J Mater Sci: Mater Electron
DOI 10.1007/s10854-015-3731-7
Structure-magnetic property correlations in nickel-polymer
nanocomposites
K. P. Murali1,2 • Himani Sharma1 • P. Markondeya Raj1 • Dibyajat Mishra1
Manik Goyal1 • Kathleen Silver3 • Erik Shipton3 • Rao Tummala1
•
Received: 20 June 2015 / Accepted: 31 August 2015
Ó Springer Science+Business Media New York 2015
Abstract Epoxy matrix nanocomposites with nickel
nanoparticles of two different sizes were processed and
characterized to investigate their structure-magnetic property correlations. Crystal structure, morphology, density,
resistivity and magnetic properties of the nanocomposites
with different filler contents were compared for different size
scales. Nanocomposites with 25 nm nanoparticles showed
higher coercivity, higher frequency stability and lower loss,
though the permeability was suppressed. Coarser nickel
particles (100 nm) showed a permeability of *5.5 but stability only up to 200 MHz. The structure-magnetic property
correlations were validated using analytical models to provide valuable design guidelines for permeability and frequency-stability in particulate nanocomposites.
1 Introduction
Magnetic components play a critical role in smart systems
for power conversion in voltage regulators and DC–DC
convertors, electromagnetic interference (EMI) isolation,
or in radio frequency (RF) front-end as antennas, filters or
matching networks [1]. Integrating such components as
thin-films onto ICs and packages leads to miniaturization
and simultaneous performance-enhancement [2–4]. Component integration has been actively pursued by the
& P. Markondeya Raj
[email protected]
1
Packaging Research Center, Georgia Institute of Technology,
Atlanta, GA 30332-0560, USA
2
Center for Materials for Electronic Technology (C-MET),
Athani, Thrissur, India
3
Georgia Tech Research Institute, Atlanta, GA, USA
electronics industry and academia for the past two decades,
though resulting in only a few examples of commercialization. The main reasons for this are the limited properties
that are achieved with such thin films, and the high manufacturing costs resulting from testability and low yield.
Novel nanoscale materials with superior properties and
silicon- or glass-compatible processing can address this
barrier. This paper focuses on processing and characterization of metal-polymer nanocomposites for their suitability as such magnetic components.
Ferrites, ferrite composites or metal composites are the
most common magnetic materials used for thin-film passive power components today. Ferrite films require hightemperature processing that make them incompatible with
silicon or organic packages, and also have inherent frequency instabilities [5, 6]. On the other hand, metallic
magnetic films are unsuitable for passive components
because of the high losses from eddy currents unless they
are at micro or nanoscale. Therefore, composites are the
most logical way to integrate magnetic components.
Although ferrite composites have recently been shown to
have attractive properties at high frequencies [7–9], metal
composites are more promising because of their higher
saturation magnetization and inherent higher frequencystability. Metal micropowder compacts consisting of iron
and permalloy powders are commercially utilized as
magnetic cores in power inductors [10] as discrete surfacemount components but not as thin films.
Metal composites having micro- and sub-microscale
fillers, however, suffer from high losses beyond a few MHz
[11, 12] from hysteresis, domain-wall and eddy-current
losses. Metal-oxide nanocomposites from thin-film deposition routes such as co-sputtering are shown to result in
higher permeability, softness and frequency stability [13,
14]. The nanometallic domains, present in these thin films,
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J Mater Sci: Mater Electron
interact through exchange-coupling resulting in the reduction in anisotropy, suppression of demagnetization with
minimal eddy current losses [15]. These nanostructures are
explored for on-chip power inductors [16]. However, the
high cost from thin-film deposition to form films with
adequate thickness is still of concern.
