MOLECULAR CLUSTER MAGNETS

JEFFREY R. LONG
Department of Chemistry, University of California, Berkeley, CA 94720, USA
E-mail: jlong@cchem.berkeley.edu

Molecular clusters with a high spin ground state and a large negative axial zero-field
splitting possess an intrinsic energy barrier for spin reversal that results in slow relaxation of
the magnetization. The characteristics of [Mn1 2O1 2(MeCO2 ) 1 6(H2 O)4 ]—the first example
of such a single-molecule magnet—leading up to this behavior are described in detail. Other
clusters known to exhibit an analogous behavior are enumerated, consisting primarily of
oxo-bridged species containing MnI I I, FeI I I, NiI I, VI I I, or CoI I centers as a source of
anisotropy. The progress to date in controlling the structures and magnetic properties of
transition metal-cyanide clusters as a means of synthesizing new single-molecule magnets
with higher spin-reversal barriers is summarized. In addition, the phenomenon of quantum
tunneling of the magnetization, which has been unambiguously demonstrated with molecules
of this type, is explained. Finally, potential applications involving high-density information
storage, quantum computing, and magnetic refrigeration are briefly discussed.

1 Introduction

Over the course of the past decade, a rapidly increasing number of molecular clusters
have been shown to exhibit magnetic bistability. These species, dubbed single-
molecule magnets, possess a combination of high spin S and axial anisotropy D in
the ground state that leads to an energy barrier U for reversing the direction of their
magnetization. The ensuing slow magnetic relaxation observed at low temperatures
is in many ways analogous to the behavior of a superparamagnetic nanoparticle
below its blocking temperature [1].
With 2-30 transition metal centers and diameters in the 0.5-2 nm regime,
established single-molecule magnets reside at the smaller end of the spectrum of
nanostructured materials. As molecular compounds, they can generally be isolated in
pure form and crystallized, permitting the precise determination of atomic structure
via X-ray crystallography. Hence, with essentially no size dispersion, these species
exhibit well-defined and remarkably reproducible physical properties. This, along
with the massively parallel production scheme associated with solution-based
molecular assembly reactions, provides impetus for the current optimism
surrounding the development of spin-based molecular electronic devices. Other
applications envisioned for such molecular magnets include high-density
information storage, quantum computing, and magnetic refrigeration. Moreover,
these clusters are positioned at the frontier between molecular and bulk magnetism,
allowing study of new physical phenomena such as quantum tunneling of the
magnetization.
Herein, the state of the nascent field of molecular cluster magnets is

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summarized, with an eye toward elucidating new and existing challenges. In view of
the considerable effort devoted to this area of research of late, surprisingly few
review articles on the subject are presently available [2-5].

2 A Mn12 Cluster Magnet

In 1980, Lis reported the synthesis and structure of [Mn12O12(MeCO2)16(H2O)4]·

2MeCO2H·4H2O, a compound containing an unprecedented dodecanuclear cluster
with the disc-shaped geometry depicted in Figure 1 [6]. Its structure features a central
MnIV4O4 cubane unit surrounded by a ring of eight MnIII centers connected through
bridging oxo ligands. Bridging acetate and terminal water ligands passivate the
surface, such that each Mn center possesses an approximate octahedral coordination
environment. Variable temperature magnetic susceptibility data were also reported
by Lis, along with the prescient observation that “such a complicated dodecameric
unit should have interesting magnetic properties”.

Figure 1. Structure of the disc-shaped cluster [Mn1 2O1 2(MeCO2 ) 1 6(H2 O)4 ] [6]. Black, shaded, and
white spheres represent Mn, C, and O atoms, respectively; H atoms are omitted for clarity. White
arrows indicate relative orientations of local spins in the ground state; note that the four central MnI V
centers have a lower spin (S = 3 /2 ) than the eight outer MnI I I centers (S = 2).

More than a decade later, magnetization data for this compound collected at high
magnetic field strengths and low temperatures were interpreted as indicating an S =
10 ground state with significant axial anisotropy [7,8]. Coordinated by weak-field
oxo donor ligands, the MnIV and MnIII centers possess the electron configurations
t2g3eg0 and t2g3eg1, imparting local spins of S = 3/2 and S = 2, respectively. The total
spin of the ground state can then be understood as arising from a situation in which

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the spins of the four central MnIV centers are all aligned antiparallel to the spins of
the eight outer MnIII centers, to give S = |(4 ¥ 3/2) + (8 ¥ -2)| = 10 (see Figure 1).
Reduced magnetization curves for the compound were found to deviate significantly
from a simple Brillouin function, suggesting that the S = 10 ground state is subject
to a substantial zero-field splitting. Indeed, fits to the magnetization data indicate an
axial zero-field splitting parameter with a magnitude of |D| = 0.5 cm-1. High-field,
high-frequency EPR spectra are consistent with this value, and further indicate the
sign of D to be negative.
The negative axial zero-field splitting removes the degeneracy in the M S levels
of the ground state, placing the higher magnitude levels lower in energy, as depicted
in Figure 2. Together with the selection rule of DM S = ±1 for allowed transitions,
this results in an energy barrier U separating the two lowest energy levels of M S =
+10 and MS = -10. In general, for an integral spin state, the energy barrier will be U
= S 2|D|, while for a half-integral spin state it will be U = (S 2 - 1/4)|D|. Thus, for the
S = 10 ground state of the Mn12 cluster, we have a spin-reversal energy barrier of U
= S 2|D| = 102|-0.5 cm-1| = 50 cm-1. Note that a positive D value would result in the
M S = 0 level being lowest in energy, such that there is no energy cost for losing
direction of the spin (i.e., in going, for example, from to MS = +10 to M S = 0).

