The magnetic moebius strip: Synthesis, structure, and magnetic studies of odd-numbered antiferromagnetically coupled wheels

Article abstract of DOI:10.1002/anie.200460211

Understanding frustration: The control of structure through the choice of the template has allowed the synthesis of nonanuclear metal wheels that contain {Cr₈Ni} or {Cr₇(VO)₂} cores. Magnetic studies (see picture) of one of these wheels shows that it behaves as a magnetic Moebius strip. These are the first detailed magnetic studies of an odd-numbered ring larger than trinuclear and should help in the understanding of spin-frustrated systems.

Full text of DOI:10.1002/anie.200460211

Communications
Magnetic Properties
possible; hopefully the understanding gained here can later
be applied more generally to other frustrated systems.
In a preceding paper[9] we have shown how the chemistry
of [Cr8F8(O2CCMe3)16] can be exploited to produce a series of
heterometallic analogues [R2NH2][Cr7MF8(O2CCMe3)16], in
which M = NiII 1, CoII, MnII, or FeII and R can be a range of
alkyl groups from methyl to n-octyl.The secondary ammo-
nium cation is found encapsulated within the metal wheel,
and this suggested that if we varied the size of the cation we
might be able to vary the size of the wheel.
The Magnetic Möbius Strip: Synthesis, Structure,
and Magnetic Studies of Odd-Numbered
Antiferromagnetically Coupled Wheels**
Olivier Cador, Dante Gatteschi, Roberta Sessoli,*
Finn K. Larsen, Jacob Overgaard, Anne-Laure Barra,
Simon J. Teat, Grigore A. Timco,* and
Richard E. P. Winpenny*
The reaction of hydrated chromium(iii) fluoride with basic
nickel carbonate in pivalic acid in the presence of dicyclo-
hexylamine, followed by crystallization from THF/toluene
produced well-shaped hexagonal crystals.Elemental analysis
and electrospray mass spectroscopy (ESMS) provide con-
vincing evidence for the formation of [(C6H11)2NH2][Cr8Ni-
F9(O2CCMe3)18] 2.The ESMS spectrum of 2 contains a peak
for the anionic wheel in the negative-ion spectrum and two
significant peaks in the positive-ion spectrum for the molec-
ular ion plus one sodium as well as for the ring plus two
sodium ions.These are the only significant high-mass peaks.
The crystals of 2 appear to be single, but the X-ray
diffraction pattern has an extraordinary distribution.Proper
Bragg diffraction spots are found within a rather flat
spheroidal shaped volume of reciprocal space and with
pronounced diffuse scattering in the reciprocal planes per-
pendicular to the apparent sixfold crystal axis of rotation.This
makes it difficult to integrate the Bragg intensities for
determining structure factors and thus also creates a problem
in assigning the space group.The structure can either be
described in some hexagonal space groups or in the ortho-
rhombic Pbna space group, which gives the lower internal R
value of integrated reflections.Solving the structure in Pbna
reveals a nona-metallic core, bridged by single atoms.Atoms
of the nearest-neighbor octahedral coordination sphere can
be located but the atomic structure does not develop further
by subsequent least-squares refinement and difference Four-
ier methods.Undoubtedly there is much disorder of the outer
parts of the pivalate ligands.The combined information of
Bragg intensities and distribution of diffuse scattering sup-
ports the following model of the structure: The molecules that
have a nine-membered ring form layers, and these molecules
are stacked to form columns that are close-packed.The
distribution of diffuse scattering over the reciprocal plane
perpendicular to the stacking direction indicates disorder
between the stacks of molecules.Little information concern-
ing the identity of ligands attached to the metal core could be
discerned, but existence of the nine-membered ring with
indication of an ordered Ni position could be substantiated
from the analysis of the Bragg intensities.The equivalent
{Cr8Co} wheel compound was synthesized; it showed very
similar cell constants and intensity distribution but had even
more pronounced diffuse scattering, and full structural
characterization remained elusive.