Composites synthesized from particle-loaded polymers
are easier to process to the required geometries and are
hence more attractive [17]. Several extensive studies have
been reported on magnetic metal-polymer composites,
particularly focusing on the iron-polymer and NiFe-polymer systems [18–20]. With large microsized particles,
permeabilities of above 100 up to frequencies of *1 MHz
are reported. These particles show lower coercivity and
higher intrinsic permeability. However, the magnetic losses
become significant even at 1 MHz. With finer nanoscale
particles, the losses are suppressed, but at the expense of
permeability. The particles usually do not interact through
exchange coupling and hence are demagnetized because of
the shape and size effects [21–23]. In addition, they show
high field anisotropy that arises from the exchange anisotropy at the metal-oxide interfaces and surface anisotropy
effects [24, 25] which suppress the permeability and limit
their applicability in spite of lower losses. A systematic
study on the role of particle size, filler content and oxide
passivation was performed to investigate these effects and
provide material selection guidelines for power and RF
applications in different frequency domains. Permeability
and magnetic loss as a function of frequency was measured
up to 1 GHz and correlated with the structure and formulations. Simple analytical equations are used to explain the
behavior and, therefore, act as modeling guidelines for
nanocomposite design for required permeability and frequency stability.
2 Experimental details
2.1 Materials and processes
Spherical nickel nanopowder (JFE Mineral Company Ltd,
Japan), Epoxy resin—EPON828 and its curing agent Epikure 3300 (both from Momentive Performance Materials,
USA) and a suitable solvent—Propylene glycol methyl ether
acetate (PGMEA) (Sigma Aldrich, USA) were used as the
starting materials. Due to their high reactivity, nanopowders
remain as aggregates in their powder form. In order to
effectively coat each individual Ni nanoparticle with the
epoxy resin, these aggregates were broken down by ball
milling using PGMEA as the solvent, dispersants (Byk-106,
Byk-Chemie, Wallingford, CT, USA) and stabilized zirconia
balls as the milling media. The process results in the disintegration of the aggregates to obtain finely dispersed
123
spherical Ni nanopowders in PGMEA. EPON828 resin was
added to this suspension and again ball-milled for 6 h, followed by the addition of the curing agent and final mixing by
ball-milling for 2 h. The process resulted in a nickel suspension in the epoxy monomer solution. The nanocomposite
mix was then dried at 100 °C to obtain dry powder. Toroids
with an outer diameter of 12.5 mm, inside diameter of 4 mm,
and 1 mm thickness were prepared from uniaxial pressing
with 3.5 T load (*300 MPa). The vol% of nickel in the
polymer matrix was varied from 30 to 70. For finer
nanoparticles (25 nm), formulations with high metal content
(1:1 metal:polymer volume ratio), but with adequate handling strength were studied.
2.2 Characterization
X-ray diffraction (XRD, Philips 1813 diffractometer,
Westborough, MA, USA) was performed to study the nickel
and its oxide phases after the nanocomposite compaction.
Chemical characterization was performed by X-ray photoemission spectroscopy (XPS) using monochromatic Al
K-alpha X-ray source, which was operated in the constantpass energy mode. The working pressure in the analysis
chamber was typically 5 9 10-8 Torr. The binding energy
scale was calibrated by measuring the C1s peak at 285.0 eV
and the accuracy of the measurement was ±0.1 eV. The
composition and chemical state were investigated on the
basis of the areas and binding energies of Ni 2p and
O1s photoelectron peaks. Peak deconvolution was performed by a peak-fitting program (Avantage) using Lorentzian–Gaussian functions after linear background
subtraction. SEM (LEO 1530) was performed to study the
particle morphology, dispersion of the fillers in the polymer
matrix and porosity. Real and imaginary parts of permeability (l0 and l00 ) up to 1 GHz were found out using
impedance spectroscopy (Agilent 4291B Impedance Analyzer). Vibrating sample magnetometer (VSM, Lakeshore
736 Series) was used to analyze the hysteresis behavior of
the composites. Densities were obtained from the mass and
volume measurements of square substrates with controlled
dimensions. Resistivities of the composite samples were
obtained from metallized disks.
3 Results and discussion
3.1 Crystal structure
The XRD patterns for the composites with different particle systems are compiled in Fig. 1. The diffraction peaks at
44.5° and 51.8° are the characteristic XRD peaks for facecentered cubic (fcc) metallic nickel crystals. The peaks
were matched with JCPDS card #04-0850 and indexed as
J Mater Sci: Mater Electron
10000
(a) 25 nm Ni
(200)
Counts (a.u.)
