Magnetic interactions of iron nanoparticles in arrays and dilute dispersions

Article abstract of DOI:10.1021/jp050161v

The magnetic properties of monodisperse Fe nanoparticles with over 4 orders of magnitude difference in concentration are studied by a combination of ordinary and remanent hysteresis loops, zero field cooled magnetization as a function of temperature, and magnetic relaxation rates. We compare the behavior of dilute dispersions with different concentrations, dispersions, and arrays made from the same particles, and nanoparticle arrays with different particle sizes and separations. The results are related to theoretical predictions and are used to create a unified picture of magnetostatic interactions within the assemblies. ? 2005 American Chemical Society.

Full text of DOI:10.1021/jp050161v

J. Phys. Chem. B 2005, 109, 13409-13419
13409
FEATURE ARTICLE
Magnetic Interactions of Iron Nanoparticles in Arrays and Dilute Dispersions
Dorothy Farrell,†,‡ Yuhang Cheng, R. William McCallum, Madhur Sachan, and
†
§
†
Sara A. Majetich*,†
Physics Department, Carnegie Mellon UniVersity, Pittsburgh, PennsylVania 15213-3890, London Centre for
Nanotechnology, UniVersity College London, London, WC1E 7HN, UK, and Ames Laboratory, Iowa State
UniVersity, Ames, Iowa 50011
ReceiVed: January 10, 2005; In Final Form: May 11, 2005
The magnetic properties of monodisperse Fe nanoparticles with over 4 orders of magnitude difference in
concentration are studied by a combination of ordinary and remanent hysteresis loops, zero field cooled
magnetization as a function of temperature, and magnetic relaxation rates. We compare the behavior of dilute
dispersions with different concentrations, dispersions, and arrays made from the same particles, and nanoparticle
arrays with different particle sizes and separations. The results are related to theoretical predictions and are
used to create a unified picture of magnetostatic interactions within the assemblies.
Introduction
length scale Landau-Lifschitz-Gilbert modeling of magnetization
dynamics beaks down due to the granularity of the particle
assemblies.
Monodisperse monodomain magnetic nanoparticles1-5 are an
ideal system for studying magnetostatic interactions, since they
act like giant magnetic moments. There have been numerous
studies of these nanoparticles in ferrofluids,5
particle concentration is a few volume percent or less, and also
in self-assembled nanoparticle arrays,2
fraction is limited only by the thickness of the surfactant coating.
Here we describe how the magnetic properties of monodis-
perse Fe nanoparticles are modified by changing the particle
concentration and particle size. Unlike previous studies, we study
similar particles with over 4 orders of magnitude difference in
the volume fraction, ranging from highly dilute dispersions to
close-packed arrays. Because of the surfactant coating, the
particle assemblies can have high density without exchange
coupling between particles that would otherwise dominate the
magnetic properties. The goal of this work is to develop an
improved understanding of the magnetization pattern within a
-19
where the
0-26
where the volume
Magnetostatic forces are long-range and have subtle effects.
These have been documented by studying the peak temperature
in the imaginary susceptibility as a function of frequency over
8
5
orders of magnitude as a ferrofluid is diluted. Dilute
ferrofluids have also been shown to behave like dipolar spin
9
glasses. In a more concentrated assembly, where the interactions
are stronger, it is theoretically possible to have a purely dipolar
ferromagnet. For a two-dimensional hexagonal lattice of point
dipoles, the magnetic ground state is ferromagnetic, but for a
square lattice, the minimum energy configuration has alternating
rows of aligned spins.27 It is therefore interesting to see if the
interactions in nanoparticle arrays are sufficiently strong to test
these predictions at finite temperatures.
Different groups have reported conflicting results on whether
the coercivity, remanence, and relaxation rate go up or down
19
with increasing particle concentration. The self-assembled
nanoparticle arrays show some collective behavior, but the
magnetostatic forces that cause it are weak and long range,
compared with the exchange forces that couple atomic spins
within a particle. It is unclear under what conditions mean field
theories based on dipolar interactions will be valid, or on what
Sara Majetich received an A. B. in chemistry at Princeton University,
and a Masters Degree in Physical Chemistry at Columbia University.
She earned a Ph.D. in Solid State Physics from the University
of Georgia and did postdoctoral work at Cornell University before
joining the faculty at Carnegie Mellon University in 1990. She is
the recipient of a National Young Investigator Award from the NSF.
More about the Majetich group research can be found at http://
www.andrew.cmu.edu/user/sm70/index.html.
*
Corresponding author. E-mail: sm70@andrew.cmu.edu.
Carnegie Mellon University.
†
‡
§
University College London.
Iowa State University.
1
0.1021/jp050161v CCC: $30.25 © 2005 American Chemical Society
Published on Web 06/23/2005

13410 J. Phys. Chem. B, Vol. 109, No. 28, 2005
Farrell et al.
dense nanoparticle assembly, through macroscopic measure-
ments of the magnetization as a function of the applied field,
temperature, and time.
Experimental Methods
A. Sample Preparation and Structure. Monodisperse Fe
nanoparticles 4.5 to 9.3 nm in diameter were prepared under
an argon atmosphere via thermal decomposition of iron pen-
tacarbonyl, Fe(CO)5, using a heterogeneous nucleation technique
that has been reported elsewhere.32 To vary the particle size,
an additional stage of growth followed. The volume of octyl
ether was doubled to reduce the concentration of particles in
solution and heating began again. Fe(CO)5 was again added at
1
00 °C, and heating continued until 260 °C, after which the
sample was cooled and removed to an argon atmosphere
glovebox for washing. Reactions were done with and without
a 1:1 molar ratio mixture of oleic acid (OA) and oleylamine
(OY) present. The surfactant binds to the Fe particle surface
and provides a barrier against agglomeration. OA is used for
strong binding to the Fe surface, and OY is mixed with OA to
reduce the oxidation reactivity of the OA. The molar ratio of
the first stage Fe to surfactant in these syntheses was varied
between 2.2:1 and 4.6:1, treating each OA/OY pair as a single
2
molecule. Assuming a headgroup area of 0.25 nm for OA and
OA/OY mixes, comparisons of surfactant concentration (15-
4
5 mM) and particle concentration indicate that surfactant
concentration is greater than that needed to coat the surfaces of
the particles. The samples were washed by adding ethanol in a
3
:1 volume ratio to the octyl ether, causing the particles to
aggregate. The aggregates were then collected with a magnet,
the supernatant was decanted, and hexane added to redisperse
the particles. Surfactant was added at a concentration of 15 to
45 mM during each washing stage. The hexane suspensions were
typically 2-20 times more dilute than the original octyl ether
suspensions.
