Mn7 species with an S = 29/2 ground state: high-frequency EPR studies of a species at the classical/quantum spin interface.

Abstract

A high spin (S) compound has been synthesized whose properties straddle the interface between the classical and quantum mechanical spin descriptions. The cluster [Mn(7)O(4)(pdpm)(6)(N(3))(4)](ClO(4))(2) (Mn(7)) has an unprecedented core structure comprising an octahedral [Mn(III)(6)(μ(4)-O)(μ(3)-O)(3)(μ(3)-N(3))(4)](6+) unit with one of its faces capped by a Mn(II) ion. Magnetization and susceptibility studies indicate an S = (29/2) ground state, the maximum possible. Variable-temperature, high-frequency electron paramagnetic resonance (HF-EPR) spectra on powder and single-crystal samples of Mn(7) exhibit sharp spectral features characteristic of a quantum spin that are well resolved in a certain temperature range but which transform to a continuum of peaks characteristic of a classical spin in another; these features have been well reproduced by computer simulations. A fast Fourier transform analysis of the sharp spectral features and the low temperature EPR spectra suggests that more than one spin state are involved.

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Published:October 09, 2011
r2011 American Chemical Society
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pubs.acs.org/JACS
Mn7Species with an S =29/2Ground State: High-Frequency EPR
Studies of a Species at the Classical/Quantum Spin Interface
Zhenxing Wang,†Johan van Tol,*,†Taketo Taguchi,‡Matthew R. Daniels,‡George Christou,‡and
Naresh S. Dalal*,†
†Department of Chemistry and Biochemistry, and National High Magnetic Field Laboratory, Florida State University,
Tallahassee, Florida 32306, United States
‡Department of Chemistry, University of Florida, Gainesville, Florida 32611-7200, United States
b
S Supporting Information
ABSTRACT: A high spin (S) compound has been synthe-
sized whose properties straddle the interface between the
classical and quantum mechanical spin descriptions. The
cluster [Mn7O4(pdpm)6(N3)4](ClO4)2(Mn7) has an un-
precedented core structure comprising an octahedral
[MnIII6(μ4-O)(μ3-O)3(μ3-N3)4]6+unitwithoneofitsfaces
capped bya MnIIion. Magnetizationand susceptibility studies
indicate an S =29/2ground state, the maximum possible.
Variable-temperature, high-frequency electron paramagnetic
resonance (HF-EPR) spectra on powder and single-crystal
samples of Mn7exhibit sharp spectral features characteristic of
a quantum spin that are well resolved in a certain temperature
range but which transform to a continuum of peaks character-
istic of a classical spin in another; these features have been
well reproduced by computer simulations. A fast Fourier
transform analysis of the sharp spectral features and the low
temperature EPR spectra suggests that more than one spin
state are involved.
T
fertile area for developing molecular electronics as well as for a
fundamentallynewwayofunderstandingthequantumchemistry
and physics of the electron spin.3It was noted early on that a
prerequisiteforSMMbehaviorwastheexistenceofalargebarrier
tospin reversal whose upper limit isgivenbyDS2,where Dis the
zero-field uniaxial anisotropy parameter and S is the total spin.
Thus, in general, a large spin S in combination with a large
negative anisotropy parameter D is required for possible SMM
applications, e.g., in quantum computing.2?4
For the above reasons, we and others have been developing
new synthetic methods for Mn clusters of various sizes and, to
date, have successfully isolated and studied a wide variety, with
nuclearities up to 84.5While these compounds have provided a
plethora of new structural, magnetic, and spectroscopic data, it
was noted that the spin dynamics exhibited by clusters with
particularly large values of S showed spectroscopic features that
could not be well simulated using a quantum mechanical
description of the spin S. A clear example of this is that the
electronparamagneticresonance(EPR)spectraofmanyofthese
compounds6?8were found to yield spectra that exhibited a
continuum rather than the series of well resolved peaks that
have been the hallmark of compounds with S = 10 or smaller.9
hediscovery ofsingle moleculemagnets(SMMs),1inwhich
each molecule behaves as a magnetic domain,2has opened a
These observations suggested that there might be a spin-phase
classical-quantum boundary, and we have been searching for
compounds at this boundary among the various Mn clusters that
we have been synthesizing and studying in recent years, con-
centrating on moderate size clusters with large spin S. Here, we
report the magnetic and EPR characterization of a new cluster
[Mn7O4(pdpm)6(N3)4](ClO4)2 (Mn7). It has an unprece-
dented core structure, but more significant is the discovery that
thepropertiesofthisclusterwithanS=29/2groundstateplaceit
at the classical/quantum spin interface.
