Magnetic properties and spin dynamics in single molecule paramagnets Cu6Fe and Cu6Co

Abstract

The magnetic properties and the spin dynamics of two molecular magnets have
been investigated by magnetization and d.c. susceptibility measurements,
Electron Paramagnetic Resonance (EPR) and proton Nuclear Magnetic Resonance
(NMR) over a wide range of temperature (1.6-300K) at applied magnetic fields,
H=0.5 and 1.5 Tesla. The two molecular magnets consist of
CuII(saldmen)(H2O)}6{FeIII(CN)6}](ClO4)38H2O in short Cu6Fe and the analog
compound with cobalt, Cu6Co. It is found that in Cu6Fe whose magnetic core is
constituted by six Cu2+ ions and one Fe3+ ion all with s=1/2, a weak
ferromagnetic interaction between Cu2+ moments through the central Fe3+ ion
with J = 0.14 K is present, while in Cu6Co the Co3+ ion is diamagnetic and the
weak interaction is antiferromagnetic with J = -1.12 K. The NMR spectra show
the presence of non equivalent groups of protons with a measurable contact
hyperfine interaction consistent with a small admixture of s-wave function with
the d-function of the magnetic ion. The NMR relaxation results are explained in
terms of a single ion (Cu2+, Fe3+, Co3+) uncorrelated spin dynamics with an
almost temperature independent correlation time due to the weak magnetic
exchange interaction. We conclude that the two molecular magnets studied here
behave as single molecule paramagnets with a very weak intramolecular
interaction, almost of the order of the dipolar intermolecular interaction.
Thus they represent a new class of molecular magnets which differ from the
single molecule magnets investigated up to now, where the intramolecular
interaction is much larger than the intermolecular one.

Full text

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Magnetic properties and spin dynamics in single
molecule paramagnets Cu6Fe and Cu6Co

P.Khuntia
F.Borsa

1Dipartimento di Fisica” A.Volta” e Unita’ CNISM-CNR, Universita’ di Pavia, I-27100
1,2, M.Mariani
1, M. Andruh
1,5, M.C.Mozzati1, L.Sorace3, F. Orsini4,5, A.Lascialfari
6, C.Maxim6
1,4,5,
Pavia, Italy
2Department of Physics, Indian Institute of Technology Bombay, Powai, Mumbai-
400076, India
3Laboratory for Molecular Magnetism and INSTM Research Unit, University of
Florence, I-50019 Sesto Fiorentino, Italy
4Dipartimento di Scienze Molecolari Applicate ai Biosistemi DISMAB, Università di
Milano, I-20134 Milano, Italy
5 S3-CNR-INFM, I-41100 Modena, Italy
6Inorganic Chemistry Laboratory, Faculty of Chemistry, University of Bucharest, Str.
Dumbrava Rosie 23, 020464 Bucharest, Romania


Abstract

The magnetic properties and the spin dynamics of two molecular magnets have been
investigated by magnetization and d.c. susceptibility measurements, Electron
Paramagnetic Resonance (EPR) and proton Nuclear Magnetic Resonance (NMR) over a
wide range of temperature (1.6-300K) at applied magnetic fields, H=0.5 and 1.5 Tesla.
The two molecular magnets consist of CuII(saldmen)(H2O)}6{FeIII(CN)6}](ClO4)3·8H2O
in short Cu6Fe and the analog compound with cobalt, Cu6Co. It is found that in Cu6Fe
whose magnetic core is constituted by six Cu2+ ions and one Fe3+ ion all with s=1/2, a
weak ferromagnetic interaction between Cu2+ moments through the central Fe3+ ion with
J = 0.14 K is present, while in Cu6Co the Co3+ ion is diamagnetic and the weak
interaction is antiferromagnetic with J = -1.12 K. The NMR spectra show the presence of
non equivalent groups of protons with a measurable contact hyperfine interaction

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consistent with a small admixture of s-wave function with the d-function of the magnetic
ion. The NMR relaxation results are explained in terms of a single ion (Cu2+, Fe3+, Co3+)
uncorrelated spin dynamics with an almost temperature independent correlation time due
to the weak magnetic exchange interaction. We conclude that the two molecular magnets
studied here behave as single molecule paramagnets with a very weak intramolecular
interaction, almost of the order of the dipolar intermolecular interaction. Thus they
represent a new class of molecular magnets which differ from the single molecule
magnets investigated up to now, where the intramolecular interaction is much larger than
the intermolecular one.

