Inter-particle interactions in composites of antiferromagnetic nanoparticles

Article abstract of DOI:10.1016/S0304-8853(03)00453-0

We have prepared mixtures of α-Fe₂O₃, CoO, and NiO nanoparticles by drying aqueous suspensions of the particles. The magnetic properties were studied by Mo?ssbauer spectroscopy. The measurements showed that interactions with CoO particles suppress the superparamagnetic relaxation of both α-Fe₂O₃ and ⁵⁷Fe-doped NiO particles. The effect of NiO particles on α-Fe₂O₃ particles was a shorter relaxation time and an induced Morin transition, which usually is absent in α-Fe₂O₃ nanoparticles. Spectra of α-Fe₂O₃ particles, prepared by drying suspensions with added Co²⁺ and Ni²⁺ ions, showed that the suspension medium can affect the magnetic properties of the α-Fe ₂O₃ particles significantly, but not in the same way as the CoO or NiO nanoparticles. Therefore, a strong inter-particle exchange interaction between particles of different materials seems to be responsible for the magnetic properties of the nanocomposites.

Full text of DOI:10.1016/S0304-8853(03)00453-0

ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 266 (2003) 36–48
Inter-particle interactions in composites of
antiferromagnetic nanoparticles
Cathrine Frandsen*, Steen M^rup
Department of Physics, Technical University of Denmark, Bldg. 307, Lyngby DK-2800 KGS., Denmark
Received 24 October 2002; received in revised form 19 December 2002
Abstract
2 3
We have prepared mixtures of a-Fe O , CoO, and NiO nanoparticles by drying aqueous suspensions of the particles.
The magnetic properties were studied by M o. ssbauer spectroscopy. The measurements showed that interactions with
7
5
CoO particles suppress the superparamagnetic relaxation of both a-Fe O and Fe-doped NiO particles. The effect of
2
3
NiO particles on a-Fe
absent in a-Fe nanoparticles. Spectra of a-Fe
Ni ions, showed that the suspension medium can affect the magnetic properties of the a-Fe O particles significantly,
2 3
O particles was a shorter relaxation time and an induced Morin transition, which usually is
2
+
2
O
3
2 3
O particles, prepared by drying suspensions with added Co and
2
+
2
3
but not in the same way as the CoO or NiO nanoparticles. Therefore, a strong inter-particle exchange interaction
between particles of different materials seems to be responsible for the magnetic properties of the nanocomposites.
r 2003 Elsevier B.V. All rights reserved.
PACS: 75.50.Tt; 76.80.+y; 75.70.Cn
Keywords: Nanoparticles; M o. ssbauer spectroscopy; Inter-particle interactions; Superparamagnetic relaxation; Nanocomposite
1
. Introduction
results of these studies, it also seems interesting to
investigate the interaction between different anti-
ferromagnetic materials.
Many studies have been undertaken on samples
of magnetic nanoparticles in order to characterise
the influence of inter-particle interactions on the
magnetic properties. Both dipole–dipole interac-
tion between ferro- or ferrimagnetic particles and
exchange interaction between epitaxially grown
ferro- and antiferromagnetic thin films have
attracted considerable attention. Based on the
Previous studies of samples of antiferromagnetic
nanoparticles have shown that the superparamag-
netic relaxation of a-FeOOH [1], a-Fe O [2], and
2
3
5
7
Fe-doped NiO [3] nanoparticles can be strongly
influenced by inter-particle interactions. The re-
laxation of the sublattice magnetisation is signifi-
cantly suppressed when the particles are allowed to
aggregate. Because of the small dipole moment of
the antiferromagnetic particles, the dipole–dipole
interaction is negligible and the interaction is
dominated by exchange interactions across the
particle interfaces [1,2]. Only a few exchange
*
Corresponding author. Tel.: +45-45-25-31-68; fax: +45-45-
3-23-99.
E-mail address: cathrine.frandsen@fysik.dtu.dk
C. Frandsen).
9
(
0304-8853/03/$ - see front matter r 2003 Elsevier B.V. All rights reserved.
doi:10.1016/S0304-8853(03)00453-0

