![(Color online) Effective (open squares) and median (closed circles) particle moment as a function of the substrate position (angle θ; Fig. 1). These values have been extracted from fits to a simple Langevin function and to a log-normal moment-weighted Langevin function [Eq. (1)], respectively. Also shown are the widths (σ MAG ) from the latter fits (right axis). The dashed lines are guides to the eye. The inset displays the room temperature magnetic response for selected samples across the series. Each curve has been normalized to its saturation magnetization.](https://www.researchgate.net/profile/Jose-De-Toro/publication/234545693/figure/fig2/AS:393572504358912@1470846405115/Color-online-Effective-open-squares-and-median-closed-circles-particle-moment-as-a_Q320.jpg)
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PHYSICAL REVIEW B 85, 054429 (2012)
Energy barrier enhancement by weak magnetic interactions in Co/Nb granular films assembled by
inert gas condensation
J. A. De Toro,1J. A. Gonz´
alez,1P. S. Normile,1P. Mu ˜
niz,1J. P. Andr´
es,1R. L´
opez Ant´
on,1
J. Canales-V´
azquez,2and J. M. Riveiro1
1Instituto Regional de Investigaci´
on Cient´
ıfica Aplicada (IRICA) and Departamento de F´
ısica Aplicada, Universidad de Castilla-La Mancha,
13071 Ciudad Real, Spain
2Instituto de Energ´
ıas Renovables, Universidad de Castilla-La Mancha, 02006 Albacete, Spain
(Received 21 September 2011; revised manuscript received 8 December 2011; published 27 February 2012)
A series of nanogranular Co/Nb samples has been prepared using an unfiltered beam of Co nanoparticles
preformed by inert gas condensation. The preparation technique is shown to be a simple and effective method for
fabricating, in a single deposition step, a sample series across which both particle size and concentration vary.
We estimate the presence of weak interparticle (dipole-dipole) interactions ranging from 7 to 19% in strength
(normalized to the median anisotropy energy barrier) across the present series. With the aim of elucidating the
effect of such interactions on the blocking behavior of such nanogranular material, we have studied the field and
temperature dependence of the magnetization in the films. For each sample, the temperature of the maximum
in the zero-field-cooled magnetization curve (TMAX) is found to lie between the values of blocking (TB)and
freezing (TF) temperature estimated from the experimentally determined particle size and concentration; i.e.,
TB<T
MAX <T
F. Furthermore, the deviation of TMAX with respect to TBcorrelates with the estimated strength
of the interparticle interaction. These results support the Dormann-Bessais-Fiorani model, which predicts an
enhancement of the effective particle anisotropy barrier in the weak-interaction regime. Our study also provides
information on (i) the oxidation of nanoparticles in granular systems and (ii) the size-dependent divergence of
nanoparticles ejected from a cluster source.
DOI: 10.1103/PhysRevB.85.054429 PACS number(s): 75.50.Tt, 75.75.Cd
I. INTRODUCTION
Interest in magnetic nanoparticles (NPs) has grown over
the last decades as new phenomena, often in stark contrast
with bulk properties, have been reported.1,2Recently this
interest has intensified in part due to progress in synthesis
techniques, which has allowed an ever finer control of the
NP properties, paving the way toward new technology.2–4
In particular, the issue of magnetic particle stability against
thermal fluctuations, and the search for strategies to enhance
it in the quest for higher magnetic storage density, has been
the focus of much attention.4–9A related subject of intense
debate is that of the influence of interparticle interactions on the
stability (blocking behavior) of particle moments.8–12 Long-
standing controversy surrounds the question as to whether
the N´
eel-Brown relaxation time13,14 (or, equivalently, the
blocking temperature) of superparamagnetic particles should
increase or otherwise under the introduction of weak dipolar
interparticle interactions.8,9Opposing results from studies
employing experimental techniques probing different time
scales are found in the literature.10,15,16 Namely, as a function of
increasing interaction, magnetometry measurements, reported
by Dormann et al.,10 showed enhanced blocking temperatures
in iron NPs dispersed in an alumina matrix prepared by
co-sputtering, whereas M¨
ossbauer spectroscopy, carried out
on weakly interacting γ-Fe2O3NPs,11,17 showed reduced
relaxation times. The magnetometry results could be success-
fully explained by a model predicting an interaction-enhanced
energy barrier,10 while a different model, developed by Mørup
and Tronc,11 was used to explain the M¨
ossbauer results.