The previously reported cyclic 3d-metal structures, from the
first—the ferric wheel of Lippard and co-workers[1]—to the
largest all contain an even number of metal centres.[2] There
are very few odd-numbered cyclic structures larger than
three; all are pentametallic and feature polydentate inflexible
ligands.[3] Raptis and co-workers have very recently reported
a nine-membered ring but only as part of higher nuclearity
structures.[4] It is difficult to rationalize the absence of odd-
numbered wheels, especially as odd-numbered metalloc-
rowns, that is, wheels centered with a further metal cation,
are known.[5] This is particularly frustrating because the
magnetic properties of such wheels should be of great interest
to physicists interested in magnetic frustration.[6] Spin frus-
tration is, in turn, important in areas as diverse as high
temperature superconductors[7] and CMR materials.[8] Herein
we report the first detailed magnetic characterization of an
odd-numbered wheel larger than a triangle.The new molec-
ular species synthesized allows us to study frustration at a
mesoscopic scale at which quantum calculations are still
[*] Dr. O. Cador, Prof. D. Gatteschi, Prof. R. Sessoli
Laboratorio di Magnetismo Molecolare
Dipartimento di Chimica & INSTM
Università degli Studi di Firenze
Polo Scientifico Universitario
Via Lastruccia n. 3, 50019 Sesto Fiorentino (Italy)
Fax: (+39)055-4573372
E-mail: roberta.sessoli@unifi.it
Dr. G. A. Timco, Prof. R. E. P. Winpenny
Department of Chemistry
The University of Manchester
Oxford Road, Manchester, M13 9PL (UK)
Fax: (+44)161-275-4616
E-mail: grigire.timco@man.ac.uk
richard.winpenny@man.ac.uk
Prof. F. K. Larsen, Dr. J. Overgaard
Department of Chemistry
University of Aarhus
Aarhus (Denmark)
Dr. A.-L. Barra
Laboratoire des Champs Magnetiques Intenses-CNRS
38042 Grenoble Cedex 9 (France)
Dr. S. J. Teat
CCLRC Daresbury Laboratory
Warrington, Cheshire, WA4 4AD (UK)
In an attempt to improve the knowledge of the nona-
nuclear wheel structure we decided to investigate a system in
which the metal sites are more likely to be ordered.Whereas
in 1 the nickel site is disordered over the eight metal positions,
if vanadyl is used the octanuclear wheel that results, [Et2NH2]
[**] This work was supported by the EPSRC(UK), the EC-TMR Networks
“MolNanoMag” (HPRN-CT-1999-00012) and “QuEMolNa”
(MRTN-CT-2003-504880), the German DFG (SPP 1137) and INTAS
(00-00172).
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[Cr6(VO)2F8(O2CCMe3)15] 3, has ordered metal sites, with the
two VO2+ units next to each other within the wheel.[12]
Therefore we treated chromium trifluoride with pivalic acid
and dicyclohexylamine in the presence of vanadyl acetate.
The product that formed was isolated as [(C6H11)2NH2]
[Cr7(VO)2F9(O2CCMe3)17] 4 (Figure 1).X-ray characteriza-
between the nearest neighbors where the spins cannot be
arranged antiparallel.More interesting and much less obvious
is how the presence of this knot in the ring manifests itself in
the magnetic properties.
The temperature dependence of the magnetic molar
susceptibility, cM, is shown in Figure 2.At room temperature
Figure 2. Variation of cM with temperature for 2. The solid line corre-
sponds to the calculated values with J=16 K, J’=70 K, and hgi=2. In
*
the inset the magnetization versus field measured at 1.6 K ( ) and
~
2.0 K ( ) is shown.
the cMT value is equal to 13.2 emuKmolꢀ1, lower than
expected (16 emuKmolꢀ1) for eight CrIII and one NiII isolated
spins with g = 2.00. This may indicate that strong antiferro-
magnetic interactions are already operative at room temper-
ature. cM increases when the temperature is lowered down to
T
max1 = 30 K, at which it passes through a broad maximum,
Figure 1. The structure of 4 in the crystal. The hydrogen atoms have
been omitted for clarity. Bond length ranges [Š]: Cr–F 1.9098–1.9338,
Cr–O 1.915–1.968, V–F 1.9494–2.0114, V–O(oxide) 1.580, V–O(piva-
late) 1.989–2.185 (av esd 0.002). Cr dark green; V purple; F yellow;
O red; N blue; C grey.
and then decreases when the temperature is lowered further.
