Structural, electrical and magnetic properties of Mg-Zr co-substituted Ni0.5Zn0.5Fe2O4

Journal of Science: Advanced Materials and Devices 4 (2019) 310e318

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Original Article

Structural, electrical and magnetic properties of Mg-Zr co-substituted
Ni0.5Zn0.5Fe2O4
K. Jalaiah a, b, *, K. Chandra Mouli c, K. Vijaya Babu d, R.V. Krishnaiah e
a

Chebrolu Engineering College, Chebrolu, Guntur, 522212, India
Department of Physics, Andhra University, Visakhapatnam 530003, India
c
Department of Engineering, Physics, Andhra University, Visakhapatnam 530003, India
d
Advanced Analytical Laboratory, Andhra University, 530003, India
e
Institute of Aeronautical Engineering and Technology, Hyderabad, 500043, India
b

a r t i c l e i n f o

a b s t r a c t

Article history:
Received 2 October 2018
Received in revised form

15 December 2018
Accepted 16 December 2018
Available online 23 December 2018

Zr and Mg co-substituted Ni0.5Zn0.5Fe2O4 ferrites have been synthesized by the sol-gel auto-combustion
method. The X-ray diffraction patterns evidenced the single phase cubic spinel structure. The lattice
parameter and cell volume are in resemblance trend with the variation of the dopant concentration. The
similar trend is observed for the crystallite and particle size. The porosity and sintered density, however,
vary in an opposite way with a variation of the dopant concentration. The same variation is found for the
drift mobility and DC resistivity. The Arrhenius graphs of DC resistivity exhibit the semiconductor nature,
for which the activation energy decreased with increasing the dopant concentration. Moreover, as the
dopant contents increased, the saturation magnetization, net magnetic moment and permeability are
reduced, while the coercivity is reinforced. These findings can be correlated with the variation of the
porosity and grain size.
© 2018 The Authors. Publishing services by Elsevier B.V. on behalf of Vietnam National University, Hanoi.
This is an open access article under the CC BY license ( />
Keywords:
Ferrites
XRD
TEM
SEM
Permeability
Saturation magnetization
Anisotropy constant

1. Introduction
In early days iron based magnetic alloys are used in various
applications. However, their low resistivity made these materials
inefficient at high frequencies, which encouraged the eddy current
through them. This wasted energy is created a serious problem that

generated the heat in the circuit. Hence, iron based magnetic materials are not favorable in high frequency applications. Ferrite
materials, in opposite, possess high resistivity and dielectric performances and do not conduct the electric current readily. The
advantage of ferrites over magnetic alloys is that they formed a
different combination of ferrites with transition metals because the
transition metals exhibit magnetic as well as semiconductor
properties. The porosity is an insignificant factor for ferrites so that
the ferrites have been investigated for several years based on this
issue. In order to get the high resistivity of ferrites researchers

* Corresponding author. Chebrolu Engineering College, Chebrolu, Guntur,
522212, India.
E-mail address: (K. Jalaiah).
Peer review under responsibility of Vietnam National University, Hanoi.

choose different combination here we also choose a new combination with transition metals to get the high resistivity of ferrite
material [1,2]. Spinal ferrites are a class of magnetic oxides with the
general formula of AB2O4. They are categorized as soft and hard
ferrites according to their magnetic performance. Soft ferrites are
easily demagnetized without significant energy need, i.e. only a
small energy amount is wasted in the form of eddy currents to
demagnetize the soft magnetic materials. In case of hard ferrites, a
significantly higher energy is needed to demagnetize. This means
that soft magnetic materials possess higher electrical resistivity,
thus, they are used in inductors and transformers. The magnetic
oxides are made from the blend of iron, nickel, zinc, manganese
oxides. By using these oxides, different combinations of soft ferrites
like Manganese-Zinc and Nickel-Zinc have been prepared. For
inductor cores, the magnetic permeability is the chief parameter
[3,4]. In order to improve the core performance at high frequency
the grain size, which can be controled by the ferrite preparation

technique, plays an important role. The solid state ceramic technique is a general ferrite fabricated technique, in which the constituent oxides react at higher temperatures. In this case, an
unusual grain growth usually occurs due to the non stoichiometry

