The shape dependence of magnetic and microwave properties for Ni nanoparticles

Article abstract of DOI:10.1016/j.jmmm.2011.08.013

The magnetic and microwave properties of Ni nanospheres and conical nanorods have been investigated through experimental and theoretical methods. Ni nanospheres and conical nanorods have the same crystal structure and close particle size, whereas the remanence ratio, coercivity, dynamic permeability and microwave absorbing properties show great dependence on their shape. Ni conical nanorods self-assembled into urchin-like structure have higher natural resonance frequency due to the large shape anisotropy compared to the Ni nanospheres. Supposing random spatial distribution of magnetic easy axes and using the LandauLifshitzGilbert equation associated with the Bruggemans effective medium theory, we simulate the complex permeability of Ni nanoparticles, which agrees well with the experimental results.

Full text of DOI:10.1016/j.jmmm.2011.08.013

Journal of Magnetism and Magnetic Materials 324 (2012) 205–209
Contents lists available at SciVerse ScienceDirect
Journal of Magnetism and Magnetic Materials
journal homepage: www.elsevier.com/locate/jmmm
The shape dependence of magnetic and microwave properties for
Ni nanoparticles
Fei Ma n, Ji Ma, Juanjuan Huang, Jiangong Li n
Institute of Materials Science and Engineering, Lanzhou University, Lanzhou 730000, China
a r t i c l e i n f o
a b s t r a c t
Article history:
The magnetic and microwave properties of Ni nanospheres and conical nanorods have been
investigated through experimental and theoretical methods. Ni nanospheres and conical nanorods
have the same crystal structure and close particle size, whereas the remanence ratio, coercivity,
dynamic permeability and microwave absorbing properties show great dependence on their shape. Ni
conical nanorods self-assembled into urchin-like structure have higher natural resonance frequency
due to the large shape anisotropy compared to the Ni nanospheres. Supposing random spatial
distribution of magnetic easy axes and using the Landau–Lifshitz–Gilbert equation associated with
the Bruggeman’s effective medium theory, we simulate the complex permeability of Ni nanoparticles,
which agrees well with the experimental results.
Received 20 April 2011
Received in revised form
20 July 2011
Available online 11 August 2011
Keywords:
Wet-chemical synthesis
Shape anisotropy
Complex permeability
Microwave absorption
& 2011 Elsevier B.V. All rights reserved.
Ferromagnetic metals have been paid much attention in
microwave application due to their higher saturation magnetiza-
tion and permeability compared to ferrite. Such materials which
were expected as high density recording media, magnetic field
sensor or electromagnetic wave absorption material should have
high value of complex permeability, tunable resonance frequency
and low eddy current loss in microwave range [1–5]. Considerable
works have investigated the complex permeability of metal-based
magnetic material through experimental or theoretical method. It
is widely proved that the magnetic properties and microwave
properties of ferromagnetic nanoparticles are related to their size
and shapes [6–8]. As the particle size decreases, eddy current loss
can be considerably suppressed and when it comes into nan-
ometer scale, surface effect [9], size effect [10,11] combined with
shape anisotropic effect [12–14] become dominant in the mag-
netic and microwave properties. The behavior of the complex
permeability in microwave frequency should ascribe to such
mixed effect to clarify which we should find a proper way to
separate the size, surface and shape effect. In our present work, we
compared Ni nanospheres with Ni conical nanorods to research
the shape effect on the static magnetic properties (coercivity and
remanence ratio), complex permeability and microwave absorbing
properties. Landau–Lifshitz–Gilbert equation associated with the
Bruggeman’s effective medium theory were used to simulate the
complex permeabilities of Ni nanospheres and conical nanorods
supposing random spatial distribution of magnetic easy axes.
To prepare Ni nanospheres, 25 ml alcoholic solution of 0.1 M
NiCl2 ꢀ 6H2O, 25 ml alcoholic solution with 0.2 g polyvinyl pyrro-
lidone (PVP, K¼30), 50 ml alcoholic solution of 0.5 M NaOH and
6 ml hydrate hydrazine (N2H4 ꢀ H2O 80%) were mixed together.