(111)
Intensity (a.u.)
8000
6000
(b) Ni 100 nm
4000
2000
0
35
Ni (0)
Ni (+2)
Ni (+3)
Ni (0)
(a) Ni 25 nm
40
45
50
55
60
0
2θ
3.2 Chemical structure
XPS was used to determine the oxidation states of Ni in the
nanocomposites with 25 and 100 nm nickel nanoparticles.
Since the oxide shell on the metal nanoparticles play a
critical role in determining the magnetic properties of the
composite, including the field anisotropy and coercivity,
surface oxide were investigated in detail using XPS. The
effect of oxide thickness on magnetic properties is
explained in detail in Sect. 3.6. The survey scan (not shown
here) did not show any extraneous elements indicating the
high level of purity in the nanocomposite. The Ni2p XPS of
the nanostructure Ni, appears as a doublet shown in Fig. 2,
comprising of 2p1/2 and 2p3/2 peaks corresponding to the
two edges split by spin–orbit coupling in elemental nickel.
The XPS spectra for Ni2p in 25 nm and 100 nm
nanocomposites were deconvoluted to determine the extent
of oxide formation on the metal. The metallic Ni(0)
appeared at 852.4 and 869.6 eV along with the corresponding satellites at 858.6 and 875.8 eV respectively [27].
In addition, deconvolution of the core levels showed the
Counts (a.u.)
(111) and (200) respectively. The processed nanocomposites show only metallic peaks with no signature from the
surface nickel oxide layer. This may be indicative of a very
thin and amorphous natural oxide on as-received 25 and
100 nm nickel nanoparticles which could be below the
detection level of XRD. The particle sizes were calculated
using Scherrer’s formula, Dhkl ¼ Kk=ðBhkl cos hÞ [26],
where Dhkl is the crystallite size, hkl are the Miller indices,
K is the crystallite-shape factor, k is the wavelength of the
X-rays, Bhkl is the width (full-width at half-maximum) and
h is the Bragg angle, as 30 and 95 nm respectively for the
as-received nanoparticles, closely agreeing with the manufacturer’s data. As can be seen from Fig. 1, the peaks
corresponding to finer nanoparticles (25 nm) are broader
than the composite with larger Ni particles, confirming
finer crystallite size of the metallic nickel.
840
(b) 100 nm Ni
2p3/2
Ni (0)
2p1/2
Ni (+2)
Ni (+3)
Ni (0)
0
880
870
860
850
Binding Energy (eV)
840
Fig. 2 Deconvoluted XPS core-level scan of Ni a 25 nm; b 100 nm
presence of Ni(?2) and Ni(?3) states at 854 and 855.4 eV
respectively in both 25 and 100 nm nanocomposite. These
states indicate the presence of mixed oxide, NiO and Ni2O3
on the metal surface. The deconvoluted data is in good
agreement with the literature [28, 29].
3.3 Density
Figure 3 shows the variation of density with metal loading.
The error bars are the standard deviation obtained from the
average reading of four samples. The densities of epoxy and
nickel are assumed to be 1.16 and 8.9 g/cc respectively. The
density of the nanocomposites increases with filler loading
till *50 vol%, stabilizes beyond that, and even starts to
8
Theoretical
Dennsity (g/cc)
Fig. 1 XRD plot comparison for nanocomposites with 100 and
25 nm nickel nanoparticles
880
6
100 nm Ni
4
25nm Ni
2
20
40
60
80
100
Ni Vol. %
Fig. 3 Variation of density with respect to nickel vol% in the epoxy
matrix
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J Mater Sci: Mater Electron
decrease beyond 70 vol%. The deviation from the measured
and calculated densities is attributed to the porosity induced
in the samples due to the insufficient volume of the polymer
to completely fill the voids between the metal nanoparticles.
The porosity depends on the size, morphology, aggregate
formation and distribution of the filler dispersed in the
polymer matrix. With larger metal particles, the density of
the composites could be much higher than that achieved here.
