Single-molecule magnet behavior for an antiferromagnetically superexchange-coupled dinuclear dysprosium(III) complex

Article abstract of DOI:10.1021/ja109706y

A family of five dinuclear lanthanide complexes has been synthesized with general formula [Ln^III₂(valdien)₂(NO ₃)₂] where (H₂valdien = N1,N3-bis(3- methoxysalicylidene)diethylenetriamine) a

Full text of DOI:10.1021/ja109706y

ARTICLE
pubs.acs.org/JACS
Single-Molecule Magnet Behavior for an Antiferromagnetically
Superexchange-Coupled Dinuclear Dysprosium(III) Complex
Jꢀer^ome Long,†,‡ Fatemah Habib,†,‡ Po-Heng Lin,†,‡ Ilia Korobkov,† Gary Enright,§ Liviu Ungur,||
Wolfgang Wernsdorfer,^ Liviu F. Chibotaru,|| and Muralee Murugesu**,†,‡
†Department of Chemistry, University of Ottawa, 10 Marie-Curie, Ottawa, ON, K1N6N5, Canada
‡Centre for Catalysis Research and Innovation, 30 Marie-Curie, Ottawa, ON, K1N6N5, Canada
§Steacie Institute for Molecular Sciences, NRC, 100 Sussex Drive, Ottawa, ON, K1A0R6, Canada
Division of Quantum and Physical Chemistry and INPACꢀInstitute for Nanoscale Physics and Chemistry, Katholieke Universiteit
Leuven, Celestijnenlaan, 200F, 3001, Belgium
^Institut Nꢀeel, CNRS and Universitꢀe J. Fourier, BP 166 25, Avenue des Martyrs, 38042, Grenoble, France
S Supporting Information
b
ABSTRACT: A family of five dinuclear lanthanide complexes has been synthesized with
general formula [LnIII2(valdien)2(NO3)2] where (H2valdien = N1,N3-bis(3-meth-
oxysalicylidene)diethylenetriamine) and LnIII = EuIII 1, GdIII 2, TbIII 3, DyIII 4, and HoIII
5. The magnetic investigations reveal that 4 exhibits single-molecule magnet (SMM)
behavior with an anisotropic barrier Ueff = 76 K. The step-like features in the hysteresis
loops observed for 4 reveal an antiferromagnetic exchange coupling between the two
dysprosium ions. Ab initio calculations confirm the weak antiferromagnetic interaction with
an exchange constant JDyꢀDy = ꢀ0.21 cmꢀ1. The observed steps in the hysteresis loops
correspond to a weakly coupled system similar to exchange-biased SMMs. The Dy2 complex
is an ideal candidate for the elucidation of slow relaxation of the magnetization mechanism
seen in lanthanide systems.
’ INTRODUCTION
Retrospectively, the synthesis and study of these pure 4f systems
has literally been boosted since the discovery that a single-ion
lanthanide complex displays slow relaxation of the magnetization.7
Indeed, the first unquenched orbital moment of some lanthanides
(TbIII, DyIII, HoIII) in association with the ligand field leads to high
magnetic anisotropy.8 Interestingly, several relaxations of the mag-
netization pathways can occur in lanthanide systems, such as direct
Orbach9 or Raman processes.10 As a proof of concept, the approach
of modulating the ligand field has been recently extended to actinide
complexes11 and to a transition-metal complex where slow relaxation
of the magnetization has been evidenced.12 Although considerable
efforts have been dedicated to the understanding of the mechanisms
in these single-ion SMMs, little attention has been devoted to
elucidating the relaxation processes in polynuclear 4f SMMs. The
main reason lies in the difficulty in correlating the structure to the
superparamagnet property. Particularly, it is still difficult to evaluate
the real consequence of the lanthanideꢀlanthanide exchange inter-
action on the SMM property where the single-ion magnetism seems
to be the dominant phenomenon.
The coordination and supramolecular chemistry of lanthanide
ions have been the center of dynamic research, especially for their
optical1 and magnetic properties.2 In particular, lanthanide
coordination complexes have recently attracted much attention
in the field of molecular magnetism. Indeed, these systems may
hold the key to obtain high anisotropic barrier single-molecule
magnets (SMMs).3 These discrete molecules exhibit superpara-
magnet-like behavior of slow magnetic relaxation at low tem-
perature. As a consequence, this new class of molecular
nanomagnets can be viewed as potential candidates for electro-
nics based on molecules and high-density storage devices.4
One of the most important issues for technological applications
remains the low blocking temperature, TB, observed in SMMs. To
date, the largest effective anisotropic barrier reported for a transition-
metal SMM is found in a hexanuclear manganese complex with an
effective energy barrier of 86 K.5 This value slightly exceeds the ones
observed in the archetype SMMs [Mn12O12(O2CR)16(H2O)4]
where Ueff < 74 K.6 While in the case of transition-metal d SMMs,
the slow relaxation arises from the combination of a large spin
ground-state S and an uniaxial anisotropy D, the mechanisms
involved in pure 4f systems are more difficult to grasp. This is mainly
due to the fact that, in such systems, the magnetic anisotropy D is
much greater than the exchange interaction J between the lanthanide
centers (weak exchange limit).3c
The synthetic strategy to obtain polynuclear 4f SMMs funda-
mentally relies on the same concepts as transition-metal SMMs:
the use of polydentate bridging ligands which can mediate
Received: October 28, 2010
Published: March 22, 2011
r
2011 American Chemical Society
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Scheme 1. H2valdien Ligand
Ligand Synthesis. The ligand, H2valdien (Scheme 1), (N1,N3-
bis(3-methoxysalicylidene)diethylenetriamine) was synthesized by mix-
ing o-vanillin (0.025 mol) with diethylenetriamine (0.0125 mol) in
40 mL of EtOH. The orange solution was refluxed for 1 h, and after
cooling down, the solvent was removed under reduced pressure to afford
an orange oil. The latter oil was left to stand overnight to form a yellow
precipitate, which was collected by suction filtration and washed with
diethyl ether. Yield = 96%. NMR 1H (CDCl3, 400 MHz): δ 2.97 (t, 2H,
CH2ꢀN), 3.69 (t, 2H, CH2ꢀN), 3.88 (s, 3H, OCH3), 6.90 (t, 1H, Ar),
6.99 (d, 2H, Ar), 8.32 (s, 1H, NdCH); 13C (CDCl3, 400 MHz): 166.0,
152.1, 148.1, 123.1, 118.6, 117.9, 114.1, 59.3, 56.1, 49.9. Calcd for
C20H25N3O4: C, 64.67; H, 6.78; N, 11.31. Found: C, 64.59; H, 6.49; N,
11.25. IR (KBr, cmꢀ1): 3419, 3056, 2995, 2935, 2900, 2835, 1629, 1468,
1416, 1376, 1335, 1269, 1146, 1128, 1080, 1024, 964, 875, 838, 778, 734.