Since the surfactant chain provides the steric repulsion that
keeps particles separated even in a dried state, the interparticle
spacing in dried assemblies of particles can be reduced by
exchanging surfactants. A mixture of hexanoic acid (HA), C5H11-
COOH, and hexylamine (HY), C6H13NH2 was used as a
replacement short chain surfactant. The shorter chain length of
these molecules results in smaller surfactant volume, allowing
them to penetrate the larger surfactant coating and displace the
larger molecules. Like OA and OY, HA and HY reacted upon
mixing, and were therefore also considered to be a double-
chained surfactant in the mixed state.
Figure 1. TEM images of (a) 6.7 ( 0.7 nm and (b) 8.5 ( 1.0 nm Fe
particles coated with OA/OY. Size distributions and Gaussian fits to
determine the average particle diameter and standard deviation, σ, for
(
c) the particles from Figure 1a, with a total of 2140 particles, and (d)
for the particles from Figure 1b, with a total of 5695 particles. These
data could also be fit to a log-normal function with the same average
size and a normalized σ of 0.12. The “spikes” in the data arise from
variations between arrays but size uniformity within an array.
The as-made particle concentrations of the samples were
The degree of oxidation can be minimized by flocculating the
particles first, but this makes it more difficult to determine
32
33
determined from calibrated X-ray fluorescence. The energies
of the emitted X-rays are specific to the elements in the sample,
and the relative concentrations of the elements are determined
by pattern intensities. The results indicate a roughly 40% yield
for the synthesis, based on the initial amount of Fe(CO)5 and
the average particle size found from TEM. These results were
used to estimate the concentrations of the hexane dispersions
made from them. The particle arrays were generally formed from
the size and spacing information, which are critical to this study.
The particle size and the separations between particles in the
arrays were determined from TEM images taken with a Philips
EM420 microscope operating at 120 keV. NIH Image 1.6.2
software was used to analyze the digitized images for the particle
size distributions. The distributions were then fit to Gaussian
functions to determine the average particle sizes and standard
deviations, σ. Figure 1 shows TEM images of arrays with
different particle sizes but the same edge-to-edge interparticle
spacing. Figure 2 shows images of particle arrays made from
the same batch of nanoparticles, but with different surfactant
coatings to change the interparticle spacing. Note how the length
scale of structural ordering is reduced in the sample with the
shorter chain surfactant. The surfactant coating plays a signifi-
cant role in the mobility of the particles during self-assembly.
The images of Figures 1 and 2 are from arrays prepared by the
15
dispersions with number densities between 2 × 10 and 3 ×
particles per cubic centimeter.
Once particle dispersions were prepared with the desired
14
1
0
surfactant and particle concentration, transmission electron
microscopy (TEM) grids were prepared. For the particle size
and separation determination, grids were prepared by dropping
a single drop of particle dispersion on the grid with a pipet.
The Fe particles imaged in the arrays are partially oxidized
because of the brief exposure during transfer to the microscope.

Feature Article
J. Phys. Chem. B, Vol. 109, No. 28, 2005 13411
B. Magnetic Measurements. Evidence for interactions
between Fe nanoparticles is obtained by comparing the mag-
netization of samples with isolated particles with more concen-
trated solutions. The temperature, applied magnetic field, and
time-dependent response of the magnetization all reveal different
aspects of these interactions.
Magnetic measurements were done with a Quantum Design
MPMS over a range of temperatures (T ) 10-300 K) and
applied fields (H ) 0-50 kOe). This system can detect magnetic
-
5
moments in the range of 10 to 1 emu with good signal-to-
noise ratios. The particles used for magnetic measurements were
maintained in a low oxygen environment at all times. For the
magnetic studies, grids were dipped into the particle suspension
using tweezers, and then held aloft in the glovebox to dry. The
dip method was utilized to maximize the particle concentration.
In the concentrated samples, stacks of TEM grids containing
multilayer arrays, embedded in silicone grease, were used. For
the dilute samples, glass ampules containing hexane dispersions
were used. In all cases the diamagnetic background was
subtracted.
The zero-field cooled magnetization as a function of tem-
perature was used to identify the blocking temperature, TB, and
to identify the temperature range over which hysteresis loops
and interaction effects are observable. To determine the blocking
temperature, the sample was cooled in zero field from room
temperature to 10 K. Once the temperature stabilized, a 100
Oe field was applied so that the magnetization would be
nonzero. The moment was measured at this and subsequent
higher temperatures to determine MZFC(T).
For standard hysteresis loops, M(H), a 50 kOe field was
applied to saturate the sample, and then the magnetization was
measured as the field is reduced and reversed in direction. The
remanent magnetization, Mr, is the magnetization of the material
following the removal of this field. The coercivity or coercive
field, Hc, is the reverse field that must be applied to a previously
saturated material to reduce the magnetization to zero.
In contrast with a standard hysteresis loop where the
magnetization is measured at each value of the applied field H,
in a remanent hysteresis loop, Mr(H), the magnetization at zero
field, or remanence, is measured after applying H. In the absence
of an applied field, the particle moment aligns with the easy
magnetization axis of the particle. In this sense, the remanent
coercivity is a measure of the field necessary to flip the
orientations of one-half of the moments along the easy axes.
Remanent hysteresis loops are particularly useful for fine
particles because they remove rotational contributions from the
particles as well as any signal from paramagnetic or superpara-
magnetic species in the sample.
Figure 2. TEM images of 6.7 ( 0.7 nm Fe particles with different
surfactant coatings. (a) Particles coated with OA/OY; (b) particles
coated with HA/HY. The contraction in interparticle spacing can be
seen in HA/HY-coated particles, which had an average edge-to-edge
interparticle spacing of 1.2 nm, compared to 2.5 nm for the OA/OY-
coated particles.
The time dependent magnetic properties were studied by
applying a 50 kOe field to the sample, removing the field and
measuring the remanent moment at intervals over a 10 hour
period, with the first measurement taken approximately one
minute after the field stabilized.
We also measured the real and imaginary parts of the AC
susceptibility. The susceptibility ø is defined as M/H. Its real
part ø′ is the component that is in-phase with the AC driving
field H, and the imaginary part ø′′ corresponds to the out-of-
phase component. ø′′ is a maximum under conditions where
the energy dissipation is greatest. Here the driving field had an
amplitude of 2 Oe and the temperature ranged between 6 and
Figure 3. TEM image of nanoparticle arrays prepared by dipping into
particle suspensions.
