Metal-semiconductor transition in NiFe2O4 nanoparticles due to reverse cationic distribution by impedance spectroscopy

Abstract

We have investigated the magnetic and electrical response of the sol-gel synthesized NiFe 2 O 4 nanoparticles. Changes in the impedance plane plots with temperature have been discussed and correlated to the microstructure of the material. Thermally activated hopping carriers between Fe³⁺-Fe²⁺ and Ni²⁺-Ni³⁺ ions have been determined for a decrease in the resistance of the sample and a change in the conduction mechanism around 318 K. The mixed spinel structure and broken exchange bonds due to small size effects are due to the canted spin structure at the surface of the nanoparticles. The magnetization is found to be influenced by the surface spin canting and anisotropy. We have established the semiconducting to metallic transition (SMT) temperature to be around 358 K in terms of localized and delocalized e g electrons along with a transition from less conductive [Fe³⁺–O^2-–Fe³⁺] and [Ni²⁺–O^2-–Ni²⁺] linkage to more conductive [Fe³⁺–Fe²⁺] and [Ni²⁺–Ni³⁺] linkage at the octahedral B site. A decrease in the dielectric constant with temperature has been discussed in terms of the depletion of space charge layers due to the repulsion of delocalized e g electrons from the grain boundary planes. The anomalies in tangent loss and conductivity data around 358 K are discussed in the context of the SMT.

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Metal-semiconductor transition in NiFe2O4nanoparticles due to reverse
cationic distribution by impedance spectroscopy
M. Younas,1M. Nadeem,1,a)M. Atif,2and R. Grossinger2
1EMMG, Physics Division, PINSTECH, P.O. Nilore, Islamabad, Pakistan
2Institute of Solid State Physics, Technical University of Vienna, Wiedner Hauptstrasse 8-10,
A-1040 Vienna, Austria
(Received 1 December 2010; accepted 24 March 2011; published online 6 May 2011)
We have investigated the magnetic and electrical response of the sol-gel synthesized NiFe2O4
nanoparticles. Changes in the impedance plane plots with temperature have been discussed and
correlated to the microstructure of the material. Thermally activated hopping carriers between
Fe3þ-Fe2þand Ni2þ-Ni3þions have been determined for a decrease in the resistance of the sample
and a change in the conduction mechanism around 318 K. The mixed spinel structure and broken
exchange bonds due to small size effects are due to the canted spin structure at the surface of the
nanoparticles. The magnetization is found to be influenced by the surface spin canting and
anisotropy. We have established the semiconducting to metallic transition (SMT) temperature to be
around 358 K in terms of localized and delocalized egelectrons along with a transition from less
conductive [Fe3þ–O2?–Fe3þ] and [Ni2þ–O2?–Ni2þ] linkage to more conductive [Fe3þ–Fe2þ] and
[Ni2þ–Ni3þ] linkage at the octahedral B site. A decrease in the dielectric constant with temperature
has been discussed in terms of the depletion of space charge layers due to the repulsion of
delocalized eg electrons from the grain boundary planes. The anomalies in tangent loss and
conductivity data around 358 K are discussed in the context of the SMT. V
of Physics. [doi:10.1063/1.3582142]
C 2011 American Institute
I. INTRODUCTION
Spinel ferrite nanoparticles by virtue of their unique elec-
tronic, magnetic, and physical structure may be harnessed for
technological applications.1,2Nano ferrites are an important
class of materials because of their high resistivity and low
eddy current losses.3Bulk spinel ferrites are described by the
formula (A)[B]2O4, where (A) and [B] represent the tetrahe-
dral and octahedral sites, respectively. Nanocrystalline ferrite
systems usually have a mixed spinel structure having the
chemical formula, ðM2þ
metal ion M2þcan occupy the either tetrahedral (A) or octahe-
dral [B] sites or both sites of the spinel structures, depending
upon the nature of the system. The inversion parameter, d, is
defined as the fraction of the (A) sites occupied by Fe3þcati-
ons and its value depends on the method of preparation.4,5
NiFe2O4is a well-known inverse spinel structure, with Ni2þ
ions occupying only the B sites. Chinnasamy et al.6have
shown that nanocrystalline NiFe2O4exhibits a mixed spinel
structure with Ni2þions occupying both (A) and [B] sites.
