Structure-magnetic property correlations in nickel-polymernanocomposites

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

� 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 prop-

erty correlations. Crystal structure, morphology, density,

resistivity and magnetic properties of the nanocomposites

with different filler contentswere 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 sta-

bility only up to 200 MHz. The structure-magnetic property

correlations were validated using analytical models to pro-

vide valuable design guidelines for permeability and fre-

quency-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]. Com-

ponent integration has been actively pursued by the

electronics industry and academia for the past two decades,

though resulting in only a few examples of commercial-

ization. The main reasons for this are the limited properties

that are achieved with such thin films, and the high man-

ufacturing 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 characteri-

zation of metal-polymer nanocomposites for their suit-

ability as such magnetic components.

Ferrites, ferrite composites or metal composites are the

most common magnetic materials used for thin-film pas-

sive power components today. Ferrite films require high-

temperature processing that make them incompatible with

silicon or organic packages, and also have inherent fre-

quency 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 frequency-

stability. Metal micropowder compacts consisting of iron

and permalloy powders are commercially utilized as

magnetic cores in power inductors [10] as discrete surface-

mount 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 depo-

sition 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,

& P. Markondeya Raj

raj@ece.gatech.edu

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

123

J Mater Sci: Mater Electron

DOI 10.1007/s10854-015-3731-7

interact through exchange-coupling resulting in the reduc-

tion 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-poly-

mer 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 aniso-

tropy 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 formu-

lations. Simple analytical equations are used to explain the

behavior and, therefore, act as modeling guidelines for

nanocomposite design for required permeability and fre-

quency stability.

2 Experimental details

2.1 Materials and processes

Spherical nickel nanopowder (JFE Mineral Company Ltd,

Japan), Epoxy resin—EPON828 and its curing agent Epi-

kure 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 disin-

tegration of the aggregates to obtain finely dispersed

spherical Ni nanopowders in PGMEA. EPON828 resin was

added to this suspension and again ball-milled for 6 h, fol-

lowed by the addition of the curing agent and final mixing by

ball-milling for 2 h. The process resulted in a nickel sus-

pension 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 han-

dling 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 pho-

toemission spectroscopy (XPS) using monochromatic Al

K-alpha X-ray source, which was operated in the constant-

pass 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 per-

formed by a peak-fitting program (Avantage) using Lor-

entzian–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 perme-

ability (l0 and l00) up to 1 GHz were found out using

impedance spectroscopy (Agilent 4291B Impedance Ana-

lyzer). 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 parti-

cle systems are compiled in Fig. 1. The diffraction peaks at

44.5� and 51.8� are the characteristic XRD peaks for face-

centered cubic (fcc) metallic nickel crystals. The peaks

were matched with JCPDS card #04-0850 and indexed as

J Mater Sci: Mater Electron

123

(111) and (200) respectively. The processed nanocompos-

ites 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 man-

ufacturer’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.

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 corre-

sponding satellites at 858.6 and 875.8 eV respectively [27].

In addition, deconvolution of the core levels showed the

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

35 40 45 50 55 600

2000

4000

6000

8000

10000

(200

)

(111

)

(b) Ni 100 nm

(a) Ni 25 nm

Inte

nsity

(a.u

.)

2θ

Fig. 1 XRD plot comparison for nanocomposites with 100 and

25 nm nickel nanoparticles

880 870 860 850 8400

2p1/2

2p3/2

(b)

Ni (0)

Ni (0)

Ni (+3)

Ni (+2)

Binding Energy (eV)

Cou

nts

(a.u

.)

100 nm Ni880 840

0

(a)

Ni (0)Ni (+3)

Ni (+2)

Ni (0)25 nm Ni

Cou

nts

(a.u

.)Fig. 2 Deconvoluted XPS core-level scan of Ni a 25 nm; b 100 nm

2

4

6

8

20 40 60 80 100

Den

nsit

y (

g/cc

)

Ni Vol. %

Theoretical

100 nm Ni

25nm Ni

Fig. 3 Variation of density with respect to nickel vol% in the epoxy

matrix

J Mater Sci: Mater Electron

123

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 bemuch higher than that achieved here.

