A Dy4 Cubane: A New Member in the Single-Molecule Toroics Family

Article abstract of DOI:10.1002/anie.201810156

Molecular materials that possess a toroidal moment associated to a non-magnetic ground state are known as single-molecule toroics (SMTs) and are usually planar molecules. Herein, we report a Dy₄ cubane, namely [Dy₄(Bppd)₄(μ₃-OH)₄(Pa)₄(H₂O)₄]?0.333 H₂O (where BppdH=1,3-Bis(pyridin-4-yl)propane-1,3-dione and PaH=2-Picolinic acid) for which magnetometry measurements and state-of-art ab initio calculations highlight SMT behavior in a tridimensional structure (3D-SMT). The in-depth theoretical analysis on the resulting low-lying energy states, along with their variation in function of the magnetic exchange pathways, allows further light to be shed on the description of single-molecule toroics and identify the coupling scheme that better reproduces the observed data.

Full text of DOI:10.1002/anie.201810156

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Accepted Article
Title: A Dy4 Cubane: A New Member in the Single-Molecule Toroics
Family
Authors: Guglielmo Fernandez Garcia, Djamilla Guettas, Vincent
Montigaud, Paolo Larini, Roberta Sessoli, Federico Totti,
Olivier Cador, Guillaume Pilet, and Boris Le Guennic
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To be cited as: Angew. Chem. Int. Ed. 10.1002/anie.201810156
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Angewandte Chemie International Edition
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COMMUNICATION
A Dy Cubane: A New Member in the Single-Molecule Toroics
4
Family
[
a,b]
[c]
[a]
[d]
Guglielmo Fernandez Garcia,
Djamilla Guettas, Vincent Montigaud, Paolo Larini, Roberta
[
b]
[b]
[a]
[c]
[a]
Sessoli, Federico Totti, Olivier Cador,* Guillaume Pilet,* and Boris Le Guennic*
Abstract: Molecular materials that possess a toroidal moment
associated to a non-magnetic ground state are known as Single-
Molecule Toroics (SMTs) and are usually planar molecules. Herein,
molecule more than one paramagnetic center coupled through
exchange interactions. The magnetic interactions between
lanthanide magnetic moments in homometallic polynuclear
complexes are, in general, very small (of the order of few
we
report
(Pa) (H
a
Dy
4
cubane,
(where
namely
4 4 3
[Dy (Bppd) (µ -
[
10,11]
OH)
4
4
2
O)
4
]·0.333H
2
O
BppdH=1,3-Bis(pyridin-4-
Kelvin)
relaxation process between the two low-lying exchange
and not always able to quench the tunneling
yl)propane-1,3-dione and PaH=2-Picolinic acid) for which
magnetometry measurements and state-of-art ab initio calculations
highlight SMT behavior in a tridimensional structure (3D-SMT). The
in-depth theoretical analysis on the resulting low-lying energy states,
along with their variation in function of the magnetic exchange
pathways, allows to shed further light on the description of Single-
Molecule Toroics and identify the coupling scheme that better
reproduce the observed data.
[
12]
multiplets, even if radical ligands strongly modify this picture.
Indeed parallel and axial principal magnetic axes of the
[
13]
individual centers are needed. On the other hand, polynuclear
lanthanide systems can show very peculiar magnetic moments
configurations at low temperature which are due to a subtle
balance between anisotropy directions and exchange
interactions.
Single Molecule Magnet (SMM) behavior was discovered more
[
1]
than twenty years ago in polynuclear 3d complexes and ten
[
2]
years later, in mononuclear 4f complexes, the latter being
[
3]
nowadays the most popular. These objects fascinate chemists
and physicists because they might be components of spintronic
[
4,5]
devices.
They are conceptually based on axial magnetic
anisotropy to create a potential barrier separating the two
orientations of the magnetic moment. Magnetic orbitals of
lanthanide are largely subject to spin-orbit coupling but slightly
perturbed by the coordination because of the small radial
extension of 4f orbitals. Therefore, the amplitude of the magnetic
anisotropy is much stronger for lanthanide ions and this turns to
[
6]
be an advantage to produce mononuclear SMMs. However,
the fast relaxation observed in these systems at zero magnetic
[
7]
field is
a
long-standing problem.
To overcome it, the
suppression of hyperfine couplings through isotopic substitution
and the dilution in diamagnetic matrices are efficient
[
8,9]
4
Figure 1. Representation of the crystal structure of Dy . BppdH are in yellow
alternatives.