Mn7was prepared from the 1:1:1:1 reaction of Mn(ClO4)2,
NaN3, NEt3, and phenyl(dipyridin-2- yl)methanol (pdpmH) in
MeCN/MeOH (20:1 v/v) and isolated in ∼50% yield as dark
red crystals of Mn732MeCN on layering of the filtered solution
with Et2O. The Mn7cation (Figure 1) has C3symmetry, and its
core consists of a [MnIII6(μ4-O)(μ3-O)3(μ3-N3)4]6+unit, with
one of its faces capped by a MnIIatom. Three η2-chelating and
three η2:μ-chelating/bridging pdpm?groups provide the peri-
pheral ligation.
Variable-temperature magnetic susceptibility measurements
were performed on a microcrystalline powder sample, restrained
Figure 1. The structure of the Mn7cation. The C3-axis is vertical,
passing through Mn3, O4, and N4. H atoms have been omitted for
clarity. Color code: MnII, yellow; MnIII, green; O, red; N, blue; C, gray.
Received: August 12, 2011

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in eicosane, in a 0.1 T field and in the 5.0?300 K range. The χMT
gradually increases from 30.59 cm33K3mol?1at 300 K to a value of
102.81cm33K3mol?1at8K,andthenslightlydecreasesto102.09at
5.0K.Theplotprofileindicatesdominantferromagneticinteractions,
andthe5.0KvaluesuggestsanST=29/2groundstatewithg∼1.91;
the spin-only value is 112.38 cm33K3mol?1. ST=29/2is the
maximum possible for Mn7, indicating a completely ferromagneti-
cally coupled system.
In order to confirm the ground state and determine the zero-
field splitting parameter D, magnetization vs applied field data
were collected on a restrained sample in the 0.1?7 T and
1.8?10.0Kranges.Theresultingdatawerefit,usingtheprogram
MAGNET,10by diagonalization of the spin Hamiltonian matrix
assuming that only the ground state is populated, incorporating
axial anisotropy (D^Sz2) and Zeeman terms, and employing a full
powder average.
The resulting data are shown in Figure 2 as reduced magnetiza-
tion(M/NμB) vsB/T,whereNisAvogadro’snumber.Theisofield
lines are essentially superimposed, indicating minimal anisotropy
(D-value).Thefit(solidlinesinFigure2)wasobtainedwithST=29/2,
g = 1.89(2), and D = 0.03(1) cm?1. An equally good fit was
obtainedwithST=29/2,g=1.89(1),andD=?0.020(5)cm?1.Itis
commontoobtaintwoacceptablefitsofmagnetizationdatafora
given spin S, with D > 0 and D < 0, because magnetization fits
are not very sensitive to the sign of D. The unusually low g-value
is undoubtedly an artifact reflecting the presence of a very low-
lying excited state populated even at these low temperatures
(vide infra) and the generally low reliability of g-values from
powder susceptibility fits; for MnIII-containing complexes, a g-
value only slightly less than 2 is expected and usually observed.
For an independent assessment of the ground state S, the g-
valueandthesignandmagnitudeoftheaxialZero-FieldSplitting
(ZFS) parameter D, EPR measurements11,12were carried out on
Mn7 in the solid state. Figure 3A shows the temperature
dependence of the EPR spectrum of the powder sample at
331.2 GHz. The spectrum is a broad peak at 300 K, but new
features start to develop at lower temperatures. At the lowest
temperature, the spectrum resembles a typical powder pattern
for axial symmetry. The transitions for the field along the
principal axis of the ZFS tensor appear on the high field side
(FigureS1,Supporting Information),whichindicatesthatDis
positive. In cases like this with a very large ground spin state,
the 2S EPR fine-structure peaks are not resolved when the
magnitude of D is smaller than the line-width, and it is only
possible to estimate the product DS.6,7However, the g-value
can be determined with a good precision. To simulate the
powder EPR spectra, we utilized the following Hamiltonian
^ H ¼ gμBB3^S þ Dð^Sz
in which we now also include the strain parameters ΔD and ΔE,
whicharethefullwidthathalfmaximum(fwhm)ofaLorentzian
distribution around average D and E values due to the spread of
the local crystal-field distortions of the molecules.13Because of
the 3-fold symmetry, we have kept E = 0 but allow ΔE to vary.