NiFe2O4 nanoparticles with a mixed spinel structure have
been shown to exhibit interesting electrical, magnetic, gas,
and humidity sensing properties.6,7
The NiFe2O4sample exhibits paramagnetic, superpara-
magnetic, or ferrimagnetic behavior depending on the
microstructure.8
Scherrer9
observed
superparamagnetic behavior in NiFe2O4nanoparticles with
grain sizes of 17 and 10 nm, respectively. A reduction in the
1?dFe3þ
dÞ½M2þ
dFe3þ
2?d?O2?
4. The divalent
ferromagnetic and
saturation magnetization of NiFe2O4due to a reduction in
grain size has been reported to result from the noncollinear-
ity of the magnetic moments at the surface.10Core-shell
morphology is appropriate to explain the magnetic properties
of the nanoparticles. Chinnasamy et al.6reported the high
value of magnetocrystalline anisotropy in the mixed spinel
NiFe2O4sample with a canted spin structure at the surface
and the core. Several methods have been used for the prepa-
ration of ferrite nanoparticles such as ball milling, thermal
decomposition, and the sol-gel technique.11,12The properties
of the ferrites are very sensitive to the synthesis techniques.
The sol-gel method is a versatile technique to vary the prop-
erties of the material by controlling different parameters
such as temperature, time of reaction, pH of the medium,
and the reagent’s concentration.13Atif et al.4observed more
reverse cationic distribution in the ZnFe2O4nanoparticles
prepared in urea (i.e., a basic medium) rather than in citric
acid (i.e., an acidic medium). In the present study we pre-
pared NiFe2O4nanoparticles in a basic medium and carried
out magnetic and electrical measurements to determine any
possible change in the conduction mechanism. To the best of
our knowledge, any possible correlation between the electri-
cal parameters and the microstructure for NiFe2O4nanopar-
ticles above room temperature has not yet been reported.
Impedance spectroscopy is a powerful technique in solid
states because of its ability to differentiate the transport char-
acteristics in grains and grain boundaries.14The grains and
the grain boundaries are the two main components that com-
prise the microstructure and the correspondence between the
grains and grain boundaries is important in understanding
the overall properties of these materials.15Impedance
a)Author to whom correspondence should be addressed. Electronic mail:
mnadeemsb@gmail.com.
0021-8979/2011/109(9)/093704/8/$30.00
V
C 2011 American Institute of Physics 109, 093704-1
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Page 2

spectroscopy can be used to study the electrical behavior of
different microstructures (phases) inside a polycrystalline
material. Using the impedance technique, data equivalent to
the real and imaginary parts of complex electrical quantities
are measured as a function of the frequency of the applied
electric field.16These complex quantities include electrical
impedance, dielectric permittivity, and loss tangent, tan d.
The electric and dielectric properties of the ferrites are pre-
dominantly controlled by the grain boundaries.17The dielec-
tric properties of the NiFe2O4 nanoparticles will be
constructive for extending the range of applications. The
electrical properties of ferrites provide supportive informa-
tion about the behavior of the localized electric charge car-
riers and an understanding of the dielectric polarization
mechanism. Cation–cation interactions are distinguished
from cation–anion–cation interactions by affecting the elec-
trical and magnetic properties of oxides containing transition
metal elements.18In this respect, impedance spectroscopy
has been successfully employed to explore the possible role
of these interactions in changing the electrical and magnetic
properties. The temperature did not exceed 373 K to inhibit
any possible grain growth during experimentation.
II. EXPERIMENTAL
NiFe2O4 nanoparticles were prepared by the sol-gel
method. Analytical grade Ni(NO3).6H2O, Fe(NO3)3.9H2O
and urea were used for material preparation. We separately
dissolved 0.1 M of Ni(NO3).6H2O and Fe(NO3)3.9H2O in a
minimum amount of distilled water. This solution was then
mixed in the aqueous solution of urea in a molar ratio of 1:3.
