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PAPER
Cite this: DOI: 10.1039/c7cp06310e
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Long-range magnetic order in the porous
metal–organic framework Ni(pyrazine)[Pt(CN)4]†
J. Alberto Rodrı́guez-Velamazán, *a Olivier Roubeau, b Roberta Poloni,
Elsa Lhotel,d Elı́as Palacios, b Miguel A. Gonzáleza and José A. Reale
c
A combined study involving DFT calculations, neutron scattering, heat capacity and magnetic measurements
at very low temperatures demonstrates the long-range magnetic ordering of Ni(pyrazine)[Pt(CN)4] below
Received 14th September 2017,
Accepted 16th October 2017
1.9 K, describing its antiferromagnetic spin arrangement. This compound belongs to the family of porous
DOI: 10.1039/c7cp06310e
combinations of porosity and magnetic properties. The possibility of including long-range magnetic
rsc.li/pccp
this class of compounds.
coordination polymers M(pyrazine)[Pt(CN)4] (M = divalent metal), renowned for showing interesting
ordering, one of the most pursued functional properties, opens new perspectives for the multifunctionality of
Introduction
In the design of molecular functional materials, the functional
properties of magnetic origin concentrate a great deal of attention
due to their potential use in a variety of applications.1,2 Several
examples in the last years making the most of the playground for
chemical design offered by molecular systems illustrate this
fact, with compounds featuring e.g. electric and magnetic order
(molecular multiferroics),3 porosity and magnetism,4 conductivity
and magnetism,5 or superconductivity and magnetism.6 These
examples make also evident the potential of the molecular
approach for combining different functional properties in the
same compound.
Based on the classical Hofmann clathrate compounds,7 the
three-dimensional frameworks {M(pz)[M 0 (CN)4]} (M = Fe, Co,
Ni; pz = pyrazine; M 0 = Ni, Pd, Pt)8 constitute a family of
molecular systems with one of the richest displays of functional
properties. The nanoporosity of these materials confers them
host–guest function,9,10 which in the case of M = FeII is
combined with spin-crossover properties11 yielding switchable
porous coordination polymers with remarkable features including,
for example, chemo-12 and photo-switching13 between the
paramagnetic high-spin and the diamagnetic low-spin state,
molecular rotation correlated with the change of spin state,14 or
pressure-tunable bistability.15 Moreover, these materials can be
a
Institut Laue-Langevin, F-38042, Grenoble, France. E-mail: velamazan@ill.eu
Instituto de Ciencia de Materiales de Aragón (ICMA),
CSIC and Universidad de Zaragoza, E-50009, Zaragoza, Spain
c
SIMAP, CNRS and Université Grenoble Alpes, F-38000, Grenoble, France
d
Institut Néel, CNRS and Université Grenoble Alpes, F-38042, Grenoble, France
e
Instituto de Ciencia Molecular (ICMol), Universidad de Valencia, Paterna,
E-46980, Valencia, Spain
† Electronic supplementary information (ESI) available. See DOI: 10.1039/c7cp06310e
b
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conveniently nanostructured16 enabling the integration into
functional devices. Nevertheless, long-range magnetic ordering
(LRMO), one of the most pursued magnetic properties,1,2
remains a challenge in this type of coordination polymers.
