Molecular spin clusters: new synthetic approaches and neutron scattering studies.

Abstract

We review our recent work in the field of molecular spin clusters and single-molecule magnets, showing how inelastic neutron scattering (INS) can be used to determine magnetic exchange interactions and anisotropy splittings. A general introduction to neutron scattering precedes selected examples, building upon the first determination of exchange coupling in a transition metal complex using INS, through anisotropic exchange in cobalt(II) spin clusters to the determination of exchange interactions in a dodecanuclear nickel(II) wheel. The strength of INS for the accurate determination of anisotropy splittings in single-molecule magnets is revealed. Not only can one determine the axial zero-field splitting parameter D, which plays a key role in single-molecule magnet behavior, but also higher-order terms important in understanding the quantum tunneling behavior. Finally, we review two of our synthetic approaches towards new single-molecule magnets based on nickel, manganese, and iron.

Full text

Page 1

910
¹ 2003 Wiley-VCH Verlag GmbH&Co. KGaA, Weinheim
DOI: 10.1002/cphc.200300689
CHEMPHYSCHEM 2003, 4, 910±926

Page 2

CHEMPHYSCHEM 2003, 4, 910±926
DOI: 10.1002/cphc.200300689
¹ 2003 Wiley-VCH Verlag GmbH&Co. KGaA, Weinheim
911
Molecular Spin Clusters: New Synthetic
Approaches and Neutron Scattering Studies
Reto Basler, Colette Boskovic, Gre ¬gory Chaboussant, Hans U. G¸del,* Mark Murrie,
Stefan T. Ochsenbein, and Andreas Sieber[a]
We review our recent work in the field of molecular spin clusters
and single-molecule magnets, showing how inelastic neutron
scattering (INS) can be used to determine magnetic exchange
interactions and anisotropy splittings. A general introduction to
neutron scattering precedes selected examples, building upon the
first determination of exchange coupling in a transition metal
complex using INS, through anisotropic exchange in cobalt(II) spin
clusters to the determination of exchange interactions in a
dodecanuclear nickel(II) wheel. The strength of INS for the accurate
determination of anisotropy splittings in single-molecule magnets
is revealed. Not only can one determine the axial zero-field splitting
parameter D, which plays a key role in single-molecule magnet
behavior, but also higher-order terms important in understanding
the quantum tunneling behavior. Finally, we review two of our
synthetic approaches towards new single-molecule magnets based
on nickel, manganese, and iron.
KEYWORDS:
exchange interactions ¥ inelastic neutron scattering ¥ mag-
netic properties ¥ single-molecule magnets ¥ spin clusters
1. Introduction
Polynuclear complexes of transition-metal ions with unpaired
electrons have long served as molecular models for magnetic
materials with extended interactions. They are appealing to
chemists, because molecular concepts can be used both in their
experimental investigation and in theoretical approaches to
treat the exchange interactions. In contrast to magnetic systems
with extended interactions, exact solutions of the appropriate
effective Hamiltonian of a spin cluster can often be obtained.
This enables the determination of the relevant exchange and
anisotropy parameters from experimental data. Since nearest-
neighbor interactions are also the dominant interactions in
extended magnets, the results obtained for a dimer are relevant
and transferable to the systems with extended interactions.
Whereas anisotropy is still poorly understood and thus difficult
to control and tune in real systems, there has been considerable
progress in understanding and thus controlling exchange
interactions. Magnetostructural correlations, that is, the depend-
ence of the exchange coupling on the nature of the bridging
ligands as well as on bond angles and distances, were
established in the 1970s, following the pioneering work of
Goodenough, Kanamori, and Anderson.[1]Molecular orbital (MO)
approaches at various levels of sophistication were then used to
rationalize the correlations.[2, 3]On the experimental side there
has been an enormous development in the general field of
molecular magnetism in the past three decades, and this has
been mainly transdisciplinary including chemistry and physics.
Our contribution has been the introduction of inelastic neutron
scattering (INS) for the study of spin clusters. INS allows the
direct spectroscopic determination, in zero magnetic field, of
exchange interactions and anisotropy parameters in the cluster
ground state. In Section 2, both experimental and theoretical
aspects of the application of INS to molecular magnetic clusters
will be briefly reviewed. Starting with the acid rhodo complex,
the first spin cluster studied by INS,[4]Section 3 will illustrate the
power of INS for the determination of exchange interactions.
Similarly, examples of anisotropy splittings, determined by INS,
will be presented in Section 4.
The discovery, about ten years ago, of so-called single-
molecule magnets (SMMs) has provided an enormous boost to
the research of spin clusters.[5]They are no longer just molecular
models for extended magnets; their own properties have
become the focus of a very extensive and intensive research
activity. This includes experiment and theory, physics and
chemistry, as well as materials sciences. It is not the objective
of this article to review this field, and we refer to references
[5c, d, 6, 7] for this. We provide a selective review of our own
activities in this field. In light of the interdisciplinary nature of this
research area, the article is divided into two parts. Firstly, we
focus on INS of molecular clusters (Sections 2±4) and then upon
the structure and magnetic properties of new clusters synthe-
sized in our group (Sections 5±6).
[a] Prof. Dr. H. U. G¸del, R. Basler, Dr. C. Boskovic, Dr. G. Chaboussant,
Dr. M. Murrie, S. T. Ochsenbein, A. Sieber
Departement f¸r Chemie und Biochemie
Universit‰t Bern, Freiestrasse 3
3000 Bern 9 (Switzerland)
Fax: (?41) 31±631±4399
E-mail: hans-ulrich.guedel@iac.unibe.ch

Page 3

H. G¸del et al.
912
¹ 2003 Wiley-VCH Verlag GmbH&Co. KGaA, Weinheim
www.chemphyschem.org
CHEMPHYSCHEM 2003, 4, 910±926
2. Neutron Scattering: General Background
2.1 Introduction
Over the last 40 years neutrons have become an extremely
useful tool for studying basic properties of matter. For this
purpose, neutrons are generally produced either by specially
designed nuclear reactors or by pulsed sources. In both cases
monochromatic neutron beams are generated by use of
monochromators or disk choppers and directed to the target
sample. Characteristics such as wavelength (energy) and direc-
tion (wave vector) of the incoming and outgoing neutrons are
then recorded using detectors and monitors.
The interaction between an incoming beam of neutrons and
the sample under investigation is extremely rich and provides
invaluable information about the structure, atomic motion and
Reto Basler was born in 1974. He
studied chemistry and physics at the
University of Berne and graduated in
1998. Since 1999 he has been working
in the G¸del group as a Ph.D. student
on the topic of inelastic neutron scat-
tering of molecular magnets.
Colette Boskovic obtained her Ph.D.
from the University of Melbourne in
1998. From 1999±2001 she was a
postdoctoral fellow at Indiana Uni-
versity with George Christou. Since
2001 she has been a postdoctoral
fellow at the University of Berne in the
group of Hans G¸del. Her current
research interests are focused on the
synthesis and characterization of
polynuclear transition-metal com-
plexes as high spin molecules and
single-molecule magnets.
Gre ¬gory Chaboussant was born in
1970 in Argenteuil (France). He re-
ceived his Ph.D. in Physics from the
Joseph-Fourier University of Grenoble
in 1997. During 1998±2000, he in-
vestigated spin excitations in Giant
magnetoresistant (GMR) manganite
oxides at the ISIS neutron facility (RAL,
UK) with a TMR Marie-Curie postdoc-
toral fellowship. Since 2000, he has
been working on molecular-magnetic
systems using inelastic neutron scat-
tering.
Hans U.G¸del obtained his Ph.D. from
the University of Berne in 1969. Fol-
lowing postdoctoral positions in Co-
penhagen (1970±71) and at the
Australian National University in
Canberra (1972±74), he has been
Professor of Chemistry at the Uni-
versity of Berne since 1978. His re-
search interests are in physical inor-
ganic chemistry: optical spectroscop-
ic and magnetic properties of transi-
tion-metal and lanthanide
compounds.
Mark Murrie, born in 1971, received
his Ph.D. in chemistry from the Uni-
versity of Manchester in 1997. From
1997 to 1999, he was a postdoctoral
fellow at the University of Edinburgh
in the group of Richard Winpenny.
Subsequently, he moved to the group
of Hans G¸del, where his research
interests are in the synthesis, structure
and magnetic properties of transition-
metal spin clusters and single-mole-
cule magnets.
Stefan T. Ochsenbein was born in
1977 in Berne (Switzerland). He stud-
ied chemistry at the University of
Berne and graduated in 2001. He is
currently working as a Ph.D. student
in the group of Hans U. G¸del on the
synthesis of spin clusters and on
inelastic neutron-scattering studies.
Andreas Sieber was born in 1974 in
Berne (Switzerland). He studied
chemistry at the University of Berne
and graduated in 2000. He is currently
working as a Ph.D. student in the
group of Hans U. G¸del on inelastic
neutron scattering on spin clusters.