For example, literature reports that more than 80 % theo-

retical 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%, indicatingmuch poorer particle packing with these

finer nanoparticles having high surface area. The SEM

images for 40 and 60 vol% nickel-loaded polymer com-

posite (Fig. 4) illustrate that the fillers are uniformly dis-

tributed 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 withfrequency. 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 mul-

timeter 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

J Mater Sci: Mater Electron

123

3.5 Magnetization curves

The B–H loops for different nanocomposite systems are

shown in Fig. 6. The induced internal magnetization (Y-

axis) 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 hys-

teresis 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 nanocom-

posites (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 accor-

dance 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 frequency-

stability

3.6.1 Permeability

The real and imaginary parts of the permeabilities (l0 andl00) 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-

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 perme-

ability 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:

cala � leffla þ 2leff

þ cblb � lefflb þ 2leff

¼ 0 ð1Þ

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 per-

meability. Different particle permeabilities were chosen to

generate a set of curves for the nanocomposite perme-

ability. The permeability variation as a function of metal

loading is also plotted with the nonmagnetic grain bound-

ary model (NMGB) in Fig. 10, again with different particle

permeabilities. The constitutive equation for NMGB is

represented as:

0

2

4

6

8

10

12

14

16

0.2 0.3 0.4 0.5 0.6

Log

(Res

istiv

ity in

Ohm

-m)

Effective Ni Volume Fraction

100 nm Ni

Fig. 5 Variation of resistivity with respect to the effective nickel

vol% (including porosity) in the epoxy matrix

-60

-40

-20

0

20

40

60

-1000 -500 0 500 1000

50

30

70100 nm

B (e

mu/

gm)

H (Oe)

(a)

-50

-40

-30

-20

-10

0

10

20

30

40

50

-1000 -500 0 500 1000

Ni 25 nm

Ni 100 nm

B (e

mu/

g)

H (Oe)

(b)

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 nanocom-

posite systems are compared in (b)

J Mater Sci: Mater Electron

123

Xc ¼XiD

Xigþ D¼ Xi

Xið2p�0:333 � 1Þ þ 1ð2Þ

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 sat-

uration 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 par-

ticle 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

systems, the intrinsic particle permeability of nickel is

much lower than that for the bulk because of the demag-

netization 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

2

3

4

5

6

7

0.0 400.0 800.0Frequency (MHz)

Perm

eabi

lity

30

40

70

60

50

(a)

0

0.2

0.4

0.6

0.8

1

0.0 400.0 800.0Frequency (MHz)

Mag

netic

Los

s Ta

ngen

t

30

40

70

60

50

(b)

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

10M 100M 1G1.0

1.5

2.0

2.5

3.0

3.5

4.0

Perm

eabi

lity

(μ' )

Frequency (Hz)

40% 80% 70%

Ni (25 nm)/Epoxy Composites(a)

10M 100M 1G

0.0

0.5

1.0

1.5Ni (25 nm)/Epoxy Composites

μ"Frequency (Hz)

40% 80% 70%

(b)

Fig. 8 Variation of l0 (a) and l00 (b) as a function of frequency for

nanocomposites with 25-nm nickel particles

0

1

2

3

4

5

6

7

0 0.2 0.4 0.6

10

30

20

Nan

ocom

posi

tePe

rmea

bilit

y

Filler Volume Fraction

100 nm Ni

25 nm Ni

6

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

J Mater Sci: Mater Electron

123

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 contri-

bution of eddy current losses to l00 is simplistically esti-

mated as [37] [38]:

l00

l0¼ 2pl0l

0D2f

3Xð3Þ

X is the particle resistivity, D is the particle size, lr is therelative 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 4qpl0ð1þ XÞD2

ð4Þ

where q is the conductivity and X is the magnetic sus-

ceptibility. 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 modifi-

cations, 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 fre-

quency (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 micro-

sized ferrites and metallic nanoparticles [39, 40]. The fre-

quency (FDW) where the domain wall resonance occurs is

given as [11]:

FDW ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

2dðnþ 1Þ3pð1þ XÞD

s

cJs2pl0

ð5Þ

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 polariza-

tion. The domain wall thickness is dependent on the

exchange constant (A) and the magnetic anisotropy energy

(K). The domain structure varies with the particle dimen-

sions. In case of microscale particles, domain wall reso-

nances lead to magnetic losses at lower frequencies. Finer

particles show domain wall resonance at higher frequen-

cies, 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 par-

ticles 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 res-

onance losses and eddy current losses are suppressed [43].