Figure 2. Energy level diagram for an S = 10 ground state with a negative axial zero-field splitting, D,
in the absence of an applied magnetic field. Arrows represent the relative orientation of the spin with
respect to the easy axis of the molecule. As indicated, the spin reversal barrier is given by U = S2 |D| =
100|D|. For [Mn1 2O1 2(MeCO2 ) 1 6(H2 O)4 ], D = -0.5 cm- 1, resulting in a barrier of U= 50 cm- 1.

As a consequence of the energy barrier U intrinsic to its ground state, the

magnetization of the Mn12 cluster can be pinned along one direction, and then
relaxes only slowly at very low temperatures. This effect is readily probed through

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AC magnetic susceptibility measurements, which provide a direct means of gauging
the relaxation rate. Here, the susceptibility of a sample is measured using a weak
magnetic field (usually of ca. 1 G) that switches direction at a fixed frequency. As
the switching frequency increases and starts to approach the relaxation rate for the
magnetization within the molecules, the measured susceptibility—referred to as the
in-phase or real component of the AC susceptibility and symbolized as c’—begins
to diminish. Accordingly, the portion of the susceptibility that cannot keep up with
the switching field—referred to as the out-of-phase or imaginary component of the
AC susceptibility and symbolized as c”—increases. If just a single relaxation
process is operational, then a plot of c” versus temperature will display a peak with
a maximum at the temperature where the switching of the magnetic field matches
the relaxation rate, 1/t , for the magnetization of the molecules. Furthermore, since
1
/t increases with temperature, this peak should shift to higher temperature when the
switching frequency is increased. As shown in Figure 3, such behavior has indeed
been observed for [Mn12O12(MeCO2)16(H2O)4]·2MeCO2H·4H2O [8]. More precisely,
the relaxation time for the magnetization in a single-molecule magnet can be
expected to follow an Arrhenius relationship:
t = t 0e(Ueff/kBT) (1)
where the preexponential term t 0 can be thought of as the relaxation attempt
frequency. Thus, a plot of lnt versus 1/T should be linear, with the slope and
intercept permitting evaluation of U eff and t 0. Analysis of data for the
[Mn12O12(MeCO2)16(H2O)4] cluster in this manner gave Ueff = 42 cm-1 and t0 = 2.1 ¥
10-7 s [9]. Note that, as is generally the case, the effective energy barrier Ueff
obtained is slightly lower than the intrinsic spin reversal barrier U calculated from S

Figure 3. Schematic representation of the out-of-phase component of the molar AC magnetic

susceptibility observed for a polycrystalline sample of [Mn1 2O1 2(MeCO2 ) 1 6(H2 O)4 ]·2MeCO2 H·4H2 O
in zero applied DC field (adapted from reference 8). From left to right, peaks correspond to data
collected in an AC field oscillating at a frequency of 55, 100, and 500 Hz, respectively.

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and D, owing to the effects of quantum tunneling of the magnetization (see Section
5). Importantly, AC susceptibility measurements performed on the analogous
[Mn12O12(EtCO2)16(H2O)4] cluster dissolved in polystyrene reveal the same behavior,
indicating that the slow magnetic relaxation is indeed associated with individual
clusters and is not a bulk phenomenon [10].
The slow relaxation of the magnetization in a single-molecule magnet also
leads to magnetic hysteresis. Figure 4 depicts a hysteresis loop collected for a
sample of [Mn12O12(MeCO2)16(H2O)4]·2MeCO2H·4H2O at 2.1 K [11]. This
hysteresis has a substantially different origin from that in an ordered ferromagnet.
Here, rather than inducing domain wall motion, increasing the applied magnetic field
shifts the relative energies of the M S levels (see Figure 2), decreasing the thermal
activation barrier for reversing spin direction and thereby accelerating the relaxation
process. As a consequence, the coercivity of the sample changes dramatically with
temperature. For example, at 2.6 K, the hysteresis loop shown in Figure 4 narrows
to one having a coercive field of less than 0.5 T [11]. As explained below in Section
5, the unusual steps apparent in the hysteresis curve are due to quantum tunneling of
the magnetization.

Figure 4. Schematic representation of a magnetic hysteresis loop observed for a single crystal of
[Mn1 2O1 2(MeCO2 ) 1 6(H2 O)4 ]·2MeCO2 H·4H2 O at 2.1 K (adapted from reference 11).

The presence of an energy barrier for reversing spin orientation suggests the
possibility of storing a bit of information as the direction of the spin in an
individual molecule (in addition to the other applications discussed in Section 6).
With Ueff ª 40 cm-1, the Mn12 cluster exhibits a magnetization relaxation half-life of
more than 2 months at 2 K; however, above 4 K this half-life is dramatically
reduced and magnetic hysteresis is no longer observed [9]. Thus, in order for these
molecules to be capable of storing information at more practical temperatures there

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is a clear need for clusters possessing a larger spin reversal barrier U. To meet this
challenge, one would like to identify or synthesize molecules bearing ground states
with exceptionally high spin S and a large negative axial anisotropy D.