I) Introduction
The development of molecular chemistry in synthesizing transition metal-ion
based molecular clusters whose properties are midway between atoms and bulk systems
provides a unique opportunity to the scientific community for the study of nanoscale
magnetism [1]. Because of the presence of non-magnetic organic ligands that prevent
magnetic interactions, the intermolecular interactions are weak in comparison to
intramolecular super-exchange interactions. Hence, the molecules are isolated
magnetically from each other and it is of great interest to investigate spin dynamics of
these nanomagnets, often called single molecule magnets (SMM). In the SMM reported
up to now, a strong exchange magnetic interaction exists among the magnetic moments
within each individual molecule which leads to a low temperature ground state
characterized by either a high total moment S or a singlet antiferromagnetic (AFM) state
S=0 depending on the topology of the magnetic ions and on their mutual magnetic
coupling. In the case of high spin ground state and high magnetic anisotropy, quantum
tunneling of magnetization and quantum coherence at low temperature have been
observed, making these nanomagnets promising candidates for magnetic storage and
quantum computing among other applications [2,3].
In this paper we present the magnetic properties of heptanuclear molecular magnets
Cu6Fe and Cu6Co with very small intramolecular magnetic coupling. These molecules are
thus a prototype of single molecule paramagnets. As it will be shown by the experimental

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results, the Cu6Fe compound consists of six Cu2+ magnetic ions with a weak
ferromagnetic interaction via the bond to a central Fe3+ ion. The isostructural Cu6Co
compound, instead, appears to be formed by six Cu2+ magnetic ions and a central
diamagnetic Co3+ ion with a small antiferromagnetic coupling between Cu2+ ions via the
bond to the central Co3+ ion.
The paper is organized as follows. In section II we summarize briefly the synthesis
of the compounds and their crystal structure. The detailed description of the results of this
section will be presented in a separate publication [4]. In Section III we present the
experimental results and data analysis. The results are presented in separate subsections
for the magnetization, the EPR, the static and the dynamic NMR. Section IV contains a
comparison between Cu6Fe and Cu6Co and a discussion of the results obtained with the
different techniques and the relevant conclusions.

II) The Samples
(A) Cu6Fe
Polycrystalline sample[{CuII(saldmen)(H2O)}6{FeIII(CN)6}](ClO4)3·8H2O (i.e,
C72H118C13Cu6FeN18O32) was synthesized from the reaction of binuclear copper(II)
complex, [Cu2(saldmen)2(µ-H2O)(H2O)2](ClO4)2·2H2O, with K4[Fe(CN)6] (H saldmen is
the Schiff base resulted by reacting salicylaldehyde with N,N-dimethylethylenediamine
as will be described elsewere [4]). In this molecule, 16 out of 118 protons belong to 8
crystallization water molecules and the remaining 102 protons arise from the organic
ligands and from six water molecules co-ordinated to six Cu2+ ions.
The lattice is of hexagonal symmetry (R-3c) with cell constants a=27.8777(16) Å,
b=27.8777(16) Å, c=21.369(13) Å, α=β=90° and γ=120°. The six Cu2+ ions are located at
the corners of an octahedron and are connected by the cyano groups and one Fe3+ at the
center of the octahedron. The Cu-Fe-Cu angles are 180˚ and the Fe-Cu angles across the
CN bridges are Cu-N-C=171.76(54)˚ and Fe-C-N=176.54(57)˚.
The nearest neighbor bond distances are Fe-H=4.0482Å and Cu-H=2.9649Å.