At Tmin = 7.4 K it passes through a minimum then increases
again, and finally reaches a second maximum at Tmax2 = 2 K.
This behavior is unusual and to our knowledge has never been
observed before.What is common, and expected, is the
presence of one maximum in a cM vs. T curve as observed for
antiferromagnetic homometallic even-membered wheels, for
example, 1.
The magnetic properties of the system are determined by
Heisenberg-type superexchange interactions between the
magnetic centers.The simplest Hamiltonian describing the
system is the following:
tion demonstrates,[10] beyond doubt, that we have made nona-
nuclear metal wheels.Each Cr···Cr and Cr···V edge is bridged
by one fluoride and two pivalate ions while the V···V edge is
bridged by one fluoride ion and one pivalate ion.
The magnetic behavior of these nonanuclear wheels is
fascinating.Compound 2 contains an even number of
unpaired electrons due to the presence of a NiII ion, with
S = 1, and eight CrIII ions with S = 3/2 spins; this allows a
diamagnetic ground state, and therefore 2 is not a typical
example of a frustrated system: for example, the doubly
degenerate S = 1/2 ground states predicted to occur in odd-
membered rings of half-integer spins.Nevertheless in 2 not all
the antiferromagnetic interactions can be simultaneously
7
X
h ¼ J0ðSCr SNi þ SCr SNiÞ þ J
SCr SCr
iþ1
ð1Þ
1
8
i
i¼1
in which J’ and J are the superexchange coupling parameters
between the nickel spin and its two chromium neighbors and
between the nearest neighbor chromium ions, respectively.
The Si values are the spin quantum operators associated with
spin values SNi = 1 and SCr = 3/2 of nickel and chromium ions,
respectively.The presence of two maxima strongly indicates
an S = 0 ground state.The first step was to simulate the cM
versus T curves for several sets of parameters J and J’.Based
on previous work on Cr8 wheels, we set J/kB to 16 K. J’/kB was
varied between zero and 70 K.Only when J’/kB > 36 K are
two maxima in the susceptibility observed (Figure 3).
satisfied and therefore it can be regarded as frustrated.[13]
A
way to visualize the problem is its analogy with the Möbius
strip, which better reflects the finite size of this system,
compared to standard soliton or domain-wall pictures.The
odd number of spins makes it impossible for all spins to align
antiparallel to their nearest neighbor—as preferred where the
exchange is antiferromagnetic.We can think of the region
where the neighboring spins are alternately “up and down” as
the flat region of the Möbius strip, while a “knot” occurs
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Figure 4. Representation of the spin frustration in 2 as a Möbius strip,
with the white circle as the Ni site, and black circles as Cr. The knot is
the point at which the thick grey line is discontinuous: a) with J’@J
and the knot on the chromium chain; b) with J’<J and the knot is at
nickel.
A measurement of the magnetization does not usually
provide information on the wave function composition and
more sophisticated techniques must be used.As Ni II and CrIII
ions have significantly different g values, 2.2 versus 1.98,
respectively, an accurate measurement of the g values of the
lowest excited state will directly reflect the composition of the
wave function.By using the spin projection techniques it is
relatively easy to calculate the g factor of the different fi
Figure 3. Simulation of the variation of cM as a function of both T (log
scale) and J’. J has been set equal to 16 K.
Qualitatively the observation of two maxima in the c
versus T curve can be explained by the presence of several
states with low total spin values (ST) that are very close in
energy to the ground ST = 0 state.If J’ = 0 the ground state is
ST = 1 because the spin of the nickel is not correlated to the
antiferromagnetic chain of chromic spins.Inclusion of an
antiferromagnetic J’ rapidly stabilizes a diamagnetic ground
state, with the first three excited states being characterized by
ST = 1.A ferromagnetic J’, even if does not remove spin
frustration, stabilizes an S = 2 ground state with disappear-
ance of the maxima in the c versus T curve.An antiferro-
magnetic CrIII–NiII interaction has been unambiguously
observed in a similar {Cr7Ni} ring.[9]
states starting from the values of the single ions.For the STCr
=
0 ST = 1 > state g = gNi = 2.2, whereas for STCr = 2 ST = 1 > g =
3
1
= gCrꢀ = gNi = 1.86. In intermediate cases the calculation of g
2
2
requires us to consider the contribution of all fi states which
appear in y1 with a ci ¼ 0.The same procedure can be applied
to any state y.