ARTICLE IN PRESS
C. Frandsen, S. M^rup / Journal of Magnetism and Magnetic Materials 266 (2003) 36–48
37
bridges between surface atoms of neighbouring
crystallites are needed to account for the interac-
tion strength [2].
of about 20 nm and a minor impurity (o10%) of
metallic Co.
5
7
Samples of pure particles (a-Fe O and Fe-
2
3
The results of studies of interaction between
magnetic nanoparticles of the same material open
the question of possible interaction effects in
samples containing magnetic nanoparticles of
different materials. Studies of multilayers of
different magnetic materials have already shown
interesting features. For example, van der Zaag
et al. [4] have shown that the N e! el temperature of
doped NiO) and mixtures of a-Fe O +NiO, a-
2
3
57
Fe O +CoO, and Fe-doped NiO+CoO (all in
2
3
weight ratios 1:1) were prepared by pouring 50 mg
of each compound into 100 ml of a ‘‘suspension
medium’’. Within this liquid, the particles were
exposed to intense ultrasound for 15 min in order
to break apart agglomerates of particles and to
obtain homogeneous mixtures. The particles were
then allowed to settle and dry at room temperature
in an open petri bowl. Initially, we had chosen
demineralised water as the suspension medium.
We also studied samples of a-Fe O nanoparticles,
(
thin antiferromagnetic CoO layers (o50 A) is
enhanced above its bulk value (293 K), when
epitaxially grown on ferrimagnetic Fe O . If
3
4
similar interaction effects are present in compo-
sites of nanoparticles, it may be possible to design
magnetic materials with new properties by mixing
nanoparticles of different materials.
2
3
prepared by drying suspensions of particles in
aqueous solutions of NiCl or Co(NO ) . Samples
2
3 2
of a-Fe O particles were also prepared by drying
2
3
Here we present the results of a study of
interactions in mixtures of antiferromagnetic
nanoparticles. By use of M o. ssbauer spectroscopy
we have studied how the magnetic dynamics of a-
aqueous suspensions with a range of pH values
(1–8). The suspensions with different pH values
were prepared by first adjusting the pH value of a
suspension of hematite particles to 13.5 by adding
NaOH. This results in formation of a stable
suspension of the particles. Then in eight separate
batches the pH was decreased to 1, 2,y, or 8 by
5
7
Fe O and
Fe-doped NiO nanoparticles is
2
3
affected by neighbouring antiferromagnetic nano-
particles of other materials. The mixtures we
investigated are a-Fe O +CoO, a-Fe O +NiO,
adding HNO and the samples were allowed to dry
2
3
2
3
3
5
7
and Fe-NiO+CoO. The results of some pre-
liminary studies have been published elsewhere [5].
In the present work, we have also assessed whether
the effects seen in the spectra are solely caused by a
pure particle–particle interaction or as an effect of
the mixing process, e.g. ion adsorption on the
particle surfaces.
at room temperature. As a reference for the
measurements of the interacting particles, a
suspension of non-interacting a-Fe O particles
2
3
was made by coating the suspended particles with
oleic acid and then permanently suspending them
in heptane. The concentration of a-Fe O in the
2
3
suspension was 0.13 vol%. This corresponds to
ꢁ
1
7
1
mg a-Fe O ml . The amount of surfactant was
2
ꢁ
3
1
2 mg ml . This sample will be referred to as the
2
. Experimental details
‘‘a-Fe O ferrofluid’’.
2
3
5
The samples were studied by F e M o. ssbauer
7
A batch of several grams of 9 nm a-Fe O
hematite) nanoparticles was synthesized by means
spectroscopy using constant-acceleration spectro-
2
3
5
7
(
meters with sources of Co in rhodium. Spectra in
the temperature range 17–300 K were obtained
using a closed cycle helium refrigerator from APD
Cryogenics Inc and a temperature controlled
liquid nitrogen cryostat. The spectrometers were
calibrated with a 12.5 mm thick a-Fe foil at room
temperature. Isomer shifts are measured relative to
that of the calibration spectra.
of a modified gel–sol method developed by
Sugimoto et al. [6]. NiO nanoparticles were
prepared by annealing chemically precipitated
5
7
Ni(OH) (with and without Fe doping) [3,7] at
2
ꢀ
3
00 C in air for 3 h. These particles are disc shaped
with an average diameter of 12 nm and a thickness
of about 2 nm [3]. Particles of CoO were synthe-
sized by annealing cobalt acetate in an argon
X-ray diffraction (XRD) was performed using a
PW 1390 Philips diffractometer with a CuKa
ꢀ
atmosphere at 350 C for 4 h yielding a particle size

ARTICLE IN PRESS
38
C. Frandsen, S. M^rup / Journal of Magnetism and Magnetic Materials 266 (2003) 36–48
radiation source. In addition to identifying the
structure of the particles by XRD, the particle size
was determined from the broadening of the line
profiles.
temperature, defined as the temperature at which
the sextet and the doublet have identical areas, is
about 70 K.
Fig. 1b shows spectra of a-Fe O particles that
2
3
Transmission electron microscopy (TEM)
images were obtained by a Philips EM 430
operated at voltages up to 300 kV.
have been allowed to aggregate during drying of
an aqueous suspension and thus interact. Compar-
ison with the spectra in Fig. 1a clearly shows that
the magnetic properties have changed dramatically
because of the enhanced interaction. The spectra
of the interacting particles do not collapse into a
doublet even above 250 K, but with increasing
temperature the average hyperfine field decreases
and the lines of the sextet become asymmetrically
broadened. Similar spectra have been observed in
several other studies of interacting magnetic
nanoparticles [1–3,8,9] and have been explained
by an ordering of the sublattice magnetisation
directions of the particles induced by inter-particle
exchange interactions of varying strengths. This is
discussed in Section 4.1.
3
. Results
3
nanoparticles
.1. Relaxation in samples of pure a-Fe O3
2
The M o. ssbauer spectra of the a-Fe O ferrofluid
2
3
(Fig. 1a) show a typical superparamagnetic beha-
viour. At low temperatures the spectra are
dominated by a sextet, but at the highest
temperature (180 K) the spectrum consists of a
doublet. At intermediate temperatures the spectra
can be described as a superposition of a sextet and
a doublet, both with relatively narrow lines,
indicating that most of the particles have either
much longer or much shorter relaxation times than
the time scale of M o. ssbauer spectroscopy
3.2. Relaxation in mixtures of different
nanoparticles
Figs. 2a and b show the M o. ssbauer spectra of
the a-Fe O particles mixed with CoO and NiO
ꢁ
9
(
B5 ꢂ 10 s). The superparamagnetic blocking
2
3
α-Fe O ferrofluid
α-Fe O
2
3
2
3
(a)
(b)
1
80 K
20 K
300 K
250 K
1
1
00 K
180 K
120 K
80 K
8
0 K
0 K
5 K
5
2
25 K
-
12
-8
-4
0
4
8
12 -12
Velocity (mm/s)
-8
-4
0
4
8
12
Fig 1. M o. ssbauer spectra obtained at the indicated temperatures of: (a) the a-Fe
2 3 2 3
O ferrofluid and (b) dried a-Fe O nanoparticles.