For particle composites, the FMR frequency is written as

[41]:

FFMR ¼ c2p

HEff ð6Þ

while K and Heff are related as [44]:

K ffi 0:75 l0MsHEff ð7Þ

where c is the gyromagnetic ratio and Heff is the effective

field anisotropy and K is the effective anisotropy energy.

1

2

3

4

5

6

0 0.2 0.4 0.6

10

30100 nm Ni

25 nm Ni 20N

anoc

ompo

site

Perm

eabi

lity

Filler Volume Fraction

5

4

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

J Mater Sci: Mater Electron

123

Based on the permeability and loss spectra, FMR is esti-

mated to be *650 MHz for the system with 100 nm par-

ticles. 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-passi-

vated 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 nanocom-

posite density increased with filler content up to 60 vol%,

beyond which the increased-filler content reduced the

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.

References

1. P. Chakraborti, H. Sharma, P.M. Raj, R. Tummala, in ECTC 63rd

IEEE, 1043–1047 (2013)

2. S. Mathuna, T. O’Donnell, N. Wang, K. Rinne, IEEE Trans.

Power Electron. 20(3), 585–592 (2005)

3. H. Sharma, K. Sethi, P.M. Raj, R. Tummala, J. Mater. Sci. Mater.

Electron. 23, 528–535 (2012)

4. P. Muthana, K. Srinivasan, A.E. Engin, M. Swaminathan, R.

Tummala, V. Sundaram et al., IEEE Trans. Adv. Packag. 31(2),234–245 (2008)

5. T. Nakamura, J. Appl. Phys. 88, 348 (2000)

6. S. Shannigrahi, K. Pramoda, F. Nugroho, J. Magn. Magn. Mater.

324(2), 140–145 (2012)

7. H. Bayrakdar, J. Magn. Magn. Mater. 323(14), 1882–1885 (2011)8. J. Lee, Y.-K. Hong, S. Bae, J. Jalli, G.S. Abo, J. Park et al., J.

Appl. Phys. 109, 07E530 (2011)

9. L. Yang, L.J. Martin, D. Staiculescu, C. Wong, M.M. Tentzeris,

IEEE Trans. Microw. Theory Tech. 56(12), 3223–3230 (2008)

10. Magnetics, A Critical Comparison of Ferrites with Other Mag-

netic Materials. (Magnetics, 2000), http://mag-inc.com. Accessed

22 April 2015

11. F. Mazaleyrat, L. Varga, J. Magn. Magn. Mater. 215, 253–259(2000)

12. P. Gramatyka, R. Nowosielski, P. Sakiewicz, J. Achiev. Mater.

Manuf. Eng. 20(1–2), 115–118 (2007)

13. Y. Hayakawa, A. Makino, H. Fujimori, A. Inoue, J. Appl. Phys.

81, 3747–3752 (1997)

14. S. Ohnuma, H. Fujimori, T. Masumoto, X. Xiong, D. Ping, K.

Hono, Appl. Phys. Lett. 82, 946–948 (2003)

15. S. Ge, D. Yao, M. Yamaguchi, X. Yang, H. Zuo, T. Ishii et al., J.

Phys. D Appl. Phys. 40, 3660 (2007)

16. D.S. Gardner, G. Schrom, F. Paillet, B. Jamieson, T. Karnik, S.

Borkar, IEEE Trans. Magn. 45(10), 4760–4766 (2009)

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 FMR (MHz)

100 234 5.8 9 103 51 2 27 650

25 1240 3.1 9 104 22 4.4 5 3500

J Mater Sci: Mater Electron

123

17. P.M. Raj, H. Sharma, G.P. Reddy, N. Altunyurt, M. Swami-

nathan, R. Tummala et al., J. Electron. Mater. 43(4), 1–10 (2014)