Synthesis of [LnIII2(valdien)2(NO3)2] Complexes. To a stirred
magnetic interactions between the metallic centers. The choice
of the bridging group is critical in the case of lanthanide systems
in order to overcome the core nature of 4f orbitals and subse-
quently induce significant exchange interaction between the
paramagnetic centers. In addition, the ligand field as well as the
coordination geometry strongly influence the local anisotropy of
the lanthanide ion. In brief, the interplay between the ligand field
effect, the geometry, and the strength of the magnetic interaction
between the lanthanide sites will govern the SMM behavior.
Taking into account the coordination preference of 4f ions for
hard Lewis bases (HSAB theory),13 it is possible to design
polytopic ligands in order to direct the assembly of polynuclear
lanthanide complexes. Schiff base ligands14 obtained from the o-
vanillin moiety have proven to be particularly suitable for the
synthesis of 4f SMMs.3a,g,h
solution of H2valdien (0.125 mmol, 0.046 g) and Ln(NO3)3 6H2O
3
(0.125 mmol) in 9 mL of MeOH/DMF 2:1 (or MeCN/DMF 2:1 for 2),
triethylamine (0.250 mmol, 35 μL) was added. The resulting clear
yellow solution was stirred for 30 s then filtered. The filtrate was placed
into a diethyl ether bath to help crystallization. After 2ꢀ3 days,
rectangular-shaped yellow crystals were collected. Yields = 55ꢀ65%.
IR and EA data for all complexes are given in the Supporting Informa-
tion.
EA, IR, and NMR Spectroscopy. Elemental analyses were carried
out with a Perkin-Elmer 2400 CHN analyzer. Infrared analyses were
obtained using a Nicolet Nexus 550 FT-IR spectrometer in the
4000ꢀ650 cmꢀ1 range. The spectra were recorded in the solid state
by preparing KBr pellets. NMR analyses were conducted on a Bruker
Avance 400 spectrometer equipped with an automatic sample holder
and a 5 mm auto-tuning broadband probe with Z gradient.
Single Crystal X-ray Diffraction Studies. Crystals were grown
from a mixture of MeOH/DMF (compounds 1 and 3ꢀ5) or MeCN/
DMF (2) solutions. A single rectangular yellow crystal suitable for X-ray
diffraction measurements was mounted on a glass fiber. Unit cell
measurements and intensity data collections were performed on a
Bruker-AXS SMART 1 k CCD diffractometer using graphite mono-
chromated MoKR radiation (λ = 0.71073 Å). The data reduction
included a correction for Lorentz and polarization effects, with an
applied multiscan absorption correction (SADABS).
The crystal structure was solved and refined using the SHELXTL
program suite.23 Direct methods yielded all nonhydrogen atoms, which
were refined with anisotropic thermal parameters. All hydrogen atom
positions were calculated geometrically and were riding on their
respective atoms. For compound 3, O(4)ꢀC(20) methoxy group of
one ligand is disordered through 36ꢀ rotation around C(19)ꢀO(4) axis.
Disorder was successfully modeled with the occupational ratio refined as
35:65%.
Magnetic Measurements. The magnetic susceptibility measure-
ments were obtained using a Quantum Design SQUID magnetometer
MPMS-XL7 operating between 1.8 and 300 K for dc-applied fields
ranging from ꢀ7 to 7 T. Dc analyses were performed on polycrystalline
samples of 13.4, 14.9, 13.5, 6.6, and 7.5 mg of 1ꢀ5, respectively, wrapped
in a polyethylene membrane (1, 2, 5) or in grease (3, 4) and under a field
ranging from 0 to 7 T between 1.8 and 300 K. Ac susceptibility
measurements were carried out under an oscillating ac field of 3 Oe
and ac frequencies ranging from 1 to 1500 Hz. The magnetization data
were collected at 100 K to check for ferromagnetic impurities that were
absent in all samples. Diamagnetic corrections were applied for the
sample holder and the core diamagnetism from the sample (estimated
with Pascal constants).
Among the lanthanide family, the DyIII ion has indisputably
led to the largest number of pure 4f SMMs. The explanation
resides in the reduced quantum tunneling of the magnetization
(QTM) experimentally observed in these systems compared to
other lanthanide ions. However, the real physical origin of this
behavior remains unclear. The flexibility of the coordination
chemistry has been employed to synthesize polynuclear
dysprosium(III) complexes with various nuclearities ranging
from dinuclear,3a,k,m trinuclear,15 tetranuclear,3g,16ꢀ19 pentanuclear,3i
and hexanuclear3l,20,21 to a Dy26 cluster.22 Nevertheless, in a
similar fashion to transition-metal SMMs, the smaller systems
tend to present higher anisotropic barriers.3a,g
In order to answer the fundamental questions raised pre-
viously, model systems are needed. In our efforts to obtain high
TB SMMs as well as understanding the underlying concepts
involved, we report here five isostructural dinuclear complexes
[LnIII2(valdien)2(NO3)2] (LnIII = EuIII 1, GdIII 2, TbIII 3, DyIII 4,
HoIII 5). Compound 4 exhibits a slow relaxation of the magne-
tization associated with SMM behavior. The characterizations of
this SMM property show an antiferromagnetic superexchange
coupling between the two DyIII centers exhibiting superpara-
magnetic-like behavior. The simplicity of the symmetric molec-
ular entity allows the evaluation of the exchange interaction
between the two LnIII ions by computational methods. The
observed magnetic properties for all complexes were validated by
ab initio calculations.