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Fig. 1. Crystal structure of Cu6Fe . Cu6Co is isostructural, with Fe replaced by Co

(B) Cu6Co
The Cu6Co crystals were obtained by adding an acetonitrile-water (1:1) solution (20
mL) containing 0.3 mmol of [Cu2(saldmen)2(µ-H2O)(H2O)2](ClO4)2·2H2O, 10 mL
acetonitrile-water (1:1) solution containing 0.1 mmol of K3[Co(CN)6] under stirring.
Green crystals suitable for X-ray diffraction were obtained directly from the reaction
mixture, by slow evaporation of the filtrate at room temperature [4].
The lattice is also of hexagonal symmetry (R-3c) with cell constants a=27.9545(19)Å,
b=27.9545(19)Å, c=21.3938(16)Å, α=β=90° and γ=120°. The six Cu2+ ions are located at
the corners of an octahedron and are connected by the cyano groups and one Co3+ at the
center of the octahedron. The Cu-Co-Cu angles are 180˚ and the Co-Cu angles across the
CN bridges are Cu-N-C=174.21˚ and Co-C-N=173.712˚.
The nearest neighbor bond distances are Co-H=3.9836Å and Cu-H=2.9628Å.

III) Experimental results and analysis

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A. Magnetic susceptibility
The temperature dependence of the magnetic susceptibility (χ=M/H) in the
temperature range 2-210 K at two applied magnetic fields, 0.1 Tesla and 1Tesla for
Cu6Fe, and in the temperature range 2-160 K at 1Tesla for Cu6Co, was measured with a
Superconducting Quantum Interference Device (SQUID) magnetometer. The raw data
were corrected by the sample holder and the single ion diamagnetic contributions before
analysis.
The results of the susceptibility measurements are shown in fig. 2 for both Cu6Fe and
Cu6Co samples. Over most of the temperature range the χT vs T data show a simple
paramagnetic behavior. At very low temperature it is evident that a departure from the
simple Curie law due to a small ferromagnetic (FM) coupling for Cu6Fe and a small
antiferromagnetic (AFM) coupling for Cu6Co.
The data for Cu6Fe can be fitted with a Curie-Weiss law with C = 2.72±0.2 (emu.K /mol)
and TF =+0.07 K. This corresponds to an average g factor for the seven spins s=1/2 per
molecule of g = 2.035. This is surprisingly low, given the supposedly unquenched orbital
momentum characterizing the 2T2g state of low spin Fe(III) in octahedral symmetry which
should lead to a much larger average g value [5]. The same behavior has been recently
reported for a linear, cyanide bridged, CuFeCu complex, and attributed to the peculiar
geometrical distortion of Fe(CN)6 unit, leading to an almost complete quench of the
angular momentum [6]. The obtained value of the Weiss constant correspond, in the
framework of simple Molecular Field Approximation (MFA),
B
F
k
Js
3
zs
) 1
+
(2
=
θ
, to a
weak ferromagnetic interaction JF = 0.14 K.
On the other hand the data for Cu6Co were fitted with a Curie-Weiss law with C =
2.44±0.06 (emu K /mol) and TN = -0.56 K. This correspond to six spins s=1/2 with an
average g factor g = 2.075. Again, by using the MFA expression for the Weiss constant
one finds an antiferromagnetic interaction JAF = -1.12 K.

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Fig.2. Magnetic susceptibility times the temperature vs temperature for (a) Cu6Fe and (b)
Cu6Co. The solid lines are theoretical fits in terms of a Curie-Weiss law as discussed in
the text.
As a whole, these results point to the existence of only a very weak exchange coupling
interaction between the magnetic centers. This conclusion is reinforced by the isothermal
magnetization curves which can be fitted reasonably well in terms of non-interacting
paramagnetic ions [4].
0 50100150 200250
2.5
2.6
2.7
2.8
2.9
3.0
(a)


χ χ χ χT ( emu K /mol)
T(K)
Cu6Fe
Exp.
Fit
0 204060 80
T (K)
100 120140 160180
1.5
1.6
1.7
1.8
1.9
2.0
2.1
2.2
2.3
2.4
2.5
2.6
(b)


χT ( emu K /mole)
Cu6Co
Exp.
Fit

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While this is not much surprising for the Cu6Co derivative, for which the interacting
centers are located far apart from each other, and mutually counterbalancing interactions
may occur, the situation is more puzzling for the Cu6Fe derivative. For this system the
magnetic orbitals of Cu(II) and those of Fe(III), respectively eg and t2g in octahedral
symmetry, should be orthogonal, leading to a substantial ferromagnetic interaction. While
the observed interaction is indeed of the expected sign, its magnitude is much lower than
expected. It is however to be noted that a negligibly small value of the exchange coupling
of Cu(II) with Fe(CN)63- units has been recently reported [7].