4
00 K.
Results
A. Dilute Dispersions. The minimum Fe particle size where
evaporation method; Figure 3 shows a typical TEM image is a
dipped grid, or the sort used in magnetic measurements. Note
that the length scale of the ordered regions is smaller.
appreciable interaction effects were observed in the hysteresis

13412 J. Phys. Chem. B, Vol. 109, No. 28, 2005
Farrell et al.
Figure 5. Magnetic relaxation as a function of time, for dilute hexane
dispersions of 7.0 ( 0.8 nm particles with different volume fractions,
at 10 K with H ) 0.
TABLE 1: Comparison of Dilute Dispersions of 7.0 ( 0.8
nm Particles as a Function of Concentration
volume
remanent
blocking magnetic
fraction, hysteresis
hysteresis remanence temperature, viscosity,
xV
loop Hc(Oe) loop Hc(Oe) ratio, Mr/Ms
TB (K)
S
0
0
.0003
.00003
240
460
430
720
0.27
0.29
40
30
0.010
0.019
the field was turned off. The data are normalized relative to the
magnetization and time at the first H ) 0 data point.
An ensemble of identical noninteracting particles is theoreti-
cally predicted to relax exponentially, with a time constant τ
related to the energy barrier height, relative to the thermal energy
Figure 4. (a) Hysteresis loops at 10 K for 7.0 ( 0.8 nm particles
31
available. Here the theoretical time dependent remanence is
frozen in hexane, for different particle concentrations; (b) Low field
given by Mr ) Ms exp(-t/τN), where the N e´ el decay time is
region of the hysteresis loops. H ) 240 Oe for the 0.03 vol. % sample,
c
-1
defined by τN ) f0 exp(-KV/kBT), and f0 is a constant related
and 460 Oe for the 0.003 vol. % sample.
to the Larmor precession frequency of the magnetic moment
9
-1
and is on the order of 10 s . In all known systems where
there are detectable interactions between nanoparticles, the
remanence actually decays much more slowly than in this simple
model. Logarithmic decay has been reported for many systems,
including magnetic recording media. This is understood in terms
of a distribution of energy barriers, which may result from a
distribution of particle volumes, variations in the particle
orientations or local values of the magnetocrystalline anisotropy,
K, or differences in the local effective field due to magnetostatic
interactions. Using a simple model with a uniform energy barrier
loops was ∼6 nm, though smaller moment particles have shown
5
pronounced differences in AC susceptibility studies. We
compared the properties of samples of 7.0 ( 0.8 nm Fe
nanoparticles dispersed in hexane with different volume frac-
tions, ranging from 0.003 to 0.03%. This corresponds to aVerage
spacings between particle centers of 84 to 181 nm, which may
seem sufficient to neglect particle interactions, but significant
differences were observed.
For dilute dispersions of this particle size, there were only
small changes in the zero field-cooled magnetization as a
function of temperature. Small reductions were observed with
increasing concentration, but the error in determining the peak
temperature from our plots was ( 5 K, so this is only marginally
significant.
34
density over a finite energy width, the remanence has a
35
logarithmic time dependence, Mr(t)/M0 ) 1 - S ln(t/t0). Here
M0 is the magnetization at the time, t0, of the first remanent
measurement, and S is the characteristic slope of the decay. The
magnetic viscosity, S, is 0.019 for the 0.003 vol % sample and
Figure 4 shows the hysteresis loops. There are two main
changes as the particle concentration increases: the coercivity
decreases and the sample saturates at lower fields. The rema-
nence ratio was roughly constant at 0.29, but in all cases less
than the value of 0.5 expected for noninteracting uniaxial
particles. For cubic materials such as Fe that have (100) easy
axes, the theoretical remanence ratio is even higher, 0.8660.
Similar coercivity and rate of saturation trends were also seen
in the remanent hysteresis loops.
0
.010 for the more concentrated 0.03 vol % sample. The
magnetic viscosity can also be related to the distribution of
energy barriers, f(∆E), which is given by S/kT.
34,35
A large
viscosity indicates a large fraction of energy barriers within the
time window of the measurement. Table 1 summarizes the
magnetic properties of these dilute dispersions as a function of
concentration.
B. Dilute Dispersions Versus Arrays. The nanoparticle
arrays obviously have far greater concentrations than the dilute
dispersions, ranging from 28 to 46 vol % for the samples
discussed here. Comparison of the hysteresis loop for a
dispersion with that of an array made from the same particles
(Figure 6) shows similar characteristics to the dilute dispersions
with different concentrations, only more pronounced. The arrays
3
3
The magnetic relaxation in zero field (Figure 5) shows that
both samples have nearly logarithmic decay over the time
window studied (approximately one minute to 10 hours, or
2
4
∼
10 -10 s), and that the more concentrated sample has a
slower relaxation rate. Here the sample was saturated, and then

Feature Article
J. Phys. Chem. B, Vol. 109, No. 28, 2005 13413
Figure 6. Hysteresis loops for 9.3 ( 1.4 nm particles, as a 0.002 vol.
%
solution in hexane, and in nanoparticle arrays, at 10 K. The
magnetizations are normalized to the values at 50 kOe. The dilute
sample has a slower approach to saturation and a higher coercivity
than the arrays sample.
show much more rapid saturation than the dilute sample, and
they have a smaller coercivity (250 Oe versus 600 Oe). If we
compare the rate of magnetic relaxation for arrays made from
the same particles in Figure 7, the viscosity increases to 0.0225.
Table 2 summarizes the magnetic properties of these larger
particles in dilute dispersions and in arrays.
Figure 7. (a) Remanent hysteresis loops taken parallel and perpen-
dicular to the plane of arrays of 7.0 ( 0.8 nm Fe particles; (b) Magnetic
relaxation as a function of time, parallel and perpendicular to the plane
of the arrays.
In dilute ferrofluids there may be two peak temperatures of
the imaginary AC susceptibility, ø′′, but the higher temperature
occurs when the fluid is in a liquid rather than frozen state and
is associated with Brownian relaxation, in which the particles
TABLE 2: Comparison of Dilute Dispersions and Arrays of
9.3 ( 1.4 nm Particles
8
themselves rotate. A dilute, frozen ferrofluid therefore has a
single peak associated with magnetic moment rotation within
the particle. Figure 8 shows the temperature dependence of M′
and M′′ (corresponding to ø′ and ø′′, respectively) for arrays of
volume
remanent
blocking magnetic
fraction, hysteresis
hysteresis remanence temperature, viscosity,
xV
loop Hc(Oe) loop Hc(Oe) ratio, Mr/Ms
TB (K)
S
8
.5 nm nanoparticles, for two different excitation frequencies,
0.0002
0.602
600
400
850
0.32
0.20
0.32
120
75
0.023
0.014
and shows a peak plus a broad shoulder at higher temperatures.