’ EXPERIMENTAL SECTION
Micro-SQUID Measurements. Magnetization measurements on
oriented single crystals were carried out with an array of micro-
SQUIDs.24 This magnetometer works in the temperature range of
0.04 to ca. 7 K and in fields of up to 0.8 T with sweeping rates as high
Materials. All manipulations were performed under aerobic/ambi-
ent conditions. All chemicals were purchased from Aldrich or Strem
Chemicals and used without any further purification.
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Table 1. Crystallographic Data for Analogous [LnIII2(valdien)2(NO3)2] Complexes
1
2
3
4
5
formula
C
40H46Eu2N8O14
C20H23GdN4O7
588.67
C40H46Tb2N8O14
1180.69
C40H46Dy2N8O14
1187.85
C40H46Ho2N8O14
1192.71
fw
1166.77
200(2)
temp. (K)
crystal system
space group
a/Å
200(2)
200(2)
100(1)
200(2)
triclinic
triclinic
triclinic
triclinic
triclinic
P-1
P-1
P-1
P-1
P-1
10.5977(5)
10.6420(5)
11.5192(6)
65.341(2)
64.813(2)
80.419(2)
1068.32(9)
1
10.5766(5)
10.5991(5)
11.5192(6)
65.1840(10)
65.4820(10)
80.2930(10)
1066.38(8)
2
10.5536(3)
10.5537(3)
11.4994(3)
66.1710(10)
65.0160(10)
80.0090(10)
1061.98(5)
1
10.4807(5)
10.5015(5)
11.4678(5)
64.937(2)
66.519(2)
79.836(2)
1048.63(8)
1
10.5104(4)
10.5297(4)
11.4828(4)
66.414(2)
65.126(1)
79.981(2)
1056.59(7)
1
b/Å
c/Å
R/ꢀ
β/ꢀ
γ/ꢀ
vol/ Å3
Z
DC/ mg mꢀ3
μ/mmꢀ1
reflns collected
R1, wR2 (I > 2σ(I))a
R1, wR2 (all data)
1.814
1.833
1.846
1.881
1.875
2.986
3.160
3.381
3.614
3.795
19 057
10 345
8893
56 987
16 595
0.0181, 0.0440
0.0215, 0.0532
0.0206, 0.0542
0.0145, 0.0354
0.0130, 0.0347
0.0194, 0.0447
2
0.0221, 0.0536
2 2
0.0215, 0.0538
2
0.0155, 0.0358
2
0.0131, 0.0346
a R = R1 = ||Fo| ꢀ |Fc||/|Fo|; wR2 = {[w(Fo ꢀ Fc2)2]/[w(Fo ) ]}1/2; w = 1/[σ2(Fo ) þ (ap)2 þ bp], where p = [max(Fo , 0) þ 2Fc2]/3; and Rw = [w(|
Fo| ꢀ |Fc|)2/w|Fo|2]1/2, where w = 1/σ2(|Fo|).
as 0.28 T sꢀ1 and exhibits field stability of better than μT. The time
The exchange interactions between magnetic centers have been
included within the Lines model.30 In this approach, the exchange
interaction between different spin terms in the absence of spinꢀorbit
coupling is modeled by a singleꢀparameter isotropic exchange Hamil-
tonian for each metal pair. This Hamiltonian model is written on the
basis of the ab initio computed spinꢀorbit multiplets of the metal
fragments and then diagonalized. The obtained exchange states corre-
spond to the solutions of an anisotropic exchange Hamiltonian of the
complex. The advantage of the Lines model is the use of a single
parameter to describe the anisotropic exchange interaction for a given
pair of interacting metal sites, which in the simplest bilinear approxima-
tion is described by 3 ꢁ 3 exchange matrix containing nine Jik
parameters. The Lines model becomes exact in two limiting cases: (1)
isotropic Heisenberg exchange coupling and (2) extremely anisotropic
(Ising) exchange coupling. The described approach has been imple-
mented in the computer program POLYꢀANISO, which is interfaced
with the routine SINGLEꢀANISO.36 The obtained exchange spectrum
and eigenfunctions were used to calculate the magnetic properties of the
dinuclear complexes.
3
resolution is approximately 1 ms. The field can be applied in any
direction of the micro-SQUID plane with precision greater than 0.1ꢀ
by separately driving three orthogonal coils. In order to ensure good
thermalization, a single crystal was fixed with apiezon grease.
Computational Methodology. The basis sets used for the
calculations were taken from the ANOꢀRCC basis library included in
MOLCAS program package.
For magnetic electrons localized in the 4f orbitals of the metal sites
the spinꢀorbit coupling and the crystal field are much stronger than the
intramolecular exchange interaction, making these effects a priority in
our study. The competition between the spinꢀorbit coupling, the
crystalꢀfield, and the intrinsic multiconfigurational nature of the multi-
electronic wave function of the 4f electrons can only be treated
adequately by an explicitly correlated ab initio method. Therefore, we
used a combined approach for studying magnetic properties of com-
plexes 1ꢀ5 which implies ab initio calculations of mononuclear lantha-
nide centers with a model description of the exchange interactions
between the centers. This methodology has been already successfully
applied for the calculation of the magnetic properties of other poly-
nuclear complexes containing lanthanide and transition-metal ions.25ꢀ27
The ab initio calculations on individual lanthanide fragments have
been carried out with MOLCAS 7.4 program package.28 In this
approach, the relativistic effects are treated in two steps, both based
on DouglasꢀKrollꢀHess Hamiltonian. Scalar terms were included in
the basis set generation and used to determine the spin-free wave
functions and energies in the multiconfigurational self-consistent field
(CASSCF) method. In the second step, spinꢀorbit interaction was
taken into account within the restricted active space state interaction
(RASSI) method, which uses the spin free multiconfigurational wave
functions as input states. The obtained wave functions and energies of
the molecular multiplets were used for the calculation of the anisotropic
magnetic properties and the g tensors of the lowest states using a
specially designed routine SINGLEꢀANISO.29 As a result, the magnetic
properties of a single magnetic ion are calculated by a fully ab initio
approach, in which the spinꢀorbit coupling is considered nonperturba-
tively.