For example, literature reports that more than 80 % theoretical density ([7 g/cc) was reported with 30–50 micron Fe
particles [30] with adequate metal volume fraction in the
polymer. Such high densities were not seen with the 100 nm
nanoparticles. The densities were further lower (3.1–3.2 g/
cc) with nanocomposites having 25 nm particles. The
porosity was *35 vol% with 25 nm nanocomposites while
it is less than 1 % with 100 nm nanoparticles below
50 vol%, indicating much poorer particle packing with these
finer nanoparticles having high surface area. The SEM
images for 40 and 60 vol% nickel-loaded polymer composite (Fig. 4) illustrate that the fillers are uniformly distributed throughout the polymer matrix. As observed from
the density measurements, the coarser 100 nm particles had
much better packing compared to the finer 25 nm particles
that form stronger aggregates with more open structure with
entrapped porosity.
3.4 Resistivity
Resistivity relates to the l00 of the composite through eddy
current losses and the associated degradation of l0 with
frequency. Figure 5 shows the variation of resistivity with
nickel (100 nm nanoparticles) loading in the polymer
matrix, with error bars indicating standard deviation from
the plotted average of three measurements. The resistivity
decreases with increased metal volume fraction indicating
that the native nickel oxide is not a good insulation. At
higher metal loading, more semiconducting paths are
formed through the nickel particles in the composite, which
results in a further reduction in the resistivity. Composites
with finer nanoparticles (25 nm) showed high resistivities
(overload) that are not accurately measurable with a multimeter or a 4-point probe. Therefore, they are not plotted
on the graph. The oxide passivation layer in this case is
insulating and completely blocks electronic conduction.
Fig. 4 a SEM images of the fractured surfaces for 40:60 (left) and 60:40 (right) vol% nickel:epoxy nanocomposites (100 nm nanoparticles).
b SEM images of the fractured surfaces for nickel-epoxy nanocomposites (25 nm nanoparticles) for 50:50 nickel:epoxy nanocomposites
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J Mater Sci: Mater Electron
16
(a)
100 nm Ni
12
B (emu/gm)
Log (Resistivity in Ohm-m)
60
100 nm
14
10
70
50
40
30
20
8
0
6
-1000
4
-500
0
-20
500
H (Oe)
1000
2
0
-40
0.2
0.3
0.4
0.5
0.6
Effective Ni Volume Fraction
50
B (emu/g)
Fig. 5 Variation of resistivity with respect to the effective nickel
vol% (including porosity) in the epoxy matrix
-60
(b)
3.5 Magnetization curves
The B–H loops for different nanocomposite systems are
shown in Fig. 6. The induced internal magnetization (Yaxis) is plotted as a function of the applied external field
applied (H) for composites loaded with different Ni
(100 nm) vol%. The saturation magnetization (Bmax),
remanence (Br), coercive force (Hc) and area of the hysteresis loop (B–H loop) are the main parameters that can be
obtained from the plot. From the figure, it can be seen that
Bmax and Br increased with the vol% in the non-magnetic
polymer. However, the coercivity (Hc) of the nanocomposites (130 Oe) did not vary with the filler loading. At
50 vol%, the magnetic nanocomposites show a Ms of
46 emu/g (230 emu/cc) with a coercivity of 130 Oe.
The coercivity and saturation magnetization for different
nanoparticle systems are shown in Fig. 6b. The finer
nanoparticles showed much higher coercivity in accordance with the Herzer’s theory [31]. With finer particles,
the particles only support single domain within them which
enhances the coercivity. The coercivity is further increased
with various surface effects such as metal-oxide exchange
anisotropy [32]. The coercivity is also related to internal
defects in the material structure which in turn restricts the
magnetic domain movement [24, 33].