The latter authors suggested that the increase in blocking
temperature observed by Dormann et al. could be due to
collective spin freezing resulting from strong interactions,
supporting this argument with a phase diagram to describe
the stabilization of magnetic particle moments in different
interaction regimes.16 In turn, Dormann et al. modified their
model to allow for variations in the attempt frequency prefactor
(τ−1
0)intheN
´
eel-Brown expression for the relaxation time,
τ=τ0exp[KV/(kBT)], where KV is the anisotropy energy
barrier. This modification was later criticized by Hansen et al.8
In the present work we study the blocking behavior in
a series of nanogranular films comprising cobalt particles
enclosed in a niobium matrix. The eleven films compared,
which differ from each other in NP size and concentration,
constitute a collection of granular samples with estimated
interparticle interactions ranging from 7 to 19% (normalized
to the median anisotropy energy barrier), thereby allowing
us to comprehensively study the effect on blocking behavior
of interparticle interactions in the weak regime. As will be
shown, the films exhibit systematically higher energy barriers
than would be expected if the same particles (within each
sample) were isolated, with a progressively larger deviation as
the interaction strength increases.
Sample synthesis is carried out by co-deposition of pre-
formed NPs with the matrix material, a method generally
referred to as “cluster assembly.” To date, the employment of
this technique has commonly involved filtering of the NPbeam
formed by inert gas condensation (a cluster source), allowing
independent control of particle size and concentration in each
deposition session.18,19 In the present work we have exploited
the profile in particle flux across an unfiltered, divergent beam
of NPs ejected from a cluster source in order to prepare, in
a single deposition session, a sample series across which
both particle size and concentration vary. Two secondary
results, relating to the synthesis technique, to be presented are
054429-1
1098-0121/2012/85(5)/054429(7) ©2012 American Physical Society
J. A. DE TORO et al. PHYSICAL REVIEW B 85, 054429 (2012)
Nb
cathode
Rotary
sample holder
Co NPs
Cluster
Source QCM
Linear
shift
TEM grid
holder
Linear
shift
θ
FIG. 1. Cross section of the sample preparation setup (plan view).
Substrates were mounted at positions corresponding to different
divergence angles θof the beam of nanoparticles (NPs).
(i) the conditions under which cluster-assembled granular
films are stable against room temperature oxidation and (ii)
an unexpected asymmetric size-dependent divergence of the
NP beam.
Section III is divided into two parts. The first part presents
characterization of NP size and concentration across the series
of Co/Nb nanogranular films. In the second part, the blocking
behavior of the films is presented and discussed in the light of
the analysis in the first part; namely, the variation in the strength
of interparticle interactions across the series is estimated using
the experimentally determined NP sizes and concentrations,
and is then used to explain the blocking behavior. Conclusions
are made in Sec. IV.
II. EXPERIMENTAL
The sample preparation setup is shown in Fig. 1.Small
Si substrates, of dimensions 6 ×3mm
2, were mounted on
the cylindrical rotary sample holder at different horizontal
positions corresponding to different divergence angles θ
measured with respect to the NP beam axis (dashed line). These
substrates were equally spaced with each short dimension
(3 mm) perpendicular to this axis and in the plane of
the figure. Particles and matrix material (sputtered from
high-purity Co and Nb targets, respectively) were deposited
quasisimultaneously—achieved by rotation of the sample
holder at 14 rpm—for a total time of 1 hour. The parameter θ
is used throughout the present paper to reference the different
samples prepared in this single deposition session. We define
the positive sense of this angle to be the downward direction
with respect to the beam axis in the plan view in Fig. 1
(the specific θmarked in the figure is, hence, negative). The
distance, measured along the beam axis, from the aperture at
the end of the particle condensation chamber (cluster source)
to the near side of the sample holder was 250 mm.