’ RESULTS AND DISCUSSION
Synthesis and Structural Analysis. The compartmental
acyclic Schiff base H2valdien ligand is obtained from the con-
densation reaction of o-vanillin and diethylenetriamine. This
ligand displays two distinct coordination pockets which can
encapsulate lanthanide centers. The large size of the inner
compartment, formed by the donor set N3O2, is particularly
appropriate to accommodate a sizable 4f ion. Only a few
examples of coordination complexes are reported with
H2valdien.31 In 2007, Dou et al. structurally characterized two
mononuclear complexes with large LaIII and NdIII ions where
only the outer donor O4 set of H2valdien was involved in the
coordination.31b Moreover, in some cases, ortho positions on the
aromatic rings are substituted with methoxy groups in order to
prevent the formation of bridged complexes;31b however, in our
synthetic methodology we employed the latter functionality to
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Table 3. Lanthanide Geometry Analysis by SHAPE Software
LnIII
square antiprism (D4d)
dodecahedron (D2d)
EuIII
GdIII
TbIII
DyIII
HoIII
4.38503
4.26909
4.30761
4.20132
4.24485
2.37483
2.18035
2.02714
1.90380
1.89277
Figure 1. The molecular structure of [DyIII2(valdien)2(NO3)2], 4.
Color code: orange (Dy), red (O), blue (N), and grey (C). Hydrogen
atoms have been omitted for clarity.
Table 2. Selected Bond Distances and Angles
LnIII
LnIIIꢀLnIII (Å)
LnIIIꢀO3 (Å)
LnIIIꢀO3ꢀLnIII (ꢀ)
EuIII
GdIII
TbIII
DyIII
HoIII
3.830(3)
3.811(1)
3.788(1)
3.768(3)
3.754(3)
2.374(3)ꢀ2.383(3)
2.347(3)ꢀ2.371(2)
2.330(2)ꢀ2.351(2)
2.317(2)ꢀ2.334(3)
2.307(2)ꢀ2.328(3)
107.26(6)
107.76(8)
108.05(8)
108.22(3)
108.17(5)
Figure 2. Temperature dependence of the χT product at 1000 Oe for
complexes 1ꢀ5 (with χ being the molar susceptibility per dinuclear
complex defined as M/H). The solid line corresponds to the best fit
for 2.
promote coordination in both pockets. The stoichiometric
reaction of H2valdien and Ln(NO3)3 6H2O in the presence of
an organic base (NEt3, 2 equiv) in a MeOH/DMF mixture (or
CH3CN/DMF for 2) affords the crystallization of the five
dinuclear compounds [LnIII2(valdien)2(NO3)2] (LnIII = EuIII
1, GdIII 2, TbIII 3, DyIII 4, HoIII 5). Slight variation in metal to
ligand ratio still gave the same complexes.
3
dihedral angle between the planes defined by the atoms
O3ꢀDy1ꢀO3a and O3ꢀDy1aꢀO3a. Despite the isostructur-
ality, small differences appear between the five dinuclear com-
pounds (Table 2). For instance, the general trend observed is a
decrease of the intramolecular LnIIIꢀLnIII distance from EuIII to
HoIII (3.830(3) to 3.762(6) Å), while the bridging
LnIIIꢀO3ꢀLnIII angle increases slightly (Table 2). In the case
of lanthanides, the geometry of the metallic center is strongly
correlated to the local anisotropy of the paramagnetic ion. Thus,
a systematic analysis of the coordination geometry must be
performed. With this in mind, exact geometry of the octacoordi-
nated lanthanide ions was determined using the SHAPE32 soft-
ware. Close analysis of the resulting data reveals that the values
obtained differ from zero (which represents the case of the ideal
geometry considered). Therefore, an intermediate geometry
between square antiprism (D4d) and dodecahedron (D2d) is
observed for all complexes (Table 3 and Figure S1, Supporting
Information). The slight variation observed along the family can
be directly correlated to the general decrease of the ionic radius of
the lanthanide ion from EuIII to HoIII (Figure S2, Supporting
Information). Moreover, the intermediate/distorted geometry
seen even for GdIII might lead to non-negligible local magnetic
anisotropy. The latter assumption can be verified by the compar-
ison of the coupling constants (J) obtained by fitting the
susceptibility data using an isotropic model with calculated J
value from an anisotropic model (vide infra).
The single X-ray crystallography studies reveal that all five
compounds are isostructural and crystallize in the triclinic P-1
space group (Table 1). As an example, the structure of the
dysprosium analogue, compound 4, will be described (Figure 1).
The asymmetric unit consists of one DyIII ion, one valdien2ꢀ
ligand and a nitrate ion. The centrosymmetric dinuclear complex
is composed of two eight-coordinate DyIII ions bridged by
phenoxo groups (O3, O3a) of the valdien2ꢀ ligands with a
Dy1ꢀO3ꢀDy1a angle of 108.22(3)ꢀ and a DyꢀDy distance
equal to 3.768(3) Å. The central core Dy2O2 appears to be nearly
rhombic, the two DyꢀO3 distances being 2.31 and 2.33 Å. One
terminal phenoxo group coordinates the dysprosium ion with a
short distance DyꢀO2 of 2.19 Å. Interestingly, the methoxide
groups are not involved in the coordination of the lanthanide
centers and thus remain strictly in the flexible inner N3O2
compartment of the ligand. In contrast with the previously
reported mononuclear complexes based on LaIII and NdIII,31b
the inner N3O2 compartment is more adequately sized for the
encapsulation of smaller lanthanide ions, such as DyIII. More-
over, the dimerization of the molecule is most likely due to the
presence of NEt3 as base promoting the full deprotonation of
H2valdien, which subsequently provide phenoxides as bridging
groups. The coordination sphere is completed by a bidentate
nitrate ion leading to an overall N3O5 coordination environment.