3 Other Oxo-Bridged Cluster Magnets

Since the discovery of the remarkable magnetic properties of the Mn12 cluster, much
effort has been devoted to searching for other examples of molecules exhibiting such
behavior. The fruits of that effort are enumerated in Table 1 [7-9,12-40], with the
clusters arranged in order of decreasing Ueff. In most cases, Ueff was established using
AC susceptibility measurements, while S and D were determined by fitting
magnetization data and high-field EPR spectra [41], respectively. A variety of other
physical techniques can also be of utility in probing the magnetic anisotropy of
these systems, including high-field torque magnetometry and the use of micro-
SQUID arrays [42,43].

Table 1. Examples of Single-Molecule Magnets.

S D (cm-1) Ueff (cm-1) ref

[Mn12O12(CH2BrCO2)16(H2O)4] 10 56a 12
[Mn12O12(CHCl2CO2)8(But CH2CO2)8(H2O)4] 10 -0.45 50 13
[Mn12O12(CHCl2CO2)8(EtCO2)8(H2O)4] 10 -0.42 49 13
[Mn12O12(MeCHCHCO2)16(H2O)4] 10 -0.44 45 14
[Mn12O12(p-PhC6H4CO2)16(H2O)4] 10 -0.44 45 14
[Mn12O12(p-MeC6H4CO2)16(H2O)4]b 10 44 15
[Mn12O12(MeCO2)16(H2O)4] 10 -0.5 42 7-9
[Mn12O12(MeCO2)8(Ph2PO2)8(H2O)4] 10 -0.41 42 16
[Mn12O12(PhCO2)16(H2O)4]1- 19
/2 -0.44 40 17
[Mn30O24(OH)8(But CH2CO2)32(H2O)2(MeNO2)4] 7 -0.79 39c 18
[Mn12O12(CHCl2CO2)16(H2O)4]2- 10 -0.27 27c 19
[Mn12O12(p-MeC6H4CO2)16(H2O)4]d 10 26 15
[Mn12O8Cl4(PhCO2)8(hmp)6]e 7 -0.6 21 20
[Mn9O7(MeCO2)11(thme)(py)3(H2O)2]f 17
/2 -0.29 19 21
[Fe8O2(OH)12(tacn)6]8+ g 10 -0.19 15 22
[V4O2(EtCO2)7(bpy)2]1+ h 3 -1.5 14c 23
[Mn4(MeCO2)2(pdmH)6]2+ i 8 -0.24 12 24
[Mn4O3(p-MeC6H4CO2)4(dbm)3]j 9
/2 -0.62 12c 25
[Mn4(hmp)6Br2(H2O)2]2+ e 9 -0.35 11 26
[(Me3tacn)6MnMo6(CN)18]2+ k 13
/2 -0.33 10 27
[Fe19O6(OH)14(metheidi)10(H2O)12]1+ l 33
/2 -0.035 9.5c 28
[Mn4O2(MeO)3(PhCO2)2L2(MeOH)]2+ m 7
/2 -0.77 9.2c 29

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 [Mn4O3Br(MeCO2)3(dbm)3]j 9
/2 -0.50 8.3 30
[Mn4O3Cl(MeCO2)3(dbm)3]j 9
/2 -0.53 8.2 31
[Ni12(chp)12(MeCO2)12(H2O)6(THF)6]n 12 -0.047 7 32
[Mn10O4(biphen)4Br12]4- o 12 -0.037 4.9 33
[(tetren)6Ni6Cr(CN)6]9+ p 15
/2 4.2 34
[Fe10Na2O6(OH)4(PhCO2)10(chp)6(H2O)2-
(MeCO2)2]n 11 3.7 35
[Ni4(MeO)4(sal)4(MeOH)4]q 4 3.7 36
[Mn9(O2CEt)12(pdm)2(pdmH)2(C14H16N2O4)2]i 11
/2 -0.11 3.1 37
[Ni21(OH)10(cit)12(H2O)10]16- r 3 2.9 38
[Fe4(MeO)6(dpm)6]s 5 -0.2 2.4 39
[Fe2F 9]3- 5 -0.15 1.5 40
a
This sample also displays a second relaxation process with U eff = 23 cm- 1. b Crystallized with three
water solvate molecules. cEstimated value (U), based upon S and D; typically, the measured value
(U eff) is somewhat lower, owing to quantum tunneling of the magnetization. d Crystallized with one p-
MeC6 H4 CO2 H solvate molecule. ehmpH = 2-hydroxymethylpyridine. fthmeH3 = 1,1,1-
tris(hydroxymethyl)ethane. g tacn = 1,4,7-triazacyclononane. h bpy = 2,2¢-bipyridine. ipdmH2 =
pyridine-2,6-dimethanol. jdbmH = dibenzoylmethane. kMe3 tacn = N,N¢,N¢¢-trimethyl-1,4,7-
triazacyclononane. lmetheidiH3 = N-(1-hydroxynethylethyl)iminodiacetic acid. m L = 1,2-bis(2,2¢-
bipyridine-6-yl)ethane. n biphen = 2,2¢-biphenoxide. o chp = 6-chloro-2-pyridonate. p tetren =
tetraethylenepentamine. q salH = salicylaldehyde. rcit4 - = citrate. sdpmH = dipivaloylmethane.