The cluster source (from Mantis Deposition Ltd.) was
operated at 44 W, employing an aggregation length of 5 mm,
and a flow rate of 40 sccm for both the incoming sputtering
(Ar) and carrier (He) gases. Considering recent work using
similar experimental setups,20–24 the combination of short
aggregation length and carrier gas was employed in order to
prepare NPs small enough for the aim of the present work. The
NP deposition rate measured at the beam axis position using
a quartz crystal monitor (QCM; Fig. 1) was 0.20 ˚
A/s. Due
to the sample holder rotation, the actual rate, onto the on-axis
(θ=0) substrate, was approximately three times smaller. This
relatively high rate, due to the lack of any beam filtering,
together with the long deposition time (1 hour), gave rise to
films thick enough to allow direct concentration measurements
by energy-dispersive x-ray spectroscopy (EDX) to be carried
out. The matrix was rf sputtered at 35 W, with a corresponding
QCM deposition rate of 0.42 ˚
A/s. The large size of the Nb
target together with its close proximity to the sample holder
ensured a uniform sputtering of the matrix (Nb flux) across
the series of substrates. Following Co/Nb deposition, the Nb
plasma was switched off and the sample holder was shifted in
order to collect a sample of Co NPs on a carbon-coated Cu grid
(shifted to the beam axis position) for subsequent analysis by
transmission electron microscopy (TEM). Obviously, being
deposited without the matrix material, the NPs on this grid
were subject to postdeposition oxidation.
EDX measurements of NP (Co) concentration were per-
formed on each sample by probing at four equally spaced
positions along the film’s long dimension, using an integration
time sufficient to register 200 peak counts at the Co Kαenergy
for each position. TEM was performed using a Jeol JEM-2100
electron microscope operating at 200 kV and equipped with
a side entry, double tilt (±20◦) specimen holder and an Orius
Gatan CCD camera (11 Mp). Field-cooled (FC) and zero-
field-cooled (ZFC) magnetization curves were recorded upon
heating from 5 to 300 K using an EverCool MPMS SQUID
magnetometer (Quantum Design), after sample cooling in zero
field and 200 Oe, respectively. In addition, magnetic hysteresis
loops were measured at 5 and 300 K up to a maximum applied
field of 50 kOe. The 5 K loops were recorded after field cooling
from room temperature in a saturating field (50 kOe).
III. RESULTS AND DISCUSSION
A. Characterization of nanoparticle size and concentration
Figure 2shows a TEM micrograph of the particles collected
on the grid placed at the beam axis position, along with the
diameter histogram extracted from several such micrographs
after correcting for particle oxidation (assuming a maximum
thickness of 2 nm for the passivating CoO shell, and bulk
densities for fcc Co and CoO). The TEM grid was somewhat
overexposed and, therefore, some of the particles appear form-
ing small groups (mostly dimers). Only isolated particles—or
particles clearly visible within a group—were used for the
histogram. The log-normal fit to the distribution yields a
median diameter dTEM =4.0nmandawidthσTEM =0.19. As
expected,20,21 the short aggregation length and the introduction
of the carrier gas (He) have led to the production of smaller NPs
054429-2
ENERGY BARRIER ENHANCEMENT BY WEAK MAGNETIC ... PHYSICAL REVIEW B 85, 054429 (2012)
01234567
()
3.8 0.1
0.32
nm
MAG
MAG
d
σ
=±
=
()
4.0 0.1
0.19
nm
TEM
TEM
d
σ
=±
=
PDF (arb. units)
Diameter (nm)
(b)
(a)
FIG. 2. (Color online) (a) TEM micrograph of NPs deposited
on the grid placed at the beam axis. (b) The corresponding particle
diameter histogram (determined measuring 200 particles and cor-
recting for particle oxidation), fitted to a log-normal function (black
curve). The red curve is the diameter distribution (probability density
function) extracted from a Langevin fit [Eq. (1)] to the room temper-
ature magnetic response of the corresponding Co/Nb granular film
(θ=0).