ARTICLE IN PRESS
C. Frandsen, S. M^rup / Journal of Magnetism and Magnetic Materials 266 (2003) 36–48
39
α-Fe O3 + CoO
α-Fe2O3 + NiO
2
(a)
(b)
295 K
250 K
180 K
120 K
250 K
180 K
120 K
100 K
80 K
80 K
20 K
20 K
-
12
-8
-4
0
4
8
12 -12
Velocity (mm/s)
-8
-4
0
4
8
12
Fig. 2. M o. ssbauer spectra of a-Fe
2 3
O nanoparticles mixed with (a) CoO and (b) NiO nanoparticles.
nanoparticles, respectively. When the a-Fe O
180 K and above, the spectra also contain a
doublet with narrow lines. Thus, interaction between
the a-Fe O nanoparticles and NiO nanoparticles
2
3
particles are mixed with the CoO particles the
spectra consist of sextets with relatively sharp lines
up to 180 K. At temperatures of 250 K and above,
a doublet appears in the spectra. At temperatures
above 80 K the lines of the sextet are clearly
narrower than those of the sample consisting
2
3
affects the relaxation behaviour of a-Fe O particles
2
3
in a way that is different from the interaction
between a-Fe O and CoO particles.
Fig. 3a and b show, respectively, M o. ssbauer
2
3
5
spectra of a sample of interacting Fe-doped NiO
7
solely of interacting a-Fe O
(
nanoparticles
Fig. 1b). In Fig. 1b, there is, however, not a
2
3
5
7
nanoparticles and Fe-doped NiO nanoparticles
from the same batch mixed with CoO nanoparti-
cles. In both samples, the spectra consist of a
superposition of a singlet and a sextet in a
relatively large temperature range. The blocking
temperature in the sample of interacting NiO
particles is about 140 K, but it increases when the
particles are mixed with CoO particles.
clearly visible doublet even at the highest tem-
peratures. Therefore, it seems that the relaxation
behaviour of the hematite particles mixed with
CoO is quite different from that in the sample
consisting solely of interacting a-Fe O particles.
2
3
The spectra of the a-Fe O +CoO sample have
2
3
similarities with those of non-interacting a-Fe O
2
3
particles, but the blocking temperature is much
higher. The same behaviour was seen for a-Fe O
3.3. The Morin transition in a-Fe O nanoparticles
2
3
2
3
nanoparticles mixed with CoO particles, which
contained no metallic Co impurity [5].
In bulk a-Fe O , the Morin transition takes
2
3
The evolution with temperature of the spectra of
a-Fe O particles mixed with NiO, shown in
place as a first-order transition at T C263 K [10].
At this temperature, the spin structure changes
M
2
3
Fig. 2b, is somehow between those seen in
Figs. 1a and b. The sextets are considerably
broadened at the highest temperatures, but at
from being confined to lie in the rhombo-
hedral (1 1 1) plane above TM to lying along
the [1 1 1] axis below TM: This magnetic phase

ARTICLE IN PRESS
40
C. Frandsen, S. M^rup / Journal of Magnetism and Magnetic Materials 266 (2003) 36–48
5
7
57Fe-NiO + CoO
Fe-NiO
(a)
(b)
3
2
1
1
00 K
50 K
80 K
20 K
295 K
250 K
180 K
120 K
80 K
8
0 K
20 K
20 K
-
12
-8
-4
0
4
8
12 -12
-8
-4
0
4
8
12
Velocity (mm/s)
57
57
Fig. 3. M o. ssbauer spectra of: (a) Fe-doped NiO nanoparticles and (b) Fe-doped NiO nanoparticles mixed with CoO nanoparticles.
transition is clearly visible in M o. ssbauer spectra
because the quadrupole shift changes sign and
to the width of line 1. The presence of a Morin
temperature was also observed in several other
samples consisting of mixtures of a-Fe O and
ꢁ
1
magnitude (from e ¼ ꢁ0:1 mm s
above TM to
2
3
ꢁ
1
e ¼ þ0:2 mm s below TM). In small particles of
a-Fe O , the transition temperature decreases with
NiO nanoparticles with other particle sizes and
morphologies. The low-temperature spectra were
fitted with two sextets. One of these corresponds to
2
3
decreasing particle size and it has been reported
that there is no Morin transition above liquid
helium temperature in particles with diameters
below about 20 nm [11–13].
ꢁ
1
the low-temperature state with e ¼ þ0:2 mm s
The other component did not show a quadrupole
.
ꢁ
1
shift of about ꢁ0.1 mm s as expected for a-Fe O
2
3
In the spectra of the samples of pure 9 nm a-
Fe O nanoparticles (Figs. 1a and b) there is as
particles above the Morin transition, but a value
close to zero. In some studies of a-Fe O
2
3
2
3
expected no indication of a Morin transition.
The quadrupole shift is negative in all the
magnetically split spectra at low temperatures
nanoparticles and Al-substituted hematite sam-
ples, similar values for the quadrupole shift have
been found [12]. The observations suggest that the
sublattice magnetisation in a temperature range is
neither fixed in the [1 1 1] direction nor in the (1 1 1)
plane.
ꢁ
1
(
eD ꢁ 0:1 mm s ) as in bulk a-Fe O above the
2
3
Morin transition temperature. This is also the case
in all spectra of a-Fe O nanoparticles mixed with
2
3
CoO (Fig. 2a). However, surprisingly, the a-Fe O3
2
particles mixed with NiO nanoparticles (Fig. 2b)
show a Morin transition at low temperature. At
3.4. Influence of added cations and pH
2
+
0 K the spectrum has a quadrupole shift close to
We have made a number of experiments to
investigate the possible influence of adsorbed
ꢁ
1
0.2 mm s . With increasing temperature up to
2
Co or Ni ions on the magnetic properties of
+
2+
B160 K there is a gradual change of the spectra,
indicating a Morin transition. This is most clearly
seen in the broadening of line number 6 compared
the a-Fe O nanoparticles. The samples were
2
3
prepared by using suspension media with various