A quick inspection of Table 1 reveals that by far the majority (30 out of 33) of
the known single-molecule magnets are clusters in which the metal centers are
bridged by oxygen donor atoms. Of these, most are manganese-containing species,
with only a few clusters featuring iron or nickel and just one containing vanadium.
Ground state spins range from S = 3 to S = 33/2, while the D values measured vary
between -0.037 and -1.5 cm-1. Significantly, the highest values of Ueff are still held
by [Mn12O12(RCO2)16(H2O)4] clusters with an S = 10 ground state and the core
structure depicted in Figure 1.
The all-important magnetic anisotropy of these clusters stems from anisotropy
in the electronic structure of the individual metal centers, which in turn arises from
spin-orbit coupling. Metal ions with orbital angular momentum and a strong
tendency to undergo a Jahn-Teller distortion are particularly suitable for generating a
large overall D value. For example, the manganese-oxo clusters listed in Table 1 all
contain octahedral MnIII centers with a t 2g3eg1 electron configuration. In the
[Mn12O12(MeCO2)16(H2O)4] cluster (see Figure 1) the MnIII centers all display a
distorted coordination environment consisting of a tetragonal elongation, which
occurs roughly perpendicular to the disc of the molecule and coincident with its easy
axis. Indeed, variants of the Mn12 cluster structure in which some of the tetragonal
elongation axes are not so aligned show significantly reduced spin-reversal energy
barriers [15,16]. The anisotropy in other metal-oxo single-molecule magnets results
from pseudooctahedral VIII (t 2g2eg0), FeIII (t 2g3eg2), or NiII (t2g6eg2) centers. Very
recently, [Co4(hmp)4(MeOH)4Cl4] (hmpH = hydroxymethylpyridine), an S = 6

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ground-state cluster containing pseudooctahedral CoII (t2g5eg2) centers, was reported to
behave as a single-molecule magnet with an exceptionally large overall anisotropy
estimated at D = -3 cm-1 [44]. It is worth noting that metal centers such as VIII and
CoII, which typically display an individual anisotropy where D is positive, can in
fact give rise to clusters with a negative overall D value [23,44]. In fact, systems
involving these two metal ions in particular would seem to hold considerable
promise for the development of new single-molecule magnets with high spin-
reversal barriers. Unfortunately, not much is yet understood about how to control or
predict the overall magnetic anisotropy of a cluster, even knowing the nature of the
anisotropy associated with its constituent metal centers [45].
The molecules listed in Table 1 represent only a rather low percentage of the
metal-oxo clusters that have been prepared and investigated for their magnetic
properties. It is not sufficient for a cluster simply to have a large number of
interacting paramagnetic metal centers, since very frequently these will conspire to
produce a ground state of low or zero net spin. For the most part, the clusters are
synthesized in one-step self-assembly reactions, from which it is usually impossible
to predict the structure of the product a priori. The difficulty lies in the enormous
structural variability encountered in metal-oxo cluster systems, which, while
fascinating from many perspectives, waylays most attempts at developing rational
approaches to their synthesis. For a given cluster product considerable variation is
possible in the nuclearity, the M-O-M angles (90-180°), and the coordination
number of the bridging oxygen atoms (2-6). Moreover, the pairwise magnetic
exchange interactions within a cluster are highly sensitive to geometry, making it
all but impossible to predict the magnetic properties of a complex metal-oxo
cluster. Thus, the discovery of new metal-oxo single-molecule magnets remains
very much a serendipitous process.

4 Cyano-Bridged Clusters

As an alternative system where some control over structures and magnetic properties
can be anticipated, a number of researchers have turned to metal-cyanide clusters. In
a bridging coordination mode, cyanide binds only two metal centers and exhibits a
distinct preference for a linear geometry. Thus, assembly reactions can be set up
with the expectation that the product will feature linear M’-CN-M moieties.
Moreover, given this bridging arrangement, it is possible to predict the nature of the
magnetic exchange interactions between M’ and M (see Figure 5) [46,47].
Assuming an octahedral coordination geometry for both metal centers, unpaired
electrons in orbitals of compatible symmetry (t2g + t 2g or e g + eg) will couple
antiferromagnetically, while those in orthogonal orbitals (t2g + eg) will couple
ferromagnetically. The antiferromagnetic interaction is typically stronger than the
ferromagnetic interaction, and will dominate the superexchange in a competitive

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situation. Furthermore, the strength of the exchange interaction depends critically
upon the degree of overlap between the metal- and cyanide-based orbitals, and,
consequently, is high when the radially-extended d orbitals of low-valent early
transition metals are involved.

Antiferromagnetic:
M' C N M

t2g
t2g M
M' C N

M' C N M

Ferromagnetic:
eg
M
t2g

M' C N

Figure 5. Orbital interactions across a bridging cyanide ligand giving rise to magnetic superexchange.
Upper: Unpaired electrons in symmetry compatible t2g orbitals interact through cyanide p * orbitals,
resulting in antiferromagnetic coupling (via the Pauli exclusion principle). In actuality, this is a bit of an
oversimplification, as electronic structure calculations indicate that the p orbitals of cyanide are
responsible to nearly the same extent [47]. Lower: Unpaired electrons from incompatible metal-based
orbitals leak over into orthogonal cyanide-based orbitals, resulting in ferromagnetic coupling (via
Hund’s rules).