Another strategy resides in having inside the
rods, PaH in green rods, while Dy, O and N are in gold, red and blue balls,
respectively. Hydrogen atoms have been omitted for clarity.
[a]
Dr. G. Fernandez Garcia,V. Montigaud, Prof. Dr. O. Cador, Dr.
B. Le Guennic
Probably, Single-Molecule Toroics (SMTs) are the most
Institut des Sciences Chimiques de Rennes
UMR 6226 CNRS-Université de Rennes 1
[
10]
aesthetic examples of atypical magnetic structures.
SMTs
263 Avenue du Général Leclerc, 35042 Rennes Cédex (France)
have attracted the attention of the scientific community, since
E-mail: olivier.cador@univ-rennes1.fr
boris.leguennic@univ-rennes1.fr
Prof. Dr. R. Sessoli, Dr. F. Totti
they offer ways to design multiferroic materials at the
[10]
nanoscale.
This class of compounds is characterized by a
[
b]
c]
“
vortex-like” spatial distribution (e.g. a torus disposition) of the
Dipartimento di Chimica ‘Ugo Schiff’
Università degli Studi di Firenze
single ion easy-axes that leads to a zero total magnetic
Via della Lastruccia 3-13, Sesto Fiorentino 50019 (Italy)
Dr D. Guettas, Dr. G. Pilet
momentum, but a non-vanishing toroidal magnetic moment.
[
III
Several examples of Dy -based polynuclear complexes (Dy
3
Laboratoire des Multimatériaux et Interfaces (LMI)
UMR 5615 CNRS-Université Claude Bernard Lyon 1
Bâtiment Chevreul, Avenue du 11 novembre 1918, 69622
Villeurbanne cedex (France)
[
10,11,14,15]
[16,17]
[18-20]
triangles,
Dy
4
coplanar,
3
coupled Dy triangles,
[
21]
[22]
6
Dy wheel
or 3d-4f metallocycles ) have been reported so
far with a non-magnetic Kramers doublet ground state resulting
from such magnetic vortex on wheel-shaped topologies.
Molecular symmetry, magnetic anisotropy direction and
magnetic interactions are the key ingredients to produce
E-mail: guillaume.pilet@univ-lyon1.fr
Dr. P. Larini
[d]
Institut de Chimie de Lyon, C2P2
UMR 5265 CNRS-CPE Lyon-UCBL
[
10]
III
43 Bd du 11 Novembre 1918, 69616 Villeurbanne (France)
SMTs.
In such a framework, Dy ions are ideal candidates
Supporting information for this article is given via a link at the end of
the document
since it easily leads to an easy magnetic anisotropy axis.
Even if the clusters that have shown toroidal-like spin
structures so far are arranged in a planar configuration, in
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Angewandte Chemie International Edition
10.1002/anie.201810156
COMMUNICATION
principle, toroidal-like spin structures, and so SMTs, might
emerge as well from non-planar arrangements of the
paramagnetic centers. Indeed, the requirement for a toroidal
ground state is only a spatial distribution of weakly coupled
magnetic moments that results in a quenching of the total
momentum of the ground state, but also to a residual toroidal
4
moment. In this regard, we investigated a novel Dy cubane
complex that shows a non-trivial toroidal magnetic moment
despite its tetrahedral core. In this work, we report the structure,
the magnetic characterizations along with the ab initio
calculations and the spin Hamiltonian model which support the
existence of uncommon toroidal magnetic moment in a non-
planar complex (3D-SMT).
The
(Pa)
yl)propane-1,3-dione and PaH=2-Picolinic acid), hereafter
abbreviated Dy , is represented on Figure 1. The synthesis and
the details of the crystal structure are given in SI and Table S1.
Dy crystallizes in the centrosymmetric P4 /n tetragonal space
group. The asymmetric unit is composed by one Dy metal
structure
of
4 4 3
[Dy (Bppd) (µ -
OH)
4
4
(H
2
O)
4
]·0.333H
2
O
(where BppdH=1,3-Bis(pyridin-4-
4
4
2
III
-
-
center, one Bppd and one Pa both disordered on two positions
-
Figure 2. Thermal variation of the magnetic susceptibility in black dots with the
calculated one (red line) according to the model developed in main text; (inset)
Field variation of the magnetization at 500 mK and the calculated curve (red
line).