Page 4

Molecular Spin Clusters
CHEMPHYSCHEM 2003, 4, 910±926
www.chemphyschem.org
¹ 2003 Wiley-VCH Verlag GmbH&Co. KGaA, Weinheim
913
magnetic properties (magnetic order, phase transitions, mag-
netic excitations) of materials. This unique set of information,
that only neutron scattering can gather,arises from the following
basic properties of the neutron:
1) The neutron mass mNimplies that its wavelength ??h/mNv (v
is the neutron velocity and is of the order of 200±3000 ms?1)
is comparable to the interatomic distances (in ängstrom) in
liquid and solid phases, and so provides insight into the
structural and dynamic properties of the sample.
2) Neutrons have no electrical charge, which results in a highly
penetrating probe that is sensitive to the nuclei of the target.
For instance, the hydrogen atom is a strong neutron scatterer
but interacts very little with X-rays. In this respect, neutron
and X-ray scattering are complementary tools for investigat-
ing magnetic properties.
3) The neutron energy E?h2/2mN?2?? h2k2/2mNis comparable
to many excitations in condensed matter (k?2?/?). Neutrons
can interact inelastically with the sample, thus providing
information about the energy of those excitations, and
neutron wavelengths between 1 and 10 ä are commonly
used to probe these excitations.
4) Finally, the magnetic moment of the neutron couples to
those of the unpaired electrons of magnetic materials such
that neutron scattering provides detailed information about
the magnetic properties. Magnetic elastic scattering is widely
used to study magnetic ordering transitions, whereas mag-
netic inelastic scattering is a key technique to address
questions such as excitations and spin±spin correlations in
magnetic systems.
Given their unique characteristics, neutrons are perfectly
suited for investigating magnetic and lattice excitations in the
thermal range (E?100 meV), in contrast to resonance techni-
ques (NMR, EPR?electron paramagnetic resonance).
2.2 Neutron Scattering Cross-Sections
When a neutron hits the sample, three important things can
happen: 1) it is scattered by the nuclei in the sample, 2) it is
absorbed by the nuclei, and 3) it is scattered through the
magnetic interaction between the intrinsic neutron magnetic
moment (?) and the magnetic field (B) generated by the
unpaired electrons in the sample.
Nuclear scattering and absorption can have an important
impact on the feasibility of a magnetic neutron-scattering
experiment. The nuclear scattering has a very rich structure
and is responsible for elastic scattering (Bragg diffraction for
instance) and phonon scattering. The absorption leads to a loss
of intensity that can greatly influence the time needed to obtain
good statistics. In the task of determining the magnetic proper-
ties of a given system both the absorption and the nuclear
scattering are undesirable and we wish them to influence the
final result as little as possible.
During the scattering process, neutrons with initial energy (Ei)
and initial momentum (ki) are scattered by the sample. After the
scattering, detectors will collect neutrons with final energy (Ef)
and final momentum (kf). The conservation rules during this
scattering process impose the following definitions for the
energy transfer (? h?) between the neutron and the target
sample, and the momentum transfer (Q) [see Figure 1 and
Equation (1)]:
Figure 1. Schematic representation of a time-of-flight direct geometry neutron-
scattering spectrometer. A polychromatic (™white∫) neutron beam is produced at
the reactor. A monochromator selects the desired incident neutron energy Eiwith
kientirely defined. After the sample target, scattered neutrons are collected in an
array of time-resolved detectors. The time of arrival of the scattered neutrons is
recorded, from which the final neutron energy Efis determined. The final wave-
vector kfis deduced from the scattering angle 2? and Q?ki?kf.
? h? ? Ei?Ef? (? h2/2m)(ki2?kf2) and Q ? ki?kf
(1)
where ki?2?/?iand kf?2?/?fare the initial and final neutron
wave-vectors, respectively. Very generally, one can decompose
the overall scattering profile into two terms, the magnetic
scattering and the nuclear scattering: S(Q,?)?Smag(Q,?)?
Snuclear(Q,?), where the nuclear scattering itself is decomposed
into two terms, coherent scattering SC(Q,?) and incoherent
scattering SINC(Q,?). The nuclear scattering arises from the
isotropic scattering of the incoming neutrons by the various
nuclei present in the sample. The interaction potential between
a neutron (r) and a nucleus (Rj) is well described by the Fermi
pseudopotential: Vj(r)?bj?(r?Rj) where bj is the scattering
length of the jth nucleus. The scattering lengths depend in an
unsystematic way on the kind of nuclei (isotopes, nuclear spin)
that are present in the sample. The nuclear scattering intensity
for a system of N molecules can be expressed in terms of these
scattering lengths [Equation (2)]:
Inuclear(Q,?) ? N¥(kf/ki)¥[?CSC(Q,?)??INCSINC(Q,?)] (2)
where the coherent/incoherent cross-sections for the jth atom
are: ?jC??bj?2and ?jINC??bj2? ? ?bj?2(unit: 1 barn?
10?24cm2). The coherent and incoherent cross-sections can be
considered to be characteristic properties of the materials: a
complete list of cross-sections can be found in reference [8]. For
polyatomic materials, one has to add up the elemental cross-
sections according to the sample composition to get the total
coherent and incoherent cross-sections. ?C(tot)??jxj?jC and
?INC(tot)??jxj?jINC. The coherent scattering gives the nuclear
Bragg scattering and phonon peaks and the incoherent scatter-
ing gives usually broad quasielastic and inelastic (phonons)
features. The incoherent scattering is the main source of
background in the spectra of spin clusters due to their high
hydrogen content. The incoherent cross-section of hydrogen
(1H) is about40 times larger than that of deuterium (2H), and is by
far the single largest contribution to ?INC (tot) in most