The mixed solution was heated to a temperature of 338–343 K
with vigorous stirring until the gel was formed, which was sub-
sequently dried at 393 K for 3 h in an oven. The dried gel was
heat treated at 573 K for 3 h to remove volatile species. Then
the powder was pressed into a pellet 13 mm in diameter and
1.5 mm in thickness. Finally, the pellet was sintered at
873 K for 4 h. The structural characterization was performed
by an x-ray diffractometer (XRD) having Cu Ka radiation
(1.5418 A˚). The intensities were recorded for 20o?2h?70o
with a step scan of 0.02owith a time of 1 s/step. The measure-
ments of the hysteresis loops were performed by using a physi-
cal property measurement system (PPMS-9 T, Quantum
Design) applying a magnetic field of 5 T.
Impedance spectroscopy on the sintered pellet of NiFe2O4
was performed in the frequency and temperature range of
1?frequency?107Hz and 298 K?temperature?373 K,
respectively, using an Alpha-N analyzer (Novocontrol, Ger-
many). The surfaces of both sides of the pellet were properly
cleaned and contacts were made by silver paint on opposite
sides of the pellet, which were cured at 423 K for 3 h. Before
the impedance experiments, the dispersive behavior of the
leads were carefully checked to exclude any extraneous induc-
tive and capacitive coupling in the experimental frequency
range. The ac signal amplitude used for all of these studies
was 0.2 V. WINDETA software was used for data acquisition,
which was fully automated by interfacing the analyzer with a
computer. ZVIEW software was used for the fitting of the meas-
ured results. The sample was arranged inside a homemade
sample holder and a dc power supply was connected to the
sample holder to stabilize the temperature. Measurements
were made after stabilizing the temperature for about 10 min
prior to each reading.
III. RESULTS AND DISCUSSION
Figure 1 shows the XRD pattern of the synthesized nickel
ferrite nanopowder. All XRD peaks are indexed well with the
standard pattern for NiFe2O4 reported in PCPDF card #
74-2081. The average crystallite size has been calculated from
the most intense peak (311) using Scherer’s formula d¼kk/b
cos h where d is the particle size, b is the full width at half
maximum of the peak (311) and k is an instrumental con-
stant.19The average calculated particle size has been found to
be 2263 nm. The lattice parameter (8.339 A˚), computed
using respective (hkl) values, is less than that of the bulk ma-
terial. This reduction in lattice parameter may be attributed to
the increased degree of inversion, more surface energy, and
surface tension which can lead to the distortion of the lattice
constant.4,20Fig. 2 shows the field dependent magnetization
of the NiFe2O4sample measured at different temperatures in
an applied field up to 5 T. From these measurements, it has
been found that the magnetization does not saturate at the
maximum available field (i.e., 5 T) and the values of magnet-
ization obtained at 300, 350, and 400 K are 15, 14, and 13
emu/g, respectively. The room temperature magnetization
value is considerably smaller than the bulk value of 56 emu/g
for nickel ferrite.21This can be explained on the basis of the
core-shell morphology of the nanoparticles with a ferrimag-
netically aligned core surrounded by the surface shell, which
is found to be structurally and magnetically disordered due to
the nearly random distribution of cations and the canted spin
arrangement. The origin of this surface disorder may be due
to broken exchange bonds, high anisotropy on the surface, or
a loss of the long-range order in the surface. Furthermore,
canted or disordered spins at the surface of the nanoparticles
are difficult to align along the field direction causing an unsat-
urated magnetization in these particles.22–24As a consequence
FIG. 1. X-ray diffraction pattern of the NiFe2O4sample recorded at room
temperature.