The peak temperature shifted upward from 47 ( 2 K at 1 Hz
to 60 ( 5 K at 1000 Hz. There was no clear shift in the position
of the shoulder. The shape of this curve reflects the distribution
of energy barriers at zero field, which suggests that there are
many weakly coupled particles plus a smaller proportion of more
strongly coupled clusters. The upward shift in peak temperature
as the frequency increases reveals that as the time scale of
measurement is changed from 1 to 10 s, the proportion of
particles that are blocked over that time scale increases. This is
the reason that the blocking temperature that would be estimated
from Figure 8a is higher than that for the SQUID magnetometer
data, where the measurement time is much longer. The fact that
the shoulder is insensitive to frequency indicates that its
magnetization is stable over periods longer than 1 s.
C. Arrays with Different Conditions. To test for evidence
of significant interactions, the same sample was first measured
with the field parallel and then perpendicular to the applied field.
If there were no interaction effects, the results would be
identical. Because the arrays are essentially a thin film of
nanoparticles, interacting particles would be expected to show
shape anisotropy and should favor an in-plane magnetization.
Figure 7 shows remanent hysteresis loops for arrays 7.0 ( 0.8
nm particles, the same as those used for Figures 4 and 5. When
the applied field is perpendicular to the plane of the arrays, there
is a slower approach to saturation and a higher coercivity (450
Oe versus 330 Oe), which is consistent with a preference for
in-plane magnetization. At saturation, all of the particle moments
are perpendicular to the plane. When the field is reduced,
interactions cause the magnetization to rotate back into the plane,
and then larger fields in the opposite direction are needed to
rotate them out of plane again. Figure 7b shows that the
magnetic relaxation is faster when the applied field is perpen-
dicular to the sample plane. All remaining magnetic measure-
ments were made with the applied field parallel to the plane of
the TEM grids.
-
3
Next, changes in the magnetic behavior as a function of the
particle size were assessed by comparing the properties of 6.7
( 0.7 nm and 8.5 ( 1.0 nm particles. These particles had the
same oleic acid/oleylamine surfactant coating and an average
edge-to-edge interparticle spacing of 2.5 nm.

13414 J. Phys. Chem. B, Vol. 109, No. 28, 2005
Farrell et al.
Figure 8. (a) Real part of the AC magnetization as a function of
temperature, for 8.5 nm nanoparticle arrays; (b) Imaginary part of the
AC magnetization.
Figure 9a shows that the zero field-cooled magnetization
curve shifts to higher temperatures (TB ) 35 K versus 105 K)
and broadens considerably. The zero field cooling freezes in a
nearly random distribution of particle moments. When the field
is applied at low temperature, the measured magnetization is
low, unlike in the case for a bulk ferromagnet. As the
temperature is increased with the field on, more and more of
the particles have sufficient energy to surmount the barrier and
align with the applied field, so the magnetization increases. At
a certain point, the thermal energy exceeds the magnetic
potential energy associated with alignment, so the moments
become more disordered again and the magnetization decreases
at high temperature. The zero field cooled magnetization curve
will show a peak at the blocking temperature. A field cooled
magnetization curve is also measured, and some groups have
identified the point of deviation between the zero field cooled
and field cooled curves as TB, which typically gives slightly
higher values. The field that is applied during measurement can
also shift TB; ideally the smallest field that leads to a good
signal-to-noise ratio is used.
Figure 9. (a) Zero field cooled magnetization for 6.7 and 8.5 nm
particles; (b) Remanent hysteresis loops; (c) Magnetic relaxation as a
function of time.
is 100 seconds, while for M o¨ ssbauer spectroscopy or neutron
scattering, it is closer to a nanosecond time scale.
In dilute dispersions, the blocking temperature can be used
to estimate the magnetocrystalline anisotropy, K, found from
the relation KV ≈ kTln(τmf0) ≈ 25kT for the measurement time
of the SQUID magnetometer. Using this method, we estimated
5
3
K ) 7.7 ×10 ergs/cm for the 6.7 nm particles, and K ) 1.1
6
3
×
10 ergs/cm for the 8.5 nm particles. The bulk value for Fe
5
3
Above the blocking temperature thermal fluctuations are
sufficient to randomize the magnetic moment directions within
the measurement time, and they are said to be superparamag-
netic. Below TB, hysteresis is still observed and the particles
are said to be blocked. This is not a true phase transition, like
that between ferromagnetic and paramagnetic states at the Curie
temperature, because it depends on the measurement time. For
magnetometry measurements, the time between data points, τm,
is 5.2 × 10 ergs/cm . Our values could be slightly higher due
32
to their thin oxide shells (∼0.5 nm). K could also be
overestimated because of the finite size distributions. The zero
field cooled magnetization curve contribution from particles of
a given size depends on the fraction of particles with that size
times the particle volume, so larger particles are weighted more
heavily. Simulations as a function of the normalized size
36
distribution suggest that K could be overestimated by as much

Feature Article
J. Phys. Chem. B, Vol. 109, No. 28, 2005 13415
as a factor of 1.7 for the 8.5 nm particles and 1.3 for the 6.7
nm particles, based on the size distribution alone. When particles
interact magnetostatically, the peak temperature of the zero field
cooled magnetization may increase, but it cannot strictly be
interpreted in terms of a single particle volume and anisotropy.
The asymmetric nature of dipolar interactions makes it hard to
treat the results in terms of an effective anisotropy, though this
may be appropriate for the most dilute systems where there are
only pairs of interacting particles. The changes in the zero field
cooled magnetization as a function of temperature are best
understood as a shift in the energy barrier distribution. Here
the larger particles have on average higher energy barriers to
switching, and also a broader distribution of barriers that cannot
be attributed simply to the size distribution.
Remanent hysteresis loops show that the coercivity is slightly
smaller for the larger particles, but the most notable different
is in the rate of approach to saturation (Figure 9b). Arrays with
the larger particles also have a slower rate of magnetic relaxation
(Figure 9c). Over the first few data points collected, the magnetic
relaxation drops sharply and then decays logarithmically. Here
we have chosen M0 and t0 at the beginning of the logarithmic
portion. In all relaxation measurements, some drop is observed
due to the effect of changing the field in the magnetometer.