3.6 Magnetic properties and their frequencystability
3.6.1 Permeability
The real and imaginary parts of the permeabilities (l0 and
l00 ) for the nanocomposites were measured up to 1 GHz
and shown in Fig. 7 for 100 nm particles and Fig. 8 for
25 nm particles. Both l0 and l00 are strongly dependent on
frequency. A resonance behavior is observed till the filler-
Ni 100 nm
40
30
Ni 25 nm
20
10
0
-1000
-500
-10
0
500
H (Oe)
1000
-20
-30
-40
-50
Fig. 6 Magnetization curves for 30, 50, 70 vol% nickel (100 nm
nanoparticles) in the epoxy matrix (a). The numbers in the figure
indicate the nickel vol%. The curves for 100 and 25 nm nanocomposite systems are compared in (b)
loading reaches 60 vol%, with the permeability reaching a
minimum and magnetic loss reaching its peak at
*650 MHz. It is evident from the figures that l0 and l00
increase with higher metal volume fractions. The permeability variation as a function of metal loading was fitted
with the Bruggeman’s Effective Medium Theory Model
(EMT) [34] as shown in Fig. 9. The EMT equation is
represented as:
la leff
lb leff
ca
þ cb
¼0
ð1Þ
la þ 2leff
lb þ 2leff
where la and lb refer to the permeabilities of the filler and
matrix, ca and cb refer to the volume fraction of the filler
and matrix, and leff is the effective nanocomposite permeability. Different particle permeabilities were chosen to
generate a set of curves for the nanocomposite permeability. The permeability variation as a function of metal
loading is also plotted with the nonmagnetic grain boundary model (NMGB) in Fig. 10, again with different particle
permeabilities. The constitutive equation for NMGB is
represented as:
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J Mater Sci: Mater Electron
(a) 4.0
7
6
Permeability
Ni (25 nm)/Epoxy Composites
3.5
70
5
Permeability (μ')
(a)
60
50
4
40%
80%
70%
2.5
2.0
1.5
40
3
3.0
30
1.0
10M
100M
2
0.0
(b) 1.5
Ni (25 nm)/Epoxy Composites
40%
80%
70%
1
1.0
70
0.8
Magnetic Loss Tangent
800.0
μ"
(b)
400.0
Frequency (MHz)
1G
Frequency (Hz)
60
0.6
0.5
50
40
0.4
0.0
30
0.2
10M
100M
1G
Frequency (Hz)
0
Fig. 8 Variation of l0 (a) and l00 (b) as a function of frequency for
nanocomposites with 25-nm nickel particles
400.0
800.0
Frequency (MHz)
Fig. 7 Variation of l0 (a) and l00 (b) as a function of frequency for
nanocomposites with 100-nm nickel particles. Numbers on the curves
indicate the nickel volume fraction
Xc ¼
Xi D
Xi
¼
0:333
Xi g þ D Xi ð2p
1Þ þ 1
ð2Þ
Where Xc and Xi refer to the susceptibility of the
composite and filler respectively, D is the particle size, and
g is the spacing, and p refers to the volume fraction. An
effective metal volume fraction that incorporates both
polymer and pore volume along with the metal volume is
used in this analysis. Epoxy is a non-magnetic material
having a permeability of *1 and nickel is a ferromagnetic
material with a bulk DC permeability of *600 and a saturation magnetization of 485 emu/cc. The permeabilities
for submicro- and nanonickel particles are strongly
dependent on the size, shape, surface state and internal
coupling between the particles [35, 36]. An effective particle permeability (nickel ? nickel oxide) was extracted by
mapping the experimental measurements with permeability
plots. Best fit was obtained when the particle permeability
is *10–15 for EMT model, as shown in the curves for
100 nm particles in Fig. 9. For NMGB model fit shown in
Fig. 10, the experimental data matches well with a particle
permeability of *20–30. For 25 nm nanoparticles, the
particle permeability is estimated as *5. For both the
123
7
Nanocomposite Permeability
0.0
6
30
100 nm Ni
5
20
25 nm Ni
4
10
3
6
2
1
0
0
0.2
0.4
0.6
Filler Volume Fraction
Fig. 9 Permeability (at 100 MHz) as a function of effective metal
volume fraction. The curves derived from Effective Medium Theory
(EMT) using particle permeabilities of 6, 10, 20 and 30 are also
shown
systems, the intrinsic particle permeability of nickel is
much lower than that for the bulk because of the demagnetization associated with size and shape, and additional
surface anisotropies [24, 33].