than those obtained in previous work using the same synthesis
technique.22–24
The variation in the particle volume concentration across
the series of Co/Nb granular films is shown in Fig. 3. Each
data point (error bar) in the plot is the mean (error in the
mean) of the four EDX measurements made per sample. As
expected, the concentration is highest for the sample prepared
at the beam axis (θ=0), and a similar maximum is observed
in the saturation magnetization (not shown). From the particle
and matrix (QCM) deposition rates, corrected for the sample
holder rotation (factors 0.3 and 0.5, respectively), a peak of
24% is expected, which is in good agreement with the value in
Fig. 3(27%). The particle concentration in the sample prepared
at the most negative θvalue (−9.6◦) lies just at the sensitivity
limit of EDX (≈2%).
The particles dispersed in films prepared at positions at
θ>5◦were found to partially oxidize under ambient (postde-
position) conditions—for this reason the θ>5◦concentration
values have been omitted from Fig. 3. This oxidation was
manifested by a significant exchange-bias effect (a hysteresis
loop shift along the applied field axis) in the low-temperature
hysteresis loops acquired after sample cooling in a saturating
magnetic field. The inset of Fig. 3shows an example of such
a loop. Exchange bias is absent in films deposited at θ<5◦.
The temperature dependence of the exchange-bias field (i.e.,
FIG. 3. (Color online) Nanoparticle concentration, measured by
EDX, as a function of substrate position on the sample holder (angle
θ;seeFig.1). Films prepared at θ>5◦(region colored in gray) were
not stable against postdeposition NP oxidation. This was evidenced
by the form of their low-temperature magnetic hysteresis loops (see
text). The inset shows such a loop.
the horizontal loop shift) exhibits an “onset temperature” of
approximately 200 K in the θ>5◦films (data not shown).
This value is typical of nanostructures comprising Co-CoO
interfaces with thin CoO components.24,25 Naturally, these
oxidized (θ>5◦) samples were eliminated from the study
of weak magnetic interactions, and, hence, from all the
related analysis (presented below). A possible explanation for
the oxidation will be discussed later, after presenting the θ
dependence of the median NP moment.
Room temperature (300 K) hysteresis loops have been fitted
using a log-normal moment-weighted Langevin function:
M=MS∞
0
LμH
kBTf(μ)dμ, (1)
where L(x)=coth(x)−1/x, with x=μH /(kBT), is the
Langevin function, and
f(μ)=1
√2πμ∗σexp ln2(μ/μ∗)
2σ2(2)
is the log-normal distribution function, with μ∗and σbeing
the median moment and width, respectively, of the distribution.
Figure 4shows two representative fits for the series of films.
The use of Eq. (1), which assumes a negligible anisotropy
barrier compared to the thermal energy, is justified by the
fact that the measurement temperature (300 K) is at least four
times higher than the “blocking temperature” of any of the
samples (see below).26 Under these circumstances, the fit of
the magnetic response to Eq. (1) has previously been shown
to be a reliable technique to estimate the magnetic particle
size distribution—see, e.g., Refs. 27 and 28. For each sample
in the present study, the solution of the fit using Eq. (1)isa
global minimum; i.e., we have confirmed that the fit of each
room temperature hysteresis loop converges to the same result
regardless of the starting parameter values.
054429-3
J. A. DE TORO et al. PHYSICAL REVIEW B 85, 054429 (2012)
FIG. 4. (Color online) Room temperature magnetic response
(symbols) and fits to a log-normal distribution of particle moments
with a Langevin response (solid lines) for the samples prepared at
θ=0and−4.6◦.