However, this effect is particularly pronounced in the arrays
and could be related to the rapid generation of flux closure
pathways.
If the particle spacing is reduced from 2.5 to 1.2 nm by
exchanging the oleic acid/oleylamine surfactant for hexanoic
acid/hexylamine, the properties of the arrays are also modified.
There is a small increase in the blocking temperature with the
smaller spacing, and the zero field cooled magnetization curve
is slightly broader (Figure 10a). With the reduced spacing, there
is a much more gradual approach to saturation in the remanent
hysteresis loop (Figure 10b). Figure 10c shows that arrays with
a smaller interparticle spacing have a slightly slower magnetic
relaxation rate. Table 3 summarizes the effects of changing the
particle size and spacing in self-assembled arrays.
Discussion
The overall picture of magnetic interactions in dilute disper-
sions and nanoparticle arrays is at first confusing. In the dilute
solutions, stronger interactions cause the sample to saturate at
lower fields, but in the arrays higher concentrations lead to
higher saturation fields. Going from a dilute to a more
concentrated dispersion decreased the viscosity; however,
concentrating the particles further by forming an array increases
S again. Finally, changing the dipole energy per pair of particles
in the arrays by roughly a factor of 2 leads to different results,
depending on whether this is accomplished by increasing the
particle size or by decreasing the interparticle spacing.
Figure 10. (a) Zero field cooled magnetization for 6.7 nm particles
with average edge-to-edge inteparticle spacings of 2.5 and 1.2 nm; (b)
Remanent hysteresis loops; (c) Magnetic relaxation as a function of
time.
A variety of models have been used to simulate the behavior
of monodomain particles based on magnetostatic interactions
that modify the distribution of energy barriers to switching.
of particles and mimimize the overall energy of the system to
6,7,19-21
find the magnetic ground state.
This energy includes the
5-19
sum of magnetostatic, anisotropy, and Zeemann terms. In
addition to this Monte Carlo approach, Landau-Lifshitz dynami-
There are two main theoretical approaches to understanding
magnetic nanoparticle interactions. The first builds on the
statistical nature of the interactions as a function of the
separation between particle moments, but does not explicitly
model the positions and orientations. Some groups have used
mean field methods15,17 or an empirical Vogel-Fulcher law.
The interacting particles have also been treated as a cluster glass.
Here the particles within a cluster switch collectively and the
stability of a cluster is determined by its size, but interactions
between clusters are ignored.10-12 The second group of models
explicitly monitors the moment directions within an ensemble
1
8
cal simulations have also been used to find the relaxed state
configuration. As the particle assembly becomes more concen-
trated, the approach of these granular models becomes more
important. Due to the finite volume of the particles and the
preference for self-assembling into close-packed structures, the
experimental distributions of particle separations may not agree
with simple statistical models. In addition, there is a need for
more realistic time- and temperature-dependent models in order
to develop a more intuitive understanding of the complex
collective behavior.
8

13416 J. Phys. Chem. B, Vol. 109, No. 28, 2005
Farrell et al.
TABLE 3: Comparison of Nanoparticle Arrays with Different Particle Size and Spacing
avg.
separation
(nm)
remanent
hysteresis
blocking
temperature,
size
nm)
volume
fraction, x
hysteresis
loop H (Oe)
remanence
magnetic
viscosity, S
(
V
c
loop H
c
(Oe)
ratio, M
r
/M
s
T
B
(K)
6
6
8
.7
.7
.5
2.5
1.2
2.5
0.280
0.458
0.460
300
415
250
660
760
400
0.31
0.35
0.32
35
45
105
0.025
0.028
0.013
TABLE 4: Comparison of Magnetostatic and Anisotropy Energies
avg.
sep.
(nm)
vol.
fraction,
V
pt
µ
pt
E
ms
-15
K
E
K
(10- cm3)
20
(10 emu)
-17
(10 ergs)
(10 ergs/cm )
4
3
(10 ergs)
-15
E
ms /E
K
size (nm)
x
v
5
7
7
9
6
6
8
.0 [1]
69
84
182
128
9.5
7.9
10.0
0.0002
0.0003
0.00003
0.0002
0.280
0.458
0.460
6.54
18.0
18.0
42.1
15.8
15.8
32.2
2.8
24.5
24.5
65.7
21.5
21.5
43.9
0.028
1.26
0.13
258
722
1180
2421
2.3
64
64
98
64
64
97
1.50
115
115
413
101
101
310
0.02
.0 ( 0.8
.0 ( 0.8
.3 ( 1.4
.7 ( 0.7
.7 ( 0.7
.5 ( 1.0
0.011
0.001
0.006
7.16
11.7
7.80
Experimentally there is consensus that time-dependent quanti-
ties such as the AC susceptibility and magnetic viscosity are
especially sensitive to interactions. However, there are conflict-
ing reports about whether the coercivity and the remanence ratio,
Mr/Ms, will increase or decrease with stronger interactions.
Unfortunately, there have been fewer studies of interaction
effects on the shape of hysteresis loops. Because the energy
barriers will change as the applied field magnitude increases,
this is a much more challenging problem to solve.
A particularly enlightening paper by Kechrakos and Trohidou
uses Monte Carlo methods to simulate the coercivity and
19
remanence at different temperatures. These results were scaled
as a function of the ratio of the dipolar and magnetocrystalline
anisotropy energies. The magnetostatic energy in different
systems was compared using values of the energy per pair of
Figure 11. Coercivity multiplied by the cube of the particle core
diameter, as a function of the magnetic volume fraction, x . (After
v
2
3
aligned dipoles, given by Ems ) µpt /4πa , where µpt ) MsV is
the particle moment and a is the center-to-center separation. In
Figure 9 the magnetic properties of samples with different
particle size are compared. Here Ems varies by a factor of 1.7.
Figure 10 shows data for samples with different interparticle
separation, where Ems is changed by a factor of 2.0. The
anisotropy energy was given by EK ) KV, where K is the
magnetocrystalline anisotropy and V is the particle volume.
Particles were placed in random but nonoverlapping positions,
and the magnetic properties were simulated both with and
without periodic boundary conditions. When these authors
compared their results with previous experimental findings,
however, they used a different expression for the magnetostatic
reference 19.)