The centrosymmetry of the complex leads to the absence of a
An intramolecular H-bond appears between N2ꢀH and the
methoxide oxygen (O4) with a distance of 2.11 Å and an angle of
165.8ꢀ, close to linearity (Figure S3, Supporting Information).
The analysis of the packing arrangement (Figures S4ꢀS6,
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Figure 3. Temperature dependence of the in-phase χ0 (left) and out-of-phase χ00 (right) ac susceptibility signals under zero dc field for 4.
Supporting Information) reveals the shortest intermolecular
Dy Dy distance of 7.36 Å, confirming the spatial isolation of
3 3 3
the dinuclear units.
Magnetic Properties. The dc magnetic properties of com-
pounds 1ꢀ5 were investigated under a 1000 Oe field in the
temperature range 1.8ꢀ300 K (Figure 2). Field dependence of
the magnetization for all complexes between 1.8 and 8 K are
shown in Figures S7ꢀS12, Supporting Information. For all
compounds, the observed paramagnetism arises uniquely from
the 4f LnIII ions. At room temperature, the χT values of
complexes 1ꢀ5 are 3.2, 15.7, 22.7, 28.7, and 28.4 cm3 K molꢀ1
,
3
3
respectively. These values are in good agreement with the
expected theoretical values (2: 15.76; 3: 23.63; 4: 28.34; 5:
28.16 cm3 K molꢀ1) for two noninteracting lanthanide ions:
3
3
GdIII (8S7/2, S = 7/2; L = 0, g = 2, C = 7.88 cm3 K molꢀ1), TbIII
ꢀ3 1
3
(7F6, S = 3, L = 3, g = 3/2, C = 11.82 cm3 K mol ), DyIII (6H15/2
,
3
3
S = 5/2, L = 5, g = 4/3, C = 14.17 cm3 K molꢀ1) and
3
3
HoIII (5I8, S = 2, L = 6, g = 5/4, C = 14.08 cm3 K molꢀ1).
3
3
Figure 4. Out-of-phase susceptibility χ00 vs frequency v (logarithmic
scale) in the temperature range 2ꢀ25 K for 4.
Due to the presence of thermally populated excited states, the
magnetic properties of the europium analogue 1 remain difficult
to interpret even at room temperature. However, the typical
nonmagnetic ground state (7F0) is observed at low temperatures
as suggested by the χT value of 0.04 cm3 K molꢀ1 at 1.8 K.33
contribute toward the negative deviation of the χT at low
temperature. This will be verified using ab initio calculations
(vide infra).
3
3
The strength of the magnetic interaction between the two
lanthanide ions in the dinuclear complexes can be easily quanti-
fied with the gadolinium analogue 2. Indeed, the GdIII ions
present no spinꢀorbit coupling at the first order. Thus, the
decrease of the χT when lowering the temperature for 2 reveals
directly the presence of an antiferromagnetic interaction between
the GdIII ions. Application of the van Vleck equation to the
Kambe’s vector coupling scheme by using the isotropic spin
Magnetization measurements performed at low temperatures
reveal a saturation of 13.46 μB at 7 T, in good agreement with the
expected theoretical value of 14.00 μB (g = 2.00). The solid line
corresponding to the Brillouin function for two uncoupled spins
S = 7/2 (g = 2.00) is slightly higher than the magnetization curve
of 2. This may confirm that the antiferromagnetic interaction is
operative (Figures S7 and S9, Supporting Information). How-
ever, ab initio calculation results show that the isotropic exchange
interaction is overestimated. This could arise from the presence
of non-negligible ZFS that results in larger isotropic J values (see
Computational Section).
Hamiltonian H = ꢀJSa Sb with Sa = Sb = 7/2, it is possible to
3
reproduce the variation of χT vs T. The best-fit parameters
obtained are J = ꢀ0.178(1) cmꢀ1 and g = 2.00(0). As expected
for pure lanthanide systems, the exchange interaction is rather
weak as a consequence of the shielded f orbitals that have little
overlap with bridging ligand orbitals. Although the obtained values
are in good agreement with the reported coupling constants for
other phenoxo-bridged GdIII systems,34 especially for centro-
symmetric complexes,35,36 it is important to verify that the
lowered symmetry of the GdIII ion (Table 3) in 2 might lead
to non-negligible zero-field splitting (ZFS). The latter can also
For compounds 3ꢀ5, the thermal variation of χT shows a
negative deviation upon cooling to reach a value of 10.2, 5.2, and
7.1 cm3 K molꢀ1 at 1.8 K for compounds 3ꢀ5, respectively
3
3
(Figure 2). For such lanthanide ions with an unquenched orbital
moment associated with a ligand field, the decrease of the χT can
originate from the following possible contributions: (i) antifer-
romagnetic interactions between the lanthanide centers; (ii) the
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Figure 5. ColeꢀCole (Argand) plot for 4 obtained using the ac
susceptibility data. The solid lines correspond to the best fit obtained
with a generalized Debye model.
Figure 7. Field dependence of the normalized magnetization of 4
between 0.04 and 4 K for dc applied field ranging from ꢀ1.5 to 1.5 T.
Figure 6. Relaxation time of the magnetization ln(τ) vs Tꢀ1 (Arrhenius
plot using ac data) for 4. The line corresponds to the fit.
Figure 8. Sweep rate dependence of the normalized magnetization of 4
at 0.04 K for dc applied field ranging from ꢀ1.5 to 1.5 T.
thermal depopulation of the Stark sublevels; and (iii) the
presence of significant magnetic anisotropy.
