Electrical and magnetic properties of nanocrystalline Fe100-xNix alloys

Article abstract of DOI:10.1016/j.jmmm.2007.05.021

The electrical and magnetic properties of nanocrystalline binary Fe_100-xNi_x alloys, where x ranges from 0 to 100, prepared by a combination of aqueous and solid-state reduction processes have been studied vis-à-vis their microstructure. The microstructural studies indicate the formation of near-equilibrium phases in the alloys with crystallite size in the range 20-40 nm. The crystallite size in the case of pure Fe and Ni, however, is in the range 40-80 nm. The electrical transport in the temperature range 20-300 K exhibits a typical ferromagnetic metallic behavior in all the cases and the absolute resistivity of nanocrystalline Fe_100-xNi_x alloys decreases monotonically with increasing Ni content. The saturation magnetization of the alloys on the other hand decreases progressively with Ni addition towards that of pure Ni value. The coercivity of alloys is found to be independent of temperature in the range 5-300 K except in the case of pure Ni wherein it increases from 30 Oe at 300 K to 65 Oe at 5 K. The electrical and magnetic properties of the nanocrystaline Fe-Ni alloys do not follow the predictions of simple itinerant band model for alloys. The temperature dependence of saturation magnetization in all the cases has a T^3/2 Bloch variation while the average atomic moment of the alloys has an effective medium composition dependence.

Full text of DOI:10.1016/j.jmmm.2007.05.021

ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 320 (2008) 182–189
www.elsevier.com/locate/jmmm
Electrical and magnetic properties of nanocrystalline Fe100ꢀxNix alloys
Ã
Satish Vittaa, , A. Khuntiaa, G. Ravikumarb, D. Bahadura
aDepartment of Metallurgical Engineering and Materials Science, Indian Institute of Technology Bombay, Mumbai 400076, India
bBhabha Atomic Research Center, Mumbai 400085, India
Received 4 January 2007; received in revised form 27 April 2007
Available online 3 June 2007
Abstract
The electrical and magnetic properties of nanocrystalline binary Fe100ꢀxNix alloys, where x ranges from 0 to 100, prepared by a
combination of aqueous and solid-state reduction processes have been studied vis-a-vis their microstructure. The microstructural studies
indicate the formation of near-equilibrium phases in the alloys with crystallite size in the range 20–40 nm. The crystallite size in the case
of pure Fe and Ni, however, is in the range 40–80 nm. The electrical transport in the temperature range 20–300 K exhibits a typical
ferromagnetic metallic behavior in all the cases and the absolute resistivity of nanocrystalline Fe100ꢀxNix alloys decreases monotonically
with increasing Ni content. The saturation magnetization of the alloys on the other hand decreases progressively with Ni addition
towards that of pure Ni value. The coercivity of alloys is found to be independent of temperature in the range 5–300 K except in the case
of pure Ni wherein it increases from 30 Oe at 300 K to 65 Oe at 5 K. The electrical and magnetic properties of the nanocrystaline Fe–Ni
alloys do not follow the predictions of simple itinerant band model for alloys. The temperature dependence of saturation magnetization
in all the cases has a T3/2 Bloch variation while the average atomic moment of the alloys has an effective medium composition
dependence.
r 2007 Elsevier B.V. All rights reserved.
PACS: 61.46.Df; 73.63.Bd; 75.50.Tt
Keywords: Nanoparticles; Electronic transport; Magnetic properties
1. Introduction
magnetic behavior of transition metals, however, under-
goes continuous changes as a function of physical size.
A typical ferromagnetic material undergoes a magnetic
phase transition to superparamagnetism when the size is
reduced and this critical size varies between 10 and 100 nm
for most materials. Such magnetic nanoparticles have
diverse applications such as information storage to drug
delivery because of which they are of significant interest.
A detailed study of the effect of alloying the metal
nanoparticles on the magnetic behavior and also the
nature of magnetic state below the superparamagnetic
limit, size and temperature, have not been investigated in
detail and these are addressed in the present work [1–7].