A true fitting procedure of the c versus T curve is
hampered by the strong g dependence on the spin state that
has a stronger effect on the value of c than J’.To take into
account the wavefunction composition of the excited states is
an unmanageable task, given the dimension of the S
subspaces in the spin Hamiltonian matrix.In Figure 2 we
report the c versus T curve calculated for J = 16 K and J’ =
70 K.The spectrum of low-lying energy states shows the first
and second S = 1 states at ꢁ 3.7 and ꢁ 10.7 K from the S = 0
ground state, respectively.The first S = 2 is calculated to occur
at ꢁ 22 K above the ground state.This energy scheme is not
significantly varied if J’ is reduced by a factor of two, as is
usual in the presence of spin frustration.The M versus H
curve shows a first plateau at about 1.8 mB ,which is in
agreement with the predicted g < 2 value.Interestingly a
maximum in the dM/dH curve at 1.6 K is observed around
28 kOe (not shown).This observation suggests a gap between
the ground and the first excited S = 1 state of about 3 K, which
is in agreement with the calculated energy spectrum.The
further increase of M above 100 kOe, without reaching the
plateau at about 4 mB expected for an S = 2 state, suggests that
the first S = 2 state starts to be populated at these fields, but
that it is at least 15 K above the first S = 1 state, as calculated.
To confirm our interpretation, we have used electron
paramagnetic resonance (EPR) spectroscopy.In Figure 5 we
report the polycrystalline powder high field EPR spectra
recorded at a frequency of 285 GHz; an unconventionally
high frequency has been used to better resolve the difference
in the g value.At 20 K a single isotropic line is observed
centered at g ꢁ 2, as a result of many populated spin states.On
To discuss the “knot” of the Möbius strip, that is, the point
at which the spins on nearest neighbors are not antiparallel,
the eigen vectors of the low lying states are needed.In this
particular case it is very convenient to use for the basis set the
representation in which we couple the chromic spins on odd
sites to give an intermediate spin Sodd and analogously for the
spins on the even sites, Seven.These two intermediate spins are
coupled together, to give the total spin for the chromium
chain, STCr, and this last is coupled to the spin of the nickel to
give the total spin, ST.There are 2764 different ways of
obtaining an ST = 1 state, therefore the wave functions of
2764
P
Hamiltonian (1), are linear combinations y ¼
ci fi.How-
ever, for the states lowest in energy only i¼f1ew ciꢀs are
significantly different from zero.The composition of the
first excited ST = 1 state strongly depend on the J’/J ratio.If
J’ < Jy1 is mainly given by Seven = 6, Sodd = 6, with STCr = 0 and
can be seen as mainly given by the uncorrelated spin of the
nickel ion.The knot is then localized on the nickel site, as
shown in Figure 4b.On the contrary when J’ @ J the largest
contribution comes from STCr = 2 antiferromagnetically cou-
pled with the nickel spin to give ST = 1.In this case the “up–
down” orientation of spins is more rigid at the nickel site and
the knot is instead delocalized on the chromium chain as
shown in Figure 4a.
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in air.The product was separated by column chromatography on silica
gel by using toluene as eluent.It was eluted as the first band from the
column.The solution was then evaporated to dryness under reduced
pressure and the residue was redissolved in warm hexane (150 mL).
Slow evaporation of the solvent at ambient temperature produced X-
ray quality green crystals of 4 after two weeks.Crystals were collected
by filtration washed with cold hexane and dried on air at room
temperature; yield 2.15 g (30%; calculated from [VO(O2CCMe3)2]n).
Elemental analysis calcd (%) for C97H177Cr7F9N1O36V2: Cr 14.16,
V 3.96, C 45.33, H 6.94, N 0.54, F 6.65; found: Cr 14.08, V 4.10,
C 45.49, H 6.62, N 0.48. F 6.37. ESMS m/z (%): ꢀ2387 (100%)
[Cr7(VO)2F9(O2CCMe3)17]ꢀ.