The simulation in Figure 3B was obtained with the following
spin Hamiltonian parameters: S =
0.0320(2) cm?1, ΔD = 0.010(2) cm?1, E = 0, ΔE = 0.008-
(2) cm?1.14Although this simulation assumes that only the
S=29/2spinstateispopulatedoverthewholetemperaturerange,
itcanbeseenthattheoverall changeofspectrawithtemperature
iswellsimulated,andthesimulationconfirmsapositivesignofD
and gives a much more accurate g-value than can be deduced
from susceptibility fits. The sharp peaks in the center of the
spectra correspond to the ΔmS= (1 transitions involving spin
sublevelswithsmallquantumnumbersmS=(1/2,(3/2,(5/2,
2?^S2=3Þ þ Eð^Sx
2?^Sy
2Þð1Þ
29/2, g = 1.996(1), D =
Figure 2. Plots of reduced magnetization (M/NμB) vs B/T. The solid
lines are the fit of the data; see the text for the fit parameters.
Figure 4. EPR spectra of a single crystal at 240 GHz with the field
parallel to the z-axis. The amplitudes are normalized.
Figure3. EPRspectraofapowdersampleat331.2GHzasafunctionof
temperature. (A) Experimental; (B) simulation (see text). The ampli-
tudes of the spectra are normalized.

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etc, which have higher transition probability and are less broa-
denedbyDandEstrain.Thesespectraareaperfectexperimental
realization of the theoretical spectral simulations by Fittipaldi15
et al. for a similarly large spin system, but with a different sign of
the ZFS parameter D.
The central peak in the experimental spectra observed at
higher temperatures is slightly stronger than in the simulations.
Also, the simulated spectra above 200 K display more of a low
field shoulder than the experiments. We suspect that these
observations are due to the deviation from a simple model that
assumes only a single well-defined ST =
populated. To clarify this, measurements were made using single
crystals. The orientational dependence of the 8 K spectra are
shown in Figure S2 (Supporting Information), whereas Figure 4
shows 240 GHz spectra at various temperatures with the
magnetic field aligned along the main axis of the axial zero-field
splitting tensor (z-axis). At 300 K, the spectra from the single
crystal also yielded a single Lorentzian peak, but as the tempera-
tureislowered,thepeakbroadens,shiftstohigher field,andfine-
structurepeaksstarttodevelopbelow110K.Thesefinestructure
peaks disappear below 20 K. The magnitude of the splitting
(∼600 G) is too large to arise from hyperfine coupling16and
must be due to the ZFS of the Mn7complex.
At low temperatures, a second broad peak (P2) appears and
becomes stronger as the temperature decreases. It is seen that P1
is not symmetric, and it is much broader and more intense than
P2.Thissuggeststhatnotonlythegroundspinstateispopulated,
but excited states are involved in the observed EPR transitions.
29/2 spin state is
These observations are not unreasonable if some exchange
coupling constants in the molecule are not too large compared
tokT.WealsoobservedsimilarphenomenaintheHF-EPRstudy
on Mn25, with S =61/2.8
In order to confirm the assumption of at least two spin states
contributing to the observed signals, we employed a relatively
unusual procedure for analyzing the fine structure of such a high
spin system. Figure 5A shows a fast Fourier transform (FFT) of
the single-crystal EPR spectrum at 40 K. The units (T?1) of the
horizontal axis correspond to the number of oscillations per
Tesla of magnetic field, which we call the “transition density” nT.
The peak at ∼0.5 T?1is assigned to the broad background that
dominates the EPR spectrum (Figure 4). Two peaks were ob-
servedataround15T?1,whicharerelatedtothefinestructurein
the cw spectrum at around 8.6 T (g ≈ 1.996). The Fourier
transform shows that two oscillation frequencies can clearly be
distinguished, which correspond to the spacing between two
neighboring mSf mS+1 EPR transitions that should be equal to
2D for this orientation. Thus, we observe two different D-values
that are presumably from two spin states. The two oscillation
frequencies (14.1 and 16.9 T?1at 20 K) appear to be slightly
temperature-dependent(insetofFigure5A),whichmightbedue
to the contribution of more spin states at higher temperatures.
The corresponding D-values are 0.0329 and 0.0274 cm?1, if we
assumeonlysecond-ordertermsintheZFS(2D=gμB/nT).Over
the temperature range of 20?80 K, the relative amplitude of the
two peaks remains similar, indicating that the energy difference
between the two spin states is small. However, in the low
temperature spectra, the position of P1and P2for S =27/2or
S =29/2corresponds to a slightly larger value of D. To account
for this discrepancy, we have introduced an additional fourth
order term in the Hamiltonian:
^ H ¼ gμBB3^S þ Dð^Sz
where O k40is the standard Stevens’ operator.16As we are only
considering the spectrum for B||z-axis, we do not include the
nonaxial second order term (E = 0, ΔE = 0).