Additionally, a frequency dependence of the maximum asso-
ciated only with a single relaxation process appears clearly on a
tridimensional plot of the variation of χ00 versus the temperature
and the frequency of the oscillating field between 1 and 1500 Hz
(Figure 4). This indicates slow relaxation of the magnetization
associated with SMM behavior.
The thermally populated diamagnetic ground state (7F0) of
the europium analogue 1 leads to a value of the magnetization
close to zero even at 7 T. For compounds 3ꢀ5, the high field
linear variation and non-saturation of the magnetization indicate
the presence of significant magnetic anisotropy and/or low-lying
excited states (Figure S7, Supporting Information). The values of
the magnetization at 7 T are 10.5, 11.6, and 10.3 μB for
compounds 3ꢀ5, respectively. The significant deviation from
the expected magnetization saturation values indicates a strong
contribution from the ligand field. However, the value obtained
for compound 4 is close to the value of 5.23 μB per DyIII ion in a
crystal field environment.3b,37
Such single peak relaxation behavior is remarkable as most
lanthanide systems exhibit multiple relaxation processes due to
significant quantum tunneling at zero field and/or to the presence of
crystallographically independent lanthanide centers.3g,21 Here, the
presence of a single relaxation process agrees with the presence of
a unique crystallographic DyIII ion in the dinuclear structure. A
close inspection of the latter relaxation process in the tridimen-
sional plot reveals two regimes of relaxation (Figure 4). For
temperatures higher than 4 K, the system follows a thermally
activated relaxation process. However, below 4 K, the relaxation
becomes temperature independent (i.e., quantum regime), and a
drop of the imaginary susceptibility, χ00, is observed. The latter
regime most likely originates from an antiferromagnetic interac-
tion between the DyIII ions which tends to create a nonmagnetic
ground state with decreasing temperature.15 The graphical
representation of χ00 vs χ0 (ColeꢀCole plot38) in the tempera-
ture range 2ꢀ12 K further confirms the single relaxation process
(Figure 5). For temperatures higher than 4 K, symmetric
In order to investigate the presence of slow relaxation of the
magnetization which may originate from an SMM behavior, ac
measurements were performed on all complexes in the tempera-
ture range 1.8ꢀ25 K with zero dc field and a 3 Oe ac field at
frequencies between 50 and 1500 Hz. The temperature and
frequency dependent ac susceptibility signal was observed below
25 K for the dysprosium analogue 4 (Figure 3). All other
complexes did not exhibit such signals. The out-of-phase (χ00)
component of the ac susceptibility (Figure 3 right) clearly
exhibits a frequency dependent full peak with one maximum.
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Figure 9. Two views of the structure of the calculated mononuclear
lanthanide fragment of 4. The structure of the fragments of 1ꢀ3 and 5
are similar.
semicircles are obtained. The data can be fitted using a general-
ized Debye model.39 The R parameter, indicating deviation from
the pure Debye model, is lower than 0.03 for this temperature
range. This low degree of disorder confirms that the magnetiza-
tion relaxes with a unique single characteristic time. When the
system enters the quantum regime (below 4 K), a slight
asymmetry in the ColeꢀCole plot appears as well as an increase
in R up to 0.18 (2 K) is observed. This indicates a narrow width of
the distribution in this single relaxation process. As observed for
the frequency dependent ac susceptibility, the antiferromagnetic
interaction between the two DyIII ions results in a drop of the
out-of-phase susceptibility, χ00, in the ColeꢀCole plot.
Figure 10. A comparison of the experimental and calculated (solid line)
magnetic susceptibility for complex 1ꢀ5.
tunneling at the steps, which is reduced by thermal activations
around the corresponding tunnel splitting.
’ AB INITIO CALCULATIONS AND SIMULATIONS OF
MAGNETISM
Computational Details. The following contractions were
used: [8s7p5d4f2g1h] for lanthanide ions, [4s3p2d] for close O
and N, [3s2p] for distant O, N, and for all C, and [2s] for H. The
active space of the complete active space self-consistent field
(CASSCF) method included all 4f electrons of the correspond-
ing lanthanide ion spanning seven orbitals. A good description of
the spinꢀorbit coupling on the metal sites usually requires the
mixing of a large number of states. In the present case we have
mixed the maximum number of spin-free states which was
possible with our hardware (Eu, 215; Tb, 215; Gd, 262; Dy,
279; Ho, 316). The free ion parentage of these states, their
spinꢀorbit energies, and the local magnetic axes of the individual
fragments can be found in Supporting Information in Tables
S1ꢀS5. The latest implementations of the MOLCAS ab initio
methodology41 (Choleski decomposition of the bielectronic
integrals, parallelization, etc.) allow the treatment of relatively large
mononuclear fragments. The structure of the calculated fragments is
shown in Figures 9 and S13 ꢀ S17, Supporting Information.
To confirm the observed dc magnetic behavior, ab initio
calculations were performed for all isolated complexes. The
temperature-dependent magnetic susceptibility results for all
complexes are shown in Figure 10. A comparison of the experi-
mental and calculated molar magnetization at 2 K for all
complexes is given in Figure 11. In the case of complex 1, EuIII
is a non-Kramers ion with a nonmagnetic ground state 7F0. The
unusually large experimental χT300 K = 3.2 cm3 K molꢀ1 can be
The anisotropic energy barrier, Ueff, can be obtained from the
high-temperature regime of the relaxation where it is thermally
induced (Arrhenius law, τ = τ0 exp(Ueff/kT)). The effective
energy barrier obtained from fitting (Figure 6) is Ueff = 76 K (τ0 =
6.04 ꢁ 10ꢀ7 s), which is comparable in magnitude to the
archetype Mn12ꢀAc SMM.6
In order to reduce the quantum tunneling effects frequently
associated with lanthanide SMMs, ac measurements in the
presence of a static dc field were carried out. Interestingly, no
significant shift in the maximum position was observed for dc
fields up to 2000 Oe. This suggests that the tunneling below the
latter field is less efficient. To further probe this, various magnetic
measurements on diluted samples are currently being investigated.