Page 5

H. G¸del et al.
914
¹ 2003 Wiley-VCH Verlag GmbH&Co. KGaA, Weinheim
www.chemphyschem.org
CHEMPHYSCHEM 2003, 4, 910±926
undeuterated molecular samples. To reduce the incoherent
background it is therefore strongly recommended to deuterate
these materials when possible, or to substitute H by another
element having a small ?INC, such as F.
2.3 Magnetic Scattering
The basic expression for the magnetic scattering cross-section is
derived by making use of Fermi's Golden Rule from first-order
perturbation theory (this is equivalent to the Born approxima-
tion for scattering processes), whereby one assumes that the
interaction potential between the neutrons and the unpaired
electrons is small enough to be treated as a perturbation.
In the case of a monoatomic system with spin-only moments,
the partial differential cross-section for nonpolarized neutrons is
obtained as Equation (3):[9, 10]
d2?/d?dEf? (?r0)2¥(kf/ki)¥[1³2g F(Q)]2
¥exp(?2W(Q))¥??,?(??,??(Q?¥Q?)/Q2)¥S??(Q,?)(3)
where ???1.913 is the gyromagnetic ratio, r0?2.818?10?15m
is the classical radius of the electron, g is the Lande ¬ g-factor, and
F(Q) is the magnetic form factor of the ion, which falls off rapidly
with Q. The Debye±Weller factor exp(?2W(Q)) is a slowly
decaying function of Q and we will usually neglect it when
dealing with magnetic scattering. The factor (??,??(Q?¥Q?)/Q2)
means that the neutron can only couple to components of the
magnetic moment that are perpendicular to the wave-vector Q
and ?, ??x, y, z. The scattering function S??(Q,?) is the space
and time Fourier transform of the time-dependent spin±spin
correlation function and contains all the information about the
magnetic structure and spin dynamics. In the Schrˆdinger
notation the scattering function S??(Q,?) is given by Equation (4):
S??(Q,?) ? ?j,j?exp(iQ(rj?rj?)) ?i,fpi
?i?S√j?,??f??f?S√j,??i??(Ei?Ef?? h?)(4)
where Sj,?is the ? component of the spin operator Sjat position
rj, ?i? is the initial state with energy Ei, ?f? is the final state with
energy Ef, pn?exp(?En/kBT)/?nexp(?En/kBT) is the Boltzmann
factor of the state ?n? and ? h? is the energy transfer between
the neutrons and the spin system during the scattering process.
Importantly, the magnetic cross-section is proportional to the
square of the magnetic moment. Since S??(Q,?) contains all the
information about the spin system under investigation, its
determination and detailed knowledge is the primary objective
of any magnetic scattering experiment.
Several pieces of information, including information about
energy levels, can be obtained experimentally from magnetic
neutron scattering, from the positions of inelastic peaks, and the
Q dependence and intensity of those peaks. The position of the
energy levels is controlled by the microscopic magnetic
Hamiltonian of the system under investigation, and the peak
intensities are controlled by the magnetic form factor f(Q), the
interference factor exp(iQ(rj?rj?)) and the matrix elements of the
form ?i?Sj,??f? whichhave to be evaluated numerically in most
cases using for instance tensor operator methods. The general
procedure has been outlined for the simple case of dimers and
trimers in reference [12]. A detailed experimental access to the
inelastic peak positions, Q dependence, and temperature
dependence allows a very reliable determination of the mag-
netic properties and microscopic parameters of most magnetic
systems.
In the majority of our experiments we use aluminum
rectangular slabs of 45?35 mm with a thickness between 1
and 3 mm to ensure a satisfactory compromise between trans-
mission and the sample mass. The neutron-scattering experi-
ments presented in this review have been carried out using
triple-axis or more often time-of-flight spectrometers. In time-of-
flight spectrometers, a monochromatic beam of neutrons is
collimated onto the sample target and scattered by the sample
towards an array of time-resolved detector tubes. The array of
detectors varies from one instrument to the other but usually
covers a range of scattering angles 2? from 10±15? to 120±140?
(see Figure 1). It is trivial to show that the scattering vector Q is
directly derived from the knowledge of ki, kfand the scattering
angle 2?: Q2?ki2?kf2?2kikfcos(2?). The available incident
energies that are commonly used for magnetic studies also
depend on the particular instrument but vary usually from Ei?
1 meV (?i?9 ä) to Ei?80 meV (?i?1 ä; note that 1 meV?8 cm?1
?11.6 K).
The Q-? space that one can probe in the course of an
experiment depends strongly on 1) the choice of the incident
energy and 2) the kinematic constraints imposed by the
scattering triangle shown in Figure 1. Instrumental resolution
should also be considered and can be up to 2±4% of the
incident energy. As an example, for ?i?6 ä (Ei?2.3 meV) the
resolution (FWHM) is approximately 50 ?eV, while it increases to
200 ?eV at ?i?4 ä (Ei?5.1 meV).
3. Exchange Splitting in Spin Clusters
3.1 Exchange Coupling
The origin of the magnetic exchange interaction between
neighboring spins can be 1) direct exchange between orbitals of
interacting paramagnetic ions or 2) superexchange, when the
exchange occurs through a diamagnetic bridge. The overall type
of exchange interaction (ferro- or antiferromagnetic) depends on
the orbital overlap integrals, and interatomic distances and bond
angles. Analytical or numerical approaches for the exact
calculation of exchange couplings can be extremely complex,
and magnetic properties are modeled using effective exchange
parameters denoted J.[13]Several experimental methods are
available for determining J, such as magnetic susceptibility, heat
capacity, EPR, and INS. The first two methods are adequate as
long as one is dealing with relatively simple clusters. For more
complex systems, having more than one or two J parameters,
INS is the technique of choice, since it allows a direct,
spectroscopic access to the energy levels and therefore the
exchange interactions.

Page 6

Molecular Spin Clusters
CHEMPHYSCHEM 2003, 4, 910±926
www.chemphyschem.org
¹ 2003 Wiley-VCH Verlag GmbH&Co. KGaA, Weinheim
915
3.2 Hamiltonian
To describe magnetic interactions, we use a Heisenberg spin
Hamiltonian [Equation (5)]:
H√ ? ?2
?
ij
JijSi¥Sj
(5)
where the sum is over all interacting spin pairs. In this definition
J, the bilinear exchange parameter, is negative for antiferro- and
positive for ferromagnetic interactions. The above description is
accurate and reasonable, if one is dealing with magnetic ions
such as Mn2?, Fe3?, Cr3?, Ni2?, Cu2?with a small orbital
contribution to the ground state. The Co2?ion, on the other
hand, often has a strong orbital contribution to the ground state,
and can be most adequately described by an anisotropic
Hamiltonian [Equation (6)]:
H√ ? ?2
?
i?j
(Jij,xS√ix¥S√jx?Jij,yS√iy¥S√jy?Jij,zS√iz¥S√jz) (6)
In some cases it is necessary to include antisymmetric
exchange interactions (JSi?Sj),[14]
?
ij
or a biquadratic term,
jij(Si¥Sj)2, as shown in our first example.[15]
3.3. Acid Rhodo- Complex [{(ND3)5CrODCr(ND3)5}Cl]¥D2O
This was the first example of an exchange-coupled transition
metal complex to be studied by INS.[4, 16]The structure consists of
two Cr3?ions, bridged by a deuteroxide ion (Figure 2). Super-
Figure 2. Schematic view of [(NH3)5CrOHCr(NH3)5]5?and the splitting of its
electronic ground state. The energies correspond to the eigenvalues of
Equation (7) and allowed ?S??1 INS transitions are depicted as arrows. The
following parameters reproduce all of the experimental data: Jab??1.92, jab?
?0.021 meV.
exchange through the OD group results in antiferromagnetic
coupling of the two Cr3?ions. For the description of this dimer,
an isotropic Heisenberg Hamiltonian, including biquadratic
exchange,[15]was used [Equation (7)]:
H√?2JabSa¥Sb?jab(Sa¥Sb)2
(7)
The resulting energy level pattern for Jab?0 is shown in
Figure 2, together with INS spectra obtained at different
temperatures. With the selection rule ?S??1 derived from
the cross-section formula, the three observed transitions shown
in Figure 3 can immediately be attributed to the transitions
shown as arrows in Figure 2. At 45 K the following parameters
were derived: Jab??1.92 meV; jab??0.021 meV.
Figure 3. Energy loss INS spectra of [(ND3)5CrODCr(ND3)5]Cl5¥D2O taken on a
triple-axis spectrometer at a neutron wavelength of ??2.34 ä at the reactor
Diorit in W¸renlingen. Full and broken curves result from least-squares fitting
procedures. From ref. [11b]
Using the cross-section formula these parameters excellently
reproduce the experimentally observed intensity ratios between
the three transitions. INS transition intensities give a direct
access to the matrix elements of ?f?S√j,??i? in Equation (4) and
are therefore very useful to validate a magnetic model. In
addition, for the acid-rhodo complex, the Q dependence of the
intensity of magnetic INS transitions is found to follow the
expected law [Equation (8)]:
I(Q)?F2(Q)¥
?
1?sin?Q ? R?
Q ? R
?
(8)
INS allowed us to determine the form factor F(Q) for Cr3?
experimentally, since the interatomic distance R was known from
diffraction experiments, see Figure 4.[11b]It turned out to be in
Figure 4. Q dependence of the INS intensity of peak I in Figure 3. The full line is
the calculation using the parameters Jaband jab. From ref. [11b]