The Fe–Ni alloys belong to a technologically important
class of alloy systems called permalloys because of their
soft magnetic properties which can be varied by varying the
alloy composition in the range 50–80 wt% Ni [8–11]. They
are used for recording applications and exhibit giant
magnetoresistance when combined with non-magnetic
The physical properties, specifically electronic and
magnetic, undergo sharp transition when the physical size
of the material reduces below certain critical values. Gaps
appear in the electron density of states leading to
quantization, which affects the electronic behavior when
the size is reduced to tens of nanometers in semiconductors
while in the case of metals the size limit to observe such
effects is much lower. Hence the transport behavior of
nanosized metals, excluding clusters, is never investigated
in detail and conventional scattering theories are used to
analyze the transport behavior. The combination of
nanosize and alloying on the other hand can change the
transport behavior and a study of this phenomenon forms
one of the objectives of this work. The macroscopic
Ã
Corresponding author.
E-mail address: satish.vitta@iitb.ac.in (S. Vitta).
0304-8853/$ - see front matter r 2007 Elsevier B.V. All rights reserved.
doi:10.1016/j.jmmm.2007.05.021

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S. Vitta et al. / Journal of Magnetism and Magnetic Materials 320 (2008) 182–189
183
metals [12]. The alloys in the composition range 30–40 wt%
Ni, known as Invar alloys, exhibit a nearly zero thermal
expansion coefficient and are extensively used. Because of
their high technological relevance, only specific composi-
tions in these alloys are investigated both theoretically and
experimentally [13–17]. A systematic investigation of the
properties of alloy particles, which are three-dimensionally
nanosized, across the binary spectrum of compositions,
however, has not been done. Hence in the present work,
nanocrystalline Fe–Ni alloy particles across the binary
composition spectrum have been synthesized and their
physical properties studied in detail vis-a-vis the structure.
The alloy particles have been synthesized using the soft
chemical borohydride reduction as this technique is well
established and has been used extensively to synthesize
even core-shell structured magnetic particles. A total of five
different compositions including Fe and Ni have been
investigated in the present work. The alloy compositions
between Fe and Ni chosen for investigation correspond to
those of the known intermetallic compounds Fe3Ni, FeNi
and FeNi3 [18]. These compounds exhibit order–disorder
transformations and all have a cubic crystal structure.
to make Fe50Ni50 alloy. The initial pH of metal salt
solutions was ꢂ5.0 while that of NaBH4 was ꢂ9.5. The
pH of the resulting solution mixture was not modified with
any additions. Aqueous state reduction of the combined
precursor solution was done by dropwise addition of
NaBH4 solution (3 M concentration) with constant magnetic
stirring of the solution mixture. Although the reactions are
highly exothermic in nature, dropwise addition of NaBH4
solution ensures that the average reaction temperature does
not rise too much above 300 K.
NiCl2 ꢁ 6H2O þ 2NaBH4 ! Ni þ 2NaCl
þ 2H3BO3 þ 7H2m;
2FeCl3 þ 6NaBH4 þ 18H2O ! 2Fe þ 6NaCl
þ 6H3BO3 þ 21H2m:
The resulting solution along with the black powder
precipitate was centrifuged at 3000 rpm and washed several
times with water to completely remove the water-soluble
products and the reactants, present if any. The precipitate
powder was dried at 423 K and then reduced further in
flowing H2 gas at a temperature of 873 K for an hour. The
chemical composition of different Fe100ꢀxNix alloys that
were prepared and investigated is given in Table 1.
2. Experimental methods
The nanocrystalline pure metal and alloy powders,
Fe100ꢀxNix where x is the wt% concentration of Ni, were
made by a combination of aqueous and solid-state reduc-
tion. The precursor for Fe is FeCl3 solution and
NiCl2 ꢁ 6H2O solution is the precursor for Ni. These
solutions were prepared from high-purity salts. In order to
prepare alloys with different compositions, metal salt
solutions with different molar concentrations but fixed
volume were prepared separately and then mixed before
adding NaBH4, the aqueous reducing agent. This will
facilitate synthesizing alloys with different compositions,
e.g., 50ml each of 1 M concentration FeCl3 and
NiCl2 ꢁ 6H2O solutions were mixed and reacted with NaBH4
The structural characterization, phase identification,
grain size determination and compositional analysis were
done by a combination of X-ray diffraction, scanning
electron microscopy and transmission electron microscopy.