The pyrazine ligands present in these compounds, however,
can act as mediators for superexchange pathways when connecting
two magnetic metal ions. The bridging ligands that can be used to
link axially the M metals keeping the desired porous architecture
are neutral aromatic species. Pyrazine is the smaller one with the
appropriate coordination topology, and therefore is the most
favorable to magnetic exchange. Indeed, pyrazine is known for
being able to mediate magnetic interactions. The interaction
through this ligand is generally weak, but many systems using
pyrazine as a building block display antiferromagnetic ordering
with Néel temperatures usually in the range of a few Kelvin.17
LRMO is in principle precluded in {M(pz)[M 0 (CN)4]} spincrossover compounds with M = FeII due to the diamagnetic
low-spin state of Fe at low temperatures.8,11 Indeed, it is a longstanding challenge in the field of spin-crossover systems to
obtain compounds where LRMO coexists with the spincrossover phenomenon. The scarce examples where this has
been achieved include a Fe–Nb metal–organic framework with
light-induced magnetic order,18 and hybrid two-network crystalline
solids that integrate FeIII 19 or FeII 20 spin-crossover cations together
with anionic magnetic networks. With the aim of demonstrating the
possibility of LRMO in {M(pz)[M0 (CN)4]} frameworks, in this work
we have focused on {Ni(pz)[Pt(CN)4]} (1),8b,9 among the reported
combinations of M and M0 ,8b,9 since NiII presents a S = 1 spin state
down to low temperatures, which makes it favorable to display
magnetic ordering (the diamagnetic M0 metals have, in principle, no
role in the magnetic behavior, and therefore are interchangeable).
This compound is isostructural with the other members of
the family.8b Its crystallographic structure can be described as
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heat pulse method. The powdered sample was sealed in an oxygenfree copper vessel whose contribution (known by a separate
experiment) was subtracted from the total heat capacity in order
to obtain the heat capacity of the sample. In the temperature
range 0.35–100 K, the heat capacity was determined on a
pressed pellet of 1 by means of semi-adiabatic relaxation
calorimetry at different applied magnetic fields up to 7 Tesla,
using a Quantum Design PPMS. The heat capacity data obtained
by both techniques show a good agreement in the common
temperature range.
Neutron scattering
Fig. 1 Scheme of the crystal structure of 1: Ni (orange), Pt (dark blue),
N (light blue), C (grey). The H atoms are omitted for clarity. The unit cell
is represented as black lines. The compound crystallizes in the tetragonal
P4/mmm space group with cell parameters a and c ca. 7.38 and 7.05 Å,
respectively (see neutron diffraction section). The pyrazine molecules are
disordered in two positions due to the 4-fold axis passing through the
N atoms, although only one position is represented for the sake of clarity.
2D {Ni[Pt(CN)4]}N layers parallel to the ab crystallographic
plane, with the pyrazine ligands (orientationally disordered in
two positions at 901 one from each other) occupying the apical
positions of the Ni octahedra and connecting the layers along the
(001) direction (Fig. 1). In the present study, we have used neutron
scattering, heat capacity and magnetic measurements at very low
temperatures, together with DFT calculations to demonstrate and
rationalize the LRMO of this compound below 1.9 K.
Methods
Preparation of the samples
Microcrystalline powder of {Ni(pyrazine)[Pt(CN)4]} was synthetized
and characterized according to the same well-established procedure described in ref. 8. The EDX and powder X-ray diffraction
analyses (Fig. S1 of the ESI†) confirmed the purity of the title
compound. Before the measurements, the samples were heated
to 150 1C for 30 min in vacuum to remove lattice water molecules.
Neutron diffraction experiments were performed on a powder
sample of ca. 0.25 g using the D1B instrument at Institut LaueLangevin, Grenoble, France, equipped with a dilution refrigerator
and using a wavelength of 2.52 Å coming from a graphite monochromator. Rietveld refinements and calculations of the nuclear and
magnetic structures were performed using the FullProf suite of
programs.22
Inelastic neutron scattering (INS) experiments were carried
out on the same sample, at the IN5 disk chopper time-of-flight
spectrometer at the Institute Laue Langevin. Data were collected
at different temperatures between 1.5 K and room temperature,
using an incident wavelength of 5 Å resulting in an instrumental
resolution of B0.1 meV at the elastic line. The sample was
placed inside an annular aluminum sample holder and presssealed with indium wire. The annular geometry was chosen to
keep the scattering probability to ca. 0.1 in order to minimize
multiple scattering effects. Temperature control was achieved
using a standard ILL Orange cryostat. An empty aluminum can
of the same dimensions as the sample holder was measured
and its spectrum subtracted from that of the sample. The
detector efficiency was corrected using data collected from a
standard vanadium sample, which is an elastic incoherent
scatterer. The data were reduced using LAMP23 transforming
the recorded time-of-flight and scattering angle into energy
transfer and wave vector.