Figure 5B shows the simulation to the spectrum at 40 K
assumingtwospinstates,anS=29/2groundstateandanS=27/2
first excited state. The resulting parameters are (a) ground state,
S =29/2, g = 1.996, D = 0.035 cm?1, ΔD = 0.007(2) cm?1, B40=
5.7(2) ? 10?7cm?1; and (b) first excited state, S =27/2, g =
1.996, D = 0.030 cm?1, ΔD = 0.009(2) cm?1, B40= 7.5(2) ?
10?7cm?1. The intrinsic line width (without D- and E-strain) is
about 35 mT, which is likely due to dipolar coupling with
surrounding molecules. The values found for the fourth order
term appear reasonable, as the ratio of D/B40is similar to that
found in systems like Mn1217and Fe8.18The same parameters
also provide a reasonable simulation of the 2.25 K spectrum, as
shown in Figure S3 (Supporting Information). It thus is possible
to describe the low temperature (<80 K) EPR spectra on the
basis of a population of two closely spaced spin states. Although
the magnetization data in Figure 2 were fitted on the basis of a
single S =29/2state, the obtained g-value of 1.89 is 5.5% lower
than the value determined experimentally by EPR. Using the
experimentally determined g-value, the saturation magnetization
agrees well with a mixture of S =29/2and S =27/2spin states. Of
course, from our analysis it cannot be excluded that additional spin
states are populated, especially at higher temperatures. This might
explain the disappearance of the structures above 80 K, but line
broadening due to increased relaxation at higher temperatures can
2?^S2=3Þ þ B0
4^ O0
4
ð2Þ
Figure 5. (A) FFT of the 40 K EPR spectrum in Figure 4 and its fitting
with two Gaussian peaks. Inset: FFT of the EPR spectra at different
temperatures. (B)EPRspectrum ofasinglecrystal at40Kwiththefield
parallel to the z-axis, and its simulation.

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alsoplayarole.Theshiftofthehigherfrequencycomponentinthe
Fourier transforms (inset of Figure 5A) at higher temperatures
might indicate that more spin states with smaller D-values are
populated above 40 K. This new FFT-analysis procedure could
provetobeusefulinthedetailedanalysisoftheEPRspectraofsuch
high spin multiplets.
In conclusion, the Mn7complex with an S =29/2ground state
wasinvestigatedindetailbyHF-EPRspectroscopyandmagnetic
susceptibility,asthissystemwasconsideredattractiveforexamining
the transition from quantum to classical behavior of a large spin
system. We indeed found that the compound yielded spectra that
exhibit both broad unresolved features but also a fine structure that
is well resolved in a limited temperature range. In other words, it
exhibits the spectral signatures of both classical and quantum spins.
Thus, this Mn7cluster provides the first clear experimental realiza-
tion of the simulated spectral predictions for such a large spin
system. In addition, the temperature dependence of the powder
spectrumillustrateschangesinthespectrumthatcouldbeexplained
solelyonthebasisofD-strainandaredistributionofthepopulation
over the spin sublevels of a single spin state, spin levels that for a
S=29/2systemat12Tspanaenergyrangecorrespondingto476K.
However, single crystal measurements resolved some of the transi-
tions and showed that at least two spin states are involved. A FFT
analysiswasintroducedasapowerfulnewproceduretoanalyzethe
newly observed splittings in the EPR spectra and to separate
transitions from different spin states. This analysis confirmed the
two peak structure that is observed in the low temperature spectra
and gave an estimate for the fourth-order term in the Hamiltonian.
NotethatMn7appearstopossessanexcellentcombinationofsmall
metal nuclearity and large value of the total spin S to facilitate the
above studies and allow the spectra to be reasonably explained, in
this case, on the basis of two well-defined spin states. However, for
larger systems such as the Mn84 cluster,5fsuch a description
becomes more problematic as many spin states are populated and
transitions remain unresolved at all temperatures.
’ASSOCIATED CONTENT
b
S
SupportingInformation. SupportingFiguresS1?S3.This
materialisavailablefreeofchargeviatheInternetathttp://pubs.
acs.org.
’AUTHOR INFORMATION
Corresponding Author
vantol@magnet.fsu.edu; dalal@chem.fsu.edu
’ACKNOWLEDGMENT
We thank the National Science Foundation (CHE-0910472)
for support of this work. The National High Magnetic Field
Laboratory is supported by NSF Cooperative Agreement No.
DMR-0654118 and by the State of Florida.
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