From the schematic plot, they are correctly predicted to have
lower coercivities. Our data from Table 4 indicate that we are
somewhere between the regimes where there are only magne-
tostatic interactions and where the magnetostatic and anisotropy
energies are equal, so that the coercivity could either rise or
drop as the volume fraction increases. We find that as the
separation is reduced, so that EK is constant while Ems increases
and Ems/EK > 1, that the coercivity rises slightly. However, for
comparable changes in the volume fraction, when both EK and
Ems increase, Hc drops, but the schematic suggests that it should
not. The behavior of the coercivity is quite complex, and this
may not be the most useful parameter to reveal interaction
effects in concentrated samples.
2
3
energy, Ems ) µpt /d , where d is the particle diameter. In a
dilute, frozen ferrofluid d , a, and this greatly overestimates
the relative strength of magnetostatic interactions. Table 4 shows
Figure 12 shows a schematic predicting the behavior of the
remanence ratio as a function of the ratio of the thermal and
anisotropy energies. This predicts a higher remanence ratio for
dilute samples than for arrays of the same particles, since EK
dominates for the former and Ems for the latter. While
demagnetizing interaction causes lower remanence ratios than
predicted for noninteracting particles, we observe that this ratio
increases with stronger interactions. It predicts higher blocking
temperatures for the arrays, which have been reported by several
2
3
the values of Ems ) µpt /a and EK for one of the dilute
dispersions discussed by Kechrakos and Trohidou5 and for
the different dispersions and nanoparticle arrays whose proper-
ties are shown in Figures 4 through 10. Our data show a range
of 4 orders of magnitude in the ratio of Ems/EK, and over 4
orders of magnitude in the magnetic volume fraction, making
it a good test of theoretical predictions.
,15
Figure 11 shows a schematic plot that compares the predicted
coercivity as a function of the volume fraction from Kechrakos
and Trohidou. On the sides of the plot we indicate the regions
spanned by our experimental results. For the dilute dispersions
EK > Ems, and under these conditions the coercivity is predicted
to drop slightly with increasing concentration. Figures 4 and 6
show that our data agree. The arrays have higher volume
fractions than the dilute dispersion and also have Ems > EK.
1
5,25,26
groups.
It also predicts a relative insensitivity to the
concentration above a fraction of 0.16, which may partly explain
why the blocking temperature changes only slightly between
the 6.7 nm samples with different spacings. When we change
the magnetic volume fraction by roughly the same amount by
changing the particle size, this simultaneously increases the
anisotropy energy 3-fold. In a plot of the remanence ratio versus

Feature Article
J. Phys. Chem. B, Vol. 109, No. 28, 2005 13417
to a lower field being required for saturation. Because the
particle moments are stabilized by the fields from their
neighbors, the magnetic relaxation in zero field is slower, as
seen in Figure 5.
If we argue that the main effect of increasing the concentration
in dilute dispersions is to favor ferromagnetic interactions of
small numbers of particles, we must consider why the remanence
ratio of the dispersions is well below the statistically predicted
values. Dynamic light scattering has shown evidence of particle
clustering, even in fairly dilute liquid dispersions,32 so the
properties may in fact be dominated by separations well below
the statistical average spacing. Both the ability of the solvent
to stabilize the dispersion and possible phase separation upon
freezing may lead to nonstatistical distributions of particle
separations.
Figure 12. The remanence ratio as a function of the ratio between the
thermal and anisotropy energies, for different values of the relative
magnetostatic and anisotropy energies. (After reference 19.) If the
magnetostatic and anisotropy energies are comparable, the remanence
v
ratio is only weakly dependent on the magnetic volume fraction, x .
The experimental distribution of switching fields is propor-
tional to the derivative of a remanent hysteresis loop, dMr(H)/
dH, which is known as the irreversible susceptibility, øirr.øirr
and S are related by the fluctuation field, Hf, such that Hf )
temperature, this would be equivalent to having a higher
blocking temperature in the larger particles, as we observe
(Figure 9a).
In addition to agreeing with much of the behavior predicted
3
5
based on the ratio of the magnetostatic and anisotropy energies,
our data show new features that are not as well understood.
The broadening of the zero field cooled magnetization curve is
a signature of collective behavior, but it is less clear whether
the arrays are a true dipolar ferromagnet, such as that predicted
SM0/øirr. Hf is in turn sometimes associated with a switching
volume, V. Here Hf ) kT/MsV, and V is not necessarily equal
7
to the particle volume. Using these relations with our experi-
mental data, we find switching volumes smaller than the particle
volumes, and so this approach reveals little about the coupled
cluster sizes.
27
by Luttinger and Tisza, or if they are an assembly of interacting
blocked particles without any domain structure. At low enough
temperatures and short enough times, they will be ferromagnetic,
but here we consider the time and temperature scales of our
measurements (T g 10 K, t g 1 min). The arrays are not dilute
enough to have a sharp cusp in the magnetization versus
temperature curve, but they likely contain clusters of coupled
particle moments over a range of sizes. This makes them “spin
glass-like” rather than a true spin glass. The cluster relaxation
rates are still perturbed by the magnetization states of nearby
clusters, but not all scaling relations and critical exponents apply.
The degree of structural disorder has been shown to affect
For the dilute dispersions, the effect of magnetostatic coupling
is effectively to introduce anisotropy, in terms of a preference
for being magnetized in a particular direction at zero applied
field. When the particles are concentrated, the effective mag-
netostatic field is more appropriately viewed as arising from
19
the Lorentz cavity field from many particles. This is analogous
to the exchange-based magnetic interactions in magnetic alloys
such as Au:Fe and Cu:Mn as a function of the concentration of
magnetic atoms. At concentrations below ∼10 at. %, the alloy
is a spin glass containing single spins and small isolated clusters.
As the concentration increases, but below the percolation
threshold, the alloy is known as a cluster glass or mictomagnet,
with large interacting clusters but no long-range behavior.37 The
behavior of cluster glasses is still not well understood. The
clusters of coupled spins in the nanoparticle arrays are likely
to be larger than in the dilute ferrofluids, and the fields they
generate at the positions of other coupled clusters are likely to
be stronger. A cluster with a larger number of parallel spins
will have a higher switching field, just as the barrier for
magnetization reversal of a single particle increases with the
number of spins (i.e., with its volume). The arrays are likely to
have a much broader range of barrier heights because of the
possibility of many different cluster sizes. The field at a
particular particle will change as its neighbors reverse their
magnetization directions, and so the energy barrier distribution
will evolve, either as the applied field is varied in a hysteresis
loop, or as time increases in magnetic relaxation, or as the
temperature increases in zero field cooled magnetization mea-
surements. The reversal of some clusters at low applied fields
or short times could then increase the barriers for reversal of
the remaining clusters. This could explain the slower rates of
approach to saturation with the more strongly interacting
particles and why this feature is so much more pronounced than
the changes in Hc, as seen in Figures 9b and 10b. Half the
magnetic volume has a lower switching field than Hc, but the
coercivity is not necessarily the aVerage switching field. This
could also explain the lower magnetic relaxation rates with
stronger interaction strength in the arrays (Figure 9c and 10c).