093704-2Younas et al. J. Appl. Phys. 109, 093704 (2011)
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of the frustrated superexchange interactions in the surface
shell, our prepared nickel ferrite sample exhibits a reduced un-
saturated magnetization which is attributed to the weakening
of the AB exchange interactions due to the effect of spin cant-
ing that dominates over the effect of site exchange of the cati-
ons in the surface shell.25
Figures 3(a) and 3(b) show the complex impedance
plane plots of the NiFe2O4sample at different temperatures
and the arrow shows the direction of the increase in fre-
quency. At each temperature, impedance plane plots show
two well resolved semicircular arcs, a larger one at low fre-
quency and a smaller one at the higher frequency side. The
appearance of two arcs in impedance plane plots at each tem-
perature indicate the presences of two types of relaxation
phenomena with sufficiently different relaxation times
(s¼RC), where R is the resistance and C is the capacitance
of the associated phase.16The size of the semicircular arcs
decreases with the increase in temperature and shows its
minima around 358 K. A further increase in temperature
causes an increase in the diameter of the impedance plane
plots as seen in Fig. 3(b). The centers of both of the semicir-
cular arcs have been found to be depressed below the real
axis indicating the heterogeneity and deviation from the ideal
behavior.16We define this temperature (358 K) as the semi-
conducting to metallic transition (SMT) temperature. The
fitting parameters derived for the equivalent circuit will be
discussed in the next paragraph.
In order to correlate the electrical properties of the
NiFe2O4sample with the microstructure of the material, an
equivalent circuit model (RgQg) (RgbQgb), shown in the inset
of Fig. 3(a) has been employed to interpret the impedance
plane plots. Here R, Q, g and gb are the resistance, the con-
stant phase element, grain interiors and grain boundaries,
respectively. The constant phase element (CPE) is used to
accommodate the nonideal behavior of the capacitance
which may have its origin in the presence of more than one
relaxation process with similar relaxation times.16The ca-
pacitance of the CPE is given by the following relation,
C ¼ Q1=nRð1?nÞ=n, where the parameter n estimates the noni-
deal behavior having a value of zero for pure resistive behav-
ior and is unity for capacitative behavior.26,27In these types
of ferrites, the grain boundary resistance is generally higher
in comparison to the grains.3Additionally, the arc represent-
ing the grain boundaries generally lies on the lower fre-
quency side since the relaxation time of the grain boundaries
is much larger than that of the grains.28Therefore, we assign
smaller (high frequency) and larger (low frequency) semicir-
cular arcs to the grains and grain boundaries, respectively.29
The parameters Rg, Rgb, Qg, Qgb, ng, and ngbwere obtained
for each temperature by fitting the impedance plane plots
(within 1% fitting error). Figure 4(a) implies that slight var-
iations in parameters n and C for the grain and grain bounda-
ries in the 298–338 K range is indicative of the
inhomogeneous distribution of the energy of the trap centers.
With an increase in temperature, there are visible increasing
and decreasing trends in the values of ngand ngb, respec-
tively, in the 338–358 K range. These trends signify that the
grain capacitance (Cg) is likely to approach ideal behavior
and the grain boundary (Cgb) deviates from the ideal behav-
ior as shown in Fig. 4(b). A decrease in the capacitance of
the grains may be due to the vanishing of defects such as the
release of trapped charges followed by the accumulation of
these charges at the grain boundaries, thereby increasing its
capacitance. Above 358 K (i.e., the SMT temperature), both
Cg and Cgb parameters start saturating. Saturation in the
capacitances of the grains and grain boundaries may be due
to the combined effect of the delocalized charge carries and
spin alignments.
Figures 5(a) and 5(b) illustrate the variations in the resis-
tances of the grain and grain boundaries with temperature.
FIG. 3. (Color online) (a) Impedance
plane plot of the NiFe2O4sample at room
temperature. Inset shows the equivalent
circuit model. Arrow shows the direction
of increase in frequency. (b) Impedance
plane plot at some selected temperatures.
Inset shows the impedance plane plot
between 363–373 K.
FIG. 2. (Color online) Magnetization against applied field at different
temperatures.
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Page 4

The inset of Fig. 5(b) shows the variations in the total resist-
ance of the sample with temperature. The decrease in the re-
sistance of grains and grain boundaries has been suggested to
be due to the thermal activation of the localized charges.