Much of the confidence in being able to control the structures and magnetic
properties of metal-cyanide clusters is predicated by extensive investigations into
magnetic Prussian blue type solids [46-54]. These compounds have proven to
exhibit highly adjustable magnetic behavior, and are generally synthesized via
aqueous assembly reactions of the following type.
x[M(H2O)6]y+ + y[M’(CN)6]x- Æ Mx [M’(CN)6]y ·zH2O (2)
The resulting structures are based on an extended cubic lattice of alternating M and
M’ centers connected through linear cyanide bridges. Two different metal sites are
present in the framework, one in which the metal, M’, is coordinated by the carbon
end of cyanide and experiences a strong ligand field, and another in which the metal,
M, is coordinated by the nitrogen end of cyanide and experiences a weak ligand field.
Recognition of how the aforementioned factors influence magnetic superexchange

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through cyanide has enabled chemists to produce solids of this type with bulk
magnetic ordering temperatures as high as 376 K [54].
A simple strategy for synthesizing molecular metal-cyanide clusters parallels
that employed in reaction 2, but utilizes blocking ligands to hinder formation of an
extended solid. The level of structural control possible is illustrated with the
assembly of clusters consisting of just one of the fundamental cubic cage units
comprising the Prussian blue structure type. Here, a tridentate ligand such as 1,4,7-
triazacyclononane (tacn) is employed to block three fac sites in the octahedral
coordination sphere of each precursor complex.
4[(tacn)M(H2O)3]x+ + 4[(tacn)M’(CN)3]y- Æ [(tacn)8M4M’4(CN)12]4(x-y)+ (3)
As in the reaction 2, the nitrogen end of the cyanide ligand displaces water to form
linear M’-CN-M linkages. Now, however, the tacn ligands, which are not so readily
displaced owing to the chelate effect, prevent growth of an extended Prussian blue
framework, and direct formation of a discrete molecular cube. Successful
implementation of this strategy has been demonstrated with the reaction between
[(tacn)Co(H2O)3]3+ and [(tacn)Co(CN)3] in boiling aqueous solution to form the
cubic [(tacn)8Co8(CN)12]12+ cluster depicted in Figure 6 [55,56]. Analogous clusters
capped by cyclopentadienyl, a mixture of cyclopentadienyl and carbonyl, or a
mixture of 1,3,5-triaminocyclohexane and water ligands have also been reported [57-
59].

Figure 6. Structure of the cubic cluster [(tacn)8 Co8 (CN)1 2] 1 2 +, as crystallized in [(tacn)8 Co8 (CN)1 2]-
(C7 H7 SO3 )·24H2 O [56]. Black, shaded, and white spheres represent Co, C, and N atoms, respectively;
H atoms are omitted for clarity.

In distinct contrast to the situation with metal-oxo clusters, once a new metal-
cyanide cluster has been discovered, one can be reasonably confident that it will be

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possible to substitute other transition metal ions having similar geometric
proclivities into the structure. This provides a potent means for attempting to
manipulate the strength of the magnetic exchange coupling, the overall spin of the
ground state, and even the magnetic anisotropy within a cluster. The maximum spin
ground state attainable for a cubic M4M’4(CN)12 cluster, however, is S = 10,
corresponding, for example, to the case where ferromagnetic coupling is expected to
arise between M = NiII (t2g6eg2) and M’ = CrIII (t2g3eg0). Note that this is the same as
the spin in the original Mn12 single-molecule magnet.
To produce the exceptionally large spin states ultimately sought in single-
molecule magnets, it is necessary to develop methods for constructing higher
nuclearity clusters in which an even greater number of metal centers are
magnetically coupled. One simple idea for accomplishing this is to carry out
assembly reactions with a blocking ligand on only one of the components in
reaction 3. Accordingly, the following reaction performed in boiling aqueous
solution was found to yield a fourteen-metal cluster (Me3tacn = N,N’,N”-trimethyl-
1,4,7-triazacyclononane) [56].
8[(Me3tacn)Cr(CN)3] + 6[Ni(H2O)6]2+ Æ [(Me3tacn)8Cr8Ni6(CN)24]12+ (4)
As depicted in Figure 7, the product exhibits a core structure consisting of a cube of
eight CrIII centers connected through cyanide bridges to six NiII centers positioned
just above the faces of the cube. Note, however, that the carbon ends of the cyanide
ligands are now bound to NiII, whereas they were initially bound to CrIII in the
reactants. Apparently, in the course of heating the reaction, sufficient thermal energy

Figure 7. Structure of the face-centered cubic cluster [(Me3 tacn)8 Cr8 Ni6 (CN)2 4] 1 2 +, as crystallized in
[(Me3 tacn)8 Cr8 Ni6 (CN)2 4](NO3 )·54H2 O [56]. Black, crosshatched, shaded, and white spheres
represent Cr, Ni, C, and N atoms, respectively; H atoms are omitted for clarity.