Then, the mixed solution was heated to 80 1C for 3 h. After
washing and desiccation, the spherical Ni nanoparticles were
obtained. To prepare Ni conical nanorods, 25 ml alcoholic solution
of 0.1 M NiCl2 ꢀ 6H2O and 25 ml alcoholic solution with 0.2 g PVP
were mixed, and 6 ml hydrate hydrazine was added into the
above solution dropwise at 70 1C. A pink suspension was obtained
immediately. The as-prepared suspension was added dropwise
into a mixed solution with 50 ml alcoholic solution of 0.5 M NaOH
and 10 ml hydrate hydrazine in a three-necked flask at 80 1C.
Then, the solution was refluxed for 3 h. After washing and
desiccation, Ni conical nanorods self-assembled into urchin-like
structure were obtained.
The scanning electron microscopy (SEM) observations were
carried out to investigate the morphology of Ni nanoparticles. Ni
nanospheres with a mean diameter of 30–50 nm are shown in
Fig. 1(a) while conical nanorods radially growing from one center
into urchin-like architectures are shown in Fig. 1(b). The nanorods
have diameters in the range of 25–50 nm and lengths up to 500 nm.
Fig. 1(c) shows the X-ray diffraction (XRD) patterns of the as-
prepared Ni nanospheres and conical nanorods. All diffraction peaks
can be indexed with the face-centered cubic (fcc) Ni. No additional
diffraction peaks from the impurities such as nickel oxide or
hydroxide were detected. The broad diffraction peaks, which are
quantified by the full-width at half-maximum (FWHM) are indica-
tive of the ultrafine Ni particles. Furthermore, the average grain
dimensions are estimated to be 30 nm for nanospheres and 35 nm
n Corresponding authors.
E-mail addresses: maf@lzu.edu.cn (F. Ma), lijg@lzu.edu.cn (J. Li).
0304-8853/$ - see front matter & 2011 Elsevier B.V. All rights reserved.
doi:10.1016/j.jmmm.2011.08.013

206
F. Ma et al. / Journal of Magnetism and Magnetic Materials 324 (2012) 205–209
Fig. 1. The SEM micrographs of Ni nanoshperes (a) and conical nanorods (b); XRD patterns of the Ni nanospheres and conical nanorods (c); TEM micrograph of the
as-synthesized coordination compound (d).
for conical nanorods with the FWHM (with the instrumental peak
width eliminated) of the (111), (200) and (220) crystallographic
planes according to the Scherrer equation. The calculated grain
sizes are consistent with the diameters of nanospheres and nanor-
ods, which suggests that both the Ni nanospheres and the conical
nanorods obtained by wet chemical methods are single crystal.
It was found that the adding sequence of the reactants plays a
dominant role in the control of crystal morphology. The adding
sequence of the reactants dominated the formation of intermedi-
ates in the reduction procedure. Conical rods were not obtained
unless the intermediate known as coordination compound
Ni(N2H4)xCl2 was formed through the reduction reaction. To
research the mechanism of the formation of conical nanorods,
we investigated the morphology and composition of the inter-
mediate. It is found that the probable chemical formula is
Ni(N2H4)3Cl2 based on the weight percentages of 26.17, 37.44
and 5.34 wt% for Ni, N and H, respectively, by atomic emission
spectrometer and elemental analysis. Fig. 1(d) shows the
transmission electron microscopy (TEM) observations of the
Ni(N2H4)3Cl2 synthesized at 70 1C. All particles are rod-like
maintaining diameters about 100–300 nm and lengths up to
400–600 nm. The formation of coordination compound is prob-
ably attributed to the nature of the electrostatic attraction. As we
know, each nitrogen in hydrazine has a couple of unbonded
electrons, so that hydrazine is eager to absorb positive charged
ions such as Ni2þ. It is reasonable to conclude that such rod-like
coordination compound can serve as an in-situ template resulting
in the Ni conical nanorods. However, the bond energy of OHꢁ and
Ni2þ is larger than that of N2H4 and Ni2þ so that the rod-like
coordination compound can only be ensured by adding
N2H4 ꢀ H2O first into the NiCl2 solution, and without the rod-like
coordination compound as the precursor, Ni conical nanorods
cannot be synthesized.