Two types of thermal activations, i.e., carrier density in the
case of band conduction and carrier mobility in case of hop-
ping, are responsible for the reduction in the resistive proper-
ties with temperature.15With the increase in temperature
above 338 K, the grain resistance shows increasing trends
while the grain boundary and total resistance (shown in the
inset of Fig. 5) still show decreasing trends. The balance
between the mobility and density of the thermally activated
hopping carriers plays a vital role in determining the change
in resistance with temperature. Above 338 K, there is a
decrease in the density of thermally activated hopping car-
riers within the grains but the mobility of the hopping car-
riers increases with temperature. The increased value of the
mobility compensates for the decrease in the density of the
hopping carriers and we observe a decrease in the total resist-
ance of the sample with a temperature up to 358 K as shown
in the inset of the Fig. 5(b). An increasing trend in the resist-
ance of the grain boundaries beyond 358 K shows its metal-
lic behavior. On the whole, the conduction mechanism can
be implicit by considering the potential of the grain boundary
and energy of the egelectrons. In ferrites, transport phenom-
ena usually arise by the hopping of localized d electrons
between valence distributions of cations that normally
occupy the oxygen octahedral site.18The electrostatic inter-
action between anion and cation electrons cause a splitting
of the cation 3d level into less stable doubly degenerate eg
electrons and more stable triply degenerate t2gelectrons.30If
Ekis the energy of egelectrons, U is the potential of the grain
boundaries, n is the number density of the egelectrons, then
mathematically, n ¼ nee/=kTe, where e is the charge on a sin-
gle electron, U is the potential applied by the grain bounda-
ries, k is the Boltzmann constant, Teis the temperature of eg
electrons, and n0 is the number density of electrons at
U?0.27If Ek>eU then the electrons will be delocalized
and actively participate in the conduction mechanism but
when Ek<eU, then eg electrons will be localized. It is
inferred here that below 358 K, in the presence of some non-
magnetic disorder (i.e., electronic trap center) and magnetic
disorder (i.e., disorientation of the surface and core spins) eg
electrons will be localized, satisfying the condition of
Ek<eU and with an increase in temperature up to 358 K, the
hopping probability of the egelectrons increases, thereby
decreasing the resistance of the sample. However, with a fur-
ther increase in temperature above 358 K, localized states
become delocalized along with alignments of the core/sur-
face spins and effective conducting channels appear. Con-
ducting channels facilitate the movement of charge carriers
thereby increasing their mobility and we observe metal-like
behavior in this temperature range. Moreover, at the SMT
temperature, all of the egelectrons might have multipotential
values that give rise to a competition between localized and
delocalized charge carriers.
The activation energy for the thermally activated charge
carriers is obtained by fitting the dc conductivity data using
the Arrhenius relation, r ¼ r0exp½?Ea=kT?, where r0is the
pre-exponential factor, Eais the activation energy, and k is
Boltzmann’s constant. The resistance values of the grains
(Rg), grain boundaries (Rgb), and geometrical dimensions
have been used to calculate the total dc conductivity by using
the relation, r ¼ L=A:R, where r is the conductivity in
S cm?1, A is area of the sample in cm2, L is length of the
sample in cm, and R is the total resistance of the grains and
grain boundaries in X.31From Fig. 5(c) a change in slope is
observed beyond 318 K, showing that a different conduction
mechanism is involved. The activation energies 0.71 and
0.41 eV have been calculated from the fitted data below and
above 318 K, respectively. A higher value of the activation
energy below 318 K suggests dominant hole hopping
between Ni2þ$ Niþ3ions at the octahedral B-site, and the
Niþ3ions are in a low spin state t6
Feþ3
t3
g
ions. With the increase in temperature above
318 K, the electrons gain enough energy to dominate the
overall conduction mechanism that causes a reduction in the
activation energy since electron hopping requires a lower
value of activation energy compared to that of hole
hopping.31
Goodenough32predicted the simultaneous existence of
the both cation–cation and cation–anion–cation interactions in
the rock salt type structures such as NiO, MnO, FeO, etc.