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is available to induce isomerization of the cyanide ligand to give the
thermodynamically-preferred NiII-CN-CrIII orientation. Unfortunately, this has the
added effect of driving the NiII centers toward a square planar coordination geometry
with a low-spin diamagnetic electron configuration, thereby destroying any exchange
coupling with the surrounding CrIII centers. The isomerization of cyanide can be
forestalled, however, by carrying out reaction 4 at -40 °C in methanol, resulting in a
metastable cluster of nominal formula [(Me3tacn)8(H2O)x (MeOH)y Ni6Cr8(CN)24]12+.
Magnetic susceptibility and magnetization data collected for samples containing this
cluster are consistent with the expected ferromagnetic coupling between CrIII and
high-spin NiII, giving rise to an S = 18 ground state.
Similar approaches have led to numerous other molecular metal-cyanide clusters
[52,60]. The highest nuclearity geometries yet uncovered occur in the tetracapped
edge-bridged cubic [(Me3tacn)12Cr12Ni12(CN)48]12+ and double face-centered cubic
[(Me3tacn)14Cr14Ni13(CN)48]20+ clusters recently reported [61]. Although these both
contain diamagnetic NiII centers as a consequence of isomerization of the cyanide
ligands, isolation of the high-spin form of the latter species would presumably
result in a cluster with an S = 34 ground state. While a spin state of this magnitude
has not yet been realized, many other high-spin metal-cyanide clusters have now
been characterized. Table 2 presents these in order of decreasing S. Topping the list
are body-centered, face-capped cubic clusters produced through reactions between
Mn2+ ions and [M(CN)8]3- (M = Mo, W) complexes in methanol or ethanol.
Magnetic susceptibility and magnetization data for [(EtOH)24Mn9W6(CN)48] clearly
indicate antiferromagnetic coupling between the MnII and WV centers to give an S =
39
/2 ground state [63]. Surprisingly, the analogous [(MeOH)24Mn9Mo6(CN)48] cluster
instead appears to exhibit ferromagnetic coupling and an S = 51/2 ground state,
although there may still be some question as to whether desolvation has complicated
the measurements [62]. Regardless, these are the highest spin ground states yet
observed for a molecular cluster, surpassing the previous record of S = 33/2 held by
[Fe19O6(OH)14(heidi)10(H2O)12]1+ (heidiH3 = N(CH2COOH)2(CH2CH2OH)) [81].
In most cases, Table 2 also lists the coupling constant J characterizing the
exchange interactions through cyanide within the clusters. Here, an exchange
Hamiltonian of the pairwise form Hˆ = -2J Sˆ 1· Sˆ 2 has been employed. Occasionally,
researchers will use an alternative convention where the exchange Hamiltonian is
instead of the form Hˆ = -J Sˆ 1· Sˆ 2, making it extremely important to cite which
convention has been adopted for the sake comparing J values. Note that with either
form, a negative J value indicates antiferromagnetic coupling, while a positive J
value indicates ferromagnetic coupling. These magnetic coupling constants are
normally obtained by fitting the temperature dependence of the measured magnetic
susceptibility using a model exchange Hamiltonian that incorporates all of the
pairwise exchange parameters for the pertinent cluster geometry. With metal-cyanide
clusters, it is usually sufficient to include only the exchange between metal centers

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 Table 2. Examples of High-Spin Metal-Cyanide Clusters.

S J (cm-1)a ref
II V 51
[(MeOH)24Mn Mo (CN)48]
9 6 /2 + 62
II V 39
[(EtOH)24Mn W (CN)48]
9 6 /2 - 63
[(Me3tacn)8(H2O)x (MeOH)y NiII6CrIII8(CN)24]12+ b 18 + 56
[(TrispicMeen)6MnII6CrIII(CN)6]9+ c 27
/2 -4.0 64
[(dmptacn)6MnII6CrIII(CN)6]9+ d 27
/2 -5 65
[(MeOH)24NiII9MV6(CN)48] (M = Mo, W) 12 ca. +16 66
[(IM2-py)6NiII3CrIII2(CN)12]e 9 +5 67
[(tetren)6NiII6CrIII(CN)6]9+ f 15
/2 +8.4 68
[(IM2-py)6NiII3FeIII2(CN)12]e 7 +3.4 69
[(Me3tacn)6MnIICrIII6(CN)18]2+ b 13
/2 -3.1 70
[(Me3tacn)6MnIIMoIII6(CN)18]2+ b 13
/2 -6.7 27
[(bpy)6(H2O)2MnII3WV2(CN)16]g 13
/2 -6.0 71
[(HIM2-py)6NiII3CrIII2(CN)12]e 6 +6.8e 72
[(tach)4(H2O)12NiII4FeIII4(CN)12]8+ h 6 +6.1 59
[(Me3tacn)2(cyclam)3(H2O)2NiII3MoIII2(CN)6]6+ bi 6 +8.5, +4.0 73
[(5-Brsalen)2MnIII2FeIII(CN)6]1- j 9
/2 +2.3 74
[(Tp)3(H2O)3FeIII4(CN)9]k 4 + 75
[(Me3tacn)2(cyclam)NiIICrIII2(CN)6]2+ bi 4 +10.9 56
[(bpm)6NiII3FeIII2(CN)12]l 4 +5.3, -1.7 76
[(bpy)6NiII3FeIII2(CN)12]g 4 +3.9 77
[(Me3tacn)2(cyclam)NiIIMoIII2(CN)6]2+ bi 4 +17.6 73
[(H2L)2NiII2FeIII3(CN)18]1- m 7
/2 +2.1 78
[(tach)(H2O)15NiII3FeIII(CN)3]6+ h 7
/2 +0.8 59
[(dmbpy)4(IM2-py)2CuII2FeIII2(CN)4]6+ n 3 +4.9 79
[(edma)3CuII3CrIII(CN)6]o 3 +9.2 80
a
For clusters where it has not been explicitly determined, only the sign of J is given. b Me3 tacn =
N,N¢,N¢¢-trimethyl-1,4,7-triazacyclononane. cTrispicMeen = N,N’,N”-(tris(2-pyridylmethyl)-N’-
methylethan)1,2-diamine. d dmptacn = 1,4-bis(2-methylpyridyl)-1,4,7-triazacyclononane. eIM2-py = 2-
(2-pyridyl)-4,4,5,5-tetramethyl-4,5-dihydro-1H-imidazolyl-1-oxy. ftetren = tetraethylenepentamine.
g
bpy = 2,2’-bipyridine. h tach = 1,3,5-triaminocyclohexane. icyclam = 1,4,8,11-
tetraazacyclotetradecane. j5-Brsalen = N,N’-ethylenebis(5-bromosalicylideneiminato) dianion. kTp =
hydrotris(1-pyrazolyl)borate. lbpm = bis(1-pyazolyl)methane. m L = 3,10-bis(2-aminoethyl)-
1,3,6,8,10,12-hexaazacyclotetradecane. n dmbpy = 4,4’-dimethyl-2,2’-bipyridine. o edma =
ethylenediaminemonoacetate.