/>2468-2179/© 2018 The Authors. Publishing services by Elsevier B.V. on behalf of Vietnam National University, Hanoi. This is an open access article under the CC BY license
( />

K. Jalaiah et al. / Journal of Science: Advanced Materials and Devices 4 (2019) 310e318

and inhomogeneity of ferrite materials [5]. To control this unusual
grain growth, we adopted the solution method known as the solgel autocombustion method in which the constituent oxides react
at lower temperatures. So, the precursor material becomes stoichiometry and homogeneity with controlled grain size. In the
present study, the correlation between structural, electrical and
magnetic properties of Mg-Zr co-substituted Ni0.5Zn0.5Fe2O4 are
discussed in connection with the dopant concentration.

mismatches between the substitute ions and host ions ionic radius.
The Fe3þ (0.67 Å) ions radius is small when compared with Zr
(0.80 Å) and Mg (0.72 Å) ionic radii. Hence the substitution of Zr
and Mg in place of the Fe3þions unit cell will bulge promptly and as
a result the lattice constant increases with increasing dopant concentration [8]. The X-ray density is estimated from the following
equation.

Dx ¼
2. Experimental
The Zr and Mg co-substituted Ni0.5Zn0.5ZrxMgxFe2-2xO4 have
been prepared by sol-gel auto combustion method, x values vary
from the 0.08 to 0.4 in steps of 0.08 with%. The starting materials of all metal nitrates with AR grade Nickel nitrate
(Ni(NO3)2.6H2O), zinc nitrate (Zn (NO3)2.6H2O), Magnesium nitrate (Mg(NO3)2.6H2O), Zirconyle nitrate (ZrO (NO3)2), ferric
citrate (Fe C6H8O7.H2O) and citric acid (C6H8O7.H2O) are used for
synthesis of Ni0.5Zn0.5ZrxMgxFe2-2xO4 (x ¼ 0.08, 0.16, 0.24, 0.32,

0.4). The stoichiometric weights of metal nitrates dissolved in
deionized water and the citric acid added to the solution as per
the oxygen ions present in chemical formula, later 50 ml
ethylene glycol added to the solution [6]. The ammonia solution
added drop wise to adjust the PH value of 7 for the final solution. Then the neutralizing solution heated to 600oCe700  C for
8e10 h with continuous stirring. After 8e10 h the solution
turned into a viscous on the formation of gel, then the temperature of a gel rise to 100  C drying, finally a powder form of
samples obtained [7]. The obtained powders processed for
simple experimental needs.
3. Structural studies
Fig. 1 shows the XRD patterns of Mg and Zr co-substituted
Ni0.5Zn0.5Fe2O4. Here the XRD patterns provide the evidence for
single phase cubic spinel and no extra peaks are observed
throughout while the doping concentration is increased. The lattice
constant is calculated from XRD peaks, using the following
equation.

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
a ¼ d h2 þ k2 þ l2
where d is the space between the lattice planes. The lattice constant
and cell volumes are shown in Fig. 2a with a variation of dopant
concentration. The increase in the lattice constant has resulted in

8M
Na a3

where M is the molar mass, Na is the Avogadro number and “a”
is the lattice constant. The X-ray density increases with increasing
dopant concentration from x ¼ 0.08 to x ¼ 0.32, later it is slightly
decreased to x ¼ 0.4. However, overall X-ray density increases with

increasing dopant concentration. The increase in X-ray density may
be due to the lattice constant which is dominated by the molar
mass as shown in the above equation because the increase in the
lattice constant decreases the X-ray density. The ratio between the
sintered density and X-ray density gives the porosity of prepared
samples. The porosity of prepared samples is estimated from the
following equation.