(
3
refined to 50:50), one µ -OH bridge, and one terminal
coordinated water molecule (Figure S1). One disordered non-
coordinated water molecule completes the unit-cell. The
structure of the complex is constructed as a tetranuclear
architecture where one half of the vertexes of the cubane core
III
-
are occupied by Dy centers and the other half by µ
3
-OH
III
Ab initio SA-CASSF/SI-SO calculations (see details in SI)
molecules (Figure 1). Each Dy is surrounded by eight oxygen
atoms (SHAPE analysis : square antiprism; Table S2), two
from one Bppd ligand, two from two Pa ligands, three from
[
23]
have been performed to i) determine the mutual orientation of
III
-
-
the principal magnetic axes of the Dy ions related to their
-
-
arrangement in the cubane core and ii) elucidate the magnetic
interactions which stabilize the non-magnetic ground state. The
three µ
ligands connect two lanthanide ions in a µ1,2 mode on four of the
six {Dy } faces. Ln-O(H O) bond lengths are greater (2.457 Å
vs. 2.369 Å) than the other Ln-O bond lengths (Table S3). All the
Dy-O(µ -OH)-Dy bond angles are very similar ranging from
06.8° to 107.1°. Likewise, Dy Dy distances within the cubane
3
-OH and one from a coordinated water molecule. Pa
III
magnetic properties of each Dy ion were calculated by a
4
O
4
2
diamagnetic substitution approach, i.e. substituting in turn the
III
III
other three Dy ions with Y ions. The Kramers ground doublet
is characterized by an axial g-tensor with a gzz ~ 19.6 in the
effective spin ½ model (Table S4) with the first excited state at
3
…
1
architecture are almost the same ranging from 3.83 to 3.85 Å, in
line with the deviation from the ideal point group symmetry. The
crystal packing is insured by π-π interactions involving aromatic
rings of Bppd ligands forming a dense 3D network (Figure S2).
The shortest Dy…Dy distance between two different Dy (center
4
to center) is equal to 14.0 Å ensuring no magnetic interaction
between neighbors.
-
1
~
100 cm (Table S5). |±15/2> M component (> 96%) prevails in
J
III
the ground state of each Dy ion (Table S6). The easy magnetic
axes are symmetry related due to the almost perfect tetrahedral
structure (Table S7). They make an angle of 30.5° with c axis
(
Figure S4). From the c axis perspective, it is possible to
evidence the circular pattern described by the easy axes. The
presence of magnetic dipole-dipole interactions (Jdip, see SI) and
exchange coupling, Jex, have been considered to account for the
magnetic inter-ions interactions. The latter was included in the
Room temperature χ
Kelvin and χ the molar magnetic susceptibility, is just slightly
smaller than expected for the
M
T value, with T the temperature in
M
6
[24]
H
15/2 multiplet ground state with
framework of the Lines model. Furthermore, it was impossible
3
-1
3
g=4/3 (52.1 vs. 56.6 cm K mol ) and collapses down to 2.5 cm
to properly reproduce the experiment with enough accuracy
-
1
either with J =0 (i.e. only dipolar interactions) or with a unique
ex
K mol on cooling down to 500 mK (Figure S3). Meanwhile, χ
M
J
ex (Figure S5). To clarify the magnetic exchange coupling
scheme, the following spin Hamiltonian was used (the subscript
ex » is omitted):
passes through a rounded maximum at 2 K which clearly
indicates that the ground state is non-magnetic (Figure 2). At the
«
lowest investigated temperature, a weak increase of χ
M
is
observed which is attributed to a low temperature paramagnetic
Curie tail, due to the impurities present in the crystal. The non-
magnetic ground state is confirmed by S-shaped first
magnetization curve at 500 mK (Figure 2) which saturates at
ˆ ˆ
ˆ
ˆ
ˆ
ˆ
ˆ ˆ
4 1
Hspin =−J1
(
S ⋅S +S ⋅S +S ⋅S +S ⋅S
)
1
2
2
3
3
4
ˆ ˆ
ˆ ˆ
2 4
−
J2
(
S ⋅S +S ⋅S
)
1
3
1
9.2 Nβ (Figure S3). This value is very close to what is expected
for four effective spins Seff=½ with g =g =0 and g =20. This
pattern corresponds to the stabilization of the two M =±15/2
x
y
z
with J
1
and J
2
referring to the exchange couplings when µ
and carboxylate or only µ
respectively, S’s are the effective spin operators at Dy sites
(Figure 3). The dipolar interaction is calculated routinely in the
point-dipole approximation. All the calculations were performed
with the POLY_ANISO routine
with the inclusion of the g tensors for each Dy center calculated
3
-OH
J
3
-OH bridging groups are involved,
III
states. All these characteristics indicate that significant
interactions operate in the cubane leading to a non-magnetic
ground state with magnetic excited states with different
contribution within few wavenumbers.