25,26
the rate of relaxation,
but since the arrays studied here were
made with the same evaporative self-assembly method, we
assume that all of them have considerable disorder like that
shown in Figure 3. We note a marked difference in the rate of
approach to saturation in both the ordinary and remanent
hysteresis loops, as seen in Figures 4, 6, 7, 9, and 10. These
differences are more pronounced for the remanent loops, which
can be viewed as the integral of the switching field distributions.
This is also a reflection of the change in the energy barrier
distribution, but, unlike with the magnetic relaxation measure-
ments, these barriers are field-dependent.
Consider first the particle moments in a highly diluted
dispersion, well below the blocking temperature. If H ) 0, the
particle moments will lie along easy axes, and the magnetoc-
rystalline anisotropy will determine the energy barrier height
for magnetization reversal, and the measured magnetic properties
will agree with Stoner-Wohlfarth theory for noninteracting
particles. If the concentration is increased so that particles begin
to interact with each other, then the anisotropy is modified by
the field of the surrounding particle moments. The effective
anisotropy can be viewed as the energetic preference for a
particle to be magnetized in a particular direction. The net
magnetostatic field from other particles is likely to be mis-
aligned, relative to the easy axes of the particle, and so the effect
is to reduce the effective anisotropy, relative to Kmx. This will
lead to reduced values of the coercivity, as observed. The
interactions will also couple moments from different particles
so that they switch together, and with the reduced Hc, this leads

13418 J. Phys. Chem. B, Vol. 109, No. 28, 2005
Farrell et al.
Conclusions and Future Directions
In all cases we observe a reduced remanence ratio, relative
to the theoretical value for noninteracting particles, which
indicates that at zero field the overall interactions are primarily
demagnetizing. However, with increasing concentration the
degree of demagnetization weakens. The hysteresis loops all
show two different regimes: a rapid change in the magnetization
near the coercivity and a gradual approach to saturation. For
the most part, the coercivity drops as the volume fraction
increases. The rate of approach to saturation shows more
complex behavior, first increasing with more concentrated
dispersions, and when moving from dispersions to arrays, but
then decreasing when the strength of the magnetostatic interac-
tions within the arrays is further increased. The magnetic
relaxation at zero field shows logarithmic decay regions for all
samples. The magnetic viscosity associated with this decay
increases with concentration for the dilute dispersions, but
decreases for arrays made from larger particles that have higher
blocking temperatures, and therefore higher anisotropy energies.
The peak temperatures of the zero field cooled magnetization
showed modest reductions in the arrays, relative to the blocking
temperatures of dilute dispersions of the same particles. The
imaginary part of the AC susceptibility shows an additional
shoulder at higher temperature, in addition to the loss peak
similar to that in a dilute ferrofluid. The insensitivity to
frequency indicates that there are magnetic regions that are stable
on a time scale of 1 s or longer.
In a simplified picture of dilute dispersions with weak
interactions, the effect of the dipolar field is to generate an
effective anisotropy in clusters with small numbers of particles.
They are strongly coupled to each other and weakly coupled to
other clusters. The reversal of spins in one cluster does not
significantly affect the state of spins in another, over the time
and temperature ranges studied here. These frozen ferrofluids
act as ensembles of weakly interacting particle clusters, rather
than as a dipolar ferromagnet. In a dense assembly such as the
self-assembled nanoparticle arrays, however, magnetostatic
interactions between neighboring clusters will affect the local
demagnetizing field. It is feasible that in intermediate applied
fields a domain-like structure develops within the arrays that
contains flux closure pathways and therefore stabilizes some
of the particle moments against switching.
Unlike in magnetic-nonmagnetic metal alloys that have
exchange coupling, we cannot compare with the bulk Curie
temperature. It is therefore difficult to determine the concentra-
tion at which the cluster glass transforms into a dipolar
ferromagnet, with long-range order that is stable over time. Our
magnetic relaxation results show a significant remanent mag-
netization 10 hours after the applied field is removed, at 10 K,
so we have made samples with magnetic stability. However,
we cannot yet determine the nanoscale magnetization pattern
within the array. The AC susceptibility data suggest that a small
fraction of the particles within the array samples may be
responsible. Small angle neutron scattering experiments are
under way to determine the magnetic coherence lengths in the
arrays.
Figure 13. Uniform structures grown with 7.0 nm Co nanoparticles.
(a) Faceted nanoparticle crystal; (b) Langmuir monolayer of 7.0 nm
Co nanoparticles showing order over large areas.
the formation of large area Langmuir layers of nanoparticles
(
Figure 13), and the synthesis of cubic nanoparticles with
3
9
controlled crystallographic orientation offer promise. There
is room for improvement in increasing the particle moment and
decreasing the interparticle separation without sacrificing the
regularity of the ordering. Improved nanoscale magnetic char-
acterization techniques applicable to small patterned structures
would be beneficial. In magnetic measurements it will be
important to determine the sizes of the coupled clusters of
magnetic nanoparticles and see how they vary as a function of
time and temperature. These clusters correspond to the domains
of a bulk ferromagnet, but little is understood about how they
evolve. AC susceptibility, neutron scattering, X-ray magnetic
circular dichroism, and electron holography may all be useful
tools for determining the domain sizes. On the theoretical front,
there is a need for improved time and temperature-dependent
simulations of the magnetic switching within nanoparticle
assemblies, so that the onset of collective behavior can be
explored more fully. Up until now, most models have treated
magnetostatic interactions as a perturbation to the behavior of
isolated particles, rather than as a new form of nanocomposite
ferromagnet without exchange effects. More detailed experi-
mental and theoretical data can provide the input for the
development of such a model.
There are a number of interesting directions for future work
on magnetic nanoparticle interactions. As we have demonstrated,
even with narrow size distributions and good control of the
interparticle spacing, it is difficult to make quantitative predic-
tions of the magnetic properties. On the synthetic front, there
is a need to prepare macroscopic samples with even greater
structural uniformity. Here the growth of nanoparticle crystals
Acknowledgment. S.A.M. thanks the National Science
Foundation (CTS-0227645) and the Petroleum Research Fund
of the American Chemical Society (ACS-PRF-37578-AC5) for
financial support. Ames Laboratory is operated by Iowa State
University for the Department of Energy under Contract No.