ARTICLE IN PRESS
C. Frandsen, S. M^rup / Journal of Magnetism and Magnetic Materials 266 (2003) 36–48
41
2
+
α-Fe2O3 + Co2+ (Fe:Co=5)
(b)
α-Fe O + Co (Fe:Co=38)
2
3
(a)
2
2
1
1
95 K
50 K
80 K
20 K
295 K
250 K
180 K
120 K
80 K
8
0 K
20 K
17 K
-
12
-8
-4
0
4
8
12 -12
Velocity (mm/s)
-8
-4
0
4
8
12
2
+
Fig. 4. M o. ssbauer spectra of a-Fe
2
O
3
nanoparticles prepared by drying suspensions of the particles in aqueous solutions of Co ions:
(a) cation ratio Fe:Co=38 and (b) cation ratio Fe:Co=5.
2
+
α-Fe2O3+ Ni2+ (Fe:Ni=4)
α-Fe O + Ni (Fe:Ni=27)
2
3
(a)
(b)
295 K
250 K
180 K
120 K
100 K
295 K
250 K
180 K
120 K
80 K
25 K
20 K
-12
-8
-4
0
4
8
12 -12
Velocity (mm/s)
-8
-4
0
4
8
12
2
+
Fig. 5. M o. ssbauer spectra of a-Fe
2 3
O nanoparticles prepared by drying suspensions of particles in aqueous solutions of Ni ions:
(a) cation ratio Fe:Ni=27 and (b) cation ratio Fe:Ni=4.

ARTICLE IN PRESS
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C. Frandsen, S. M^rup / Journal of Magnetism and Magnetic Materials 266 (2003) 36–48
2
+
2+
concentrations of Co
or Ni
ions. Some
as an introduction to the discussion of the features
of the nanocomposites.
typical temperature series of M o. ssbauer spectra
are shown in Figs. 4 and 5. By comparing the
spectra in Fig. 4a with those in Fig. 1b, it can
In the spectra of non-interacting particles
(Fig. 1a) a doublet appears at relatively low
temperatures. The relative area of the doublet
increases with temperature at the expense of the
sextet. At 180 K the spectrum only contains the
doublet component. (The small asymmetry of
the doublet is an effect of the relaxation time being
2
+
be seen that small amounts of Co
(about the
amount needed to form a monolayer on the
hematite particles) result in narrower lines of
the sextet at the highest temperatures. The spectra
in Fig. 4a do, however, not contain a doublet as
the spectra of a-Fe O particles mixed with CoO.
Larger amounts of Co
doublet component at the highest temperatures
indicating the presence of particles with short
relaxation times. When Ni ions are added (Figs.
a and b) the spectra obtained at the highest
temperatures contain a doublet, which is especially
dominating in the sample with the highest Ni
concentration. It is notable that in contrast to the
ꢁ
10
of the order of 10 s [16].) Both components have
relatively narrow lines in the whole temperature
range. Similar spectra have been found in numerous
other studies of nanoparticles of various magnetic
materials. It is often assumed that the magnetic
anisotropy of magnetic nanoparticles is uniaxial
with the anisotropy energy given by
2
3
2
+
(Fig. 4b) result in a
2
+
5
2
+
2
EðyÞ ¼ KV sin y;
ð1Þ
sample of a-Fe O particles mixed with NiO, there
where K is the magnetic anisotropy constant, V
the particle volume, and y the angle between the
(sublattice) magnetisation direction and an easy
direction of magnetisation. The expression for the
magnetic anisotropy energy of a-Fe O is more
2
3
is no Morin transition in the samples prepared
2
with Ni ions.
+
High-resolution TEM studies of agglomeration
in samples of TiO2 nanoparticles [14,15] have
shown that the pH of the suspension medium can
have an important influence on the way particles
aggregate. We therefore tried to change the pH of
the aqueous solution in which a-Fe O particles
2
3
complex than Eq. (1) [10,16], but for simplicity we
use Eq. (1) in the following discussion. A detailed
discussion of the magnetic energy of a-Fe O
2
3
2
3
nanoparticles is given elsewhere [2,16].
were suspended to see if this had an effect on the
properties of the dried samples. All samples,
prepared with pH values ranging from 1 to 8,
yielded spectra like those shown in Fig. 1b. Thus,
the pH of the suspension medium had no influence
on the relaxation behaviour of the dried samples.
The superparamagnetic relaxation time of mag-
netic nanoparticles with magnetic energy given by
Eq. (1), i.e. the average time between transitions
across the energy barrier, separating the minima at
y ¼ 0 and y ¼ 180 ; is given by the N e! el–Brown
expression [17,18]
ꢀ
ꢀ
t ¼ t0 expðKV=kBTÞ;
ð2Þ
4
. Discussion
where kB is Boltzmann’s constant and T the
ꢁ
12
temperature. t is typically in the range 10
–
10 s and depends weakly on temperature [18].
0
ꢁ
9
4
.1. M o. ssbauer spectra of non-interacting and
ꢁ11
interacting a-Fe O particles
For 9 nm a-Fe O particles, t0E10 s [13]. The
2
3
2
3
temperature dependence of the relaxation time for
non-interacting a-Fe O particles has previously
As illustrated in Fig. 1, the evolution with
temperature of the M o. ssbauer spectra of samples
of non-interacting and interacting a-Fe O parti-
cles is quite different. In both cases, the low-
temperature spectra consist of a sextet with
relatively narrow lines, but at higher temperatures,
substantial differences are seen. We will use these
spectra and the theoretical interpretation of them
2
3
[13,16] been found to be in accordance with
Eq. (2). Spectra like those shown in Fig. 1a can
be well fitted with the Blume–Tjon model [19] for
M o. ssbauer relaxation spectra when taking the
particle size distribution into account [2,13,16].
At intermediate temperatures, some of the
particles will have relaxation times of the order
2
3