(Mr/Ms) are 134 Oe, 0.32 and 279 Oe, 0.38, respectively. The Hc
and Mr/Ms of the Ni conical nanorods are both higher than that of
the Ni nanospheres. Considering that the nanospheres and conical
nanorods have close grain size and particle diameter, such
discrepancy in Hc and Mr/Ms is probably due to the effect of shape
anisotropy. As we know, the effective anisotropy, which is the
sum of magnetocrystalline and shape anisotropy, is directly
proportional to the coercivity. Along long axis of the nanorods
the demagnetizing field is much smaller compared to that of short
axis, which means the pinning of the magnetization in the long
axis direction. Such pinning effect usually makes the magnetiza-
tion harder to reverse so that higher Hc and Mr/Ms compared to
isotropic structures. This is why the Hc and Mr/Ms of Ni conical
nanorods is higher than that of Ni nanospheres.
The saturation magnetization of the bulk Ni at 300 K is
55.0 emu/g [15]. Both of the saturation magnetizations of nano-
spheres (45.02 emu/g) and nanorods (43.77 emu/g) are smaller
than that of bulk Ni. There are several reasons for the decrease in
Ms such as the surface oxidation, the nonmagnetic or weakly
magnetic interfaces [16], the ligand effect on the particle surface,
etc. It was inevitable to have oxidation layers for ultra fine
nanoparticles in our present work. The oxide layer of the Ni
particle is an antiferromagnet, so that the presence of such layers
usually has no contribution to the Ms and lowers the magnetic
moment per unit mass, and the spin of nickel which is close to the
oxide layer is pinned due to the exchange anisotropy interaction
between the antiferromagnetic layer of NiO and the ferromag-
netic core of Ni [17]. Furthermore, poor magnetic properties
found for nanoparticles were usually related to the presence of
precursor residues coordinated on the surface. It is well known
that strong p–acceptor ligands, such as carbon monoxide, induce
a dramatic collapse of the saturation magnetization [18,19]. In
our experimental system, PVP which is a widely used surfactant
serves as a dispersant. It usually absorbs on the surface of Ni
nanoparticles, so that the saturation magnetization might also
decrease through the ligand effect of carbonyl groups in PVP.
The M–H hysteresis loops of the Ni nanospheres and nanorods
are illustrated in Fig. 2(a). It can be seen that they are both
ferromagnetic and their coercivity (Hc) and remanence ratio

F. Ma et al. / Journal of Magnetism and Magnetic Materials 324 (2012) 205–209
207
Fig. 3. Comparison of experimental and calculated complex permeability for Ni
nanoshperes (a) and conical nanorods (b).
is shown in Fig. 2(b)), the magnetization and field are given as
M ¼ ðmx,my,MsÞ
H ¼ ðhx,0,HeÞ
ð2Þ
By substituting Eq. (2) into Eq. (1), considering 9hx959He9 and
Fig. 2. Magnetic hysteresis loops of the Ni nanoshperes and conical nanorods (a);
coordinate system for microwave propagation in a single anisotropic particle (b).
9m959Ms9, the diagonal element
m
and off diagonal element
k
are
as follows:
mx
hx
om
ð
o0 þiao
Þ
m
k
¼ 1þ
¼ 1þ
o0 þiaoÞ2ꢁ
omo
o
2
ð
The microwave permeability of the Ni nanoparticle–paraffin
wax composites compacted into ring shapes was measured. The
composites with 21.0 vol% Ni nanospheres and 23.3 vol% Ni
conical nanorods were investigated, respectively, in the range of
0.1–18 GHz by measuring the reflection coefficient S11 and the
transmission coefficient S21 in an APC7 coaxial mode. Fig. 3
(triangle lines) shows the frequency dependence of complex
permeability (m0 and m00) in the range of 0.1–18 GHz. The complex
permeability for Ni nanospheres and conical nanorods has similar
pattern: m0 decrease with frequency, while m00 of the composites
show a broad resonance peak, which is 2.8 GHz for nanospheres
and 4.3 GHz for conical nanorods. In gigahertz range, the reso-
nance behavior for metal magnetic nanoparticles is usually
ascribed to the natural resonance.