The lower panel of Fig. 2shows the diameter distribution
(red line) obtained from this magnetic analysis of the granular
film prepared at the beam axis position (θ=0) for its
comparison with the distribution determined by TEM analysis
of the NPs deposited on the grid. Distributions with similar
widths (within ±10 %) are found from the magnetic analysis
of the rest of the films (see below). The size distribution
is relatively broad, as expected for a fully unfiltered beam
of particles preformed in a cluster source. This result is in
good agreement with the mass spectra recently reported by
Gracia-Pinilla et al. for gas-phase Cu and Ag particles prepared
with a similar cluster source.20,21 The diameter distribution
width derived from the ‘‘θ=0” Langevin fit (σMAG =0.32)
is significantly larger than that obtained from the fit to the TEM
histogram (σTEM =0.19). Yusuf et al. recently pointed out a
similar discrepancy in their study of maghemite NPs.29 Such
difference may be understood in terms of the higher diameter
sensitivity of the SQUID measurement (∼d3) compared with
that of the TEM observations (∼d). On the other hand, the
value of the median of the derived diameter distribution
(dMAG =3.8 nm) is in close agreement with the median diame-
ter extracted from the TEM micrographs (dTEM =4.0nm).To
convert from particle moment to diameter, we have used a value
of saturation magnetization MSequal to the low-temperature
value of bulk fcc Co scaled by the ratio we find between the
saturation magnetic moments at 300 and 5 K (m300 K/m5K
).
This ratio is found to adopt a value of approximately 0.8
across the entire series. Such a large thermal reduction (20%)
in saturation magnetization is a well-known size effect in
nanoparticles.30,31
Figure 5shows the median magnetic moment of the films as
a function of the substrate position. The observed monotonic
variation of the median particle moment with position can be
directly inferred from the increasingly easier saturation of the
magnetic response at room temperature, which is shown in the
inset of the figure. The particle diameter range corresponding
to this variation in median magnetic moment is 2.6–4.0 nm.
The effective moments obtained from fits to a simple Langevin
FIG. 5. (Color online) Effective (open squares) and median
(closed circles) particle moment as a function of the substrate position
(angle θ; Fig. 1). These values have been extractedfrom fits to a simple
Langevin function and to a log-normal moment-weighted Langevin
function [Eq. (1)], respectively. Also shown are the widths (σMAG)
from the latter fits (right axis). The dashed lines are guides to the
eye. The inset displays the room temperature magnetic response for
selected samples across the series. Each curve has been normalized
to its saturation magnetization.
function are also plotted in the figure. These moment values
are systematically higher than the median moments, a tendency
that was found in similar analysis reported by Fonseca et al.32
The results in Fig. 5are remarkable in that they prove a long-
assumed size-dependent divergence of the NPs in the beam
from a cluster source, an effect underlying the utilization of
so called “aerodynamic” lenses for size filtering implemented
in cluster-assembly systems for some time.18,33 However, the
lack of symmetry (i.e., of a peak in the median moment value
at the beam axis position) in this size-dependent divergence
is rather surprising. The origin of this asymmetry may lie in
the stray magnetic fields from the magnetrons in the main
deposition chamber, since such fields were recently suggested
to explain other magnetic effects in a different magnetron-
sputtered system.34 Further investigation would be required to
elucidate this possibility.
The asymmetry in the characteristic particle size across the
series (Fig. 5) may explain why the θ>5◦samples, despite
not being the most concentrated films, are found to partially
oxidize. A previous study by Meldrim et al. reported on
how increasing NP concentration can undermine the stability
against oxidation of granular films. Namely, the authors
showed that granular Co/Cu and Co/Ag films (comprising
5.5 nm particles), grown by the same method as the films
in the present study, were stable for a NP concentration of
10% but oxidized for 30 and 50 % concentrations.35 This
observation can be understood in terms of the formation of
a porous structure that allows the penetration of oxygen in
highly concentrated samples. In the case of nanoparticle films
(no matrix), some of us recently showed that porous structures
may surprisingly propagate into relatively thick (>100 nm)
capping layers.23 The combination of the results displayed
in Figs. 3and 5of the present study indicates that not only
the particle concentration but also the particle size plays a
054429-4
ENERGY BARRIER ENHANCEMENT BY WEAK MAGNETIC ... PHYSICAL REVIEW B 85, 054429 (2012)
role in generating porosity in nanogranular films and, thus, in
determining film stability against oxidation.
B. Blocking behavior across the sample series
Having presented basic characterization (particle size and
concentration), we now turn to the blocking behavior of the
granular films. Figure 6shows four representative examples
of normalized ZFC magnetization curves from the series.