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43
of 10ꢁ9–10ꢁ8 s and these particles will give
contributions with broad lines [19]. However, if
250 K. The spectra are dominated by sextets with
broad lines far above the temperature where the
spectra of the non-interacting particles have
collapsed to a doublet. The magnetic energy of a
ꢁ10
t0o10
s, the exponential dependence of the
relaxation time in conjunction with the particle
size distribution results in a very broad distribu-
tion of relaxation times such that only a small
fraction of the particles have relaxation times in
this range. The contribution of these particles to
the spectra is therefore almost negligible. This is
discussed in more detail elsewhere [20].
particle, i; with volume V ; which interacts with its
i
neighbours, j; may be written [1,2]
Ei ¼ KVi sin y ꢁ Mi ꢃ
X KijMj:
ð4Þ
2
j
Here Mi and Mj represent the (sublattice)
magnetisation of the particles i and j; respectively.
Kij represents the effective exchange coupling
constant originating from exchange coupling
between surface atoms of the particles i and j: If
the anisotropy term (the first term) in Eq. (4) is
predominant, superparamagnetic relaxation of the
magnetisation may take place between orienta-
tions of the sublattice magnetisation along the easy
axes close to y ¼ 0ꢀ and 180 . In this case the
distribution of the values of the energy barriers
Below the superparamagnetic blocking tempera-
ture, the (sublattice) magnetisation vectors fluc-
tuate in directions close to the easy directions of
magnetisation. These fluctuations (collective mag-
netic excitations) are usually fast compared to the
time scale of M o. ssbauer spectroscopy and result in
a reduction in the magnetic splitting of the spectra
given by [21,22]
ꢀ
BobsCB f1 ꢁ k T=ð2 KVÞg;
ð3Þ
0
B
where B0 is the magnetic hyperfine field in the
absence of these fluctuations. The maximum
reduction will normally not exceed 10–15%,
because further increase of the temperature or
decrease of the particle size results in fast super-
paramagnetic relaxation [22], i.e. the spectrum
collapses to a doublet. Collective magnetic excita-
tions in conjunction with the particle size distribu-
tion results in some line broadening, but because
the reduction of the magnetic splitting is less than
(KV ) in a typical sample results in a broad
i
distribution of relaxation times leading to
M o. ssbauer spectra like those in Fig. 1a. If the
interaction term (the second term) is large, it may,
below a critical temperature, result in formation of
an ordered state of otherwise superparamagnetic
particles [1,2,8,9]. If the interaction energy is
predominant compared to the anisotropy energy,
there will be only one energy minimum, defined by
the effective interaction field. At finite tempera-
tures, the (sublattice) magnetisation vectors may
then fluctuate in directions close to that corre-
sponding to the energy minimum. The magnetic
properties of such samples have been described by
a simple mean field model, in which the summa-
tion in the last term of Eq. (4) is replaced by the
average value [1,2]. The degree of ordering can be
described by an order parameter, which is unity at
T ¼ 0 K and decreases with increasing tempera-
tures until it vanishes at the transition temperature
at which the sample becomes superparamagnetic.
The temperature dependence of the order para-
meter can be calculated by using Boltzmann
statistics [1,2]. Well below the ordering tempera-
ture there is no energy barrier, which limits the
frequency of the fluctuations of the sublattice
magnetisation directions. Therefore, it is likely
that the fluctuations are fast compared to the time
1
narrow at all temperatures. In the present case
0–15%, the lines in the sextet remain relatively
ꢁ
11
with t0E10 s, one finds from Eq. (2) that
ꢁ9
tE5 ꢂ 10 s for KV=kBTE6: Therefore, the
magnetic splitting collapses when the reduction
of the magnetic hyperfine field approaches 8%. A
substantial line broadening, like that seen in, for
example, the high-temperature spectra in Figs. 1b
and 4a, cannot be explained by collective magnetic
excitations, because these spectra contain sextets
with hyperfine fields, which are reduced by much
more than 10%.
The evolution with temperature of the spectra of
the interacting particles (Fig. 1b) is completely
different from that of the non-interacting particles.
The lines of the a-Fe O sextet become increas-
2
3
ingly broadened with increasing temperature, but
there is no clearly visible doublet at least up to

