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The Royal Society of Chemistry 2013 Chem. Commun., 2013, 49, 901--903 901
Cite this: Chem. Commun., 2013,
49, 901
A hydride-ligated dysprosium single-molecule
magnet†
Ajay Venugopal,
a
Floriana Tuna,
bc
Thomas P. Spaniol,
a
Liviu Ungur,
d
Liviu F. Chibotaru,
d
Jun Okuda*
a
and Richard A. Layfield*
b
An experimental and ab initio computational study of an unsym-
metrical, hydride-bridged di-dysprosium single-molecule magnet
is reported.
Lanthanide coordination compounds have accounted for some of
the most important developments in studies of single-molecule
magnets (SMMs), a family of molecules that exhibit magnetic
memory effects.
1
The temperatures at which Ln-SMMs function
far exceed the limits previously set by transition metal SMMs,
2
and
the benchmark SMM blocking temperature was recently re-defined
by [Tb
2
{N(SiMe
3
)
2
}
4
(thf)
2
(m-N
2
)]
, where magnetic hysteresis up to
14 K was measured.
3
Indeed, energy barriers to reversal of the
magnetization (the anisotropy barrier, U
eff
) in Ln-SMMs often exceed
100 cm
1
,
4
which has created renewed confidence that such
materials may eventually be developed for device applications.
5
Single-ion effects, such as the symmetry and electrostatic
potential of the crystal field, strongly influence the relaxation of
the magnetization in SMMs,
1e
and exploring ligands that are new to
Ln-SMMs could push the field in new directions.
6
The hydride
ligand – which has never been applied in SMM studies – offers an
interesting opportunity because its strong ligand-field effects, and
potential to promote strong exchange, could influence the relaxa-
tion in Ln-SMMs in completely different ways to oxygen-donor
ligands, which are ubiquitous in SMM studies.
1
We now report the
hydride-bridged compounds [Ln(Me
5
trenCH
2
)(m-H)
3
Ln(Me
6
tren)]
[B{C
6
H
3
(CF
3
)
2
}
4
]
2
, where Ln = Gd(III)is[1][X]
2
,Ln=Dy(III)is
[2][X]
2
,andMe
6
tren = tris{2-(dimethylamino)ethylamine. Com-
pound [2][X]
2
is the first hydride-ligated SMM.
Adding [Et
3
NH][B{C
6
H
3
(CF
3
)
2
}
4
]to[Ln(CH
2
SiMe
3
)
3
(thf)
3
]inether
at 40 1C, followed by Me
6
tren and then by dihydrogen produced
[1][X]
2
2Et
2
O and [2][X]
2
2Et
2
O (Scheme 1). Both [1][X]
2
2Et
2
O
(Fig. S1, ESI†) and [2][X]
2
2Et
2
O (Fig. 1) crystallize in the space
group P
%
1, with the Ln centres being related by crystallographic
inversion symmetry. Disorder within the ligands was resolved
with split positions for the carbons. Taking the disorder into
account, the eight-coordinate Ln(
III) ion is complexed by three
m-hydrides, four nitrogens and a carbon atom of a C–H-activated
[Me
5
trenCH
2
]
ligand. The seven-coordinate Ln(III)ioniscom-
plexed by the four nitrogens of the Me
6
tren ligand in addition to
the m-hydrides. Key parameters are presented in Tables S1 and S2
(ESI†). The coordination geometries of the Ln centres in [1]
2+
and
[2]
2+
are similar: the seven-coordinate environment of Ln(1A) can
be roughly described as mono-capped octahedral, whereas the
eight-coordinate Ln(1) occupies a very low symmetry site.
Scheme 1 Synthesis of [1][X]
2
(Ln = Gd) and [ 2][X]
2
(Ln = Dy).