Page 7

H. G¸del et al.
916
¹ 2003 Wiley-VCH Verlag GmbH&Co. KGaA, Weinheim
www.chemphyschem.org
CHEMPHYSCHEM 2003, 4, 910±926
good agreement with the calculated F(Q) obtained from
Hartree±Fock calculations.
3.4. Exchange Anisotropy in K10[Co4(D2O)2(PW9O34)2]¥22D2O
When anisotropy becomes important, magnetic susceptibility
data on polycrystalline samples do not provide enough infor-
mation to determine all the relevant parameters. We had
previously studied the tetranuclear nickel(II) cluster in K6Na4[Ni4-
(D2O)2(PW9O34)2]¥24D2O using INS,[17]and, from magnetic sus-
ceptibility measurements on the analogous cobalt cluster, an
overall ferromagnetic interaction was expected. By analyzing the
INS spectra in Figure 5, the energy level diagram presented in
Figure 5. Neutron-energy loss INS spectra of K10[Co4(D2O)2(PW9O34)2]¥22D2O
measured on the time-of-flight spectrometer IN6 at the ILL with an incident
neutron wavelength of ??4.1 ä. The experimental points are shown for three
temperatures with inclusion of least-squares Gaussian fits with equal widths.
Transitions from the ground state are labeled I±IV and those from excited states
A±C. From ref. [18].
Figure 6 was derived.[18]The Co2?ions in the tetranuclear cluster
are in a distorted octahedral environment. Spin orbit coupling
and a low-symmetry crystal field component split the4T1ground
state into six Kramers doublets. Assuming that only the lowest of
these is involved in the energy splittings below 7 meV, we used
the following empirical Hamiltonian [Equation (9)]:
H√ ?
?
??x?y?z
?2J?(S√1?¥S√3??S√1?S√4??S√2?S√3??S√2?S√4?)
?2J??S√1?¥S√2?
(9)
where the J?and J??parameters correspond to the interactions
along the edges and across the short diagonal of the rhomblike
cluster, respectively. The parameter set given in the caption of
Figure 6 reproduces the energy positions as well as the relative
intensities and the Q dependence of the observed INS tran-
sitions. In addition, these parameters also reproduce the
magnetic susceptibility and heat capacity data, clearly showing
the strength of INS.[18]
Figure 6. Energy-level diagram of the [Co4(D2O)2(PW9O34)2]10?cluster ground
state derived from INS. Transitions from the ground state and first excited states in
Figure 5 are given as full and broken lines, respectively. The transitions and levels
identified on IN4 are given as dotted lines. The following parameters, based on
Equation (9), reproduce all of the experimental data: Jx?0.70, Jy?0.43, Jz?1.51,
Jx??0.44, Jy??0.28, Jz??0.46 meV. From ref. [18].
3.5 Exchange Coupling in [Ni12(chp)12(O2CMe)12(THF)6(H2O)6]¥
9THF
The structure of the cyclic dodecanuclear complex is shown in
Figure 7a.[19]According to magnetic susceptibility measure-
ments, the net magnetic interaction between the twelve Ni2?
ions is ferromagnetic. Again magnetic susceptibility data were
Figure 7. a) Structure of [Ni12(chp)12(O2CMe)12(THF)6(H2O)6]. b) Nearest-neighbor
(J1and J2) and next-nearest neighbor (J3) exchange interactions. From ref. [19b].
insufficient to determine the exchange interactions. Due to the
molecular structure, three exchange interactions shown in
Figure 7b should be taken into account for a proper analysis,
which leads to Equation (10),
H√ ? ?2J1
?
i?1
N?2
S2i?1¥S2i?2J2
?
i?1
N?2
S2i¥S2i?1?2J3
?
i?1
N?2
S2i?1¥S2i?1(10)
with N?12 and SN?1?S1. The INS data in Figure 8a could
be reproduced by a model of six ferromagnetically coupled
Ni2?dimers (J1), each with a weak ferromagnetic interaction
to the next dimer (J2). A third interaction (J3), which is anti-
ferromagnetic and couples next-nearest Ni2?ions, was neces-
sary to account for the observed INS transitions. Values of
J1?1.4, J2?0.24, and J3??0.12 meV were derived from these