p¼1À

ds
dx

where “ds” and “dx” are sintered and x-ray densities respectively.
The porosity and sintered density are shown in Fig. 2b with a
variation of dopant concentration. From Fig. 2b it is clear that both
the parameters exhibit opposite trend with a variation of dopant
concentration. The sintered density is decreased as a result of lagging the sintering rate of material. The sintering rate of material is
lagging due to the volatilization of zinc at higher temperature. Since
the melting point of zinc is less than those of other constituent ions,
the material becomes non stoichiometry [9]. To minimize the non
stoichiometry property of the material, the excess of ferric oxide is
changed as ferrous oxide, i.e., Fe3þ ions are changed as Fe2þions in
the sintering process. The presence of Fe2þions in the material lags
the sintering rate of material, hence sintered density is decreased
[10]. The decrease in the sintered density results in the development of pores in the material.
4. Surface morphology
The crystallite size is estimated from the following equation.

D¼

Fig. 1. X-ray diffraction patterns of Ni0.5 Zn0.5ZrxMgxFe2-2xO4 samples with x ¼ 0.08,
0.16, 0.24, 0.32, and 0.4.

311

0:94*l
b cos q

where l is the wavelength of Cu radiation and b is the full width
half maximum of (3 1 1) peak. The FWMH is decreased with
increasing substituting ionic radii so that the decrease in the
FWHM increases the crystallite size since crystallite size and
FWHM are inversely related in the above equation. Fig. 2c shows
the crystallite size and particle size with a variation of dopant
concentration. The TEM pictures are shown in Fig. 3. The particle
size is measured from TEM pictures by using image-j software.
The particle size increased with increasing dopant concentration
as a result of the agglomeration nature of crystallites [11]. From
Fig. 2c we conclude that both the crystallite size and the particle
size are in comparable nano size. The SEM micrographs of prepared samples are shown in Fig. 4. The grain size is measured from
SEM micrographs by using the image-j software. The grain size
decreased with increasing dopant concentration. The decrease in
grain size is due to the development of pores in the material
during the sintering of material.


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K. Jalaiah et al. / Journal of Science: Advanced Materials and Devices 4 (2019) 310e318

Fig. 2. (a) variation of lattice parameter and cell volume with dopant concentration. (b) variations of sintered density and porosity with dopant concentration. (c) the variation of
particle size and Crystallite size with dopant concentration.

5. DC resistivity
The ferrites exhibit the semiconducting nature since ferrites are
composed of transition elements and all transition elements show
the semiconducting nature. Fig. 5 shows composition variation of
DC resistivity and drift mobility of prepared ferrite samples. The DC
resistivity of ferrite samples decreased with increasing doping
concentration. The decrease in DC resistivity because of the
increased electronic conduction between the paramagnetic region
(Fe2þions) to ferromagnetic (Fe3þions) region [12]. That is the
electronic exchange has occurred in ferrites from Fe2þ (n-type) to
Fe3þ (p-type). In Fig. 5 the drift mobility varies opposite to DC resistivity with increasing doping concentration, since the decrease
in DC resistivity increases the mobility of electrons. The Arrhenius
plots drawn between DC resistivity and inverse temperature in the
range of 300 K and 620 K show that all plots are less curved. So
these plots reveal the semiconducting nature of prepared samples.
The Arrhenius plots for the present study are shown in Fig. 6. The
semi conductivity of ferrite samples is described by the following
equation.



s ¼ so exp

DE
kB T



where so is the constant, DE is the activation energy, KB is the
Boltzmann constant and T is the absolute temperature. The graph

between s and 1/T gives more or less a curved line. The DE equals
0.1eV for stoichiometry composition and DE reaches 0.5eV for low
conductivity ferrites [13]. For the present study the Activation energy DE decreased from 0.17eV to 0.11eV i.e. the activation energy,
decreased with increasing dopant concentration and it is shown in
Fig. 7. The decrease in activation energy is due to increase of
jumping frequency of electrons from the paramagnetic region
(Fe2þ) to the ferromagnetic region (Fe3þ) [14].