Fig. 1 Structure of [2]
2+
(50% thermal ellipsoids). Only one split positi on of
disordered atoms shown. Hydrogen atoms omitted, except m-hydrides.
a
Institute of Inorganic Chemistry, RWTH Aachen University, Landoltweg 1, 52056
Aachen, Germany. E-mail: jun.okuda@ac.rwth-aachen.de
b
School of Chemistry, The University of Manchester, Oxford Road, Manchester,
M13 9PL, UK. E-mail: Richard.Layfield@manchester.ac.uk
c
EPSRC National UK EPR Facility, Photon Science Institute, The University of
Manchester, Oxford Road, Manchester, M13 9PL, UK
d
Division of Quantum and Physical Chemistry, Katholieke Universiteit Leuven,
Celestijenlaan 200F, 3001 Leuven, Belgium
† Electronic supplementary information (ESI) available: Synthetic, analytical,
crystallographic details. Magnetism graphs, computational details. CCDC
901745 and 901746. For ESI and crystallographic data in CIF or other electronic
format see DOI: 10.1039/c2cc38036f
Received 6th November 2012,
Accepted 7th December 2012
DOI: 10.1039/c2cc38036f
www.rsc.org/chemcomm
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902 Chem. Commun., 2013, 49, 901--903 This journal is
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The Royal Society of Chemistry 2013
The considerable interest in molecular rare earth hydr ides stems
from their applications in synthesis and catalysis, and from their
potential to activate dihydrogen.
7,8
Solid-state rare-earth hydrides are
valued for their magnetic, optical and semiconductor properties.
9
However, [2][X]
2
provides the first opportunity to investigate the
SMM properties of a rare-earth hydride. Mindful of the crucial role of
crystal field symmetry in SMMs, [2]
2+
also enables an investigation of
how two different, low-symmetry environments within the same
hydride species can impact upon dynamic magnetic behaviour.
Compounds [1][X]
2
and [2][X]
2
were investigated by SQUID
magnetometry in the temperature range 1.8–300 K. At 300 K in a
field of H
dc
= 1000 G, the w
M
T product for [1][X]
2
(w
M
is the molar
magnetic susceptibility) i s 15.2 cm
3
Kmol
1
(Fig. S2, ESI†), which is
consistent with the value of 15.76 cm
3
Kmol
1
predicted for two
non-interacting Gd(
III)ions(
8
S
7/2
, g =2).Oncooling,w
M
T decreases
gradually down to 50 K, and then rapidly to reach 1.22 cm
3
Kmol
1
at 1.8 K, which indicates antiferromagnetic e xchange. In agreement
with this, the magnetisation (M) versus field (H) isotherms are well
below the calculated Brillouin function of two uncoupled S =7/2
ions (Fig. S3, ESI†). The maximum M value at 2 K and 70 kG is
9.3 m
B
, which is much smaller than the calculated value of 15.0 m
B
for
two uncoupled Gd(
III) centres with g = 2. The magnetism of [1][X]
2
was modelled with the Hamiltonian H = JS
Gd1
S
Gd2
,whereJ is the
exchange coupling constant and S
Gd1
and S
Gd2
represent the spins
on the Gd(
III) ions. A good fit of the w
M
T(T) data was obtained with
g =1.995(expectedforGd
3+
)andJ = 1.22 cm
1
, thus indicating
weak antiferromagnetic coupling. Studies of hydride-mediated
exchange are hitherto unknown in lanthanide chemistry, however
the value of J determined for [1][X]
2
is similar to those measured in
other exchange-coupled gadolinium compounds.
3b
The w
M
T data for [2][X]
2
(Fig. S2, ESI†) reveal a value of
28.17 cm
3
K mol
1
at 300 K, in good agreement with the
theoretical value of 28.34 cm
3
K mol
1
for two uncoupled
Dy(
III) ions (
6
H
15/2
, g = 4/3), suggesting that all the m
J
sub-levels
within the electronic ground term of Dy(
III) are populated
at 300 K. At lower temperatures, w
M
T decreases gradually to
24.7 cm
3
K mol
1
at 25 K, and then more rapidly below 25 K, to
reach a value of 16.57 cm
3
K mol
1
at 2 K. The decrease of
w
M
T on cooling can be assigned to depopulation of excited m
J
sub-levels and weak antiferromagnetic exchange. The M(H)
data of 2, acquired at several temperatures between 1.8 and
10 K (Fig. S4, ESI†), reveal a rapid increase of the magnetisation
at small fields, followed by a more gradual increase at high
fields, without reaching saturation. Isothermal M(H/T) curves
do not superimpose, confirming the presence of significant
magnetic anisotropy and/or low-lying excited states. The value
of M at 1.8 K and 70 kG is 10.71 m
B
, (5.35 m
B
per Dy), as typically
observed in other Dy
2
SMMs.