Magnetic measurements: magnetic measurements were recorded
on a polycrystalline powder samples with an Oxford Instruments
Vibrating Sample Magnetometer (VSM) operating in the temper-
ature range 1.5–300 K with magnetic fields up to 120 kOe. It has been
checked that the magnetic susceptibility was independent of the
amplitude of the applied field by recording the magnetization with
two different magnetic fields, 1 and 10 kOe.
Figure 5. Variable-temperature EPR spectra of 2 recorded at 285 GHz
by using a laboratory built spectrometer based on a Gunn diode
source of far-infrared radiation.
lowering the temperature, a line centered at g = 1.86 increases
in intensity at the expense of the line at g ꢁ 2, confirming that
the lowest magnetic state has a g factor significantly smaller
than 2.Similar results are obtained at 190 GHz.The lines
have a nonresolved fine structure, probably due to the
magnetic anisotropy (the so called zero-field splitting) of
the states, but the observed shift to low g values on lowering
the temperature unambiguously confirms that J’ @ J as
suggested also by the presence of two maxima in the magnetic
susceptibility.The spin frustration is therefore delocalized on
the chromium chain, as represented by the Möbius strip of
Figure 4a.
This heterometallic odd-membered ring provides a fasci-
nating example of how the supramolecular approach can be
used to observe new magnetic phenomena.It possible to tune
the delocalization of the frustrated bonds in the ring and to
detect it in a very simple way, thus providing a text book
example of spin frustration.Similar phenomena are observed
in 4 and detailed studies will be reported later.
Received: April 2, 2004
Revised: July 8, 2004
Keywords: cage compounds · chromium · heterometallic
.
complexes · magnetic properties · spin frustration
[1] KL. .Taft, CD. .Delfs, GC. .Papaefthymiou, S.Foner, D.
Gatteschi, S.J.Lippard, J. Am. Chem. Soc. 1994, 116, 823 – 832.
[2] R.E.P. Winpenny, Comprehensive Coordination Chemistry II,
Vol. 7 (J.A.McCleverty, T.J.Thomas), Elsevier, Oxford, 2004,
pp.125 – 176, and references therein.
[3] a) B.Hasenknopf, -JM. .Lehn, BO. .Kneisel, G.Baum, D.
Fenske, Angew. Chem. 1996, 108, 1987 – 1990; Angew. Chem. Int.
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2001, 123, 773 – 774.
[4] G.Mezei, P.Baran, R.G.Raptis, Angew. Chem. 2004, 116, 584 –
587; Angew. Chem. Int. Ed. 2004, 43, 574 – 577.
[5] V.L. Pecoraro, A.J. Stemmler, B.R. Gibney, J.J. Bodwin, H.
Wang, J.W.Kampf, A.Barwinski, Prog. Inorg. Chem. 1997, 45,
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Experimental Section
[6] G.Toulouse, G. Comm. Phys. 1977, 2, 115 – 119.
[7] F.Nori, E.Gagliano, S.Bacci, S. Phys. Rev. Lett. 1992, 68, 240 –
243.
2: CrF3·4H2O (5.0 g, 28 mmol), (cy-C6H11)2NH (2.1 g, 12 mmol), basic
nickel carbonate (2NiCO3·3Ni(OH)2·4H2O; 0.5 g, 0.9 mmol) and
Me3CCO2H (15.0 g, 147 mmol) were heated at 1408C for 7.0 h, then
allowed to cool to room temperature.Acetone (50 mL) was added
and the resulting mixture was stirred for 15 mins.The microcrystalline
product was filtered, washed with a large quantity of acetone, dried in
air, dissolved in hot THF (75 mL), filtered, and the filtrate was diluted
with toluene (40 mL).The solution was concentrated by evaporation
at approx.40 8C to 30 mL and then very slowly cooled to room
temperature.The solution was left to stand for 24 h to yield green
hexagonal crystals, which were isolated by filtration and washed with
toluene; yield 1.7 g (17%, calculated from CrF3·4H2O).Elemental
[8] V.Caignaert, E.Suard, A.Maignan, Ch.Simon, B.Raveau,
Magn. Magn. Mater. 1996, 153, L260 – L264.
J.
[9] F.K. Larsen, E.J.L. McInnes, J. Overgaard, S. Piligkos, G.
Rajaraman, E. Rentschler, A.A. Smith, G.M. Smith, G.A.