The chemical composition of the alloys given in Table 1 is
determined by energy dispersive X-ray analysis in the
scanning electron microscope. Synthesis of metal nano-
particles by borohydride reduction in some cases results in
the formation of metal borides [19]. In the present work,
however, boron does not seem to form any borides as
observed by X-ray diffraction, discussed in the next section
and also chemical composition analysis by energy-disper-
sive X-ray analysis. The boron forms predominantly
Table 1
The chemical composition of different Fe100ꢀxNix alloys together with the various structural parameters obtained from X-ray diffraction and transmission
electron microscopy
Sample
Ni (wt%)
Phase
Size (nm)
XRD
80
Crystal structure
Lattice parameter (nm)
TEM
100
Present
0.287
Bulk
F
Fe
0
26
Fe
BCC
0.286
F3N1
Fe74Ni26
FN
Fe0.94Ni0.06
Fe0.64Ni0.36
FeNi
25
20
24
45
40
35
50
60
BCC
FCC
FCC
0.287
0.359
0.358
0.286
0.359
0.356
51
Fe49Ni51
F1N4
Fe19Ni81
N
81
FeNi3
Ni
FCC
FCC
0.354
0.352
0.354
0.352
100
Ni
The lattice parameters of the bulk phase given are from the JCPDS Table [34]. The size determined from TEM is the particle size as compared to grain size
obtained by XRD.

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184
H3BO3, which gets removed after repeated washing with
water. The electrical resistivity of the nanocrystalline alloys
was measured as a function of temperature in the range
20–300 K using the standard DC Four-probe technique.
For the purpose of resistivity measurement, the powder
was compacted into pellets of size 10 mm ꢃ 5 mm ꢃ 5 mm
in a hydraulic press at a pressure of 60 kg cmꢀ2. No binders
were used for compressing the powder into pellets and
these were found to have a porosity of ꢂ15%, measured
using the standard ASTM technique [20]. A small piece of
this pellet weighing ꢂ2–3 mg was used for magnetic
measurements. The magnetic properties, magnetization as
a function of external magnetic fields up to 40 kOe in the
temperature range from 5.0 to 300 K, were studied using a
SQUID magnetometer.
particles. This hump-like feature is clearly absent in the
alloy compositions indicating that addition of Ni to Fe
reduces the oxidation potential. In the case of Fe74Ni26
alloy, two sets of peaks can be identified corresponding to
Fe94Ni6 ‘BCC’ phase and Fe64Ni36 ‘FCC’ phase. The BCC
phase is a solid solution of Ni in Fe, while the FCC phase
corresponds to the intermetallic compound Fe3Ni. Increas-
ing the Ni concentration results in the formation of a
single-phase microstructure as seen in the Fe49Ni51 alloy.
All the peaks could be indexed to the intermetallic
compound FeNi, which has an FCC structure. The
diffraction pattern from the Fe19Ni81 alloy shows the
presence of a single-phase corresponding to the interme-
tallic compound FeNi3. The peaks in the diffraction
pattern from pure Ni could be indexed to the FCC phase.
A tetragonal phase formation due to the presence of
oxygen in Ni has been recently reported [21]. In the present
work, however, no evidence for the presence of a tetragonal
phase was observed. The average crystallite size in each of
the alloys can be determined from the half-width of the
peaks after subtracting the instrumental broadening [22]
and it is found to be E20 nm, given in Table 1. The
crystallite size in the case of pure Fe and Ni, however, is
E80 and 45 nm, respectively, much larger than the
crystallite size in alloys. These results indicate an inherent
resistance to growth of the crystallites in the case of alloys
compared to pure elements. The microstructure was also
studied by transmission electron microscopy. Fig. 2 shows
the typical microstructural image together with the selected
area diffraction pattern from Fe19Ni81 alloy. The particle
size is found to be E50 nm and the diffraction pattern
shows an FCC ring pattern, in agreement with the X-ray
diffraction results. The particle size determined by trans-
mission electron microscopy is larger than the size
determined by X-ray diffraction showing that the particles
are made of multiple crystallites. The magnetic nature of
the crystallites promotes aggregation leading to formation
of large particles as observed by transmission electron
microscopy.