directly connected to each other through a cyanide bridge. For the clusters in Table
2, measured J values range in magnitude from 0.8 to 17.6 cm-1. Overall, the
coupling tends to be a bit weaker than observed for oxo-bridged clusters. Given an
appropriate choice of metal ions, however, the coupling through a cyanide bridge
can be much stronger, and the highest J value yet observed is -113 cm-1, occurring
in the dinuclear molybdenum(III) complex [Mo2(CN)11]5- [82].

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 Ultimately, the strength of the magnetic exchange coupling is quite important
if single-molecule magnets are to be produced that retain their unusual properties at
higher temperatures. This is because J dictates how high excited spin states are
above the ground state, and if these are close in energy then the spin reversal barrier
may be compromised by their thermal population. Thus, identification of a linear
bridging ligand that could be utilized in place of cyanide and deliver stronger
magnetic exchange coupling would be of considerable value. A little-explored means
of potentially achieving molecules with well-isolated, high-spin ground states
involves use of electron delocalization to generate strong magnetic exchange
coupling via a double-exchange mechanism [83].
Although high-spin, the clusters occupying the top six entries of Table 2 all
approximate Oh symmetry. While this does not necessarily preclude development of
magnetic anisotropy (since a very slight structural distortion could accompany
magnetic polarization), it certainly might act against it. Indeed, none of these very
high-spin molecules have been shown to exhibit single-molecule magnet behavior.
Consequently, the development of strategies for synthesizing high-nuclearity metal-
cyanide clusters with a more anisotropic overall geometry presents an important
goal. An example of a high-spin species with a lower-symmetry geometry is the
trigonal prismatic cluster [(Me3tacn)6MnCr6(CN)18]2+ depicted in Figure 8 [70]. This
molecule has an S = 13/2 ground state, and was obtained serendipitously from a
reaction between Mn2+ and [(Me3tacn)Cr(CN)3] in aqueous solution. Although it
displays a unique molecular axis, the cluster still does not behave as a single-
molecule magnet, owing to the negligible single-ion anisotropy associated with its
MnII (t2g3eg2) and CrIII (t2g3eg0) centers.

Figure 8. Structure of the trigonal prismatic cluster [(Me3 tacn)6 MnCr6 (CN)1 8] 2 +, as crystallized in
K[(Me3 tacn)6 MnCr6 (CN)1 8](ClO4 ) 3 [70]. Black, crosshatched, shaded, and white spheres represent
Mo, Mn, C, and N atoms, respectively; H atoms are omitted for clarity.

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 In fact, very few of the clusters listed in Table 2 contain metal ions likely to
contribute to a large overall magnetic anisotropy. As stated previously, however, it
is frequently possible to substitute other metal ions into a known metal-cyanide
geometry, thereby potentially altering the ground state anisotropy. Accordingly, a
straightforward approach to producing single-molecule magnets might be to replace
the metal centers of the lower-symmetry clusters in Table 2 with ions known to
deliver the anisotropy in metal-oxo single-molecule magnets, particularly MnIII, VIII,
and CoII. Another idea is simply to move down the column in the periodic table and
utilize second- or third-row transition metal ions. Since spin-orbit coupling is a
relativistic phenomenon, this will generally enhance significantly any single-ion
anisotropy. For example, while [Cr(acac)3] (acac = acetylacetonate) has an axial zero-
field splitting of |D| = 0.59 cm-1 [84], [Mo(acac)3] exhibits a large negative D value
of -6.3 cm-1 [85]. Hence, replacing the CrIII centers in a cluster with MoIII might be
expected to impart magnetic anisotropy while preserving the spin of the ground
state. As an added advantage, the strength of the magnetic exchange coupling in the
cluster should also increase, owing to the more diffuse valence d orbitals of MoIII.
Synthesis of the octahedral complex [(Me3tacn)Mo(CN)3] [73] enabled a
demonstration of precisely these effects. Simply employing it in place of
[(Me3tacn)Cr(CN)3] in the preparation established for the trigonal prismatic cluster
[(Me3tacn)6MnCr6(CN)18]2+ (see Figure 8), resulted in an isostructural product
containing [(Me3tacn)6MnMo6(CN)18]2+ [27]. Incorporating MoIII, this cluster still
has a ground state of S = 13/2, but with an axial zero-field splitting of D = -0.33 cm-1
and an exchange coupling constant that has increased from -3.1 cm-1 to -6.7 cm-1.
AC susceptibility measurements indeed show it to behave as a single-molecule
magnet with Ueff = 10 cm-1.
Ultimately, it is anticipated that similar substitutions in higher-spin metal-
cyanide clusters may lead to new examples of single-molecule magnets with
significantly enhanced spin-reversal energy barriers.