Page 8

Molecular Spin Clusters
CHEMPHYSCHEM 2003, 4, 910±926
www.chemphyschem.org
¹ 2003 Wiley-VCH Verlag GmbH&Co. KGaA, Weinheim
917
Figure 8. a) INS spectra of an undeuterated sample of [Ni12(chp)12(O2C-
Me)12(THF)6(H2O)6]¥9THF measured on the triple-axis spectrometer TASP at SINQ,
PSI at 1.6 K with the final energy fixed to EF?2.7 meV for various values of Q. The
least-squares Gaussian fits are shown as solid lines. The two transitions are
labeled I and II. b) Corresponding energy level diagram. The energy splitting is
reproduced by the parameters J1?1.4, J2?0.24, J3??0.12 meV, see Equa-
tion (10). From ref. [19b].
measurements. The resulting energy levels up to 3.2 meV are
shown in Figure 8b. The Q dependence was not well pro-
nounced in the experimental INS data. This is due to the fact that
the INS sample was undeuterated; this results in incoherent
neutron-scattering processes, which both broaden the observed
signal and increase the background of the INS spectra. Again, INS
provided results which could not have been extracted by any
other method.
4. Anisotropy Splittings in Single-Molecule
Magnets
4.1 Magnetic Anisotropy
Spin clusters may show magnetic anisotropy in two ways. The
Zeeman effect is the (anisotropic) response to an external
magnetic field (Zeeman splitting), whereas the zero-field split-
ting (ZFS) reflects the magnetic anisotropy in the absence of an
external field. In the following we will discuss the ZFS, because of
its key role in single-molecule magnet behavior.
The magnetic anisotropy of spin clusters arises from the
single-ion anisotropy of all the individual magnetic centers, as
well as magnetic dipole±dipole interactions between these
centers. For ions with a ground state S?1/2, orbital contribu-
tions may be mixed into the ground state through spin-orbit
(SO) coupling H??¥L¥S.[20a]MScomponents of a given S state
are then split, which leads to a preferred orientation of the
magnetization with respect to the anisotropy axes of the
molecule. The magnitude of this splitting and therefore of the
anisotropy is proportional to ?2, the SO coupling constant.
Organic radicals, which show a small SO coupling, have a small
magnetic anisotropy, whereas transition metal ions show much
larger anisotropies. In f-block ions SO coupling is the dominant
interaction, resulting in even larger anisotropies.
The appropriate effective Hamiltonian to describe the single-
ion anisotropy is often given by Equation (11)
H√ ? D(S√z2?S(S?1)/3)?E(S√x2?Sy2)(11)
where D reflects the axial and E the rhombic anisotropy.
For a spin-only ion (S?3/2) in octahedral symmetry, no orbital
contribution is mixed into the ground state and therefore D?
E?0. In Jahn±Teller ions such as Mn(III) the symmetry is lowered
to axial, which results in D?0. An axial elongation from Ohto D4h
symmetry (Figure 9) lowers the energy and leads to occupation
Figure 9. Effect of a Jahn-Teller Oh?D4helongation on the energy splitting of
the d levels in a high-spin Mn3?complex.
of the z2orbital and therefore to a preferred orientation of the
magnetization along ?z (easy-axis anisotropy), corresponding
to a negative value of the D parameter. A positive D term
corresponds to easy-plane anisotropy with preferred orientation
of the spins in the xy plane.
The parameter E is the rhombic anisotropy parameter and
reflects distortions from purely axial symmetry. The axial term in
Equation 11 is diagonal in a ?S,Ms? basis, whereas the rhombic
term is nondiagonal and mixes basis functions differing by
?Ms??2.
The cluster anisotropy in the strong exchange limit, where the
intracluster exchange couplings are much stronger than the
single ion ZFS, is described by Equation (12)
H√ ? S¥Dcluster¥S
(12)
and Dclusteris dependent on the single ion Diand eventually upon
anisotropic exchange through dipole±dipole interactions. In the
case of collinear Di, Dclustercan be easily calculated according to
reference [20b].
Figure 10 shows the effect of a negative Dclusterfor an S?9/2
ground state with purely axial anisotropy. It is split into ?Ms
sublevels with the largest ?Ms? values lying lowest in energy. The
orientation parallel or antiparallel to the easy axis (z axis) is

Page 9

H. G¸del et al.
918
¹ 2003 Wiley-VCH Verlag GmbH&Co. KGaA, Weinheim
www.chemphyschem.org
CHEMPHYSCHEM 2003, 4, 910±926
Figure 10. Double potential well for an S?9/2 ground state with axial
anisotropy and a negative D parameter.
energetically preferred and there is an energy barrier between
the two orientations of magnetization.
This energy barrier can lead to slow magnetization relaxation
phenomena, if the thermal energy is much smaller than the
barrier height (kT??). The result is a single-molecule magnet.
Below the blocking temperature TBthe magnetization is frozen
and the relaxation is extremely slow. We will present some
examples of SMM spin clusters with S?9/2 ground states below.
The energy barrier in purely axial anisotropic spin clusters is
???Dcluster?S2for integer S and ???Dcluster?(S2?1?4) for half-
integer S. Therefore, a prime objective is to maximize both
?Dcluster? and S, in order to obtain the largest possible energy
barrier. Table 1 shows some selected SMMs and their energy
barriers.
4.2 Determination of Anisotropy Splittings by Inelastic
Neutron Scattering
Usually, information about barrier heights in SMMs is derived
from magnetization relaxation measurements as a function of
temperature. This indirect approach suffers from a number of
disadvantages. The main one lies in the fact that magnetization
relaxation in a system as shown in Figure 10 can occur by two
mechanisms: by pure thermal activation over the barrier and by
thermally assisted tunneling. Thus, the activation energies ?E
determined from magnetization relaxation measurements are
usually smaller than the energy difference ?. It is therefore
highly desirable to supplement the bulk measurements by
spectroscopic techniques, which can access the split energy
levels directly. The two main techniques are high-field EPR (HF-
EPR) measurements and INS. We have specialized in the latter. In
contrast to HF-EPR, INS does not require an external field and is
thus the technique of choice for an accurate and direct
determination of anisotropy splittings in SMMs.
Mn12Acetate
SMM behavior was first observed in the cluster [Mn12O12-
(OAc)16(H2O)4].[5a,b, 21]It has the highest energy barrier (ca.
46 cm?1) and is the most intensely studied system of this type.[22]
Figure 11 shows the structure. The molecule consists of a
Figure 11. Structure of [Mn12O12(OAc)16(H2O)4]. Small and large spheres corre-
spond to Mn4?and Mn3?ions, respectively.
tetrahedron of four Mn4?ions (S?3/2) surrounded by a ring of
eight Mn3?(S?2) ions, giving a cluster with S4 molecular
symmetry. Exchange interactions within the cluster lead to an
S?10 ground state. The molecule has a negative axial
anisotropy and exhibits slow magnetic relaxation at low temper-
atures. Below 2 K the reversal of the magnetization is governed
by quantum tunneling.[22b, 23]
INS studies on a partially deuterated polycrystalline sample
were performed on the high-energy resolution time-of-flight
spectrometer IN5 at ILL.[24]Figure 12 shows the spectra at 1.5, 14,
and 24 K. At the lowest temperature one cold transition is
observed on the neutron energy loss side. At higher temper-
atures additional transitions appear on the loss side as well as
the gain side.
The selection rules for magnetic INS transitions within the
ground state sublevels are ?MS?0,?1. The observed peaks can
thus be attributed to ?Ms??1 transitions within the split
ground state. For example the cold transition at 1.5 K is assigned
Table 1. Ground state properties of selected SMMs. ? is the spectroscopic
energy barrier, ?E the activation energy obtained from relaxation measure-
ments. The ligands in the formulae are abbreviated as follows: chp?6-chloro-
2-pyridonate; cit?citrate; tacn?triazacyclononane; dpm?monoanion of
dipivaloylmethane; bpy?2,2?-bipyridine.
S
? [cm?1]
?E [cm?1] Reference
[Mn12O12(O2CMe)16(H2O)4]
[Fe8O2(OH)12(tacn)6]Br8
[Fe4(OMe)6(dpm)6]
[Ni12(chp)12(O2CMe)12(H2O)6(THF)6]
[Ni21(cit)12(OH)10(H2O)10][Na2(NMe4)14]
[V4O2(O2CEt)7(bpy)2][ClO4]
10 45.7[a]
10 22.8[a]
5
12
3 ±
3 13.5[c]
42
17
2.4
6.3±7
2
±
[22]±[24]
[45]
[37e, 46]
[47]
[33b]
[48]
4.5±5.1[a,b]
6.7[c]
[a] From INS. [b] Different barriers due to different isomers. [c] From
magnetic measurements.