B. EPR spectra
Electron Paramagnetic Resonance (EPR) measurements were carried out at 9.45
GHz (X band) at room temperature with a Bruker spectrometer, equipped with a standard
microwave cavity. A modulation field of 0.05 mT and a microwave power of about 1.86
mW were used.
The room temperature EPR spectrum of Cu6Fe and of Cu6Co are shown in Fig. 3.
The shape of the signal for both systems is typical of octahedral Cu2+ ions with axial
distortion environment, leading to a g//>g⊥>2.00 pattern. This is in agreement with the
findings of crystal structure solution, which indicated a square pyramidal coordination
environment for Cu(II) [8]. The experimental spectrum could be satisfactorily simulated
(as a powder spectrum resulting from the superposition of spectra of axial sites with
angular orientations randomly distributed) by assuming an anisotropic g-factor with a
Lorentzian line shape. The values obtained from the simulation of the spectrum are
g//=2.172 and g⊥= 2.085. This confirms that the unpaired electron is located, as expected,
in a dx2-y2 orbital, so that the absence (or weakness) of the exchange coupling between
Fe(III) and Cu(II) should be regarded as accidental. Finally, we note that the absence of
the EPR signal arising from Fe3+ ion in the corresponding derivative at room temperature
is most likely due to the fast relaxation time of low spin Fe(III) at this temperature,
leading to an exceedingly broad line. Further studies at lower temperatures are currently
in progress to clarify this issue.

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Fig. 3 Experimental (black line) and computed from numerical analysis (red line)
derivative EPR signals in Cu6Fe (a) and in Cu6Co (b).

C. Proton NMR spectra
Nuclear Magnetic Resonance (NMR) measurements on polycrystalline Cu6Fe and Cu6Co
samples were performed with a standard TecMag Fourier transform pulse NMR
spectrometer using short π/2-π/2 radio frequency (r.f) pulses (1.9-2.2 µs) in the
temperature range 1.6 K to 300 K at two applied magnetic fields, H=0.5 T and 1.5 T. We
employed a continuous flow cryostat in the temperature range 4.2 to 300 K and a bath
cryostat in the temperature range 1.6 to 4.2 K. Fourier transform of the half echo spin
signal of the NMR spectrum was taken in the case where the whole line could be
irradiated with one r.f pulse. The low temperature broad spectra were obtained by the
2800 30003200
B (G)
3400 3600
-20
-10
0
10


(b)
Derivative EPR Signals (arb. units)
-100
-50
0
50



(a)

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convolution of lines obtained from several Fourier transforms each one collected at
different values of the irradiation frequency keeping the external field constant.
Proton NMR spectra for Cu6Fe and Cu6Co were collected as a function of frequency
at constant applied magnetic field H=1.5 T at different temperatures. The spectra thus
obtained are shown in Fig.4. They are found to broaden progressively with decreasing
temperature and to develop a structure due to the presence of a shifted small component.
The spectra at low temperatures could be fitted well with two Gaussian functions having
different width and shift. In the analysis of the data which follows we use as experimental
results for the full width at half maximum (FWHM) and for the paramagnetic shift
L
ps
K
ν
ν
∆
=
(νL is the Larmor frequency) the values used for the fitted Gaussian lines.


.

















-2.0x10
6
0.0
2.0x10
6
4.0x10
6
0.0
2.0x10
5
4.0x10
5
6.0x10
5
8.0x10
5
T=1.6 K
T= 5 K
T= 10 K
T= 20 K
Fits to Gaussian
(b)
1H NMR, Cu6Co, H=1.5 T


Intensity (arb. units)
Frequency(Hz)
-2.0x10
6
0.0
2.0x10
6
4.0x10
6
0.0
2.0x10
6
4.0x10
6
6.0x10
6
T= 1.6 K
T=3.8 K
T=6.9 K
T=20 K
Fits to Gaussian
(a)
1H NMR, Cu6Fe, H=1.5 T


Intensity (arb. units)
Frequency(Hz)

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Fig.4 Representative spectra of proton NMR at different temperatures with fitting
curves made up of the superposition of two Gaussian lines at different resonance
frequency for Cu6Fe (a) and for Cu6Co (b).