18. R. Nowosielski, J. Achiev. Mater. Manuf. Eng. 24(1), 68–77

(2007)

19. A. Taghvaei, H. Shokrollahi, K. Janghorban, Mater. Des. 31(1),142–148 (2010)

20. A. Taghvaei, H. Shokrollahi, A. Ebrahimi, K. Janghorban, Mater.

Chem. Phys. 116(1), 247–253 (2009)

21. N. Tang, W. Zhong, X. Wu, H. Jiang, W. Liu, Y. Du, Mater. Lett.

59(14–15), 1723–1726 (2005)

22. Y. Zhan, S. Wang, D. Xiao, J. Budnick, W. Hines, IEEE Trans.

Magn. 37(4), 2275–2277 (2001)

23. K. Peng, L. Zhou, A. Hu, Y. Tang, D. Li, Mater. Chem. Phys.

111(1), 34–37 (2008)

24. A. Berkowitz, K. Takano, J. Magn. Magn. Mater. 200(1–3),552–570 (1999)

25. D. Fiorani, Surface Effects in Magnetic Nanoparticles (Springer,

New York, 2005)

26. P. Scherrer, Gottinger Nachrichten Math Phys 2, 98–100 (1918)

27. A.P. Grosvenor, M.C. Biesinger, R.S.C. Smart, N.S. McIntyre,

Surf. Sci. 600(9), 1771–1779 (2006)

28. P. Prieto, V. Nistor, K. Nouneh, M. Oyama, M. Abd-Lefdil, R.

Dıaz, Appl. Surf. Sci. 258(22), 8807–8813 (2012)

29. S. D’addato, V. Grillo, S. Altieri, R. Tondi, S. Valeri, S. Frab-

boni, J. Phys. Condens. Matter 23(17), 175003 (2011)

30. H. Shokrollahi, K. Janghorban, Mater. Sci. Eng. B 134(1), 41–43(2006)

31. G. Herzer, IEEE Trans. Magn. 26(5), 1397–1402 (1990)

32. W.H. Meiklejohn, C.P. Bean, Phys. Rev. 102(5), 1413 (1956)

33. S.P. Gubin, Y.A. Koksharov, G. Khomutov, G.Y. Yurkov, Russ.

Chem. Rev. 74(6), 489 (2005)

34. I. Youngs, N. Bowler, K. Lymer, S. Hussain, J. Phys. D Appl.

Phys. 38(2), 188 (2005)

35. R. Ramprasad, P. Zurcher, M. Petras, M. Miller, P. Renaud, J.

Appl. Phys. 96, 519 (2004)

36. P. Chen, M. Liu, L. Wang, Y. Poo, R.-X. Wu, J. Magn. Magn.

Mater. 323(23), 3081–3086 (2011)

37. Y. Li, G. Li, Physics of Ferrites (Science, Beijing, 1978), p. 335

38. S.B. Liao, Ferromagnetic Physics (Science, Beijing, 1992),

pp. 17–81

39. M.A. Abshinova, A.V. Lopatin, N.E. Kazantseva, J. Vilcakova, P.

Saha, Compos. A Appl. Sci. Manuf. 38(12), 2471–2485 (2007)

40. M. Wu, Y. Zhang, S. Hui, T. Xiao, S. Ge, W. Hines et al., Appl.

Phys. Lett. 80, 4404–4406 (2002)

41. B. Lu, X. Dong, H. Huang, X. Zhang, X. Zhu, J. Lei et al., J.

Magn. Magn. Mater. 320, 1106–1111 (2008)

42. G. Bertotti, Hysteresis in Magnetism, 1st edn. (Academic Press,

New York, 1998)

43. C. Kittel, Phys. Rev. 73(2), 155 (1948)

44. X. Zhang, X. Dong, H. Huang, Y. Liu, W. Wang, X. Zhu et al.,

Appl. Phys. Lett. 89, 053115 (2006)

45. F. Fonseca, G. Goya, R. Jardim, R. Muccillo, N. Carreno, E.

Longo et al., Phys. Rev. B 66(10), 104406 (2002)

J Mater Sci: Mater Electron

123