3.6.2 Magnetic losses
The magnetic losses arise from various mechanisms. The
coercivity is an indication of the hysteresis loss in the
Nanocomposite Permeability
J Mater Sci: Mater Electron
6
100 nm Ni
5
25 nm Ni
30
20
10
4
5
3
4
2
1
0
0.2
0.4
Filler Volume Fraction
0.6
Fig. 10 Permeability (at 100 MHz) as a function of effective metal
volume fraction. The curves derived from Nonmagnetic Grain
Boundary Model (NMGB) using particle permeabilities of 4, 5, 10,
20 and 30 are also shown
material. For larger particles with multiple domains within
the particle, domain walls contribute to losses. Finally, the
intrinsic ferromagnetic resonance (FMR) creates additional
losses as the frequency reaches the FMR frequency. These
losses are added to the eddy current losses to give the total
magnetic loss of the material. The eddy current losses in
metal-nanocomposites are a strong function of the particle
size, particle conductivity and the frequency. The contribution of eddy current losses to l00 is simplistically estimated as [37] [38]:
l00 2pl0 l0 D2 f
¼
3X
l0
ð3Þ
X is the particle resistivity, D is the particle size, lr is the
relative permeability, and f is the frequency. A linear
change in l00 /(l0 )2 with frequency is an indication of eddy
current loss. However, the data analysis did not show such
linear behavior. Hence, eddy currents are not considered
significant in this system. The frequency (FEC) above
which the eddy current losses dominate is estimated using
the equation [11]:
FEC ¼
4q
pl0 ð1 þ XÞD2
ð4Þ
where q is the conductivity and X is the magnetic susceptibility. Estimated FEC for 100 nm particles is much
more than 10 GHz, again indicating that eddy currents are
not dominant. Ramprasad’s analysis [35] also predicts that
the eddy currents do not contribute to net losses at
microwave frequencies when the particle size is *100 nm.
For filler content above 70 vol%, the permeability
degrades at a much lower frequency due to the reduction in
resistivity from percolation conduction between the nickel
particles. The lower resistivity creates eddy currents, which
start to dominate at much lower frequencies in this case and
no resonance-like behavior is observed. By introducing a
coupling agent such as aminosilane, significant reduction in
magnetic loss was demonstrated by Taghvaei et al. [20].
The reduction in loss is attributed to better insulation and
separation between the particles. A self-passivating oxide
layer by treating the particles with an alkaline solution was
also shown to improve the loss [19]. With these modifications, the properties such as frequency stability and
mangetic loss in nanocomposites with 100 nm particles can
be further enhanced even at higher loadings. From the
results, it is clear that 60 vol% Ni loaded composite has the
optimum properties of good permeability (5) at high frequency (up to 200 MHz) and low magnetic loss (\0.02).
The losses from domain wall resonance occur when
multiple domains are present within the particles, and are
usually dominant at 1–250 MHz frequencies for microsized ferrites and metallic nanoparticles [39, 40]. The frequency (FDW) where the domain wall resonance occurs is
given as [11]:
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2dðn þ 1Þ cJs
FDW ¼
ð5Þ
3pð1 þ XÞD 2pl0
where c is the gyromagnetic ratio, d is the domain wall
thickness, n is the number of domains in a particle with
diameter D, lo is the permeability of free space, X is the
susceptibility of the material, Js is the saturation polarization. The domain wall thickness is dependent on the
exchange constant (A) and the magnetic anisotropy energy
(K). The domain structure varies with the particle dimensions. In case of microscale particles, domain wall resonances lead to magnetic losses at lower frequencies. Finer
particles show domain wall resonance at higher frequencies, while these losses are absent in single-domain finer
nanoparticles [21, 41]. Literature estimates the domain wall
thickness for bulk nickel as *50 nm [42]. For finer particles with enhanced anisotropy, the domain wall thickness
reduces. However, even for these domain dimensions, for a
100 nm particle, Eq. (5) predicts that the resonance occurs
in GHz range.