6. Magnetic properties
The magnetic properties of Mg and Zr substituted Ni0.5Zn0.5Fe2O4ferrites are calculated by using the M-H loops shown in
Fig. 8. All the M-H loops are with less loss of magnetic energy and
the M-H loop data is collected at room temperature. The saturation magnetization and the corresponding net magnetic moment
are estimated from M-H loops. Both the saturation magnetization
and the corresponding net magnetic moment are in decreasing
trend with increasing dopant concentration as shown in Fig. 9a.
The decrease in saturation magnetization is due to the decrease of
Fe3þ ions in general formula with the substitution of Mg and Zr
ions in place of Fe3þions. The presence of Fe3þions in the material
needs a much more flux to orient in the applied field direction.
Since Fe3þions behave like ferromagnetic ions the Fe3þions need
higher flux density to orient in the field direction [15]. The


K. Jalaiah et al. / Journal of Science: Advanced Materials and Devices 4 (2019) 310e318

313

Fig. 3. Transmission electron micrographs of Ni0.5Zn0.5ZrxMgxFe2-2xO4 along with selected area Electron diffraction patterned of samples.

decreased Fe3þions in material need lesser flux density to orient in
the field direction. Hence the saturation magnetization is
decreased with increasing dopant concentration. Father the net
magnetic moment of the material is calculated using the following
equation.

M ¼ MA À MB
here MA and MB are the magnetic moments of A-site and B-site
respectively. From the above equation the resultant magnetic


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K. Jalaiah et al. / Journal of Science: Advanced Materials and Devices 4 (2019) 310e318

Fig. 4. Schematic SEM photo graphs of Zr and Mg Co substituted Ni0.5Zn0.5ZrxMgxFe2-2xO4.

Fig. 5. Compositional variation of D.C resistivity and Drift mobility.

Fig. 6. Variation of log r with inverse temperature.


K. Jalaiah et al. / Journal of Science: Advanced Materials and Devices 4 (2019) 310e318

315

moment of material is the difference between the B-site magnetic
moment and A-site magnetic moment. The increase in A-site
magnetic moment decreases the resultant material magnetic
moment. The substituted Mg and Zr in place of Fe3þions, occupy the
A-site and B-sites for their comfortable fit in lattice sites. While Zr
enters A-site, it replaces the Fe3þions from A-site to B-site. To give
place for Fe3þions in B-site the Ni2þions are converted as Ni3þions
by releasing an electron. And by taking the electron from Ni ion,
Fe3þion is changed as Fe2þion [16,17]. Moreover the A-site spin
magnetic moment is always opposite to the B-site spins magnetic
moment, hence the net magnetic moment is decreased with
increasing dopant concentration. The Fe3þions from A-site will be
arranged anti parallel in B-site upto certain concentration, later
Fe3þions from A-site will be arranged on B-site with canting position. This gives an angle between the Aesite Fe3þions and B-siteFe3þions called Y-K angle [18]. The Y-K angle is calculated by using
the following equation.
Fig. 7. Variation of activation energy with dopant concentration.

nB ¼ ð6 þ xÞcosaYÀK À 5ð1 À xÞ

Fig. 8. Magnetization versus magnetic field (M-H) curves of Zr and Mg substituted Ni0.5Zn0.5ZrxMgxFe2-2xO4. at room temperature.


316

K. Jalaiah et al. / Journal of Science: Advanced Materials and Devices 4 (2019) 310e318

Fig. 9. Variation of net magnetic moment and saturation magnetization (a), Y-K angles (b), coercive field and porosity (c), and permeability and grain size (d) with dopant
concentration.

The variation of Y-K angles with dopant concentration is

shown in Fig. 9b. From Fig. 9b it is clear that Y-K angles increased
with increasing dopant concentration. The increase in the Y-K
angles suggests the increase of AeB interaction [19]. The coercive
field is a field where the magnetization becomes zero in reverse
order. The composition variation of Coercive field and porosity is
shown in Fig. 9c. From Fig. 9c it is concluded that the increase in
the porosity increases the coercive field. According to J. Smith and
H.P.J. Wijn the increase in the porosity of the material will affect
the reverse magnetization of material [20]. On removing the
applied magnetic field magnetic dipoles will not come to initial
orientation since the magnetic dipoles lag by field (i.e. the

magnetic dipoles suffer by residual flux). This lagging of field is
affected by the porosity of samples [21]. Hence an increase in
porosity increases the coercive filed.
7. Magnetic permeability
Permeability is the property of a magnetic material which
measures its ability to support the formation of magnetic fields
within itself. The extent of the magnetization of a material denotes
the response to an applied magnetic field. The permeability of the
material is estimated from the following equation

m¼

Fig. 10. Variation of permeability with frequency.