The SMM behavior can be further investigated through micro-
SQUID experiments between 0.04 and 4 K (Figures 7 and 8).
Hysteresis loops were measured on easy axis-oriented single
crystals. An “S-shaped” hysteresis is observed with a large step at
H = ( 0.3 T, which can be directly associated with a spin flip of
the antiferromagnetically coupled DyIII spins. Moreover, the
strong sweep-rate dependence confirms the presence of quantum
tunneling of the magnetization. The tunnel position resonance shift
at (0.3 T is due to each DyIII ion acting as bias field on its
neighboring metal ion within the molecule. Such behavior is similar
to previously observed {Mn4}2 systems where two cluster units are
entangled in their slow relaxation of the magnetization.40 It can
therefore be concluded that for 4 the hysteresis loops reveal
exchange-biased interactions between the two individually relaxing
DyIII ions. The strength of this weak exchange coupling determined
through low-temperature dc measurements corresponds to 0.32 T.
In addition to the unique aforementioned behavior, complex 4
reveals an atypical behavior: Below 1 K the coercive field increases
with increasing temperature, contrary to what is usually observed in
SMMs and traditional magnets. This can be ascribed to strong
3
3
explained by a large temperature-induced paramagnetism (TIP)
and the thermal population of excited multiplets.
The energy spectrum of 1 for several low-lying excited states is
shown in Table 4. The energy of the first excited multiplet is
already much lower than the free ion value (400 cmꢀ1) which is
the reason for the enhanced susceptibility in 1. As the table
shows, the stabilization energy of the ground spinꢀorbital singlet
is a function of the number of spin-free states included in
the spinꢀorbit coupling calculation. A good agreement with
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Figure 12. Orientation of the local main magnetic axes of the ground
Kramers doublet in 4. In Tb2 (3) and Ho2 (5) complexes, the
orientation of the main magnetic axis is analogous.
Figure 11. A comparison of the experimental and calculated (solid
lines) molar magnetization for complexes 1ꢀ5.
splitting of the ground S = 7/2 term on each GdIII site, which
appears to be non-negligible (Table S2, Supporting In-
formation). The noticeable difference between the fitted lines
exchange parameter, JGdꢀGd = ꢀ0.08 cmꢀ1, and the fitted
Table 4. Lowest Multiplets of the EuIII Fragmenta
no.
A
B
C
parameter of isotropic exchange interaction, Jisotropic
=
ꢀ0.178 cmꢀ1, is due to this zero-field splitting. The latter ZFS
arises most likely from the lowered symmetry of GdIII ions as
seen in Table 3. Considering smaller splittings of the ground 8S0
multiplet in the Lines model resulted in larger fitted values for the
exchange parameter.
1
2
0.000
101.860
273.267
429.725
628.622
676.208
802.393
859.612
874.699
1392.231
0.000
0.000
208.547
378.847
531.867
899.761
960.062
1078.854
1139.114
1156.185
1856.677
231.432
401.711
554.371
941.396
1002.795
1121.218
1181.665
1199.146
1905.155
3
4
5
For the analogous Tb2 complex 3, from the basis set of column
3, Table S3, Supporting Information, the Lines parameter of
JTbꢀTb = ꢀ0.1 cmꢀ1 was obtained, and the experimental and
fitting data can be seen in Figures 10 and 11, and Figure S20
(Supporting Information). Although the obtained fit is reason-
able, the experimental susceptibility obtained is slightly lower
than the calculated one at 300 K. This slight difference between
the experimental and the calculated magnetic susceptibility and
magnetization remains unclear.
The simulated magnetism of complex 4 with the Lines para-
meter JDyꢀDy = ꢀ0.21 cmꢀ1 is shown in Figures 10 and 11, and
the simulations correspond to the basis set of column 5 from
Table S4, Supporting Information. The calculated directions of
the anisotropy axes and the local magnetic moments in one of the
two-fold degenerate Ising ground states are shown in Figure 12.
Due to the inversion symmetry of complexes 1ꢀ5, the
orientation of the local anisotropy axes is strictly parallel, while
the local magnetic moments in both Ising ground states are
antiparallel to each other. At high temperature (300 K), the value
of χT is well approximated by the sum of the contributions of
individual centers. The experimental susceptibility obtained is
slightly higher than the calculated one at 300 K. A reduction of
8% in both experimental magnetic susceptibility and molar
magnetization is in good agreement with the calculated curves
(Figure S21, Supporting Information).
6
7
8
9
10
a A: spin-free states originating from 7F multiplet were mixed by
7
5
5
5
5
5
5
spinꢀorbit coupling. B: states coming from F, D, L, G, H, I, F,
5K, 5G, and 5D multiplets were mixed by spinꢀorbit coupling. C: states
coming from 7F, 5D, 5L, 5G, 5H, 5I, 5F, 5K, 5G, 5D, 3P, 3O, 3 M, 3K, 3H, 3F,
3I, and 1Q multiplets were mixed by spinꢀorbit coupling.
experimental data is obtained if the energy of the first excited
multiplet in the set C is reduced by 40% (Figure S18, Supporting
Information).
The apparent overestimation of the excitation energy(ies) is
probably related to the fact that the CASSCF wave function is too
“ionic” due to the lack of dynamical correlation. These effects can
be accounted for by performing a multistate CASPT2 calcula-
tion. However, due to large basis of RASSI states need to be taken
into account for a good description of the spinꢀorbit coupling
on the lanthanide ions, the multistate CASPT2 was computa-
tionally too costly.