3. Results
The X-ray diffraction patterns obtained from the
Fe100ꢀxNix nanocrystalline alloy powders after solid-state
reduction at high temperature are shown in Fig. 1. The
X-ray diffraction pattern of the as prepared powder (dried
precipitate) does not show any peaks indicating that
microstructural development takes place during the solid-
state reduction process at 873 K. The as prepared powder is
amorphous in nature and was found to be very weakly
magnetic. The diffraction pattern from Fe shows clear
peaks, which can be indexed to the ‘BCC’ phase. A broad
hump like feature is seen at a 2y value of around 251, which
could be due to the presence of an oxide layer on the Fe
∗
N
∗
∗
∗ Ni
∗
∗
∗
∗
F1N4
∗ FeNi3
∗
∗
∗
∗
It is interesting to observe that alloy formation takes
place as per the equilibrium phase diagram [23], although
the method of preparation is not an equilibrium process.
The chemical composition for the alloys develops during
the aqueous state reduction process, while the structural
development takes place during the low temperature
annealing process. Although kinetically the processes are
far from equilibrium, equilibrium phase formation indi-
cates that thermodynamic compound formation energies
are very low and override the kinetic limitations. Since the
different phases in the Fe–Ni alloy system are all cubic,
the lattice parameter can be uniquely determined from the
X-ray diffraction patterns. It is found that the lattice
parameter determined from the different peaks in all the
cases is in close agreement with the bulk phase values as
well as those obtained by atomistic simulations [17]. The
atomic size difference between Fe and Ni is only 5.8% and
hence they form substitutional solids. Since addition of Fe
FN
∗
∗ γ(Fe, Ni))
∗
∗
ο
∗ Fe0.94Ni0.06
F3N1
∗
ο
ο
ο
∗
∗
o Fe0.64Ni0.36
∗
∗ Fe
F
∗
20
30
40
50
60
70
80
90
100
Diffraction angle, 2θ
Fig. 1. The X-ray diffraction pattern from Fe100ꢀxNix nanocrystalline
alloys, Fe and Ni all show a single-phase microstructure except for the
Fe74Ni26 (F3N1) alloy which shows a mixture of two phases. The peaks
were identified using the International Centre for Diffraction Data
database [32].

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185
Fig. 2. Transmission electron microscopy image, bright field (a) and together with the selected area diffraction (b) show the nanocrystalline single-phase
nature in all the Fe100ꢀxNix alloys. The above typical micrograph is from Fe19Ni81 (F1N4) alloy. The scale bar in the micrograph corresponds to 200 nm.
to Ni or Ni to Fe, both stabilize the FCC structure, the
lattice parameters observed for the intermediate phases are
close to that of the FCC base, Ni. The lattice parameter in
general depends on the absolute crystallite size and is
known to increase as the crystallite size decreases to
nanometer scale [24,25]. The present work, however,
clearly shows that the lattice parameter depends only to a
limited extent on the absolute crystallite size and is a strong
function of the method of preparation of the nanocrystal-
line alloys. The chemical synthesis technique used results in
the formation of nearly stress-free nanocrystallites with
near-equilibrium lattice parameters.
The temperature dependence of the resistivity in the
range 20–300 K is shown in Fig. 3. A typical metallic
behavior with a positive temperature coefficient is seen in
the entire temperature range in all the cases. The absolute
value of resistivity in all the cases is found to be higher
compared to the equivalent bulk resistivity. The room
temperature resistivity of Fe is ꢂ5 orders of magnitude
higher while that of pure Ni is only an order of magnitude
higher compared to the bulk values. The resistivity
decreases monotonically with increasing Ni content at all
temperatures. The temperature dependence is non-linear in
both the alloys and pure metals, typical of ferromagnetic
systems.
The magnetization of nanocrystalline alloys, Fe and Ni,
was studied as a function of external field H and
temperature T and the results are shown in Fig. 4. The
magnetization M reaches saturation in external fields
H45000 Oe in all the cases at all temperatures. These
fields are much higher compared to the typical fields
required to saturate the magnetic moment of Fe and Ni.
This is due to the presence of nanocrystalline grains and
associated grain boundaries, which hinder the magnetic
alignment of grains and increase the effective field required
to saturate the magnetization in nanocrystalline systems.
The room temperature saturation magnetization Ms of Fe
and Ni is found to be 65 and 44 emu gꢀ1 when compared to
217.8 and 54.4 emu gꢀ1 for bulk Fe and Ni, respectively.