To reproduce the data, linear spin-wave calculations were
performed using the SPINWAVE software24 developed at Laboratoire
Léon Brillouin, which calculates the spin-correlation functions in
order to generate the powder-averaged dynamical structure factor
observed by inelastic neutron-scattering.
Magnetic measurements
Magnetization measurements were performed down to 200 mK
in a superconducting quantum interference device (SQUID)
magnetometer equipped with a dilution refrigerator developed
at the Institut Néel-CNRS Grenoble and in a Quantum Design
MPMS-XL SQUID magnetometer of the Physical Measurements
unit of the Servicio General de Apoyo a la Investigación-SAI,
Universidad de Zaragoza.
Heat capacity
The heat capacity of 1 was determined from adiabatic calorimetry in the temperature range 77–300 K with a commercial
adiabatic calorimeter from Termis Ltd21 using the conventional
Phys. Chem. Chem. Phys.
DFT calculations
Total energy calculations were performed using the PWSCF
package,25 using PAW pseudopotentials, plane waves kinetic
energy cutoffs of 120 Ry and a PBE functional. No Hubbard U
correction was applied since we compute a PBE gap between
the dz2 bands of almost 2 eV. A 1 1 2 supercell was
employed to compute the interaction through pyrazine rings,
J1, using a k-point mesh of 5 5 3, while a 2 2 1 supercell
using a 3 3 5 k-point mesh was employed to compute the
in-plane interactions: the nearest-neighbour magnetic interaction, J2, and the next-nearest-neighbour interaction through
the metallo-cyanide ligands, J3 (see below).
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Paper
Results and discussion
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Magnetic measurements
The magnetic properties of 1 were determined in the range of
200 mK–300 K and are shown in Fig. 2. The wT vs. T plot
(w being the molar magnetic susceptibility) shows a value at
high temperature of ca. 1.3 cm3 K mol1 (see Fig. 2 top), higher
than the one expected for an S = 1 spin-only case with g = 2.0
(i.e. 1 cm3 K mol1), but not unusual in NiII complexes.26,27 A fit
of the magnetic susceptibility to a Curie–Weiss law down to
12 K gives an effective g value of 2.3, in the range of the typical
values for NiII compounds,26 and a negative Weiss constant of
y = 4.5(1) K, indicative of antiferromagnetic interactions and
of a possible effect of the zero-field-splitting of the S = 1 ground
state. At low temperatures the system deviates from the paramagnetic behaviour, with w showing a maximum at TN = 1.95 K
that likely corresponds to the onset of antiferromagnetic ordering. This temperature nicely agrees with the one obtained by
heat capacity and neutron scattering, as shown in the following
sections. The value of TN/y = 0.4 points to a 1D character above
the ordering temperature.28
The magnetization versus applied magnetic field isotherms
confirm the antiferromagnetic behavior, as well as a g value
larger than 2 (see Fig. 2 middle). At 2.5 K, the magnetization
curve increases significantly more slowly than in absence of
antiferromagnetic interactions, as shown by the comparison
with a Brillouin function. In addition, below the transition
temperature, a metamagnetic-like behavior, i.e. a change in the
M vs. H slope, is observed at a field m0Hc = 2.1 T. This is
indicative of a reorientation of the magnetic moments of the
zero field antiferromagnetic state towards a field induced
structure. The feature is however broadened because the
measurements were performed on a polycrystalline sample.
The value of Hc corresponds to an energy of 3.24 K, which
nicely agrees with the energy necessary to overcome the energy
of the ground state (see the following sections).