3.6.3 Ferromagnetic resonance (FMR)
The FMR determines the ultimate operation frequency of
the material when the hysteresis losses, domain wall resonance losses and eddy current losses are suppressed [43].
For particle composites, the FMR frequency is written as
[41]:
c
FFMR ¼
HEff
ð6Þ
2p
while K and Heff are related as [44]:
K ffi 0:75 l0 Ms HEff
ð7Þ
where c is the gyromagnetic ratio and Heff is the effective
field anisotropy and K is the effective anisotropy energy.
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J Mater Sci: Mater Electron
Table 1 Properties of nickel
nanoparticles estimated from
the permeability and loss
spectra
Size (nm)
Hk (Oe)
K (J/m3)
lw (nm)
Ld (nm)
Particle permeability
27
650
5
3500
100
234
5.8 9 103
51
2
25
1240
3.1 9 104
22
4.4
Based on the permeability and loss spectra, FMR is estimated to be *650 MHz for the system with 100 nm particles. From Eq. (6), this gives a field anisotropy of 234 Oe.
The estimated particle permeability is *27, matching
more with the NMGB model than the EMT model. These
values are also tabulated in Table 1. The effective field
anisotropy is enhanced in nanoparticles because of surface
anisotropy and ferromagnetic-antiferromagnetic coupling
at the Ni/NiO interface [24, 25]. Assuming the exchange
constant for nickel as 1.5 9 10-11 J/m, the corresponding
length parameter lw, that is related to domain wall width, is
then estimated as 51 nm, using the formulations by Bertotti
[42]. These values are also tabulated in Table 1.
For 25 nm nanoparticles, the estimated permeability
from Fig. 10 is *5. Using Eq. (6), the estimated Heff and
FMR for these nanoparticles is 1240 Oe and 3.5 GHz. This
corresponds to a effective anisotropy energy (K) of
3.1 9 104 J/m3, higher than that for 100 nm nickel
(5.8 9 103 J/m3), estimated from Eq. (7). The value of K is
further reduced when the grain size approaches less than
5 nm, in the super-paramagnetism regime, where the K is
estimated as 3.75 9 103 J/m3 [45]. The length parameter
lw is 22 nm, again based on Bertotti’s formulations [42].
The critical diameter for nickel is *59 exchange length,
according to Bertotti’s particle domain models. The
exchange length is a function of anisotropy energy density,
and varies from 2 nm for 100-nm particles to 4.4 nm for
25-nm nanoparticles. The critical radius is *10–22 nm for
particles in this size domain. However, since the domain
width is much higher (20–50 nm), even particles of
60–100 nm are expected to be of single domain. Literature
reports the FMR to be close to 5.5 GHz both for 25 nm
carbon-coated nickel nanoparticles [44] and oxide-passivated 70 nm nickel nanoparticles [41]. The FMR for the
current 25 nm system cannot be directly verified here
because of the limitations of the impedance analyzer.
4 Conclusions
Nickel-based nanocomposites with two different particle
sizes were processed and test-structures fabricated to
investigate the relationships between microstructure and
properties. XPS was used to study the surface nickel oxide
chemical structure. For 100 nm particles, the nanocomposite density increased with filler content up to 60 vol%,
beyond which the increased-filler content reduced the
123
FMR (MHz)
density due to the induced porosity. The measured density
was much lower for finer (25 nm) nanoparticles compared
to that with coarser (100 nm) nanoparticles indicating
much poorer particle packing with finer nanoparticle
composites. Nickel nanocomposites with 60 vol% in the
polymer matrix showed a permeability of *5 and low loss
(0.02) up to 200 MHz. Nanocomposites with 25 nm
nanoparticles showed a lower permeability of 2.1–2.3 but
with more frequency stability till 800 MHz. The higher
frequency stability and lower loss in smaller particle
nanocomposites (25 nm) are attributed to its higher field
anisotropy, and suppression of both eddy current losses and
domain wall resonance. A consistent set of mathematical
models that predict particle and composite permeabilities,
and their frequency-stability, derived from size-dependent
field anisotropy is proposed.
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