The magnetic fraction corresponding to these values of
10-1
10-2
10-3
10-4
10-5
10-6
F
F3N1
FN
F1N4
N
50
100
150
200
250
300
Temperature T, K
Fig. 3. The DC electrical resistivity of the nanocrystalline Fe100ꢀxNix
alloy system in the temperature range 20–300 K indicates a decreasing
resistivity with increasing Ni content. The temperature dependence in all
the cases, however, is metallic.
magnetization is found to be ꢂ30% for Fe and 82% for Ni.
The saturation magnetization of the alloys decreases with
increasing Ni content from 123.6 emu gꢀ1 for the Fe74Ni26
alloy to 73.6 emu gꢀ1 for the Fe19Ni81 alloy. In the case of
bulk alloys, however, Ms is found to exhibit a peak around
50 wt% Ni, not in agreement with the present results. The
saturation magnetization in all the different compositions
is slightly lower than the equivalent bulk value [8], an effect
of reduced size or increased specific grain boundary area
and also the presence of small quantities of oxides which
are below the detection limit of X-ray diffraction, 5%. In
the case of pure Fe, however, the magnetization is
approximately three times lower than the bulk value
possibly due to the presence of an oxide covering layer
on the surface. This is seen in the X-ray diffraction pattern
also which shows a broad hump-like feature in the 20–301
2y range. The remanant magnetization Mr and coercive
field Hc, which are a measure of the magnetic nature of a
material, are found to be very low in all the cases in the

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186
80
60
80
40
0
5K
50K
100K
150K
200K
300K
40
20
0
-20
-40
-60
-80
-40
Fe
F1N4
-80
-30
-20
-10
0
10
20
30
-30
-20
-10
0
10
20
30
External Field H, 103 Oe.
External Field H, 103 Oe.
160
120
80
5K
50K
40
20
0
100K
150K
200K
300K
40
0
-40
-80
-120
-160
-20
-40
F3N1
Ni
-30
-20
-10
0
10
20
30
-30
-20
-10
0
10
20
30
External Field H, 103 Oe.
External Field H, 103 Oe.
150
100
50
0
-50
-100
FN
30
-150
-30
-20
-10
0
10
20
External Field H, 103 Oe.
Fig. 4. The magnetic hysteresis behavior of Fe100ꢀxNix nanocrystalline alloys at different temperatures in the range 5–300 K is shown. The magnetization
reaches saturation in all the cases for fields 4104 Oe.

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187
temperature range 5–300 K, clearly indicating the soft
1.0
0.8
0.6
0.4
0.2
0.0
magnetic nature. The coercive field Hc in all the composi-
tions except pure Ni is found to be p20 Oe even at 5 K. In
the case of pure Ni, it increases from 30 Oe at 300 K to
65 Oe at 5 K. These values of coercivity are quite different
compared to their bulk equivalents.
F3N1
F1N4
4. Discussion
4.1. Electrical transport
FN
The electrical transport behavior of ferromagnetic metals
and alloys below the Curie temperature TC is still not
completely understood [24,25]. The electron transport in
general is a result of electron–phonon, electron–magnon and
electron–electron scattering processes. In the case of
ferromagnetic metals and alloys, it will be dominated by
spin scattering. In the ferromagnetic state, magnetic ordering
takes place leading to a change in electron scattering cross
section compared to the magnetically disordered paramag-
netic state. The magnetic ordering parameter, however, will
be o1.0 for T40 K, and thermal demagnetization takes
place via the formation of magnons. Hence the temperature
dependence of electrical transport, resistivity r(T), for
temperatures below TC can be written in the form:
F
N
50
100
150
200
250
300
Temperature T, K
Fig. 5. The temperature dependence of resistivity in the range 20–300 K
obeys the behavior predicted by Eq. (1) in all the cases indicative of
magnon-dominated transport. The symbols represent experimental data
and the solid line through the experimental data points represents fit to
Eq. (1). The fit parameters are given in Table 2.