5 Quantum Tunneling of the Magnetization

Owing to the extremely high level of interest from physicists, a substantial body of
literature already exists on quantum tunneling of the magnetization in single-
molecule magnets. Rather than attempting a complete overview of the subject here,
we will give only a very basic description of the phenomenon.
In 1996, two groups of researchers independently proposed an explanation for
the unusual steplike features apparent in the magnetic hysteresis loops obtained
from samples of [Mn12O12(MeCO2)16(H2O)4]·2MeCO2H·4H2O [11,86,87]. Inspection
of Figure 4 reveals, for example, four steps on each side of the hysteresis loop
collected at 2.1 K. These steps originate from a loss of spin polarization in the

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molecules due to tunneling of the magnetization through the energy barrier U rather
than simple thermal activation. This tunneling only occurs with the resonant
alignment of two (or more) M S levels on the left and right sides of the energy
diagram displayed in Figure 2. As shown, in zero applied magnetic field each M S =
+N level is aligned with the corresponding M S = -N level, fulfilling the resonance
condition. Indeed, the first step in the hysteresis loop shown in Figure 4 arises at H
= 0. The tunneling does not necessarily transpire between the pair of levels lowest
in energy, and in fact the probability of tunneling increases as one progresses
upward toward M S = 0. Thus, much of the loss of magnetization is a result of
thermally-assisted tunneling between higher energy levels. As the strength of the
applied magnetic field is increased, the MS levels shift in energy, with the lower
levels going up on one side and down on the other until eventually the spin reversal
barrier disappears. Between these two extremes lie a number of field strengths at
which a resonance occurs that again permits tunneling of the magnetization.
Accordingly, the positions of the steps in the hysteresis loops can be used to map
out the M S energy levels of the ground state.
Certain differences in the rate of tunneling are observed between the various
single-molecule magnets. The distinction can be particularly evident at extremely
low temperatures, where the thermal energy no longer assists the tunneling process.
For example, this temperature-independent regime is much more readily attained in
the cluster [Fe8O2(OH)12(tacn)6]8+ (which also has an S = 10 ground state) than in the
Mn12 cluster [88]. The discrepancy has been attributed to the greater transverse
component to the anisotropy of the former molecule. That is, the Fe8 cluster shows
a significantly larger value for the rhombic zero-field splitting parameter E (as well
as fourth order terms), resulting in a greater degree of mixing between the M S = ±N
levels, which, in turn, facilitates tunneling [89].

6 Potential Applications

Several applications for single-molecule magnets have been envisioned.

Perhaps the most obvious of these is their potential future use as magnetic data
storage media. Here, the idea is that an individual molecule would be capable of
storing a single bit of binary information as the direction of its magnetization—i.e,
with spin up representing, say, a 0 and spin down representing a 1. With a diameter
of just 1-2 nm, this could lead to surface storage densities as high as 200,000
Gbits/in2, approximately three orders of magnitude greater than can be achieved with
current magnetic alloy film technology. Data storage density is of particular import
in computer hard drives, where the distance between bits of information places
constraints upon the speed and efficiency of the computer. Thus, the use of self-
assembled monolayers of single-molecule magnets as a storage media could one day
lead to extremely fast computer hard drives. Clearly, a significant challenge that

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must be met in order for this idea to come to fruition is the development of methods
for reading and writing such miniscule magnetic moments. Another challenge, and
one that is more amenable to chemists, lies in the synthesis of molecules having
larger spin reversal barriers U, which would then permit storage of information at
more accessible temperatures. As discussed previously, this entails constructing
molecules possessing a well-isolated ground state with a very high spin S and a
large negative axial zero-field splitting D. In addition, since quantum tunneling of
the magnetization could contribute to the loss of information, one would ideally like
these molecules to exhibit no transverse anisotropy.
Recently, it has been shown theoretically that single-molecule magnets could
be used as the memory components in quantum computing [90-92]. A single crystal
of the molecules could potentially serve as the storage unit of a dynamic random
access memory device in which fast electron spin resonance pulses are used to read
and write information [90]. This application would take advantage of the quantized
transitions between the numerous MS levels in the ground state of a single-molecule
magnet, but must be implemented at very low temperature (below ca. 1 K) to avoid
transitions due to spin-phonon interactions. Such a device would have an estimated
clock speed of 10 GHz and could store any number between 0 and 22S-2 (= 2.6 ¥ 105
for S = 10). Thus, to maximize the capacity of the memory, one would like to have
a single-molecule magnet with as large a spin S as feasible. In addition, to ensure
that resolution of the level structure within the ground state manifold is maintained,
it is important for the magnitude of D also to be large.
Finally, it has been suggested that single-molecule magnets might be of utility
as low-temperature refrigerants via the magnetocaloric effect [92,93]. This
application would take advantage of the large entropy change that occurs upon
application of a magnetic field to a sample of randomized spins. Since each cluster
magnet is identical, the change occurs only over a very narrow temperature window
centered at its blocking temperature (3 K for the Mn12 cluster). In order to extend the
range of accessible refrigeration temperatures, single-molecule magnets with higher
blocking temperatures (i.e., with larger spin-reversal energy barriers U) would be of
value.

7 Acknowledgments

This work was funded by NSF Grant No. CHE-0072691. I thank Ms. J. J. Sokol
for helpful discussions.

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