Heat capacity
The clearest indication of the onset of LRMO is obtained from
heat capacity measurements. The molar heat capacity (Cp) of 1
was determined from adiabatic and semi-adiabatic relaxation
calorimetry in the temperature ranges 77–300 K and 0.35–100 K
respectively and at different applied magnetic fields up to
7 Tesla in the latter low temperature range. Fig. 3 depicts the
data normalized to the gas constant R up to 100 K at zero-field
and m0H = 7 T (for clarity, only the curve at the maximum
applied field is shown; the full set of data is given in Fig. S2 of
the ESI†). The most noticeable feature is a lambda-like peak
centered at TN B 1.9 K for zero-field, in excellent agreement
with the magnetic susceptibility data and indicative of LRMO.
The anomaly is field-dependent at applied fields higher than
m0H = 0.5 T. For higher fields, the anomaly becomes rounder
and shifts to higher temperatures, indicating a decoupling
of the magnetic interactions. Indeed, the experimental curve
at the highest field of 7 T is essentially accounted for by
the Schottky heat capacity of non-interacting Ni(II) S = 1 spins
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Fig. 2 Top: Molar magnetic susceptibility (w) as a function of temperature
of 1 (the applied magnetic field is 0.05 T and 0.1 T for the 1.35–5 K and
5–300 K temperature ranges, respectively). The maximum at 1.95 K indicates
the onset of antiferromagnetic order. Continuous line: fit to a Curie–Weiss law
as explained in the text in the temperature range from 12 to 300 K. Inset:
wT vs. T plot suggesting antiferromagnetic correlations between the Ni atoms.
Middle: Molar magnetization (M) as a function of the applied magnetic field (H)
at 4.2 K (green diamonds), 2.5 K (blue circles) and 240 mK (red squares)
together with the calculation of a Brillouin function for a temperature of 2.5 K
and g = 2.3 (dashed line). The small discrepancy between the saturation value
of the Brillouin function and the measured saturated value might be due to an
uncertainty in the mass measurement of the sample. Bottom: dM/dH vs. H
above (T = 2.5 K, blue line) and below (T = 240 mK, red line) the magnetic
transition, which evidences the inflexion point in the M vs. H at about 2.1 T
indicative of a field induced transition.
(full green line in Fig. 3). At high temperatures, the signal is
dominated by non-magnetic contributions associated with
thermal vibrations of the lattice, that have been estimated as
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corresponding to one Ni(II) S = 1 spin, R Ln (2S + 1) = 1.098R.
The shape of the heat capacity anomaly and the significant
entropy above TN are indicative of a low-dimensional character
above the ordering temperature.30 Overall, the heat capacity
data corroborate the presence of a 3D LRMO of Ni(II) ions below
TN, indicating a tendency to a low-dimensional nature above it.
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Neutron scattering
Fig. 3 Molar heat capacity of 1 normalized to the gas constant R in zerofield (empty circles) and 7 T applied field (empty squares). Full circles
correspond to the zero-field data obtained by conventional adiabatic
calorimetry. The dashed line is the estimated lattice contribution, corresponding to a Debye function with yD = 69 K below 20 K. The full green line
is the Schottky contribution corresponding to a two-level system in m0H = 7 T.
The full red line is the sum of the lattice and Schottky contributions.
a Debye function with Debye temperature yD = 69 K (dashed
line in Fig. 3). This value is in the upper range for molecular
coordination compounds,29 in agreement with the stiff character arising from the 3D coordination network in 1.