Fe it cuts across both the majority and minority spin bands
[27]. Hence spin splitting effects become dominant for
alloying addition to Fe while they just increase the
concentration of minority band electrons in the case of
Ni. As a result, addition of Ni to Fe moves the Fermi
energy level downwards and increases the effective s-band
electrons, which are not localized and free for electron
transport. This increases the electrical conductivity of the
alloy with increasing Ni addition to Fe. This simple band
picture explains qualitatively the observed electrical trans-
port behavior in nanocrystalline Fe–Ni alloys, clearly
indicating that complex band structure modifications take
place only at sizes much smaller than those obtained in the
present work [28–30].
rðTÞ ¼ r0 þ AT2 þ BTn,
(1)
where r0 is the residual resistivity due to impurities such as
defects and grain boundaries, A is the electron–magnon
scattering coefficient and B and n depend on higher order
scattering mechanisms such as two magnon scattering or
electron–phonon scattering. The value of the exponent n is
found to be 4.5 for two magnon scattering dominant
conduction and 5.0 for electron–phonon scattering [26].
The resistivity ratio, r(T)/r(300 K) of all the nanocrystal-
line Fe–Ni alloys has been fitted to Eq. (1) with different
values for the exponent n. It is found that the experimental
data fit well to Eq. (1) with n ¼ 4.5, indicating that two
magnon scattering is dominant both in the pure elements
and in the Fe–Ni alloys. The results of resistivity fit
together with the experimental results are shown in Fig. 5
and the fit parameters are given in Table 2. The single
magnon scattering coefficient A in typical bulk ferromag-
netic elements Fe, Ni and Co is ꢂ10ꢀ11 O cm Kꢀ2. This
coefficient in the present nanocrystalline systems, however,
is found to be higher compared to the bulk value (Table 2).
These results show that the grain boundary, which is
structurally and magnetically, disordered leads to lowering
of the magnetic order even in the bulk of the nanocrystal-
line material. This results in an increase in the scattering
coefficient A and also contributes to increasing the absolute
value of resistivity.
4.2. Magnetic behavior
The magnetic hysteresis loops show clearly the ferro-
magnetic nature of all the alloys below 300 K. The
extremely low coercive fields observed in all the cases
indicate magnetic softness and thus the possibility of
existence of single domain state at high external magnetic
fields. The magnetization decreases (for T40 K to 0) as T
goes to TC, the Curie temperature of the ferromagnetic
material. This thermal demagnetization can follow either
the Curie–Weiss behavior or the Bloch behavior, depend-
ing on the mechanism of demagnetization. According to
the Curie–Weiss behavior, demagnetization takes place due
to random fluctuations of the spin system caused by
thermal effects and the magnetization decrease with
temperature is given by the Brillouin function. An
alternative is demagnetization by the formation of spatially
correlated spin modes known as spin waves or magnons.
The absolute value of resistivity is found to decrease
monotonically with addition of Ni to Fe. This can be
understood in the context of band formation in Fe–Ni
alloys. In the case of pure Ni the Fermi energy lies
exclusively in the minority spin band, whereas in the case of

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188
The magnetization according to this model decreases with
temperature as given by the Bloch relation:
Eq. (2) as shown in Fig. 6. These results clearly indicate
that the demagnetization phenomenon is dominated by the
formation of magnons at ToTC and is in agreement with
the electrical transport behavior which shows a predomi-
nantly magnon scattering for To300 K (Fig. 5). Typical
value of the Bloch constant C for bulk Fe is 3 ꢃ 10ꢀ6 K2/3
whereas this constant is about an order of magnitude
higher in the present work, Table 3, in all the cases.
A higher value of this constant implies a stronger
temperature dependence due to a large contribution from
the surface atoms or conversely nanosized crystals [31,32].
This agrees with the typical grain sizes determined from
microstructural studies and also the electrical transport,
which shows a high magnon scattering coefficient.