my
¼
ꢁ
¼
ð3Þ
2
hx
ð
o0 þiaoÞ2ꢁ
o
where om¼gMs and o0¼gHe. The above solutions were deduced
based on the microwave field h perpendicular to He. When the
microwave field h is not perpendicular to He, by substituting
Eq. (2) into Eq. (1) and combining with Maxwell’s equations, the
permeability tensor is given by [20]
0
1
1ꢁsin2 ycos2
f
ꢁsin2 ysin
f
cos
f
ꢁsin
ꢁsin
y
y
cos
cos
1ꢁcos2
y
y
cos
sin
y
f
f
ꢀ
ꢁ
2
B
B
@
C
C
A
1
d
o
ꢁsin2 ysin
f
cos
f
1ꢁsin2 ysin2 f
m
¼
e
i
ꢁsin
y
cos
y
cos
f
ꢁsin
y
cos
y
sin
f
ð4Þ
For the calculation of dynamic frequency dependent perme-
ability around natural resonance range, Gilbert equation has been
widely used:
(
)
1=2
k2Þsin2 yþ2
m
2½ð
7½ðm2
ꢁ
k
ꢁ
k2Þ sin4 yþ4
k
2 cos2 y 1=2
ꢃ
2
ð
m2
ꢁ
k
ꢁ
d
¼ i
oð
m0e 1=2
Þ
m
ꢁ1Þsin2 yþ1ꢃ
ð5Þ
dM
dt
a
Ms
dM
dt
¼ ꢁg
M ꢂ He þ
M ꢂ
ð1Þ
where
d is given in Eq. (5) and m and k are given in Eq. (3). Eq. (4)
can be used to calculate the intrinsic permeability ( ı) of one
magnetic domain. With a random distribution of He an equivalent
average magnetic permeability should be given as follows, in
where M is the magnetization, He is the effective anisotropic field,
is the gyromagnetic factor, is the damping coefficient and Ms
m
g
a
is the saturation magnetization. When the microwave field h is
perpendicular to the effective anisotropic field (the diagram
which 10,000 single domains with randomly generated angles y

208
F. Ma et al. / Journal of Magnetism and Magnetic Materials 324 (2012) 205–209
and
j
were considered.
was plotted as a function of frequency. The real part e0 and
imaginary part e00 of the complex permittivity maintained almost a
constant over 0.1–18 GHz except for the little fluctuation above
14 GHz. It was found that the complex permittivity for nanorods
was higher than that of nanospheres. In the metal–insulator
composites, the space charge and the dipole polarization could be
ascribed to the polarization phenomena. The space charge polariza-
tion often takes place in the interface between the metal core and
the insulator matrix. The free electrons from the metal fractions
promote the charge accumulation at the interfaces and the higher
permittivity is attained due to the improved electrical conductivity.
Nanorods have larger specific surface area, which might result to
more space charge polarization so that higher complex permittivity
compared to nanospheres. The dielectric and magnetic loss tangent
P
N1 mi
ðy,fÞ
/m
iS ¼
ð6Þ
N
An equivalent scalar permeability of mı can then be calculated by
taking the Eigen value of the permeability tensor:
ꢂ
ꢃ
mi ¼ Eigenvalue /
miS
ð7Þ
Magnetic particles with certain volume fraction P are dispersed in
a nonmagnetic matrix (paraffin wax). The effective permeability
(
m
eff) for composite can be calculated by normal Bruggeman’s
effective medium theory [21,22]
mi
ꢁmeff
1ꢁmeff
1þ2meff
p
þð1ꢁpÞ
¼ 0
ð8Þ
mi þ2meff
can be expressed as tan dE¼ / ¼ /
e00 e0 and tan dM m00 m0, respectively,
which means the ratio of energy loss to the energy storage.
Fig. 4(b) shows frequency dependence of the dielectric and magnetic
loss tangent of Ni nanospheres and conical nanorods composites. It
can be seen that the value of magnetic loss is much higher than that
of dielectric loss, illustrating that the main loss for the composites in
the range of 0.1–18 GHz is magnetic loss. Furthermore, the magnetic
loss tangent appears peaks with the increase of frequency. The peak
for the nanospheres has the maximum value about 0.5 higher than
that of conical nanorods. However, the peaks for conical nanorods
are wider and appear in higher frequency range compared to that of
nanospheres, which means conical nanorods might be more suitable
to be a broad band microwave absorber.