Page 10

Molecular Spin Clusters
CHEMPHYSCHEM 2003, 4, 910±926
www.chemphyschem.org
¹ 2003 Wiley-VCH Verlag GmbH&Co. KGaA, Weinheim
919
Figure 12. INS spectra of [Mn12O12(O2CCD3)16(D2O)4]¥2CD3CO2D¥4D2O at 1.5, 14,
and 24 K, measured with the time-of-flight spectrometer IN5 at ILL with ??5.9 ä.
Positive numbers correspond to neutron energy loss. With reference to
Equation (13), the following parameter values were determined from the INS
data: D??0.457, B40, and B44. From ref. [24].
to the Ms??10?MS??9 excitation. At 24 K all the levels are
thermally populated and all the allowed transitions are observed
(Figure 12).
The ground state is well-isolated, and in ref. [24] the ZFS was
modeled using an axial spin Hamiltonian within the S?10
ground state [Equation (13)]:
H√ ? DCluster[S√z2?1/3S(S?1)]?B40O√40?B44O√44
with
O√40? 35S√z4?[30S(S?1)?25]S√z2?6S(S ? 1)?3S2(S ? 1)2
and
O√44? 1/2(S√?4?S√?4)(13)
where B40and B44are the symmetry-allowed higher order terms
of the axial anisotropy.[25]
Figure 13 shows that the levels are split to first order by the B44
term. All the terms of Equation 4 were necessary to describe the
ZFS, and the derived parameters from the INS data are D?
?0.457, B40??2.33?10?5, and B44??3.0?10?5cm?1, in good
Figure 13. Energies of the zero-field split levels of the S?10 ground state as a
function of B44for Mn12acetate.
agreement with HF-EPR data.[26]More recent work has shown
some disorder in the crystal structure.[27]Thus, despite the
crystallographic S4molecular symmetry, individual clusters will
suffer small rhombic distortions. A small E term may therefore be
appropriate in the spin Hamiltonian, which would result in a
mixing of the Ms??2 basis functions. It therefore appears likely
that both the B44and the E term contribute to magnetization
tunneling.
Mn4Cubanes
A series of SMMs with the formula [Mn4O3X(OAc)3(dbm)3] (X?Br,
Cl, OAc, and F; dbm?monoanion of dibenzoylmethane) were
examined using INS, magnetization, and relaxation measure-
ments.[28]Figure 14a shows the structure of these clusters, which
Figure 14. a) Structure of the [Mn4O3X(OAc)3(dbm)3] (X?Cl, Br, OAc, and F)
clusters and b) exchange coupling scheme.
have approximate C3site symmetry. Three Mn3?ions (S?2) are
coupled antiferromagnetically to an Mn4?ion (S?3/2), which
leads to a S?9/2 ground state (Figure 14b).

Page 11

H. G¸del et al.
920
¹ 2003 Wiley-VCH Verlag GmbH&Co. KGaA, Weinheim
www.chemphyschem.org
CHEMPHYSCHEM 2003, 4, 910±926
Figure 15 shows the INS spectra for the four above-mentioned
compounds recorded on IN5 at 18 K. The four expected ?Ms?
?1 transitions within the ZFS ground state are observed. The
shift to lower energies of corresponding transitions in Figure 15
clearly shows the decrease of ?Dcluster?along the series of anions
Cl, Br, OAc, and F.
Figure 15. INS spectraof undeuterated samples of [Mn4O3X(OAc)3(dbm)3](X?Cl,
Br, OAc, and F) at 18 K obtained with the time-of-flight spectrometer IN5 at ILL
with ??7.5 ä. Positive numbers correspond to neutron energy loss. The observed
transitions are labeled according to Figure 16. From ref. [28].
The appropriate Hamiltonian to model these clusters is given
in Equation (14):
H√ ? Dcluster(S√z2?S(S ? 1)/3)?B40O√40?Ecluster(S√x2?S√y2) (14)
with O√40defined as in Equation (13).
Figure 16 shows the energy levels as a function of E. The E
term mixes the MS??1/2 with MS??3/2 basis functions. The
observation of transitions III and IV (Figure 15) is therefore
Figure 16. Energies of the zero-field split levels of the S?9/2 ground state as
function of ?E? for [Mn4O3X(OAc)3(dbm)3] and assignment of the INS transitions
observed in Figure 15. Parameter values are given in Table 2.
essential to determine E. Table 2 summarizes the ZFS parameters
obtained from least-squares fitting of the INS peak energies. In
Table 2 we note that ?E is smaller in the chloride than the
bromide, despite the fact that the spectroscopic barrier ? is
higher in the chloride. This is due to the smaller E term in the
bromide: as a result of the smaller E parameter, the wave-
functions MS??1/2 and MS??3/2 are significantly less mixed
in the bromide than in the chloride. This is turn leads to smaller
tunneling rates and thus a higher effective barrier ?E for the
bromide, despite the smaller D value. Thus, the rhombic term is
the key term for understanding the quantum tunneling behavior
in this series of clusters.
5. The Structure and Magnetic Properties of
New Citrate-Assembled Spin Clusters
In the past, polynuclear transition metal complexes have been
synthesized using predominantly carboxylate ligands, either on
their own or in combination with other ligands.[29]Although
polycarboxylates have the potential to act as bridging ligands in
cluster synthesis, their use has been little explored.[30]Citric acid
[see formula; H4cit, HOC(CO2H)(CH2CO2H)2] possesses three
carboxylic acid groups and one hydroxy group. Tetradeproton-
ated citric acid (citrate) can both bridge and chelate transition-
metal ions, thus increasing the stability of transition-metal
complexes. Despite these advantages only a few transition-
metal±citrate clusters have been reported,[31]alongside a variety
of dimeric compounds.[32]
The first high-nuclearity cluster with the citrate ligand
[Ni8(cit)6(OH)2(H2O)2]10?was reported in 1977 by Strouse et al.[31a]
Using a similar approach, we were able to synthesize
[Ni7(cit)6(H2O)2]10?(the anion of 1) and two stereoisomeric
clusters [Ni21(cit)12(OH)10(H2O)10]16?(the anions of 2 and 3).[33]
The structure of 1 consists of two trimeric units connected by a
central Ni2?ion (see Figure 17). The three independent citrate
ligands provide magnetic exchange pathways between the Ni2?
ions, bridging two, three and five metal centers. The NMe4?and
Na?ions in the lattice provide charge balance of the decaanionic
cluster.
The magnetic susceptibility of 1 plotted as ?T versus T in
Figure 18 reveals a predominant intramolecular ferromagnetic
Table 2. Parameters obtained from INS measurements for the [Mn4O3X-
(OAc)3(dbm)3] clusters. The activation energy ?E obtained from magnetization
relaxation measurements is included for comparison.
[cm?1]
?Ecluster?
0.022
0.017
0.017
±
X?
Cl
Br
OAc
F
Dcluster
B40/10?5
??E
?0.529
?0.502
?0.469
?0.379
?6.5
?5.1
?7.9
?11.1
10.66
10.10
9.43
7.59
8.21
8.3
±
±