The shape and width of the proton NMR spectrum is determined by two main
interactions: (i) the nuclear-nuclear dipolar interaction, (ii) the hyperfine interaction of
the proton with the neighboring magnetic ions. The first interaction generates a
temperature and field independent broadening [9] which depends on the hydrogen
distribution in the molecule and is thus similar in all molecular magnets independently of
their magnetic properties [10].
The hyperfine field resulting from the interaction of protons with local magnetic
moments of Cu2+ may contain contributions from both the classical dipolar interaction
and from a direct contact term due to the hybridization of proton s-wave function with the
d-wave function of magnetic ions. The dipolar contribution has tensorial character and is
thus responsible for the inhomogeneous width of the line due to the random distribution
of orientations in a powder sample and to the many non-equivalent proton sites. The
contact interaction, on the other hand, has scalar form and it can generate a shift of the
line for certain groups of equivalent protons in the molecule [11].
In the usual simple Gaussian approximation for the NMR line shape, the line width is
proportional to the square root of the second moment, which in turn is given by the sum
of the second moments due to the two interactions described above [9]:

md
FWHM
〉
∆
〈
+
〉
∆
〈
∝
22
νν
(1)

where <∆ν2>d is the intrinsic second moment due to nuclear dipolar interactions, and
<∆ν2>m is the second moment of the local frequency-shift distribution (due to nearby
electronic moments) at the different proton sites of all molecules. The relation between
<∆ν2>m and local Cu2+ electronic moments for a simple dipolar interaction is given by [9]

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2
,
3
,
,
2
2
0,
2
)(
1
N
∑ ∑∑


∑ ∑

R






〉〈
=





〉
−
〈
ν
=
〉
∆
〈
∈
i
∈
j
∆
∈
i
∆
RRR
tjz
ji
ji
R
tiRm
m
r
A
N
ϑ
γ
νν
(2)

where R labels different molecules, i and j span different protons and Cu2+ ions within
each molecule, N is the total number of probed protons. In Eq.2 , νR,i is the NMR
resonance frequency of nucleus i and νL = γ H is the bare Larmor resonance frequency.
The difference between the two resonance frequencies represents the shift for nucleus i
due to the local field generated by the nearby moments j. A (ϑi,j) is the angular dependent
dipolar coupling constant between nucleus i and moment j and ri,j the corresponding
distance. < mz,j> is the component of the Cu2+ moment j in the direction of the applied
field, averaged over the NMR data acquisition timescale. In a simple paramagnet one
expects
A
jz
N
m
χ
=
〉〈
,
where χ is the SQUID susceptibility in emu/mole and NA is
Avogadro’s number.
We can thus write approximately:

χν
zm
A FWHM
=
〉
∆
〈
=
2
(3)

where Az is the dipolar coupling constant averaged over all protons and all orientations .
The experimental results for the magnetic contribution to the line width are plotted as a
function of the magnetic susceptibility in Fig.5 for both Cu6Fe and Cu6Co. The linear
relation predicted by Eq.3 is well verified and the values obtained from the fit for the
average dipolar coupling are Az = 2.53×1022 cm-3 ( for Cu6Fe ) and Az = 3.44×1022 cm-3
(for Cu6Co) which are consistent with the dipolar interaction of protons not directly
coupled to the Cu2+ magnetic ions at a mean distance of 3 Å from Cu2+.

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Fig.5. Magnetic inhomogeneous broadening of the proton NMR line plotted vs. magnetic
0.0 0.20.4 0.6 0.81.01.2
0
100
200
300
400
500
600
700
800
900
Cu6Fe
Cu6Co


(FWHM)m(kHz)
χ χ χ χ(emu/mole)

susceptibility in Cu6Co and Cu6Fe. The straight lines are curve fits according to Eq.3 .