As is well understood, the position of the peak in a ZFC
curve, TMAX, marks a crossover in the main effect that
increasing thermal energy has on the particle moments: from
the deblocking of randomly oriented moments, at T<T
MAX,
to producing superparamagnetic fluctuations in such moments
(Curie-Weiss law) at T>T
MAX. Also plotted in Fig. 6are the
FC magnetization curves for the extremal θvalues (samples)
of the group selected in the figure. The observed strong
irreversibility between the FC and ZFC curves below (or below
a temperature slightly above) the peak temperature is charac-
teristic of an ensemble of magnetic particles with randomly
oriented anisotropy axes.36 Although in both examples the
FC magnetization decreases monotonically with increasing
temperature, in contrast to the behavior in spin glasses or
strongly interacting particle systems (where it is essentially
flat below the freezing transition),36,37 the shapes of the two
(FC) curves are qualitatively different. This difference and its
physical significance will be discussed below.
Figure 7presents the variation in TMAX extracted from the
ZFC curves measured across the sample series. The figure
also includes estimations for the characteristic temperatures
that would be expected for each sample (given its particle
size distribution and concentration) in two extreme scenarios:
(i) ideally isolated particles exhibiting a blocking (peak)
temperature, TB, determined exclusively by the individual
particle energy barriers, and (ii) strongly dipolar interact-
ing particles undergoing a cooperative freezing at TFto a
FIG. 6. (Color online) Selected zero-field-cooled (ZFC) magne-
tization curves (each curve is normalized to its maximum value).
The field-cooled (FC) magnetization curves of the maximum and
minimum θvalues (samples) of the selected group are also shown.
FIG. 7. (Color online) Temperature of the peak in the zero-
field-cooled magnetization curves (TMAX) as a function of substrate
position. Also plotted is the estimated blocking temperature for
isolated Co particles of the same size as those across the series (TB;
lower black line) and the freezing temperature estimated for strong
dipolar interactions between the particles (TF; upper black line). The
dashed vertical line marks the coincidence of the change in slope of
TMAX with the peak in TF.
low-temperature superspin-glass state.16 The ideal blocking
temperatures have been estimated as TB=βKV∗/(25kB),
where Kis the magnetocrystalline anisotropy constant and
V∗(=μ∗/MS) is the median particle volume. A value of
K=1.9×105J/m3has been used, which is that reported by
Woods et al. for a system of monodispersed 5.5 nm diameter
fcc Co particles38 (this value is in close agreement with that
reported for 3 nm Co particles dispersed in a Nb matrix39). The
parameter βaccounts for the distribution in particle volume in
each film. Its value for each film has been extracted from the
graph of βversus σ(width of log-normal volume distribution)
reported by Jiang and Mørup,40 using the corresponding σ
of the film (which is three times that shown in the right axis
of Fig. 5). Given the small variation in σacross the series, a
similarly small variation is obtained for the βvalue, its average
value being 1.9.