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C. Frandsen, S. M^rup / Journal of Magnetism and Magnetic Materials 266 (2003) 36–48
scale of M o. ssbauer spectroscopy. Thus, the
magnetic splitting in the M o. ssbauer spectra should
be proportional to the order parameter. In a
sample of more or less randomly packed nano-
particles there will be a variation of the effective
exchange coupling constants, K ; such that at a
ij
given temperature different parts of the sample
will have different values of the order parameter.
This will result in a distribution of magnetic
hyperfine fields, which can explain the line broad-
ening of the sextets. Detailed analyses of spectra of
this type have shown that the model can explain
quantitatively the properties of interacting
a-Fe O particles [2].
1
0 nm
Fig. 6. Transmission electron micrograph of NiO nanoparti-
cles. Note the alignment of the lattice planes of neighbouring
particles.
2
3
Qualitatively, the spectra of interacting and
non-interacting particles of maghemite (g-Fe O )
2
3
[
9], NiO [3] and goethite (a-FeOOH) [23] differ in
regions in the samples, in which the particles that
contribute to the signals in the M o. ssbauer spectra,
mainly interact with each other. In other local
regions they may interact mainly with the particles
of the other material. Therefore, the spectra may
have different types of contributions. The detailed
atomic arrangement at the interfaces is probably
also a parameter, which can have an important
influence on the exchange coupling between
particles, and which can vary considerably in a
sample. However, in all cases discussed here and
reported previously [5], the spectra of mixtures of
different nanoparticles are significantly different
from those of the samples with only one type of
particles. This shows that the mixing with other
particles has a large influence on the magnetic
properties of the composites.
the same way as those of a-Fe O particles.
2
3
Therefore, the difference in the temperature
dependence of the M o. ssbauer spectra of interact-
ing and non-interacting magnetic nanoparticles,
illustrated in Fig. 1, seems to be a common feature
of magnetic nanoparticles. If the interaction
energy gradually increases from a negligible value
to become predominant compared to the aniso-
tropy energy, one should expect a gradual change
of the spectra from being similar to those of Fig.
1
a to resemble those in Fig. 1b.
If the neighbouring particles are randomly
oriented, one might expect that the contributions
from different neighbouring particles in the second
term of Eq. (4) partially cancel, and therefore the
net interaction field may be small. However, high
resolution TEM studies of samples TiO nanopar-
2
ticles, obtained by drying aqueous suspensions,
have shown a large tendency for neighbouring
nanoparticles to align with parallel lattice planes
4.2. Interaction of a-Fe O nanoparticles with CoO
2
3
2
nanoparticles and Co ions
+
[
14,15]. If the particles in our samples have a
The spectra of the a-Fe O particles interacting
2
3
similar tendency, this might explain the strong
interaction. Indeed, preliminary TEM studies do
in fact indicate such a tendency both for a-Fe O
and NiO nanoparticles. As an example, Fig. 6
shows an electron micrograph of NiO nanoparti-
cles. It is seen that several neighbouring NiO
nanoparticles have well aligned lattice planes.
When analysing the M o. ssbauer spectra of
mixtures of different particles in the present work,
it should be realised that there may be local
with CoO particles (Fig. 2a) consist up to 180 K of
a sextet with lines that are much narrower than
those of the corresponding spectra of pure inter-
acting hematite particles. This indicates that
interactions with CoO significantly reduce mag-
netic fluctuations in the a-Fe O particles. At 250
and 295 K a coexistence of a sextet and a doublet is
seen and there is only a moderate broadening of
the sextet compared to the spectra in Fig. 1b.
Thus, the shape of these spectra is more similar to
2
3
2
3