Subtracting this lattice contribution to the zero-field data
yields the magnetic heat capacity Cm (Fig. 4 left) which has a
characteristic T2 tail for T 4 5.5 K. On the other hand, the Cm
data below the peak extrapolate to a power law as a function of
temperature with an exponent between 2 and 3, which would
agree with the spin-wave contribution of a 2D or a 3D antiferromagnet, respectively.28 Considering a T3 extrapolation in
combination with the experimental Cm(T) data, the magnetic
energy, Um, and entropy, Sm, can be derived by integration of
Cm over T and Ln T, respectively. The magnetic energy of the
ground state is found to be of 3.3 K. The results for Sm are
shown in Fig. 4 right and the total Sm is found to tend to 1.15R
at high temperatures, value slightly larger than the full content
Fig. 4 Left: Magnetic heat capacity of 1 normalized to the gas constant R
in zero-field. The dashed lines are aT2 and bT3 extrapolations (with a = 8.9
and b = 0.257) of the higher and lower temperature data, respectively and
as indicated. Right: Magnetic entropy as a function of temperature. The
dashed line is the expected entropy content for one Ni(II) S = 1 spin
normalized to the gas constant R, i.e. Ln 3.
Phys. Chem. Chem. Phys.
In order to gain a deeper insight into the nature of the magnetic
ordering of the title compound, we have performed neutron
scattering experiments. At temperatures above the magnetic
ordering, powder neutron diffraction patterns fairly correspond
(Fig. S3, ESI†) to the crystal structure of the isostructural
compounds.8b,9 Measurements between 50 mK and 10 K and
with a wavelength of 2.52 Å did not show any evidence of the
LRMO (Fig. 5), in contrast with the above described observations. Almost identical patterns are observed at 50 mK and at
10 K – well below and well above the anomaly observed in the
heat capacity, respectively. No increase of intensity is observed
in any of the reflections, neither the appearance of new reflections of magnetic origin is detected. Several reasons can explain
this fact. First, the low magnetic density of the system would
lead to weak magnetic reflections. Second, the hydrogen content of the compound produces an elevated incoherent background that can mask weak signals. Third, the crystal size of
the compound is small, as reflected by the width of the nuclear
reflections, and this can spread out the magnetic intensity
making it difficult to distinguish from the background.
To verify these hypotheses, we have calculated the magnetic
contribution for different possible magnetic structures
Fig. 5 Neutron diffraction patterns of 1 collected at D1B instrument at a
wavelength of 2.52 Å at 50 mK (blue open circles) and at 10 K (red full
circles). The line at the bottom is the difference pattern. Inset: Experimental data in the low Q region and comparison with the calculation of
the magnetic contribution (summed to the background) for two possible
magnetic structures, with moments along c, schematized in the top part of
the figure: with k = [0, 0, 21 ] (black line and arrows) and with k = [21 , 0, 21 ]
(green line and arrows). The vertical bars mark the positions of the
magnetic reflections.
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(we illustrate two of these in Fig. 5). As the bulk measurements
point to an antiferromagnetic ordering, and given that only one
magnetic atom is present in the unit cell, the magnetic propagation
vector, k, should be nonzero. We assume that the antiferromagnetic
interactions can occur through the pyrazine rings – which
corresponds to the shorter distance between magnetic atoms –
as observed in other similar compounds,17 and in-plane,
through the metallo-cyanide ligands. This hypothesis has been
confirmed by our DFT calculations (see below) and implies that
the most likely magnetic propagation vectors are k = [0, 0, 12] and
k = [12, 0, 12] (or equivalently k = [0, 12, 12]), that is, antiferromagnetic
coupling along the c-axis, or along both the c and a (or b) axis
(see scheme in Fig. S4 of the ESI†). We have represented two
examples of these configurations in Fig. 5 (other possible
arrangements are given in Fig. S5 of the ESI†). The calculation
of the magnetic contribution assuming a magnetic moment of
2 Bohr magnetons (as corresponds to a S = 1 magnetic atom)
and applying the same peak width determined for the nuclear
reflections gives a weak magnetic signal that can certainly
remain hidden by the background.