When strong cation–anion–cation interactions dominate over
the weak cation–cation interactions, these materials have semi-
conducting/insulating behavior. In the case of strong cation–
2g;e1
g
??
as compared to the
2g;e2
??
FIG. 4. (Color online) (a) Variation of
parameters ngand ngbwith temperature,
and (b) variation of grains and grain
boundary capacitances with temperature
for the NiFe2O4sample.
093704-4 Younas et al.J. Appl. Phys. 109, 093704 (2011)
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Page 5

cation interactions between octahedral B-site, these materials
show metallic behavior, and may become semiconducting at
low temperatures. Also, the presence of cations of the same
elements with different valence states give rise to the metallic
character below the Curie temperature. In NiFe2O4with nor-
mal cation distribution (Fe3þ)[Ni2þFe3þ]O42?, the cation–
cation interaction is dominated by the cation–anion–cation
interactions between [Fe3þ–O2?–Fe3þ] and [Ni2þ–O2?–
Ni2þ].33,34In the view of crystal field and ligand field theories,
the Ni2þ–O2?–Ni2þinteractions are dominant which rendered
this material to be semiconducting. However, Ni2þions may
distribute randomly on (A) and [B] sites along with Fe3þions
due to some reverse cationic distributions in the nanocrystal-
line NiFe2O4material. The room temperature Mo ¨ssbauer spec-
troscopy (the result will be shown in a forthcoming paper)
revealed the sextet and relaxed magnetic structure with a very
broad linewidth. The broad linewidth is observed due to the
field distribution for small crystallite size which is about 22
nm in this case. The reduced value of the hyperfine field at the
B site compared to the bulk counterpart35is the result of the
distribution of the crystallite size. The inversion parameter esti-
mated from the Mo ¨ssbauer spectroscopy was 0.64. The
reduced value of the tetrahedral isomer shift as compared to
the octahedral isomer shift for this material has been attributed
to the difference in the coordination of the Fe3þfrom the four
fold site (A site) to the six fold (B site). Hence, in this material
a fraction of Fe3þand Ni2þions migrate to the [B] and (A)
sites, respectively. Shifting of the Fe3þions causes compres-
sive strains due to the smaller distance between the B-site ions
compared to the A-site ions in nanoparticles.7These compres-
sive strains may break the surface exchange bonds which
results in a canted spin structure. The canted spin structure not
only affects the [Ni2þ–O2?–Ni2þ] interactions but also weak-
ens the AB-exchange interactions that cause a lower value of
the room temperature magnetization compared to the bulk
counterpart previously discussed. An increased number
of Fe3þat [B] enhances the exchange interaction between
[Fe3þ–O2?–Fe3þ]. It is presumed here that below 258 K, an
increase in temperature causes an increase in hopping of the
localized charge carriers between the [Fe3þ–O2?–Fe3þ] and
[Ni2þ–O2?–Ni2þ] linkage at the octahedral B site, in this way
giving rise to the semiconducting character in the material.
However; the affinity of the NiO for the oxidation and creation
of defects such as oxygen vacancies during heating in the fer-
rite lattice leads to the formation of Ni3þand Fe2þions. Above
358 K, diminishing localized states and alignments of the spins
give rise to the efficient conductive channels in the form of
[Fe3þ–Fe2þ] and [Ni2þ–Ni3þ] links. These channels cause the
delocalization of the charge carriers, and in so doing creating a
metallic character above 358 K.
Figures 6(a) and 6(b) show the variation of tangent loss
with frequency at some representative temperatures. Each
spectrum possesses two loss peaks with different relaxation
times exhibiting the presence of at least two relaxations in
the system which is in accordance with the impedance plane
plot results previously discussed. The larger peak in the low
frequency region <102Hz is attributed to the relaxation pro-
cess at the grain boundaries and the smaller peak in the high
FIG. 5. (Color online) (a) Variation of
Rgwith temperature, (b) variation of Rgb
with temperature for the NiFe2O4sam-
ple; inset shows the variation of total re-
sistance with temperature, and (c) total
dc conductivity of NiFe2O4 the solid
lines are the best fit to the Arrhenius
relation.