In the case of gadolinium analogue 2 the simulated magnetism
with the Lines parameter gave JGdꢀGd = ꢀ0.08 cmꢀ1, corre-
sponding to S = 7/2, (Figures 10 and 11 and Figure S19 Table S2,
Supporting Information). Contrary to the description based on
the isotropic exchange model (Figures 2 and S7, Supporting
Information), the simulations in Figures 10 and 11 fit very well
both the susceptibility and the magnetization. The important
ingredient brought by ab initio calculations is the zero-field
Finally, the simulated magnetism of Ho2 complex (5) with the
Lines parameter JHoꢀHo = ꢀ0.44 cmꢀ1 is shown in Figures 10
and 11, and Figure S22 (Supporting Information). The simula-
tions correspond to the basis set of column 2 from Table S5,
Supporting Information. The agreement with experimental
susceptibility and magnetization is very good.
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Table 5. Calculated Exchange Coupling Constants for Di-
nuclear Complexes 1ꢀ5
LnIIIꢀO3ꢀ
LnIII (ꢀ)
Jcalc
Lines(cm-1)
ꢀ
Jcalc
lsing(cm-1)
ꢀ
LnIII
LnIIIꢀLnIII (Å)
EuIII
GdIII
TbIII
DyIII
HoIII
3.830(3)
3.811(1)
3.788(1)
3.768(3)
3.754(3)
107.26(6)
107.76(8)
108.05(8)
108.22(3)
108.17(5)
ꢀ
ꢀ
ꢀ0.08
ꢀ0.10
ꢀ0.21
ꢀ0.44
ꢀ
ꢀ3.60
ꢀ5.25
ꢀ7.04
Information as 165 K. Interestingly, this value does not match the
anisotropic barrier derived from the ac measurements (Ueff = 76
K). Despite the fact that the relaxation time follows a thermally
activated behavior at high temperature, the energy differences
observed indicate that an Orbach process might not be pre-
dominant and that further relaxation pathways have to be
considered. Another reason for this discrepancy can be the
overestimated excitation energies of the local Dy multiplets
obtained within the CASSCF approximation.
’ CONCLUSION AND OUTLOOK
Using a compartmental Schiff base ligand based on the o-
vanillin motif, a family of centrosymmetric dinuclear lanthanide
complexes has been synthesized and fully characterized. For all
complexes, an antiferromagnetic interaction between the lantha-
nide ions is observed. Furthermore, computational methods
allow us to validate observed experimental behavior. Simulations
based on ab initio calculations predict that the strength of the
interaction increases with the decrease of the intramolecular
LnIIIꢀLnIII distances as well as the increase in the bridging
LnIIIꢀO3ꢀLnIII angle. Due to the fast relaxation of the magne-
tization for TbIII and HoIII analogues, only the DyIII analogue, 4,
exhibits a slow relaxation of the magnetization associated with
SMM behavior and an anisotropic barrier of Ueff = 76 K. The
single relaxation process observed adequately correlates with the
presence of a unique crystallographic DyIII ion. Although the
observed slow magnetic relaxation is mainly due to the single-ion
relaxation, the results above demonstrate that a weak exchange
coupling (J = ꢀ0.21 cmꢀ1) between the lanthanide ions affects
the QTM. Therefore, the observed steps in the hysteresis loops
correspond to a weakly coupled system similar to exchange-
biased SMMs.40 Due to the centrosymmetry and simplicity of the
system, complex 4 can be viewed as an ideal model for under-
standing the parameters that affect the SMM behavior in poly-
nuclear 4f systems. Even though the coupling between the
lanthanide ions remains small through the superexchange path-
way, it is important to investigate simple analogous dinuclear
systems to understand the nature and the strength of the
interaction. Subsequently, their effect on the relaxation mechan-
ism involved in weakly coupled molecules can be investigated. By
modulating the superexchange pathway the nature and the
strength of the interaction can be further tuned. We believe this
may be the way forward for controlling the interactions between
4f ions and designing better SMMs.
Figure 13. Zeeman spectrum (a) and simulated magnetization curve
(b) at T = 0 K for 4.
The general trend, which can be inferred from these simulations, is
the increase of the exchange interaction when the intramolecular
LnIIIꢀLnIII distance decreases (Table 5). This is consistent with
previously reported studies on the dinuclear gadolinium comple-
xes.34 However, the change of the orbital overlap between the f
centers, caused by an increase of the bridging angle, could also lead to
the increase of the exchange interaction. It is noteworthy that the
coupling constant increases with the addition of f electrons along
with the f-orbital contraction down the series. Further investigation is
needed to confirm such trends.
In order to better characterize the distinct SMM behavior
observed for 4, several approximations were tested (Table S4,
Supporting Information). In the largest computational approx-
imation (see Supporting Information) the complete molecule
was kept as is. The only change was the substitution of the
neighboring DyIII ion with diamagnetic LaIII simulated in the ab
initio calculations by the same ANO-RCC all-electron basis set as
used for DyIII. The obtained g tensor is strongly anisotropic (gz =
19.547) pointing to an Ising interaction between DyIII ions. The
orientations of the magnetic axes are found to be almost collinear
to the shortest DyꢀO2 distance with an angle of 4.05ꢀ.
The simulated magnetization curve at 0 K (Figure 13) shows a
single magnetization step at a value of applied field strongly
dependent on its angle with the anisotropy axes of the DyIII ions.
For instance, the observed jump at 0.3 T in the micro-SQUID
experiment (Figure 8) requires a large angle of 58ꢀ between the
anisotropy axes and the applied magnetic field.
’ ASSOCIATED CONTENT
The energy of the first excited Kramers doublet on each DyIII
fragment is obtained with the set 5 in Table S4, Supporting
S
Supporting Information. Detailed description of the
b
computation data, packing diagrams, SHAPE, infrared data, and
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CIF files for all complexes.This material is available free of charge
via the Internet at http://pubs.acs.org.
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’ AUTHOR INFORMATION
Corresponding Author
*m.murugesu@uottawa.ca.
’ ACKNOWLEDGMENT
We thank the University of Ottawa, CCRI, NSERC
(Discovery and RTI grants), Early Researcher Award, Vision
2010, CFI, ORF, and FFCR for their support.
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