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45
those of non-interacting a-Fe O particles than to
anisotropy of the a-Fe O particles, which then
2
3
2
3
those of strongly interacting particles. The block-
ing temperature is, however, much higher than
that of the a-Fe O ferrofluid. It is possible that a
may become predominant compared to the inter-
action energy. This might explain the temperature
dependence of the spectra, which is typical for
particles for which the anisotropy is predominant
and it could also explain the high blocking
temperature. The spectra of the sample prepared
2
3
strong exchange interaction between the surface
atoms of the a-Fe O particles and the CoO
2
3
particles results in a strong coupling of the
sublattice magnetisation directions of the two
different types of particles. The CoO particles are
larger than the hematite particles and the magnetic
anisotropy constant is also larger. Therefore, it is
likely that the anisotropy energy for CoO particles
is large compared to the interaction energy and the
magnetic properties may be dominated by super-
paramagnetic relaxation across the anisotropy
energy barrier rather than by the inter-particle
2
+
from an aqueous solution of Co with an Fe:Co
ratio of 38 consist of sextets at all temperatures up
to 295 K (Fig. 4a). The substantial line broad-
ening, seen at the highest temperatures and the
absence of a doublet is typical for a sample in
which the inter-particle interactions dominate over
the anisotropy energy. The spectra are similar to
those of pure, interacting hematite nanoparticles
(Fig. 1b), but significantly different from those of
the mixture of hematite and CoO nanoparticles. In
the spectra of a sample with an Fe:Co ratio of 5
(Fig. 4b), a doublet appears at TX120 K, indicat-
ing that some of the hematite nanoparticles exhibit
fast relaxation. We suggest that with the relatively
interaction. A strong coupling of the a-Fe O3
2
particles to these CoO particles will result in a
situation where the relaxation of the a-Fe O
2
3
particles follows the relaxation of the CoO
particles. This may explain why the spectra in
Fig. 2a are typical for samples for which the
anisotropy energy is predominant. The presence of
a doublet at the highest temperatures may not be
due to superparamagnetic relaxation of the CoO
particles to which the a-Fe O particles are
2
+
large amount of Co ions, a paramagnetic cobalt
salt is formed during the drying of the sample.
Such a paramagnetic salt may separate the
a-Fe O particles and thereby reduce the inter-
2
3
particle interaction and lead to fast superpara-
magnetic relaxation. In both samples it is expected
that the surface of the a-Fe O particles is covered
2
3
coupled. It could be related to the transition of
CoO from an antiferromagnetic to a paramagnetic
state. The N e" el temperature of bulk CoO is 293 K.
However, even well above this temperature, the
sextets have much sharper lines than in the spectra
of pure a-Fe O particles [5]. The CoO particles
2
3
2
+
by Co ions, at least to the same extend as in the
sample consisting of a mixture of hematite and
CoO nanoparticles. Therefore, if the single ion
2
+
anisotropy of adsorbed Co
ions were respon-
2
3
therefore seem to have a much larger influence on
the relaxation of some of the a-Fe O particles
sible for the behaviour of the sample of hematite
mixed with CoO, one would expect the spectra in
Figs. 2a, 4a and b to be similar. This is not the case
and therefore it seems that the relaxation beha-
viour of hematite in the samples with CoO
nanoparticles cannot be explained by adsorbed
2
3
than expected for a paramagnetic phase. Because
the CoO is in contact with a-Fe O , which has a
much higher magnetic transition temperature, it is
2
3
possible that its N e" el temperature is increased as in
the case when CoO interacts with Fe O4 [4].
2
+
Co ions.
3
Further investigations are necessary to clarify the
mechanisms by which CoO particles influence the
relaxation of a-Fe O particles.
4.3. Interaction of a-Fe O nanoparticles with NiO
2
3
2
nanoparticles and Ni ions
+
2
3
A possible explanation of the spectra in Fig. 2a
2
+
could be that small amounts of Co
dissolved during the mixing procedure and subse-
ions are
When the a-Fe O particles are mixed with NiO
2
3
particles (Fig. 2b), the M o. ssbauer spectra obtained
at To180 K consist of sextets and the spectra
show a gradual Morin transition that is not seen in
the spectra of pure, interacting or non-interacting
quently adsorbed on the surface of a-Fe O
2
3
particles. Because of the large single-ion anisotro-
2
+
py of Co
this could result in an enhanced