Page 12

Molecular Spin Clusters
CHEMPHYSCHEM 2003, 4, 910±926
www.chemphyschem.org
¹ 2003 Wiley-VCH Verlag GmbH&Co. KGaA, Weinheim
921
Figure 17. The [Ni7(cit)6(H2O)2]10?cluster anion in compound 1. Ni atoms are
shown as black spheres, O atoms as dark gray spheres, C atoms as light gray
spheres, and H atoms are omitted for clarity.
Figure 18. The powder magnetic susceptibility at 1 kG plotted as ?T vs. T for
compound 1. The solid line is a simulation of the experimental data with the two
coupling constants JA?10 and JB??4.5 cm?1. The inset shows the field
dependence of the magnetization at 1.8 K.
interaction between the Ni2?ions. We used the following
Heisenberg exchange Hamiltonian with two different exchange
parameters JAand JBto model the data [Equation (15)]:
H√ex??2JA(S1¥S2?S1¥S3?S3¥S4?S4¥S5
?S5¥S6?S6¥S7)?2JB(S2¥S3?S5¥S7)
(15)
With the parameter values JA?10 cm?1and JB??4.5 cm?1, in
good agreement with existing magnetostructural correlations,[34]
the calculated curve fits the experimental data very well. The
resulting spin ground state of the Ni7 cluster is S?7, as
confirmed by the magnetization versus field measurements
shown in the inset of Figure 18.
One of the largest known nickel(II) clusters, the henicosanu-
clear anion found in compounds 2 and 3, is built upon a planar
edge-sharing {Ni7(OH)6} core, with Ni1 located on an inversion
center (Figure 19). The flexibility of ligation exhibited by the
ligand citrate is remarkable, with five different binding modes
observed. The clusters in compound 3 exist as a pair of
enantiomers, and are diastereoisomers to the cluster in 2, as
shown in Figure 20. Isomerism has been observed previously in
Mn12SMMs, but this is a geometric isomerism in which the
positions of H2O and carboxylate ligands differ.[35]However, in
our system, the points of ligation of the citrate and H2O ligands
are identical for the anions found in both 2 and 3.
The powder magnetic susceptibility of compounds 2 and 3
between 300 and 2 K are almost identical. The decrease from
Figure 19. The [Ni21(cit)12(OH)10(H2O)10]16?cluster anion found in compound 2 in
a polyhedral representation. Ni atoms are shown as black spheres, O atoms as
dark gray spheres, C atoms as lines, and H atoms are omitted for clarity.
Figure 20. The Ni-O skeleton of [Ni21(cit)12(OH)10(H2O)10]16?. a) is the achiral ??-
form found in compound 2, b) is the ??-enantiomer found in compound 3,
together with c) the ??-enantiomer. The configurations refer to the Ni atoms
labeled *.
26.8 emumol?1K at 300 K, consistent with 21 uncoupled S?1
spins and a g value of 2.26, down to 9.4 emumol?1K (?T
calculated for S?3 and g?2.26 is 7.7 emumol?1K) at 2 K reveals
predominantly antiferromagnetic interactions within the cluster.
Ultralow temperature magnetization measurements on a single
crystal of 2 were necessary to reveal the ground state spin S?3
(see Figure 21). At low field the magnetization increases sharply.
Figure 21. The field dependence of the magnetization of a single crystal of
compound 2 measured at 180 mK along the crystallographic c axis.
However, saturation could not be observed at a value of
M/N?B?6.8 expected for S?3 and g?2.26 (with M/N?B?gS at
saturation), due to excited spin states with higher MSvalues

Page 13

H. G¸del et al.
922
¹ 2003 Wiley-VCH Verlag GmbH&Co. KGaA, Weinheim
www.chemphyschem.org
CHEMPHYSCHEM 2003, 4, 910±926
being stabilized as the field is increased (see inset Figure 21). This
leads to at least one spin crossover showing up as a clear step in
the magnetization curve, similar to the crossovers observed in
the ™molecular ferric wheel∫.[36]
In this ultralow temperature regime, ac-magnetic susceptibil-
ity measurements on the same crystal of 2 show a frequency-
dependent out-of-phase signal (Figure 22): clear evidence for a
Figure 22. The ac-magnetic susceptibility in the mK range measured on a single
crystal of compound 2 along the crystallographic c axis. The in-phase component
is plotted as ??T vs. T, and the out-of-phase component as ??? vs. T.
slow relaxation of the magnetization and SMM behavior. The
frequency dependence of the ac signal has been correlated to an
Arrhenius law [Equation (16)]:
? ? ?0¥exp(?E/kT)(16)
Above 300 mK the relaxation follows a thermally activated
process with an estimated activation energy ?E?2.0 cm?1,
whereas at lower temperatures the relaxation is clearly faster
than expected for a thermal process.[33b]Although the cluster
does not have axial symmetry, from the activation energy we can
derive an approximate D value of ?0.22 cm?1, which is around
half that found for Mn12acetate.[6a, 24, 26]
6. The Structure and Magnetic Properties of
New Transition-Metal Spin Clusters that
Incorporate Ligands Derived from Salicylidene-
2-ethanolamine
Deprotonation of the Schiff base proligand salicylidene-2-
ethanolamine (H2L; see formula) affords the potentially triden-
tate ligands HL?and L2?, which each incorporate an {O N O}
donor set. Like citrate, the derivatives of H2L can act in both
bridging and chelating capacities, enhancing the stability of the
metal complexes formed. The ligands favor binding in a
meridional fashion, as has been observed in a number of mono-
and dinuclear transition-metal species. Although this binding
mode would appear to limit the size of clusters that can be
formed, complexes with nuclearities up to four can be readily
envisioned. With respect to possible SMM behavior, this
apparent size limitation is not necessarily a disadvantage as
tetranuclear complexes of V, Mn, Fe, Co and Ni have been
reported to act as SMMs.[37]We have synthesized the complexes
[Mn4Cl4L4] (4), [Fe3(O2CMe)3L3] (5) and [Ni4(MeOH)4L4] (6) from the
reaction of simple metal salts and H2L or L2?.[38]
The structure of complex 4 contains an [Mn4(?2-O)4(?2-Cl)4]
core (Figure 23) with the four essentially co-planar Mn centers
arranged approximately as a square. The sides of the square are
each comprised of an alkoxo and a chloro bridge linking pairs of
Mn centers, with the core O and Cl atoms lying on alternating
sides of the Mn4plane around the square. The four Mn3?centers
each display a Jahn±Teller elongation, with the axially elongated
sites occupied by the Cl atoms.
For complex 4, magnetic susceptibility measurements be-
tween 1.8 and 300 K are consistent with overall ferromagnetic
interactions (Figure 24). The ?Mand ?MT versus T data were fit in
the temperature range 20±300 K according to the exchange
Hamiltonian in Equation (17):[39]
H√ex? ?2 J(S1¥S2?S1¥S4?S2¥S3?S3¥S4) (17)
yielding values of J?1.7 cm?1and g?2.0, which result in a spin
ground state of S?8. A combination of zero-field splitting and
antiferromagnetic intermolecular interactions explain the rapid
decrease in ?MT at low temperature. The presence of intermol-
ecular interactions is supported by a maximum in the ?Mversus T
plot at 2.8 K. Variable-temperature magnetization measurements
were performed on complex 4 in the temperature range 1.8±8 K
in fields up to 5 T. At fields less than 1 Tan S shape is evident in
the M/N?Bversus H/T plot, which is characteristic of antiferro-
magnetic intermolecular interactions and consistent with the
susceptibility behavior. Nevertheless, it is possible to reproduce
the higher field data by assuming axial anisotropy with S?8,
D??0.14 cm?1and g?1.94.
These values of S and D lead to a calculated energy barrier to
reorientation of the magnetization direction ?E?9 cm?1. Al-
though this barrier is small, SMMs with comparable or smaller
energy barriers have been reported,[33b, 40]and thus complex 4
was expected to display SMM behavior at low temperature.
Indeed, hysteresis due to slow relaxation of the magnetization
was observed by microsquid measurements down to 350 mK.
However, this behavior displayed deviations from that typically
observed for SMMs, due to the intermolecular interactions
evident in complex 4. Work is currently in progress on the