i
[
25,26]
and homemade fitting code,
separately (Table S4). With this model both the crystallographic
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COMMUNICATION
disorder on each metal site and the non-collinearity of the single-
ion g tensors are considered. In this framework, the resulting
low-lying 16 states are arranged in four groups of degenerate
states (Figure 3). For the sake of simplicity, the spatial
disposition of the single magnetic moments (left-hand side in
Figure 3) for each group of states can be labeled using the
collinear “up” (↑) and “down” (↓) notation. Remarkably, the total
magnetic moment of the ground state |↑↓↑↓> is close to 0
the basis of the well-known efficiency of the super-exchange
pathway given by the carboxylate ligands,
J
1
is therefore
[
27]
4
expected to be dominating in Dy .
Such results point out the
necessity to verify the presence of equivalent set of exchange
parameters able to reproduce in the most accurate way as
[
28]
possible the experiment. Even if only seldom performed, such
a detailed analysis of the EES’s is mandatory whenever in
presence of potentially high correlated set of parameters (Figure
-
1
(
effective g=0.46), while excited states have a non-zero total
magnetic moment. Looking at the spins configuration of the
ground state along the axis (Figure 3), the toroidal
arrangement of the magnetic moments emerges.
4). We finally identified a set of J values (J
1
=-0.27 cm and J
2
=-
-
1
0.09 cm ) that match reasonably well the maximum on the χ
M
c
vs. T curve as well as the inflexion point on the M vs. H curve
(Figures 2 and S5). The slight deviation at low T may be
ascribed to small amount of paramagnetic impurities and
structural disorder on the ligands that are not taken into account
in the calculations. The selected set of exchange parameters is
not, of course, the unique set which can reproduce the
experimental data, but surely it is the most sound on the basis of
the ab initio results. Indeed, when one of the most important
parameters is fixed (the energy gap between the ground and
first excited states), all other used sets of parameters fail to
reproduce the experiment (Figure S5). The energy diagram and
the calculated total g-values in the effective spin 1/2 framework
are provided on Figure 3: The ground state is non-magnetic,
even if its global g-value is not strictly zero due to the disorder in
the crystal structure that lower the symmetry. To confirm this, we
ran
a calculation on a symmetrized spin Hamiltonian (T
d
symmetry) resulting in a strict diamagnetic ground state (see SI,
Table S8). Back to the main model, the first excited states
-
1
|
↑↑↓↓> (g=28.33) lie 2.14 cm above the ground state, while the
-1
third and fourth excited states are at 3.46 cm (g=39.05) and
.51 cm (g=67.63), respectively. One must notice that for all
-
1
9
excited states, global g tensors are not collinear (Figure S6). In
order to confirm that state |↑↓↑↓> is not only non-magnetic but
possesses a non-zero toroidal moment, we calculated the total
!
!
!
!
!
spin S
=
∑i S and the toroidal moment τ ∝ r × S , respect
∑i
tot
i
i
i
to the center of mass of the metal core (as a reference the same
quantities were calculated for the archetypal Dy triangle, see
3
[
15]
Table S9). State |↑↓↑↓> presents a quenching of the total spin
but a non-zero τ (net toroidal moment), while state |↑↑↓↓> has
both non-zero τ and Stot (mixed-moment SMT).
Figure 3. Coupling scheme within Dy
degeneracies (bottom) along two directions (x axis view for (a); c axis view for
b)) with gzz-values in the effective spin 1/2 framework and calculated toroidal
moment τ (in β.Å).
4
(top) with the calculated energy state
(
To determine under which condition state |↑↓↑↓> becomes
the ground state, we mapped the energies of the low-lying states
for J and J ranging from -0.5 to +0.5 cm . The resulting
1 2
surfaces, called Exchange Energy Surfaces (EES) in analogy
with the widely used Potential Energy Surfaces (PES), are
plotted on Figure 4. The ground state is always non-magnetic for
Figure 4. EES for states |↑↓↑↓>, |↑↑↓↓> and |↑↑↑↑>. State
|↑↓↑↑> has been omitted for clarity. The vertical black segment
-
1
-
1
corresponds to the best agreement with the experiment (J =-0.27 cm and
1
-1
2
J =-0.09 cm ).