L
L0

Fig. 11. Variation of permeability and anisotropy constant with dopant concentration.

K. Jalaiah et al. / Journal of Science: Advanced Materials and Devices 4 (2019) 310e318

where L is the measured inductance of the torroids and Lo is
calculated as follows

 
OD
t  10À9 Henry
Lo ¼ 4:606N 2 log
ID
Fig. 9d shows the variation of the initial permeability and grain
size with the dopant concentration. From Fig. 9d it is clear that the
permeability decreases with increasing dopant concentration, since
the permeability and the grain size are related as shown in the
following equation.

K ¼ cd2
here K is the permeability, c is the dimension less constant and d is
the grain size. Hence permeability is directly proportional to the
square of the grain size. The materials composed with grains
include the atomic dipoles or spin dipoles [22]. The existed atomic
dipoles or spin dipoles in grains are oriented randomly. By the
application of external fields, the atomic dipoles or spin dipoles in
grains align with the field direction. This is related to the induced
magnetic flux in the magnetic material, which continues to increase up to a certain frequency. In this case, a resonance peak will
appear where the frequency of the applied field equals the spin
dipoles or atomic dipoles. It means that the maximum magnetic
flux is induced in the material at the resonance frequency. Later

atomic dipoles will not follow the applied field. According to
literature survey the resonance peak appearance connects to: (i)
inhomogeneous material, (ii) crystalline magnetic anisotropy, (iii)
the combination of the magnetic anisotropy and the ferromagnetic exchange fields, (iv) the domain walls and (v) the electromagnetic body resonance. The frequency variation of
permeability in the present study is shown in Fig. 10. From the

317

Fig. 10 it is clear that all samples exhibit the resonance peak
around the 12 MHz to 13 MHz. The resonance effects occur in all
ferrous and paramagnets. In particular, it is not peculiar to ferrites
in its simple form. Generally, it has been considered that the
resonance in ferrites accounts for a large part of the magnetic
dispersion of ferrites. The permeability arises from the rotation of
magnetic dipoles rather than from a domain wall displacement
process. The domain wall displacement does not account for
magnetic dispersion at higher frequency [23]. More complex type
resonances are considered in ferromagnetic and antiferromagnetic materials, the sample shape anisotropy is taken into account
in this case. Sometimes there may be two or more resonance
frequencies possible in an accessible range of frequency. In this
case, domain wall effects will be considered. The moving wall sets
up a magnetic double layer in the wall, and as a result the additional energy acquires its static value. Another resonance frequency appears due to body-resonance which accounts for the
high permeability and high permittivity [24]. Both are comparable
at body resonance frequency and as a result, the permeability and
permittivity of a material may give too small values. The permeability and anisotropy constant are shown in Fig. 11 with dopant
concentration. The permeability and anisotropy constant are
related as shown in following expression.

mi ∞

M 2s D
K

From the above relation, the initial permeability is directly
proportional to the square of saturation magnetization, and
inversely proportional to anisotropy constant. The permeability
strongly depends on the homogeneity of the material. That means,
permeability depends on the grain size, intra and intergranular
porosity of material. If they are not explained well, then the

Table: 1
The structural data of Zr and Mg substituted Ni0.5Zn0.5ZrxMgxFe2-2xO4.
Dopant
concentration

Lattice
parameter(Å)

Crystallite
size (nm)

X-ray
density g/cm3

Porosity (%)

Sintered
density g/cm3

Grain

size (mm)

Particle
size (nm)