In contrast, a signal of magnetic origin is clearly noticeable
in the inelastic neutron scattering measurements performed at
1.5 K (Fig. 6). At 1.5 K, a sharp peak is observed around
0.45 meV, which upon heating rapidly broadens and shifts to
lower energy, merging with the elastic peak. The smooth
Paper
decrease of the intensity at high Q points to a magnetic origin
of the anomaly. The magnetic excitation presents weak dispersion,
with a behaviour that resembles that of the similar compound
Fe(NCS)2(pyrazine)2.17
Magnetic interactions
The experimental results can be rationalized in terms of
magnetic interactions by using DFT calculations. We computed
the magnetic couplings using a broken symmetry formalism, by
mapping DFT total energies corresponding to a few magnetic
configurations with a simple spin-Hamiltonian for isotropic
P
exchange interactions: H ¼ Jij Si Sj (spin oriented along z).
i; j
Jij are the magnetic couplings between site i and j and Si, j are
the spins of high-spin Ni2+ ions located at sites i and j.
Calculations performed with fully relativistic pseudopotentials
and including spin–orbit coupling reveal no significant magnetic anisotropy, as commonly observed in octahedral NiII
systems.26 Specifically, we found a magnetic anisotropy energy
below 0.02 meV (0.23 K) per Ni atom (energy difference between
spin aligned along the z-axis and within the plane), a value
reasonably small in comparison with other NiII octahedral
systems.26
The exchange couplings are schematically shown in Fig. 7.
A full optimization of the geometry was performed in each case.
Fig. 6 Experimental energy-momentum spectra at 1.5 K (top-left) and 3 K (top-right) recorded at IN5 instrument. Simulation of the powder-averaged
excitation spectrum using rescaled magnetic interactions obtained from DFT calculations as explained in the text (bottom-left). Inelastic spectra,
integrated over the whole Q range, at the indicated temperatures (bottom-right). Data were taken using an incident wavelength of 5 Å resulting in an
instrumental resolution of B0.1 meV.
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Fig. 7 (left) Scheme of the proposed magnetic structure for 1. The magnetic interactions are represented as thick continuous lines. (right) Two different
views of the calculated spin density distribution plotted using an isosurface level of 0.003 electrons Bohr3. This figure illustrates the dxy and dz2 character
of the spin density with localization on the CN and pyrazine ligands.
We find weak antiferromagnetic coupling along the c-axis and
within the plane, with a larger exchange coupling through the
pyrazine. We obtain J1 = 5.7 K, J2 = 0 K, and J3 = 2.2 K, that is,
two relevant antiferromagnetic interactions, J1 and J3, mediated
by the ligands, and no significant J2 interaction (with no ligand
involved). We have checked that the orientation of the pyrazine
plane has a negligible effect on the results. Fig. 7-right shows
the spin density at the metal site having a dz2 and dxy character
consistent with an elongated octahedral field splitting around
Ni and a high-spin state, S = 1. We find that 26% of the spin
density along z is carried by the pyrazine ligand while only
16% of the spin density is carried by the NC–Pt–CN ligand,
consistent with a stronger exchange coupling along z.
The two significant interactions are antiferromagnetic, in
accordance with the susceptibility results, although their values
may be overestimated, since no Hubbard U correction has been
applied to the DFT calculations (see Methods section). In the
present case, the energy of the ground state in the mean field
approximation is Um/R = J1 + 2J3, which yields an energy of
10.1 K for the values of Ji obtained from DFT. Therefore,
we need to rescale by a factor of ca. 1/3, according to the
experimental value of Um/R = 3.3 K derived from the integration
of Cm over T. The predominance of J1 is also in agreement with
the TN/y value derived from susceptibility and with the heat
capacity results, both indicative of a 1D character above TN.30
More specifically, the ratio RJ = J3/J1 = 0.4 is in accordance with
the heat capacity and entropy curves, as confirmed by Monte
Carlo simulations with total energy 3.3 K and different values of
RJ (see details in the ESI,† Fig. S6), which show that a ratio of
0.4 gives the best agreement with the experimental results.