We turn now to the analysis of the small shifted line observed in the NMR spectra of
both Cu6Fe and Cu6Co (see Fig.4). The paramagnetic shift is defined as
L
LR
ps
K
ν
νν −
=
,
where νR is the resonance frequency and νL is the proton Larmor frequency . It can be
expressed as [11]:

)(T
N
H
K
BA
eff
µ
ps
χ
=
(4)

where µB= Bohr magneton and χ(T)=paramagnetic susceptibility per mole,
NA=Avogadro’s number, Heff = local hyperfine field. The hyperfine field, which
generates the line shift, is due to a contact scalar interaction arising from the electron
density associated with the s- part of the wave function at the proton site. Thus Heff can
be expressed in terms of the atomic hyperfine coupling constant, a(s), multiplied by a
correction factor, ξ, which gives the fraction of s-character of the wave function of the
magnetic electron at the proton site [11]:

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)(saH
B eff
ξµ
=
(5)

For an atom the hyperfine constant can be expressed as
ABn
Psa
µ
h
γ
π
3
16
)(
=
, with
2
) 0 (
AA
P
ψ
=
the electron probability density at the nucleus for the free atom.
The experimental results for the shift of the satellite line in Fig.4 are shown in Fig.6
for both Cu6Fe and Cu6Co plotted also as a function of the magnetic susceptibility. As
seen in the figure the prediction of Eq.4 is well verified. From the slope of the plot of the
shift vs. the susceptibility one derives a value of 506.5 G for the hyperfine magnetic field
at the proton site for hydrogen bonded to the Cu2+ for Cu6Fe and a value of 462.4 G in the
case of Cu6Co.
The theoretical hyperfine constant for H atom is a(s)= 0.0473cm-1 [11] close to the
value reported for the molecular hydrogen ion H2+ [12] and corresponding to an hyperfine
field at the proton site of about 28 Tesla. Thus the contact term for the bridging
hydrogen’s in Cu6Fe and Cu6Co is only about 0.17% of the atomic hyperfine field for 1s
electron in hydrogen atom consistent with a very small overlap of d and s wave functions
of the magnetic ion and the hydrogen respectively.

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05101520
0,0
0,2
0,4
0,6
0,8
1,0
1,2
1,4
1,6
1,8
2,0
0,00,20,40,6 0,8 1,01,2
0,0
0,2
0,4
0,6
0,8
1,0
1,2
1,4
1,6
Cu6Fe
Cu6Co


Kps(%)
T(K)


Kps(%)
χ χ χ χ(emu/mole)

Fig. 6 Temperature dependence of paramagnetic shift of the satellite line (see Fig.4) in
Cu6Fe and Cu6Co. The inset shows the linear behavior of Kps vs. χ with temperature as an
implicit parameter.

D. Proton NMR signal intensity, T2 and wipeout effects
The normalised signal intensities for protons studied as a function of temperature in
Cu6Fe and Cu6Co are shown below. The signal intensity was measured by the area under
the echoes collected at different delay times, obtained from then usual Hahn-echo
sequence [13]. The Mxy(t) vs. t curve giving the spin-spin relaxation recovery law was
extrapolated at t=0 and normalised by multiplying by T to compensate for the Boltzmann
factor. At low temperature the spectrum broadens and so it was acquired point by point
by sweeping the resonance frequency at fixed magnetic field. As shown in Fig.7 the
decrease of the normalized intensity in the intermediate temperature regime indicates a
loss of signal. The loss of signal is a phenomenon, which has been observed in many
molecular nanomagnets [14]. The explanation of this “wipe-out” effect rests in the very

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short T2 attained by the nuclei closer to the magnetic ions. T2 was measured in our
systems from the exponential decay of the echo amplitude as a function of time delay
between two rf pulses and the results are shown in Fig. 8. The very short value of T2 and
the broad maximum observed in the T dependence of 1/T2 in Fig.8 are in qualitative
agreement with the loss of signal intensity observed in the same temperature range.

050 100 150
T(K)
200250 300
0.0
0.2
0.4
0.6
0.8
1.0
Cu6Co, H=1.5T
Cu6Co, H=0.5T
Cu6Fe, H=1.5T


I*T/Imax*Tmax

Fig. 7. Temperature dependence of normalised NMR signal intensity multiplied by
temperature