Page 14

Molecular Spin Clusters
CHEMPHYSCHEM 2003, 4, 910±926
www.chemphyschem.org
¹ 2003 Wiley-VCH Verlag GmbH&Co. KGaA, Weinheim
923
Figure 23. Ortep plots of complexes a) [Mn4Cl4L4] 4, b) [Fe3(O2CMe)3L3] 5, and
c) [Ni4(MeOH)4L4] 6 at the 50 % probability level, intramolecular hydrogen bonds
are shown as dashed lines.
synthesis of species structurally analogous to 4, but possessing
bulky organic substituents on the ligand in order to remove the
effect of intermolecular interactions.
The structure of 5 contains an [Fe3(?2-O)3]3?core (Figure 23b),
with the three Fe atoms comprising the corners of a scalene
triangle. Each pair of Fe centers is connected by an alkoxo and an
acetate bridge along the edges of the triangle. As a result of the
ligand arrangement, two of the core O atoms and one acetate
Figure 24. Plot of ?Mand ?MT versus T for complex 4 measured in a 1 kG field.
The solid lines represent the best fits to Equation (17).
ligand lie on one side of the Fe3plane, while the third core O
atom and the remaining two acetate ligands lie on the other.
For complex 5 the magnetic susceptibility data is consistent
with overall antiferromagnetic interactions (Figure 25). The ?M
Figure 25. Plot of ?Mand ?MT versus T for complex 5 measured in a 1 kG field.
The solid lines represent the best fits to Equation (18).
and ?MT versus T data were fit according to the exchange
Hamiltonian given in Equation (18)],
H√ex? ?2JA(S1¥S2)?2JB(S1¥S3)?2JC(S2¥S3) (18)
yielding values of JA??9.8, JB??9.4, JC??8.3 cm?1with g
fixed to 2.0. Frustration of the three competing antiferromag-
netic interactions results in a spin ground state of S?1/2. This is
confirmed by variable temperature magnetization measure-
ments in the temperature range 1.8±8 K in fields up to 5 T, which
can be simulated using S?1/2 and g?2.0.
The structure of complex 6, (Figure 23c) incorporates a [Ni4-
(?3-O)4] cubane core. The L2?ligands coordinate in a similar
fashion to that observed in 4 and 5, except that in 6, the ethoxo-
type O atoms are ?3- rather than ?2-bridging. The peripheral
ligation for 6 is completed by four terminal MeOH ligands, which
participate in intramolecular hydrogen bonding interactions
with the phenoxo-type O atoms of the L2?ligands, across four of
the six faces of the cubane. As a result, these four faces exhibit
shorter Ni±Ni separations and smaller Ni-O-Ni angles. In
addition, 6 possesses a tetragonal elongation of the Ni

Page 15

H. G¸del et al.
924
¹ 2003 Wiley-VCH Verlag GmbH&Co. KGaA, Weinheim
www.chemphyschem.org
CHEMPHYSCHEM 2003, 4, 910±926
coordination, which occurs along the O-Ni-O vector involving
the MeOH and trans alkoxo ligands.
For complex 6, the magnetic susceptibility behavior is
consistent with overall ferromagnetic interactions (Figure 26).
The ?Mand ?MT versus T data were fit in the temperature range
Figure 26. Plot of ?Mand ?MT versus T for complex 6 measured in a 1 kG field.
The solid lines represent the best fits to Equation (19).
10±300 K according to the exchange Hamiltonian [Equa-
tion (19)], where JAcharacterizes exchange across the two faces
of the Ni4cubane that are not bridged by hydrogen bonds, while
JBcharacterizes the remaining four pairwise interactions [Equa-
tion (19)].
H√ex??2JA(S1¥S4?S2¥S3)?2JB(S1¥S2?S1¥S3?S2¥S4?S3¥S4) (19)
This yielded the parameters JA??3.8, JB?9.0 cm?1, g?2.18,
resulting in a spin ground state of S?4. These J values are in
good agreement with the previously reported correlation
between coupling constants and Ni-O-Ni bridging angles.[34b,41]
The rapid decrease in ?MT at low temperature is attributed to a
combination of zero-field splitting and antiferromagnetic inter-
molecular interactions. Variable temperature magnetization
measurements were performed on complex 6 in the temper-
ature range 1.8±8 K in fields up to 5 T (Figure 27). The
Figure 27. Plot of M/N?Bversus H/T for complex 6. The solid lines represent
simulations.
experimental data can be simulated using S?4, D??1.01 cm?1
and g?2.24. This value of D is of greater magnitude than those
reported for structurally related Ni2?cubane complexes (?0.10±
?0.47 cm?1).[41b]However both the magnitude and sign of D
have recently been confirmed by preliminary INS studies and
may be related to the apparent distortion of the Ni2?coordina-
tion environment in 6. The values determined for S and D lead to
a calculated energy barrier to reorientation of the magnetization
direction of 16 cm?1, which should be more than sufficient for
manifestation of SMM behavior. Thus, low-temperature mag-
netic measurements are planned in order to investigate this
further.
7. Summary and Outlook
Our contributions to this field go back about thirty years, a time
when terms such as molecular magnetism, supramolecular
chemistry, spin clusters, and single-molecule magnets did not
exist. Establishing magnetostructural correlations in dinuclear
and polynuclear complexes of magnetic transition-metal ions
was one of the primary objectives in the 1970s and early 1980s.
Whereas in the majority of these studies measurements of the
bulk magnetic properties of the cluster compounds formed the
basis for the quantitative evaluation of the magnetic coupling
parameters, our approach was based on spectroscopic techni-
ques.
Using high-resolution optical spectroscopy, both in absorp-
tion and emission, it was possible to determine the exchange
parameters in a number of cluster compounds.[42]Since ex-
change splittings could be observed not only in the ground
state, but also in excited states, very detailed information about
the orbital pathways of exchange interactions could be ob-
tained. These techniques were somehow limited, however, to
transition-metal ions exhibiting sharp d±d bands, such as Cr3?,
V2?, Fe2?, Cr2?, Mn2?, and Fe3?. Nevertheless, the most accurate
determination of an exchange splitting in a spin cluster is the
optical spectroscopic work on the [LCr(OH)3L]3?(L?1,4,7-
trimethyl-1,4,7-triazacyclononane) dimer.[43]
Inelastic neutron scattering had not been used to probe the
magnetic excitations in molecular spin clusters until the study on
the acid rhodo complex, see Section 3.3. Since then, there have
been about one hundred studies of spin clusters using INS.
When the number of magnetic ions in a cluster increases, the
information content of bulk magnetic data is insufficient to
determine all the relevant parameters, and supplementing these
measurements by spectroscopic techniques becomes manda-
tory. INS can be the method of choice, because it allows direct
access to the microscopic energy levels without an external
magnetic field, that is, without any assumption about g values.
For instance, it was possible to determine accurate values of
bilinear and biquadratic Heisenberg exchange parameters in
dimeric complexes.[44]In both the acid rhodo complex and also
in dimeric copper acetate, an increase of the J value of 5±10%
between room temperature and 10 K was deduced from INS: a
fact that had remained hidden in the magnetic susceptibility
experiments. In more recent years, INS has proved to be very
powerful for the accurate determination of anisotropy splittings