Below TN, these magnetic couplings lead to a LRMO with a
magnetic structure with k = [12, 0, 12] propagation vector, as
shown in Fig. 7-left, consistent with the neutron diffraction
Phys. Chem. Chem. Phys.
results (it corresponds to the case represented in green in Fig. 5).
The absence of significant J2 coupling between nearest-neighboring
Ni sites in the plane permits this magnetic structure, implying a
certain degree of frustration if J2 is not strictly null, and presenting
different equivalent configurations (see Fig. S4 in the ESI†). This is
consistent with a low ordered magnetic moment (and therefore
low magnetic diffraction signal).
The obtained magnetic couplings allow reproducing qualitatively
the inelastic neutron scattering results (Fig. 6). Just by scaling all the
interaction values by a factor 1/3, the main features of the
experimental spectrum are reproduced, in particular the maximum
of intensity around 0.45 meV and the weak dispersion. Furthermore,
these interactions reproduce the feature emerging from ca. 0.6 Å1
noticeable in the experimental data, pointing to a magnetic Bragg
peak of a k = [12, 0, 12] magnetic structure. This supports that the
magnetic order is likely the one depicted in Fig. 7-left.
Since these materials are porous, it may be pertinent to
consider if there would be an interplay between possible guest
molecules and the magnetic ordering. In these frameworks,
guest molecules are known to hinder the movements of the
pyrazine molecules, that otherwise have remarkable rotation
freedom.14 This could in principle affect indirectly the magnetic
interaction through pyrazine but, since the magnetic interactions
are weak and the magnetic ordering takes place at very low
temperatures (where the rotation is deactivated), the possible
interplay should not be relevant.
Conclusion
We have demonstrated by means of neutron scattering, DFT
calculations, heat capacity and magnetic measurements the
existence and the nature of long-range magnetic ordering in
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{Ni(pyrazine)[Pt(CN)4]}. The main evidence of the existence of
this magnetic ordering below 1.9 K comes from heat capacity
and magnetometry results. Neutron scattering results (powder
diffraction and INS), heat capacity data and DFT calculations
draw a picture where the magnetic order is dominated by an
exchange coupling through pyrazine molecules, with a second
weaker magnetic interaction through the metallo-cyanide
ligands, yielding a spin arrangement likely described by a
magnetic propagation vector k = [12, 0, 12]. These results demonstrate
that long-range magnetic order can be added to the outstanding
list of functional properties of the family of {M(pyrazine)[M0 (CN)4]}
compounds.
Conflicts of interest
There are no conflicts to declare.
Acknowledgements
The authors are grateful to the Institut Laue Langevin and SpINS
for the neutron beam-time allocated (experiments 7-02-134 and
CRG-2042). Partial funding for this work is provided by the
Ministerio de Economı́a y Competitividad (MINECO) through
projects MAT2015-68200-C2-2-P, MAT2014-53961-R, CTQ201678341-P and MDM-2015-0538. Authors would like to acknowledge
the use of Servicio General de Apoyo a la Investigación-SAI,
Universidad de Zaragoza. Calculations were performed using the
froggy platform of the CIMENT infrastructure, which is supported
by the Rhône-Alpes region (GRANT CPER07_13 CIRA) and the
Equip@Meso project (reference ANR-10-EQPX-29-01). Also, computer resources from GENCI under the CINES grant number
A0020907211 were used for this work. This work benefited from
the support of the project ANR-15-CE06-0003-01 funded by the
French National Agency for Research. R. P. is indebted to Andres
Saul for fruitful discussions. We thank C. Paulsen for allowing us
to use his SQUID dilution magnetometers.
Notes and references
1 O. Kahn, Molecular Magnetism, John Wiley & Sons, New York,
1993.
2 J. S. Miller and A. J. Epstein, Angew. Chem., Int. Ed. Engl.,
1994, 33, 385–415.
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