for experimental
assistance, and Prof. Y. S. Lee and Drs. F. C. Chou and A. Prodi
for helpful discussions.
Figure 2. (a) Low temperature dependence of øM for compounds in the
solid solution ZnxCu4-x(OH)6Cl2 for x ) 0 (2), 0.50 (blue, 9), 0.66 (green,
[), and 1.00 (red, b) as measured under ZFC conditions at 100 Oe (inset,
x ) 0). Lines shown to guide the eye. (b) Dependence of |ΘCW| on interlayer
Zn site occupancy; the additional point is for x ) 0.80 (O).
Supporting Information Available: Synthetic protocol and mag-
netic characterization of ZnxCu4-x(OH)6Cl2 (0 e x e 1); crystallographic
tables for ZnxCu4-x(OH)6Cl2 (x ) 0.33, 0.42, 1.00) (pdf). Full X-ray
crystallographic information, in CIF format. This material is available
free of charge via the Internet at http://pubs.acs.org.
Zn-paratacamites were prepared by hydrothermal synthesis ac-
cording to the following:
3Cu2(OH)2CO3 + 2MCl2 + 3H2O f
2M{Cu3(OH)6}Cl2 + 3CO2 (1)
References
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the exclusive use of MCl2 ) CuCl2 and ZnCl2, respectively. Full
experimental details are provided in the Supporting Information.
As Figure 2a shows, the magnetic susceptibility of 2 is distinct
from that of its Cu-substituted congeners. Cu[Cu3(OH)6Cl2] shows
a ferromagnetic transition with a critical temperature, TC ) 6.5 K.
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The observed magnetism of the MCu3(OH)6Cl2 series may be
understood by a Goodenough-Kanamori analysis12 of a Cu-O-
Cu superexchange pathway. Within the kagome´ layers, a Cuintra
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