6
The dynamic magnetism of [2]X
2
was investigated using
alternating current (ac) magnetic susceptibility measurements
as a function of temperature and of frequency. In zero dc field,
an ac field of H
ac
= 1.55 G and ac frequencies (n) oscillating at
1–1200 Hz, the in-phase (w
0
M
) (Fig. S5 and S6, ESI†) and the out-
of-phase (w
00
M
) (Fig. 2 and 3) components of the magnetic
susceptibility are temperature and frequency dependent below
22 K. The maximum in w
00
M
ðnÞ gradually shifts to lower frequen-
cies as the temperature is lowered from 13 K to 1.85 K,
indicating that [2]
2+
is an SMM. The temperature dependence
of w
00
M
in [2][X]
2
shows unsymmetrical maxima at several fre-
quencies up to 1200 Hz in zero applied field (Fig. 3). Deconvo-
lution of the overlapping maxima (Fig. S8, ESI†) enabled two
Lorenzian curves to be fitted, and two relaxation processes to be
identified. At fixed temperatures in the range 1.85–12 K, semi-
circular Cole–Cole plots of w
0
M
vs. w
00
M
were obtained, and were
fitted to a generalized Debye model with a = 0.27–0.33 (Fig. S9,
ESI†). The relatively high values of the a parameters imply that
more than one relaxation process is occurring, which is con-
sistent with the unsymmetrical w
00
M
ðT Þ curves, and the presence
of two distinct Dy sites in [2]
2+
.
The relaxation of the magnetization in SMMs can be characteri zed
by a relaxation time, t.
1b
Plots of ln t versus 1/T for [2]
2+
in zero dc field
using w
00
M
ðT Þ and w
00
M
ðnÞ data are linear above 11 K (Fig. S10, ESI†),
suggesting that the magnetization relaxes via an Orbach process
involving the ground and first-excited m
J
levels. The Arrhenius
relationship t = t
0
exp (U
eff
/k
B
T) allowed the anisotropy barrier for
the slower relax ation process to be esti mated as U
eff
=65cm
1
,with
t
0
=1.04 10
7
s. Be low 11 K, a gradual c rossover to a t emperature-
independent regime is observed, suggesting relaxation via quantum
tunnelling of the magnetization (QTM). From the w
00
M
ðnÞ data, the
second relaxation process was estimated to have U
eff
=15cm
1
.
Application of a static field to [2]X
2
reduces the QTM rate. Field-
dependence studies at 4 K showed a rapid increase in t upon
increasing the field from zero to 800 G, and w
00
max
shifts to lower
frequencies. Above 800 G, t decreases rapidly, passing through a
minimum at 2.5 kG (Fig. S11, ESI†). This indicates an additional
relaxation pathway that shortcuts the energy barrier, as predicted at
level crossings when resonant QTM occurs. Application of the
optimum field of 800 G to [2][X]
2
thus shifts the maxima in w
00
M
ðnÞ
to lower frequencies (Fig. 2), and additional maxima at lower
frequencies were observed in w
00
M
ðT Þ (Fig. 3). At 800 G, the Arrhenius
analysis produced U
eff
=85cm
1
and t
0
=5.7 10
9
s (Fig. S10, ESI†).
To gain more insight into the two relaxation processes in [2]
2+
,
ab initio calculations were carried out using MOLCAS 7.6.
10
Fig. 2 w
00
M
ðnÞ isotherms in [2]X
2
with H
ac
= 1.55 G.
Fig. 3 w
00
M
ðT Þ in [2]X
2
with H
ac
= 1.55 G applied at various frequencies.
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The calculations revealed that the ground Kramers’ doublet for
each of the two Dy(
III) centres is well separated from the first
excited state, but that the energy separation is 231 cm
1
in the
eight-coordinate Dy(1) and 94 cm
1
for t he seven-coordinate
Dy(1A) (Table 2 and Table S4–S8, ESI†). The calculated g values
of the ground Kramers’ doublets for Dy(1) are g
x
= 0.0187, g
y
=
0.0298 and g
z
= 19.7236; those for Dy(1A) are g
x
= 0.0615, g
y
= 0.1374
and g
z
= 19.2638. Thus, the transverse g-values are approximately
four times smaller for Dy(1) than for Dy(1A), and the different
symmetry of the Dy coordinati on environments influences the
energies and axiality of the Kramers’ doublets.