MsðTÞ ¼ Msð0Þ½1 ꢀ CT3=2ꢄ,
(2)
where Ms is the saturation magnetization and C is the
Bloch constant which depends on the exchange energy J
and is given as B(kB/J)3/2, B is a constant which depends on
the crystal system. The saturation magnetization Ms
obtained from the experimental data shown in Fig. 4 in
the temperature range 5–300 K obeys the Bloch relation,
Table 2
The electrical transport parameters, resistivity r, scattering coefficients A
and B
The magnetization of ferromagnetic metals and alloys
depends on the band structure and hence the composition
of the alloys. The main contribution to magnetic behavior
therefore is by the 3d electrons and a change in
composition, which changes the 3d electron population,
will result in a change in magnetic behavior. The band
structure of ferromagnetic transition metal alloys is
generally understood within the framework of itinerant
electrons model. The average atomic magnetic moment of
the alloy, malloy according to this model is given by the
relation [33,34]:
Sample r(300) (O cm) r0 (O cm)
A (O cm Kꢀ2
)
B (O cm Kꢀ4.5
)
F
2.6 ꢃ 10ꢀ1
1.8 ꢃ 10ꢀ3
9.6 ꢃ 10ꢀ4
7.8 ꢃ 10ꢀ5
5.8 ꢃ 10ꢀ5
1.65 ꢃ 10ꢀ2 3.8 ꢃ 10ꢀ6
8.5 ꢃ 10ꢀ4 1.5 ꢃ 10ꢀ8
2.8 ꢃ 10ꢀ4 7.9 ꢃ 10ꢀ9
2.3 ꢃ 10ꢀ5 7.3 ꢃ 10ꢀ10
1.8 ꢃ 10ꢀ6 8.5 ꢃ 10ꢀ10
ꢀ6.3 ꢃ 10ꢀ13
ꢀ2.6 ꢃ 10ꢀ16
1.2 ꢃ 10ꢀ17
F3N1
FN
F1N4
N
ꢀ5.6 ꢃ 10ꢀ17
ꢀ1.3 ꢃ 10ꢀ16
The scattering coefficients were obtained by fitting the resistivity to
Eq. (1).
160
malloy ¼ mhost ꢀ Dzx,
(3)
140
F3N1
where mhost is the host metal moment, Dz is the difference in
valence between the two elements and x is the alloy
concentration. The magnetic moment of Fe–Ni alloys
obtained using Eq. (3) is shown in Fig. 7 along with the
experimental data. It can be clearly seen that the values
predicted by the itinerant electron model, Eq. (3) are large
and do not agree with the experimental data showing that
the band structure is more complex than predicted by the
simple itinerant electron model. The alloy magnetic
moment on the other hand can be determined using the
effective medium approximation given by
120
FN
100
80
60
40
F1N4
F
N
mFe2Ni ¼ 2:2ð1 ꢀ xÞ þ 0:6ðxÞ,
(4)
0
1000
2000
3000
4000
5000
6000
Temperature T3/2, K3/2
where x is the fraction of Ni, 2.2 and 0.6 are the atomic
magnetic moments of bulk Fe and Ni, respectively. The
alloy magnetic moment obtained using the effective
medium approximation is also shown in Fig. 7 and these
are more close to the experimental values compared to the
Fig. 6. Saturation magnetization Ms obtained from the magnetic
hysteresis at different temperatures follows the ferromagnetic Bloch
thermal demagnetization behavior. The ground state or 0 K saturation
magnetization can be obtained by extrapolation and is given in Table 3.
Table 3
The characteristic magnetic properties of nanocrystalline Fe100ꢀxNix alloys obtained from experimental results, Ms and Hc and a fit to the experimental
results, C and malloy
Sample
Saturation magnetization, Ms (emu gꢀ1
)
Coercive field, Hc (Oe)
C (K2/3
)
Average moment, mavmB at 0 K
300 K
5 K
69.6
0 K
71.8
300 K
5 K
F
65.2
123.6
120.0
73.6
20
15
15
10
30
25
20
15
10
65
1.3 ꢃ 10ꢀ5
3.7 ꢃ 10ꢀ5
1.2 ꢃ 10ꢀ5
1.3 ꢃ 10ꢀ5
9.4 ꢃ 10ꢀ6
0.69
1.56
1.31
0.79
0.49
F3Ni
FN
F1N4
N
152.7
126.8
75.4
153.6
127.8
76.3
44.1
45.9
46.4

ARTICLE IN PRESS
S. Vitta et al. / Journal of Magnetism and Magnetic Materials 320 (2008) 182–189
189
temperatures as low as 5 K suggests that the crystallite
boundaries are not effective in pinning the magnetization.
2.6
2.4
2.2
2.0
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
Exptl.
Effective Medium
Itinerant Electron
Acknowledgment
The authors wish to acknowledge the Department of
Science and Technology, Government of India, for
financial support.
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