The freezing temperatures in Fig. 7have been determined
by
TF=aμ0
4πkB
μ2
D3=aμ0
4πkB
MSCμ∗,(3)
where the first expression follows from the dipolar interaction
energy between two point dipole moments (both of value
μ∗) separated by a distance D(the mean center-to-center
interparticle separation), which has been approximated as the
length of the edge of a cube with the per-particle volume
(=1/n), i.e., D=1/n1/3, where nis the particle number
density (the substitution 1/D3=n=C/V ∗=CMS/μ∗has
been made) and Cis the volumetric particle concentration
measured by EDX (Fig. 3). This is a standard approximation in
studies of dipolar interactions in particle systems.8Following
an article by Hansen and Mørup reporting values of the
constant afor a variety of strongly interacting particle systems
054429-5
J. A. DE TORO et al. PHYSICAL REVIEW B 85, 054429 (2012)
(granular films and frozen ferrofluids),8we have used a=1
as the appropriate value for the present series of samples.41
Except for the first data point (at the lowest θ), which agrees
remarkably well with the TBestimate, the TMAX values (Fig. 7)
all lie between the two extreme scenarios described above,
falling closer to the ideal superparamagnetic blocking values
(TB). This result, along with the irreversibility between the
FC and ZFC curves (commented above), indicates that the
blocking process in the sample series is mainly driven by
single-particle dynamics. However, the progressive departure
of the TMAX from the TBcurve with increasing θ, combined
with the change in slope in the former curve (vertical dashed
line)—precisely where TFbegins to fall due to the peak in
the particle concentration (Fig. 3)—indicates that interparticle
interactions are also at play. The effect of interparticle
interactions is also reflected in the progressive evolution in
the shape of the FC magnetization curve, which shows a low-
temperature change in its second derivative only in the films
with larger TF(i.e., stronger interactions). This is exemplified
in Fig. 6for θ=1.2◦, which contrasts with the fully concave
curve for θ=−5.7◦. Such behavior is reminiscent of strongly
interacting particle systems, where the FC magnetization
flattens out below the freezing temperature.36
The strength of dipole-dipole interactions in any magnetic
particle ensemble will always be reasonably quantified by
Eq. (3); however, this expression will approximate the tem-
perature of the maximum in a ZFC curve only when such
interactions are strong enough compared to the single-particle
anisotropy barrier. The estimated TBand TFvalues (Fig. 7)
are consistent with the presence of relatively weak dipolar
interactions in the samples, since the dipolar to single-particle
anisotropy energy ratio, kBTF/(25kBTB)=TF/(25TB), takes
relatively low values across the series (ranging from 7 to 19%).
Taken within the Dormann-Bessais-Fiorani model, which
predicts an increase in the effective energy barrier upon the
introduction of dipolar interparticle interactions, the presence
of weak dipolar interactions would constitute a plausible origin
of the described features of the results summarized in Fig. 7.
Regarding Mørup and Tronc’s recourse to collective be-
havior in order to explain the enhanced blocking temperatures
observed by Dormann et al. (see Sec. I), it is clear in the present
system that the interparticle interactions are not strong enough
to yield a spin-glass-like freezing transition in any of the
samples, and, therefore, the growing (TMAX −TB) difference
in Fig. 7cannot be attributed to such a phenomenon. This state-
ment is further reinforced by the temperature and frequency
dependence of the ac susceptibility. The signal-to-noise ratio
was rather poor, but it still allowed the frequency sensitivity
of the peak (in its shift toward larger temperatures with
increasing frequency) to be determined for the sample with the
strongest interactions (θ=1.1◦). This measurement yielded
p=TMAXTMAX
(log ω)≈0.06, a typical value for superparamagnets
with weak to moderate interactions (superspin- or spin-glass
transitions have been found to exhibit values about 4–5 times
lower).10,36,37
IV. CONCLUSIONS
Nanogranular film preparation by cluster assembly using
an unfiltered beam of gas-phase Co NPs has conveniently
provided samples with different particle sizes and concentra-
tions in a single deposition session. The sample parameters
attained are such as to give rise to interparticle (dipole-
dipole) interactions along the series that scan the weak to
moderate range. An increasing enhancement of the effective
particle anisotropy energy barrier with increasing interactions
across the series is concluded, which, together with the
exclusion of the possibility of a spin-glass-like transition,
supports the Dormann-Bessais-Fiorani model. To the best of
our knowledge, the absence of any reported magnetometry
measurement of a reduction in the blocking temperature
upon the introduction of weak dipolar interactions in any
particle system is a clear weakness of the otherwise convincing
Mørup-Tronc model. Two secondary results from our study are
(i) the observation that not only the particle concentration but
also the particle size plays a role in determining the stability
against oxidation of granular films in ambient conditions, and
(ii) the detection of an asymmetric size-dependent divergence
of the NP beam.
ACKNOWLEDGMENTS
We acknowledge financial support from the Consejo Inter-
ministerial de Ciencia y Tecnolog´
ıa (Project No. MAT2008-
01158/NAN). We thank M. Rivera and E. Prado for their
technical support.
1Quy Khac Ong, Xiao-Min Lin, and Alexander Wei, J. Phys. Chem.
C115, 2665 (2011).
2H. Kronmuller and S. Parkin, editors, Handbook of Magnetism and
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