W-7405-ENG-82.
3
8
through the slow diffusion of a poorly coordinating solvent,

Feature Article
J. Phys. Chem. B, Vol. 109, No. 28, 2005 13419
References and Notes
(19) Kechrakos, D.; Trohidou, K. N. Phys. ReV. B 1998, 58, 12169-
1
2177.
(
1) Hess, P. H.; Parker, P. H., Jr. J. Appl. Polym. Sci. 1966, 10, 1915-
(20) Petit, C.; Russier, V.; Pileni, M. P. J. Phys. Chem. B 2003, 107,
1
5
1
927.
10333-10336.
(2) Griffiths, C. H.; O’Horo, M. P.; Smith, T. W. J. Appl. Phys. 1979,
(
21) Russier, V.; Petit, C.; Legrand, J.; Pileni, M. P. Phys. ReV. B 2000,
0, 7108.
6
2, 3910.
(
3) Grinstaff, M. W.; Salamon, M. B.; Suslick, K. S. Phys. ReV. B
(22) Lalatonne, Y.; Motte, L.; Russier, V.; Ngo, A. T.; Bonville, P.;
993, 48, 269.
Pileni, M. P. J. Phys. Chem. B 2004, 108, 1848-1854.
(
4) Park, S. J.; Kim, S.; Lee, S.; Zhim, Z. G.; Char, Kookrin; and
Hyeon, T. J. Am. Chem. Soc. 2000, 122, 8581-8582.
5) Luo, W.; Nagel, S. R.; Rosenbaum, T. F.; Rosensweig, R. E. Phys.
ReV. Lett. 1992, 67, 2721-2724.
6) Chantrell, R. W.; Fearon, M.; Wohlfarth, E. P. Phys. Status Solidi
A 1986, 97, 213.
(
(
23) Puntes, V. F.; Krishnan, K. M. IEEE Trans. Magn. 2001, 37, 2210.
24) Garcia-Otero, J.; Porto, M.; Rivas, J.; Bunde, A. Phys. ReV. Lett.
(
2
000, 84, 167-170.
(
25) Farrell, D.; Ding, Y.; Sanchez-Hanke, C.; Kao, C.-C.; Majetich, S.
A. J. Appl. Phys. 2004, 95, 6636.
26) Farrell, D.; Cheng, Y.; Ding, Y.; Yamamuro, S.; Sanchez-Hanke,
(
(
(
7) O’Grady, K.; El-Hilo, M.; Chantrell, R. W. IEEE Trans. Magn.
C.; Kao, C.-C.; Majetich, S. A. J. Magn. Magn. Mater. 2004, 282, 1-5.
1
993, 29, 2608.
(
27) Luttinger, J. M.; Tisza, L. Phys. ReV. 1946, 70, 954
8) Zhang, J.; Boyd, C.; Luo, W. Phys. ReV. Lett. 1996, 77, 390.
(28) Stoner, E. C.; Wohlfarth, E. P. Trans. R. Soc. London 1948, A240,
5
99.
F.; Mørup, S. Phys. ReV. Lett. 1997, 79, 5154.
10) Humfeld, K. D.; Giri, A. K.; Majetich, S. A.; Venturini, E. L. IEEE
Trans. Magn. 2001, 37, 21994.
11) Chamberlin, R. V.; Humfeld, K. D.; Farrell, D.; Yamamuro, S.;
Ijiri, Y.; Majetich, S. A. J. Appl. Phys. 2001, 91, 6961.
12) Chamberlin, R. V.; Hemberger, J.; Loidl, A.; Humfeld, K. D.;
Farrell, D.; Yamamuro, S.; Ijiri, Y.; Majetich, S. A. Phys. ReV. B 2002, 66,
72403.
13) Mørup, S.; Madsen, M. B.; Frank, J.; Villadsen, J.; and Koch, C.
J. W. J. Magn. Magn. Mater. 1983, 40, 163.
14) Jonsson, T.; Nordblad, P.; Svedlindh, P. Phys. ReV. B 1998, 57,
97.
(
(
(
(
(
29) Brown, W. F., Jr. J. Appl. Phys. 1959, 30S, 130S.
30) Meikeljohn, W. H.; Bean, C. P. Phys. ReV. 1956, 102, 1413.
31) N e´ el, L. Ann. G e´ ophys. 1949, 5, 99.
32) Street, R.; Woolley, J. C. Proc. Phys. Soc. A 1949, 62, 562.
33) Farrell, D.; Majetich, S. A.; Wilcoxon, J. P. J. Phys. Chem. B 2003,
(
(
(
1
07, 11022.
(34) Chikazumi, S. Physics of Magnetism; John Wiley and Sons: New
1
York, 1964; p. 100.
(
(35) An alternative expression is sometimes used for the magnetic
viscosity, M(t) ) Mo - S lnt. This leads to viscosities with awkward units,
and we therefore use the dimensionless version.
(36) Sappey, R.; Vincent, E.; Hadacek, N.; Chaput, F.; Boilot, J. P.;
Zins, D. Phys. ReV. B 1997, 56, 14551.
(
4
(15) Dormann, J.; Bessais, L.; Fiorani, D. J. Phys. C 1988, 21, 2015.
16) Hendriksen, P. V.; Mørup, S.; Christiansen, G.; Jacobsen, K. W.
(
Magnetization Reversal in Clusters of Magnetic Particles, In Science and
Technology of Nanostructured Magnetic Materials; Hadjipanayis, G., Prinz,
G. A., Eds.; Plenum Press: New York, 1992; p. 573.
(37) Mydosh, J. A. Spin Glasses: An Experimental Introduction; Taylor
and Francis: London, Washington, DC, 1993; p. 36.
(38) Talapin, D. V.; Shevchenko, E. V.; Kornowski, A.; Gaponik, N.;
Haase, M.; Rogach, A. L.; Weller, H. AdV. Mater. 2001, 13, 1868.
(39) Dumestre, F.; Chaudret, B.; Amiens, C.; Renaud, P.; Fejes, P.
Science 2004, 303, 821-823.
(
17) Mørup, S.; Tronc, E. Phys. ReV. Lett. 1994, 72, 3278.
(18) Held, G. A.; Grinstein, G.; Doyle, H.; Sun, S.; Murray, C. B. Phys.
ReV. B 2001, 64, 012408.