ARTICLE IN PRESS
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C. Frandsen, S. M^rup / Journal of Magnetism and Magnetic Materials 266 (2003) 36–48
a-Fe O nanoparticles. At TX180 K the spectra
and such a paramagnetic phase in the sample may
separate the a-Fe O nanoparticles and thereby
reduce the inter-particle interactions.
2
3
contain both a doublet with narrow lines and a
sextet with rather broad lines. Thus, these high
temperature spectra have similarities to both those
of pure non-interacting and interacting a-Fe O
2
3
5
7
4.4. Interactions between Fe-doped NiO
nanoparticles and CoO nanoparticles
2
3
nanoparticles. The NiO particles are much smaller
than the CoO particles and therefore they are
expected to have a smaller magnetic anisotropy
energy. In fact, the spectra in Fig. 3a show that
they are superparamagnetic at TX180 K. (Neu-
tron diffraction studies of a similar sample of NiO
nanoparticles [24] have shown that the N e! el
temperature is about 460 K, i.e. a little lower than
the N e! el temperature of bulk NiO (523 K).) We
propose that the sextets with broad lines in Fig. 2b
at TX180 K are due to hematite particles for
which the magnetic energy is dominated by
magnetic interaction with other a-Fe O nanopar-
5
7
The spectra of Fe-doped NiO nanoparticles
with and without CoO nanoparticles (Fig. 3) show
a coexistence of a sextet and a doublet in a broad
temperature range. This indicates that the mag-
netic properties are dominated by relaxation
across an energy barrier, i.e. the inter-particle
interaction energy seems to be small compared to
the anisotropy energy in both samples. The
superparamagnetic blocking temperature is high-
est in the sample with CoO nanoparticles. We
suggest that the mechanism for the suppression of
the relaxation may be the same as for the a-Fe O
2
3
ticles. The doublets in the spectra of Fig. 2b at
TX180 K may be due to hematite particles, which
perform fast superparamagnetic relaxation, be-
cause they mainly are in contact with NiO particles
with a small magnetic anisotropy energy.
2
3
nanoparticles, i.e. a strong exchange coupling at
the CoO–NiO interfaces hinders to some extend
the relaxation of the NiO particles.
5
7
Although the spectra of Fe-doped NiO nano-
particles qualitatively are similar to those typical
for non-interacting particles one cannot conclude
that the inter-particle interaction is weak. The
shape of M o. ssbauer spectra of interacting nano-
particles does not give direct information about
the absolute value of the strength of inter-particle
interactions, but it depends on the ratio between
the anisotropy and the interaction energies.
a-Fe O nanoparticles have unusually small mag-
The spectra of a-Fe O nanoparticles, prepared
2
3
by drying suspensions in aqueous solutions of
2
Ni ions (Fig. 5), contain a doublet at the highest
+
temperatures, indicating the presence of a-Fe O
2
3
particles with fast superparamagnetic relaxation.
The spectra at the highest temperatures of the
sample with a Fe:Ni ratio of 27 are similar to those
of a-Fe O nanoparticles mixed with NiO, shown
2
3
in Fig. 2b. This might suggest that the fast
relaxation in the samples consisting of a-Fe O
2
3
4
ꢁ3
netic anisotropy constants (t10 J m
[13]).
Typical values for nanoparticles of other materials
2
3
mixed with NiO in fact could be due to adsorbed
2
+
Ni ions. However, the low-temperature spectra
in Fig. 5 show no indication of a Morin
4
6
are in the range 10 –10 J m . Therefore, the
ꢁ3
magnetic energy of a-Fe O nanoparticles may
2
3
temperature in contrast to the sample of a-Fe O3
easily be dominated by inter-particle interactions,
leading to M o. ssbauer spectra like those shown in
Fig. 1b. The coexistence of sextets and singlets or
doublets (e.g. Figs. 3a and b) does not show that
the inter-particle interactions are small, but only
that the anisotropy energy is predominant.
2
particles mixed with NiO particles. Therefore,
inter-particle interaction effects in the a-Fe O +
2
3
NiO sample also seem to have an important
influence on the magnetic properties of the
particles. The spectra of the sample with an Fe:Ni
ratio of 4 (Fig. 5b) show an evolution with
temperature typical for particles for which the
anisotropy energy is predominant. Almost all the
a-Fe O particles relax rapidly at the highest
5. Conclusions
2
3
temperatures. This is presumably because a para-
magnetic nickel salt is formed during the drying,
We have studied the effects of inter-particle
interactions in mixtures of antiferromagnetic

ARTICLE IN PRESS
C. Frandsen, S. M^rup / Journal of Magnetism and Magnetic Materials 266 (2003) 36–48
47
nanoparticles prepared by drying aqueous suspen-
sions. The M o. ssbauer spectra of non-interacting
seems to be predominant compared to the inter-
action energy. The blocking temperature is in-
creased when the particles interact with CoO,
presumably because the Fe-doped NiO nano-
particles are exchange coupled to the CoO
particles with large anisotropy energy.
The present studies of composites of magnetic
nanoparticles show that inter-particle interactions
between particles of different materials can have a
substantial influence on the magnetic properties.
The results suggest that exchange coupling be-
tween surface atoms of nanoparticles of different
materials play an important role in these materials.
If such interaction effects are prevalent we suggest
that they can be used to tailor magnetic materials
with new properties from mixtures of nanoparticles.
9
nm a-Fe O particles exhibit a typical super-
2
3
5
7
paramagnetic behaviour with a blocking tempera-
ture of about 70 K. The distribution in energy
barriers results in a broad distribution of relaxa-
tion times and therefore the spectra essentially can
be described as superpositions of sextets and
doublets. If the a-Fe O particles are allowed to
2
3
interact, the superparamagnetic relaxation is
suppressed and the M o. ssbauer spectra are in
accordance with the existence of an ordered state
in which the interaction energy is predominant
compared to the anisotropy energy. The line
broadening of the sextets in these spectra can be
explained by a variation of the inter-particle
interaction strength in the sample.
When the a-Fe O particles are mixed with CoO
2
3
particles, the M o. ssbauer spectra are typical for
particles for which superparamagnetic relaxation
across an energy barrier is predominant, but the
blocking temperature is much higher than for the
non-interacting particles. We suggest that a strong
exchange coupling between the a-Fe O particles
Acknowledgements
This work was supported by the Danish
Technical Research Council and the Danish
Research Council for Natural Sciences. Lis Lille-
balle and Franz B^dker are thanked for their help
with sample preparation, Helge K. Rasmussen for
help with the M o. ssbauer spectroscopy measure-
ments, Flemming Grumsen for help with the TEM
studies and Leif Gerward for help with the XRD
measurements.
2
3
and the CoO particles, which have larger magnetic
anisotropy energy, can explain the results. In the
sample of a-Fe O particles mixed with NiO
2
3
particles, some of the particles exhibit fast super-
paramagnetic relaxation above the blocking tem-
perature of the NiO particles. This can be
explained by a-Fe O particles surrounded by
2
3
NiO nanoparticles with small anisotropy energy.
Other particles in the sample seem to be more
influenced by interactions between a-Fe O parti-
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