Fig. 3 (solid lines) shows theoretical fitting curves of the
complex permeability for Ni nanospheres (Fig. 3(a)) and Ni
conical nanorods (Fig. 3(b)). We suppose that the saturation
magnetization 4pMs is 4.90 kG based on the experimental data
of VSM for both nanospheres and nanorods, the damping para-
meters are 0.50 for nanospheres and 0.65 for nanorods from the
width of the natural resonance peak. It was found that the fitting
curves match satisfactorily with the experimental data when the
He¼0.187 kOe for nanospheres and 0.700 kOe for conical nanor-
ods. The He of Ni conical nanorods is much higher than that of Ni
nanospheres, which shows good agreement with the discussion
on Hc. Moreover, from the Kittel [8] model for natural resonance,
the natural resonance peak varies linearly with He, which is the
sum of crystalline anisotropy, shape anisotropy, surface aniso-
tropy, etc. In our case, Ni nanospheres and conical nanorods have
the same crystal structure and close particle size, so that the
major difference between the two samples is their morphology.
Ni conical nanorods have larger shape anisotropy which origi-
nated from demagnetization effect can increase He dramatically.
This is why Ni conical nanorods have larger He and higher
resonance frequency compared to Ni nanospheres.
The reflection loss (RL) of a microwave absorbing layer backed
by a perfect conductor was calculated by the following equations:
ꢄ
ꢄ
ꢄ
ꢄ
ꢄ
ꢄ
ꢄ
ꢄ
ðZinꢁ1Þ
ðZin þ1Þ
RLðdBÞ ¼ 20log10
ð9Þ
ꢀ
ꢁ
ꢅ ꢀ
ꢁ
ꢆ
1=2
mr
er
2
p
c
fd
1=2
Zin
¼
tanh j
ð
mrer
Þ
ð10Þ
where RL is a ratio of reflected power to incident power in dB, Zin
In order to explore the microwave absorbing properties of the
composites, both magnetic and dielectric loss should be considered.
As shown in Fig. 4(a), the complex permittivity of Ni nanoparticles
is the normalized input impedance relative to the impedance in
e0–je00 and mr m0–jm00 is the complex permittivity
free space, er¼ ¼
and complex permeability of the absorber material, d is the
thickness of the absorber, and c and f are the velocity of light
and the frequency of microwave in free space, respectively. The RL
curves were shown in Fig. 5 for both Ni nanospheres and conical
nanorods. The RL was less than –10 dB in the 6.7–9.5 GHz for
conical nanorods while more than –8 dB in the whole frequency
range for nanospheres with thickness of 2.5 mm. The values less
than –10 dB indicates that more than 90% of the introduced
microwaves are absorbed, so this value is the target value to be
attained for the absorber’s applications. More importantly, the
thickness of the sample is smaller than that of the usual ferrite
material indicating that the Ni conical nanorods may be good
microwave absorption filler in broad frequency band.
Fig. 4. Frequency dependences of the complex permittivity (a); frequency depen-
Fig. 5. Simulated RL for Ni nanoparticle–paraffin wax composites with the
dences of the dielectric and magnetic loss tangent (b).
thickness of 2.5 mm.

F. Ma et al. / Journal of Magnetism and Magnetic Materials 324 (2012) 205–209
209
In conclusion, the Ni nanospheres and conical nanorods have
been synthesized by wet-chemical methods. The anisotropic
growth of Ni nanoparticles should be ascribed to the formation
of one-dimensional intermediate Ni(N2H4)3Cl2. The synthesized
Ni nanospheres and conical nanorods have close particle and
grain size, which makes them the ideal candidate to investigate
the shape effect on their magnetic properties. We compared the
magnetic and microwave properties of the Ni nanospheres and
conical nanorods by both experimental and theoretical methods.
The coercivity, remanence ratio and natural resonance frequency
of Ni nanoparticles all show dependence on their shape. Ni conical
nanorods with larger shape anisotropy compared to nanospheres
have larger coercivity and higher resonance frequency.
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This work was supported by Open Project of Key Laboratory
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