0.08
0.16
0.24
0.32
0.4

8.2997
8.2996
8.3072
8.3367
8.3908

5.3857
5.3112
5.1105
5.5166
5.5663

5.5237
5.6840
5.7482
5.7665
5.733

10.99

14.34
16.16
17.31
19.12

4.9166
4.8685
4.8191
4.7682
4.6370

2.2286
2.1454
2.0556
1.9542
1.8775

25.1005
27.7178
29.6136
32.3956
37.3752

Table: 2
The DC resistivity data of Zr and Mg substituted Ni0.5Zn0.5ZrxMgxFe2-2xO4.
Dopant concentration

DC resistivity(r)
U-cm

Drift mobility(h) Â 10À36

Activation energy (DE) eV

0.08
0.16
0.24
0.32
0.4

1.92775E6
889033
430824
243293
89791

1.5834
1.7539
2.9249
4.62057
6.1224

0.1765
0.1673
0.1509
0.1411
0.1172

Table: 3
The magnetic properties of Zr and Mg substituted Ni0.5Zn0.5ZrxMgxFe2-2xO4.

Dopant concentration

Net Magnetic
momenthB

Saturation
magnetization emu/gm

Coercive
field (Hc)Oe

Anisotropy
constant(K)

Y-K angles (⁰)

Permeability

0.08
0.16
0.24
0.32
0.4

5.8800
5.6074
4.8321
3.9987
3.2924

65.4921
60.5877
51.4706
42.3480
34.7691

11.4795
12.8929
30.7264
43.6102
44.2298

80.1051
105.62
117.13
134.71
200.68

35.3507
42.7818
48.4878
54.1299
58.5468

114
84
52
33
25

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K. Jalaiah et al. / Journal of Science: Advanced Materials and Devices 4 (2019) 310e318

permeability mechanism must be governed by some other
mechanism of magnetic anisotropy and magnetostriction [25].
There are three types of magnetic anisotropy (1) crystal structure,
(2) grain shape and (3) applied stress or residual stresses. The
crystal structure anisotropy is independent of grain size and shape
and it can be easily observed by measuring the magnetic curves in
different crystal directions. The interaction of the spin magnetic
moment with the crystal lattice gives easy and hard directions.
The magnetized body produces the poles or charge distribution at
the surfaces. As a result, the magnetized body itself acts as another
source of the magnetic field called a demagnetizing field. This
demagnetizing field acts opposite to the magnetizing field, and it
happens by applying a magnetic field in the material hence the
permeability decreases. In short, decreasing the shape of
magnetizing body effects the permeability. In case of round shaped magnetized body, the anisotropy constant will be higher and
for cube shape, the anisotropy constant will be low. The permeability will be low for round shaped magnetize body, and for cube
shape it will be higher. From Fig. 4, magnetized bodies other than
the cube shape should be grown, so that the anisotropy constant
will be high. As a result, the permeability decreases with
increasing dopant concentration. The third one arises due to the
spin-orbit coupling that produces strain along the crystallographic axis. So, the magnetized body will change directions when
magnetized [13].
8. Conclusion
The Zr and Mg co-substituted Ni0.5Zn0.5Fe2O4 ferrites have
been prepared by sol-gel auto combustion method. The investigated samples revealed the semiconducting nature, in which the

activation energydecreased with increasing dopant concentration. The XRD patterns confirm the single phase cubic spinel and
no secondary phase was identified by this analysis. The lattice
constant, cell volume as well as the porosity of samples increased
with increasing the dopant concentration. The density of material,
as a consequence, decreased by pores developed in the material.
The crystallite and particle sizes are comparable in the nano scale.
As the dopant content varies, the DC resistivity and drift mobility
varied in the opposite way. The saturation magnetization, net
magnetic moments and permeability are reduced with increasing
dopant concentration, while the coercive field and anisotropy
constant are enhanced. The Y-K angles increase with increasing
dopant concentration. Electrical and magnetic properties have
been discussed in good correlation with the structural behaviour
(see Tables 1e3).
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