11
SMMs in which
the Ln centres are weakly exchange coupled relative to the measure-
ment temperature, as in [2]
2+
(see below), are likely to have their
slowly relaxing magnetization associated with individual lanthanide
ions. Thus, despite the high axiality for both dysprosiums, the eig ht-
coordinate Dy(1) will be characterized by a stronger suppression of
QTM, which can explain the observation of only one blocking centre
in the ac susceptibility measurements. In polymetallic Ln-SMMs that
featuremorethanonerelaxationprocess, assigning each processes
to a specific lanthanide is not straightforward using only bulk
susceptibility measurements,
12
so here the calculations are crucial.
The U
eff
value of 65 cm
1
in [2]
2+
inzerofieldismarkedlylessthan
the calculated energies of both first excited Kramers’ doublets. The
discrepancies can be explained by considering the possible relaxation
mechanisms, i.e. an Orbach process via the first excited Kramers’
doublet, or directly from the ground state via QTM and/or a Raman
process. The deviation from linearity of the Arrhenius plot for [2]
2+
in
zero field (Fig. S10, ESI†) shows that the QTM regime is entered below
about T = 11 K, hence the poor match between the experimental U
eff
value and the energies of the first excited Kramers’ doublets. However,
in the optimum dc field of 800 G the QTM is effectively suppressed,
and the close match of the theoretical (94 cm
1
) and experi-
mental (85 cm
1
) energy barriers in Dy(1A) suggests that relaxa-
tion probably occurs via the first excited Kramers’ doublet.
The magnetic moment s of the dysprosiums in the ground
Kramers’ doublets of [2]
2+
intersect at an angle of 4.851 (Fig. 4).
The small values of g
x
and g
y
for Dy(1) and Dy(1A) suggest that an
Ising-type exchange interaction occurs in [2]
2+
. The total magnetic
interaction (J
tot
) is a sum of the magnetic di pole–dipole contribution
(J
dip
) and the exchange part (J
exch
). The magnetic interaction between
the ground Kramers’ doublets on the two dysprosiums is described
by
^
H ¼ðJ
dip
þ J
exch
Þ
^
~
s
1;z
^
~
s
2;z
,wheres
˜
i,z
= 1/2 is the projection of the
pseudospin corresponding to the lowest Kramers doublet on Dy
i
on
the main anisotropy axis, z. Using the calculated g tensors for the
ground Kra mers’ doub lets, J
dip
was calculated exactly as +5.16 cm
1
(Table S11, ESI†). A fit of the experimental dat a allowed
J
exch
= 7.62 cm
1
to be calculated (Fig. S13–S18, Table S11, ESI†).
Whereas the dipolar interaction is ferromagnetic, the exchange
interaction is antiferromagnetic and stronger than the dipolar
contribution, hence the total interaction in [2]
2+
is antiferromagnetic
with J
tot
= 2.46 cm
1
, which is consistent with the exchange
coupling in [1]
2+
.
In summary, the hydride-bridged species [Ln(Me
5
trenCH
2
)-
(m-H)
3
Ln(Me
6
tren)]
2+
, (Ln = Gd, Dy) contain seven-coordinate and
eight-coordinate Ln(
III) centres. Two relaxation processes in the
SMM [2]
2+
were identified from ac susceptibility studies, with
anisotropy barriers of U
eff
=65cm
1
and 15 cm
1
,respectively.
Ab initio calculation of the g-values for Dy(1) and Dy(1A) in [2]
2+
allowed the process with U
eff
=65cm
1
to be assigned to the
eight-coordinate Dy(1), while fast QTM within seven-coordinate
Dy(1A) prevents detection of a blocking process.
We acknowledge the support of the EPSRC (RAL, FT), The
Humboldt Foundation (AV, RAL), the DFG (JO), the FWO-
Vlaanderen (LU), and the KU-Leuven (LU, LFC).
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Fig. 4 Orientation of the magnetic moments in the ground Kramers’ doublet of
[2]
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(dashed lines). The arrows show the antiferromagnetic coupling. Pink
atoms = hydrides, blue = N, grey = C.
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