Dy
1 K temperature in the absence of an external dc field (Figure
S7), the signature of the slowing down of the magnetic moment.
According to the calculated energy diagram of Dy (vide supra),
4
shows frequency dependent ac susceptibility in the 2-
J
1
<0 and J
couplings) there is a competition between states |↑↓↑↓> and
↑↑↓↓>. In this subset of values, states |↑↓↑↓> or |↑↑↓↓> are
stabilized when J or J dominates, respectively. However, on
2 1 2
>0. For J <0 and J <0 (only antiferromagnetic
1
|
4
1
2
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Angewandte Chemie International Edition
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COMMUNICATION
even at 2 K not only the non-magnetic ground-state is populated
but the other states are also involved. As a result, the relaxation
of the magnetic moment implies several states with different
processes. Nevertheless, the experimental data can be
analyzed in the frame of the extended Debye model which
feature one main relaxation with a relatively narrow distribution
from ferrotoroidic systems composed by two connected
[
29]
frustrated rings (interacting 2D-SMT). These findings pave the
way to the design of original three-dimensional toroics as new
objects in molecular spintronic.
(
α<0.3) (see SI, Figure S8, Table S10). While a thermally
Acknowledgements
dependent process dominates at high temperature, the
relaxation time tends to become thermally independent below 4
K. The energy diagram which results from the coupling between
local magnetic moments impacts, in a complex manner, the in-
D. G. is grateful for the PhD fellowship from University Claude
Bernard Lyon 1. Additional support was provided by the Région
Rhône-Alpes (CMIRA2015). G. F. G. gratefully acknowledges
the European Commission through the ERC-AdG MolNano-Mas
M
field relaxation dynamics. At 2 K, the in-field behavior of χ ’ in
the 1-1000 Hz frequency window is plotted on Figure 6. It
reflects the in-field evolution of the relaxation time which is not
monotonic. The slowing down at low field is commonly observed
in mononuclear SMMs. At higher field than 1 kOe the relaxation
time decreases as the surface plot moves to higher frequencies
(
project no. 267746) and the ANR (ANR-13-BS07-0022-01) for
financial support. V. M. is thankful to ERC (project no. 725184)
for fundings. B. L. G. thanks the French GENCI/IDRIS-CINES
center for high-performance computing resources. COST Action
Molspin (CA 15128) is also acknowledged.
(
Figure S9). The black line at high frequencies (1000 Hz) shows
two maxima at 2.8 and 4 kOe. These fields correspond to the
crossings between the first three states (|↑↓↑↓>, |↑↑↓↓> and
Keywords: single molecule toroics • lanthanide • dysprosium •
|
↑↓↑↑>) in agreement with Zeeman energy diagrams calculated
with the magnetic applied along the principal axis of state |↑↑↑↑>
4.3 kOe, Figure S10) and along one of the principal axes of
cubane • ab initio calculations
(
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Chem. Soc. 1993, 115, 1804-1816.
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relaxation pathways to the global magnetic moment.
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corresponds to χ ’ values at 1000 Hz and the two dots to the observed
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Significant toroidal magnetic moment in a Dy
4
cubane
complex associated to a non-magnetic ground state has been
characterized in detail by magnetometry and state-of-art ab initio
computational methods. A deep analysis of the low-lying energy
states resulting from the specific coupling scheme allows to
reliably identify the best set of parameters to properly reproduce
the magnetic data. The computed energy ladder also suggests
that in such a class of systems, the magnetic nature of the
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1 2
ground state could be easily modulated by altering the J /J ratio
6
352-6356.
and, therefore, by slight changes in the ligand nature or by
external perturbations (i.e. pressure). As far as we know, this is
one of the first cases in which a non-magnetic toroidal ground
state is found in a 3D topology (3D-SMT). This strongly differs
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3
D magnetic toroics: Molecular
Guglielmo Fernandez Garcia, Djamilla
Guettas, Vincent Montigaud, Paolo
Larini, Roberta Sessoli, Federico Totti,
Olivier Cador,* Guillaume Pilet,* and
Boris Le Guennic*
materials that possess a toroidal
moment associated to a non-
magnetic ground state are known as
Single-Molecule Toroics (SMTs)
and are usually planar molecules. It
is herein observed in a Dy
4
cubane,
Page No. – Page No.
transposing this property to a
A Dy
4
Cubane: A New Member in
tridimensional structure (3D-SMT).
the Single-Molecule Toroics Family
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