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Page 6

frequency region >104Hz is associated with the grains.36In
both relaxation processes, the peak height increases and
shifts toward the higher frequency side up to 358 K, as
shown in Fig. 6(a). In the NiFe2O4material,18the relaxation
is attributed to the cation–anion–cation interactions at the
octahedral B site. Now the increase in magnitude of the tan-
gent loss peak with temperature is attributed to the increase
in the number of thermally activated [Fe3þ–O2?–Fe3þ] and
[Ni2þ–O2?–Ni2þ] linkages responsible for the relaxation;
whereas the shift in the relaxation frequencies toward higher
values is due to the mobility activation of the charge carriers
with an increase in temperature. Above 358 K, the magni-
tude of the loss peak in the low frequency region remains rel-
ativelytemperature insensitive
discussion of delocalization of the charge carriers with an
indiscriminate distribution of the energy. Some of the charge
carriers scatter from the grain boundary planes due to the
increased lattice vibrations.37The scattering outcome in the
reduced value of the mobility that has been found to be re-
sponsible for the shift of the high frequency relaxation peak
toward a lower frequency as shown by the arrow in Fig. 6(b).
Figure 7(a) shows the frequency dependent real part of
the dielectric constant at different temperatures. The trends of
the graph show the existence of more than one type of polar-
ization in NiFe2O4 nanoparticles. Typically four types of
polarizations, interfacial, dipolar, atomic, and electronic are
reported in ferrites.38Dispersion below 102Hz is suggested to
be due to the interfacial polarization and above 104Hz, due to
rotational displacement of the dipoles. At frequencies higher
than 106Hz, a relatively independent value of the dielectric
constant with temperature is attributed to the atomic and elec-
tronic polarizations. Figure 7(a) indicates an increase in the
dielectric constant with temperature up to 358 K. It is sug-
gested here that thermally activated dipoles cause an increase
in the interfacial and rotational polarizations by accumulating
at grain boundaries. In the view of the above SMT discussion,
an increase in temperature above 358 K alters the overall
space charge capability. A decrease in the dielectric constant,
as shown in the inset of Fig. 7(a), has been endorsed due to
the scattering of the charge carriers which causes a depletion
in the space charge layers. At each temperature, a decrease in
the dielectric constant with frequency is observed owing to
the lower dipolar response to the ac field.39
which supportsour
Different types of conductivities in NiFe2O4 material
have been reported in the literature. Baruwati et al.40attrib-
uted the n-type behavior as being due to the presence of Fe3þ
in NiFe2O4nanoparticles. The electron conduction is repre-
sented as Fe3þ$ Fe2þ. The hole conduction is represented as
Ni2þ$ Ni3þ. Other reports41,42also support the existence of
n-type and p-type conductivities in Ni-Zn ferrites due to the
presence of Fe2þand Ni3þ, respectively. The values of the
activation energy (i.e., 0.41 and 0.71 eV) obtained in this
study suggest hopping and polaronic conduction between the
localized sites.43In the hopping process, the carrier mobility
is temperature dependent, which is usually characterized by
activation energy. Figure 7(b) shows the frequency dependent
ac conductivity of the NiFe2O4sample at some representative
temperatures. At low frequency, the ac conductivity is found
to be weakly frequency dependent due to the nonequilibrium
occupancy of the trap charges.27A further amplification of
frequency reduces the occupancy of the trap centers by mak-
ing them available for conduction. It facilitates the conductive
state to become more active by promoting the hopping of
electrons and holes. The conductivity increases with increas-
ing frequency and temperature up to 358 K. Above 358 K, the
frequency of the hopping ions decreases due to a reduction in
the mobility of the charge carriers after reflection from the
grain boundary plane and a decrease in conductivity as shown
in inset of Fig. 7(b) is observed. Trends in conductivity with
temperature supports our results of the dielectric constants as
both the conductivity and the dielectric constant runs parallel.