Timco, R.E.P. Winpenny, Angew. Chem. 2003, 115, 105 – 109;
Angew. Chem. Int. Ed. 2003, 42, 101 – 105.
[10] Crystal data for 2: (C102H186Cr8F9NNiO36; Mr = 2648.41 gmolꢀ1):
dark green hexangular shaped blocks, orthorhombic, space
group possibly Pbna, a = 19.587(5), b = 24.818(6), c =
33.925(9) Š, V= 16490(7) Š3, Z = 4, T= 200(2) K, 1 =
analysis calcd(%) for
C
116H202Cr8F9NNiO36: Cr 14.69, Ni 2.07,
1.067 gcmꢀ3 F(000) = 5576, m(MoKa) = 0.683 mmꢀ1.Crystal
,
C 49.19, H 7.19, N 0.49, F 6.04; found: Cr 14.51, Ni 1.83, C 49.64,
H 7.25, N 0.48, F 5.85. ESMS m/z (%): ꢀ2465 (100) [Cr8Ni-
F9(O2CCMe3)18]ꢀ; + 2671 (100) [M+Na]+; + 2511 (50) {[Cr8Ni-
F9(O2CCMe3)18] + 2Na}+.
data for 4 C101.5H187.5Cr7F9NO36V2: Mr = 2634.9 gmolꢀ1; green
prism, orthorhombic, space group Pbcn, a = 23.9765(13), b =
31.2265(18), c = 19.3562(11) Š, V= 14492(1) Š3, Z = 4, T=
150(2) K,
1 = 1.208 gcmꢀ3
,
F(000) = 5546,
m(MoKa) =
4: CrF3·4H2O (5.0 g, 28 mmol), (C6H11)2NH (2.40 g, 13.2 mmol)
and Me3CCO2H (14.0 g, 137 mmol) were heated with stirring at
1408C for 2.0 h. [VO(O2CCMe3)2]n (1.5 g, 5.6 mmol when n = 1)
was added, and the mixture then heated for 4.0 h. The reaction
mixture was cooled to room temperature, acetone (30 mL) was
added, and the solution was stirred for a further 15 mins.A green solid
was collected by filtration, washed with acetone (3 ” 15 mL) and dried
0.701 mmꢀ1.Data were collected on Bruker SMART CCD
diffractometers (MoKa, l = 0.71069 Š for 2 and 0.6898 Š for 4).
Selected crystals were mounted on the tip of a glass pin by using
Paratone-N oil and placed in the cold flow produced with an
Oxford Cryocooling device.Complete hemispheres of data were
collected using w-scans (steps of 0.68 for 2 and 0.38 for 4,
30 sframeꢀ1).Integrated intensities were obtained with
[14]
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Communications
SAINT+ [11] and they were corrected for absorption by using
SADABS.[11] Structure solution and refinement was performed
with the SHELX program.[11] The structures were solved by
direct methods and 3 was completed by iterative cycles of DF
syntheses and full-matrix least-squares refinement against F2 to
give, for 4 by using 705 parameters and 418 restraints, wR2 =
0.2241 (19676 unique reflections), R1 = 0.0681 (14946 reflections
with I > 2s(I)).For 2 the structure did not develop past the
localization of the atomic structure of the nona-metallic wheel
and the octahedral first coordination sphere of the metals.
CCDC-231873 (4) contains the supplementary crystallographic
data for this paper.These data can be obtained free of charge via
www.ccdc.cam.ac.uk/conts/retrieving.html (or from the Cam-
bridge Crystallographic Data Centre, 12 Union Road, Cam-
bridge CB21EZ, UK; fax: (+ 44)1223-336-033; or deposit@
ccdc.cam.ac.uk).
[11] G.M. Sheldrick, Programs for Crystal Structure Analysis,
University of Göttingen, 1998.
[12] F.K. Larsen, J. Overgaard, S. Parsons, E. Rentschler, G.A.
Timco, A.A.Smith and R.E.P.Winpenny,
Angew. Chem. 2003,
115, 6160 – 6163; Angew. Chem. Int. Ed. 2003, 42, 5978 – 5981.
[13] O.Kahn, Chem. Phys. Lett. 1997, 265, 109 – 114.
[14] R.C. Paul, A. Rumar, J. Inorg. Nucl. Chem. 1965, 27, 2537 –
2547.
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