In order to obtain a clear understanding of the conduc-
tion mechanism, we have divided the conductivity graph
over three frequency regions: (I) 1–100 Hz, (II) 3?102–
4?103Hz, and (III) 3?105–4?106Hz. At each frequency
region, the conductivity follows the dynamical ac power law,
such that r x;T
ð
having the unit of conductivity and s is the slope of the fre-
quency dependent region, 0.0?s?1.18Fitting of the experi-
mental data yields a value of s whose dependence on
temperature is a function of the conduction mechanism.
Figure 7(c) shows the variation of the slope parameter, s,
with different temperatures. For region (I), there is no change
in s with temperature due to a nonequilibrium occupancy of
the trap charges. In region (II) there is a linearly decreasing
trend of s with temperature suggesting a correlated barrier
Þ ¼ B T
ð ÞxS T
ð Þ, where B is the parameter
FIG. 6. (Color online) (a) Variation of
tangent loss with frequency. The direc-
tion of the arrow shows the increase in
temperature, and (b) variation of tangent
loss with frequency with the arrow in the
direction of the increase in temperature.
093704-6Younas et al.J. Appl. Phys. 109, 093704 (2011)
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Page 7

hopping conduction model in this material. At higher fre-
quencies in region (III), value of s first decreases reaching a
minimum value, and then starts increasing again as shown in
Fig. 7(c). This behavior of s is in accordance with the over-
lapping large polaron tunneling model of ac conduction.12
The higher values of activation energy in our case also sup-
port this argument.17The cations surrounded by close
packed oxygen anions can be treated as isolated from each
other due to little direct overlap of the charge clouds and
hence, the localized egelectron model is appropriate. This
localization give rise to the formation of the polaron and the
charge transport may be considered between the nearest
neighbor sites.12,44The polaronic conduction in this material
has been assumed between Fe3þand Fe2þdue to the pres-
ence of defects (i.e., oxygen vacancies, vacancies, agglomer-
ates, and nanovoids) at nanolevels.17
mechanism of ac conduction in the nanostructure NiFe2O4is
different in different frequency ranges. It is expected that
the correlated barrier hopping conduction mechanism
dominates in this material owing to the presence of the
[Fe3þ–O2?–Fe3þ] and [Ni2þ–O2?–Ni2þ] linkage in the lat-
tice. The formation of hopping ion pairs depends upon the
occupancy of Ni-ions at the octahedral B-site. However, a
clear understanding of the conduction mechanism in this
nanostructure NiFe2O4needs further investigation.
Apparently, the
IV. CONCLUSIONS
Ithasbeenshownthatimpedancespectroscopyisanexcel-
lent technique to investigate the electrical transition with the
possible correlation to the microstructure of the material. Grain
and grain boundary phases are well resolved by impedance
plan plots. The parameters Rg, Rgb, Qg, Qgb, ng, and ngbcoupled
with the grain and grain boundaries are explained using an
equivalent circuit model. Thermal activation of trapped
charges/dipoles has been found to be responsible for decreasing
the resistance of the grain and grain boundaries and an increase
in the value of the dielectric constant and tangent loss. The
change in slope of the Arrhenius plot around 318 K has been
discussed on the basis of hopping between Fe3þ–Fe2þand
Ni2þ–Ni3þions and hopping has been suggested as a dominant
ac conduction mechanism in this material. As the magnetiza-
tion study illustrated, surface spin canting of the nanoparticles
due to the broken exchange bond and anisotropy is responsible
for the weakening of the AB-exchange interaction and hence a
lower value of room temperature magnetization. Semiconduc-
tor to metallic transition around 358 K has been reported and
discussed in terms of the transition from localized charge car-
rier [Fe3þ–O2?–Fe3þ]/[Ni2þ–O2?–Ni2þ] linkages to delocal-
ized charge carrier [Fe3þ–Fe2þ]/[Ni2þ–Ni3þ] linkages.
ACKNOWLEDGMENTS
One of the authors, M. Atif, acknowledges the Higher
Education Commission (HEC), Islamabad Pakistan, for the
grant of the PhD scholarship.
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