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Effect on structural, optical, electrical, and magnetic
properties of Ce and Ni co-doped SmFeO
3
nanostructures
Surbhi Sharma
1
, Naseem Ahmad
2
, and Shakeel Khan
1,
*
1
Department of Applied Physics, Z.H. College of Engineering & Technology, Aligarh Muslim University, Aligarh 202002, India
2
Department of Physics, Aligarh Muslim University, Aligarh 202002, India
Received: 12 October 2022
Accepted: 17 January 2023
ÓThe Author(s), under
exclusive licence to Springer
Science+Business Media, LLC,
part of Springer Nature 2023
ABSTRACT
In this study, nano-crystalline powder samples of Sm
0.96
Ce
0.04
Fe
1-x
Ni
x
O
3
(0 BxB0.3; step size = 0.1) have been synthesised via cost-effective sol–gel
auto-combustion route and characterised through various analytical techniques
to probe the effect of Ce and Ni co-doping on various physical properties of the
system under investigation. Rietveld refinement of X-ray diffraction (XRD)
patterns along with FTIR spectra elucidates the successful formation of
orthorhombic crystal symmetry having Pbnm (D
2h16
) space group. Williamson–
Hall (W–H) analysis has been employed to calculate the average crystallite size
and micro-strain induced within the crystal lattice via co-doping. The average
particle size evaluated from Transmission electron microscopy (TEM) is con-
comitant with the W–H findings. UV–Visible spectroscopy corroborates a sig-
nificant redshift in the energy band-gap from 2.51 to 1.97 eV, whereas there is an
increase in the Urbach energy on increasing Ni concentration. Various optical
parameters including skin depth, extinction coefficient, and optical conductivity
have been realised. Sm
0.96
Ce
0.04
Fe
0.7
Ni
0.3
O
3
exhibits the most prominent ferro-
magnetic behaviour with remarkably higher values of the magnetisation, coer-
cive field, and remanent magnetisation. In addition, the exchange bias (EB)
effect is perceived attributed to the ‘‘cluster glass’’ states for all the samples. DC
resistivity data shows typical semi-conducting-like behaviour of all the pre-
pared samples and systematic reduction in the activation energy on the incor-
poration of Ni ions. The frequency-dependent dielectric measurements divulge
the usual dielectric dispersion behaviour. The AC conductivity data obeys the
Jonscher power law. Nyquist plots of the studied samples indicate the presence
of a non-Debye type of relaxation phenomenon.
Address correspondence to E-mail: skhanapd@gmail.com
https://doi.org/10.1007/s10854-023-09917-3
J Mater Sci: Mater Electron (2023) 34:476 (0123456789().,-volV)(0123456789().,-volV)
1 Introduction
Over the past couple of decades, condensed matter
physicists have paid keen interest in examining the
physical properties of perovskite-based ceramic oxi-
des. Perovskite oxide materials with a general for-
mula ABO
3
(where A and B represent rare-earth and
transition metal ions, respectively) show fascinating
properties like Mott transition, colossal magneto-re-
sistance (CMR), charge (orbital) ordering, supercon-
ductivity, and multiferroic nature [1]. Amongst ABO
3
systems, the rare-earth orthoferrites (RFeO
3
) crys-
tallise in an orthorhombically distorted perovskite
crystal symmetry with Pbnm/Pnma space group,
where Fe ions prefer the central symmetry and rare-
earth ions prefer the off-centre position [2]. The
multifunctional properties of these materials probe
their extra feasibility in various promising applica-
tions such as catalysts, solid oxide fuel cells (SOFCs),
spintronics, data storage applications, highly efficient
electromagnetic wave absorbers, the removal of
electromagnetic pollution, and interference in con-
sumer’s electronics [3–8]. Specifically, SmFeO
3
(SFO)
belongs to the Pbnm space group (#62) and exhibits
intriguing properties, such as G-type antiferromag-
netic ordering below the Neel Temperature,
T
N
=670 K, fast magnetic switching, highest spin
reorientation transition temperature from (C
4
)?(C
2
)
(occurs between T
SR1
=450 K and T
SR2
=480 K),
magnetisation reversal phenomenon at cryogenic
temperatures (*5 K), low dielectric loss, ferroelec-
tricity, and improved piezoelectricity at 300 K [9].
The three different magnetic interactions such as
Fe
3?
–O–Fe
3?
,Fe
3?
–O–Sm
3?
, and Sm
3?
–O–Sm
3?
and
Sm
3?
–Sm
3?
below 5 K, Fe
3?
–Sm
3?
below 140 K, and
Fe
3?
–Fe
3?
interactions above 140 K are responsible
for magnetism in SmFeO
3
[10,11]. Factors governing
spin reorientation transition in SmFeO
3
include
magnetic anisotropy, Dzyaloshinskii–Moriya (DM)
interaction, exchange interaction, and single-ion ani-
sotropy remark it a promising candidate for mag-
neto-electric (ME) and magneto-striction applications
[6]. A lot of studies have been carried out explaining
the improved magnetic behaviour with enhanced
saturation magnetisation in SmFeO
3
. For example,
Bashir et al. [12] studied the magnetic properties of
SmFeO
3
synthesised via a conventional solid-state
reaction route and reported the values of magnetic
moment 0.21 l
B
/f.u. and saturation magnetisation
0.288 l
B
/f.u. at 300 K.
Furthermore, some important works of literature
are summarised here. Zhu et al. [13] examined the
magnetic activity of Er-doped SmFeO
3
and realised
an improvement in magnetic susceptibility and sat-
uration magnetisation and a decrease in electric
polarisation in Er
3?
-doped SFO resulting in the
transformation of the system from hard to a soft
magnetic system. Fan et al. [14] illustrated that Ce-
substituted perovskite-based SmFeO
3
ceramics
would have befitting functional applicability in cat-
alytic oxidation processes. Syed Bukhari et al. [15]
have reported that Ce-doped SmFeO
3
exhibits
remarkable advancement in conductivity and stabil-
ity, making it to be a potential candidate for gas
sensors and as interconnect in anode materials for
SOFCs. Bouziane et al. [16] investigated the substi-
tution effect of Mn in the SFO system and reported a
lowering in the spin reorientation transition temper-
ature as a function of Mn concentration. Mir et al. [1]
reported an increase in porosity, dielectric constant,
ac conductivity, grain size, and reduction in optical
band-gap energy in SmFeO
3
nanostructures via Ni
substitution. Since A-site doping has a significant
influence on the magnetic anisotropy (magnetic
properties), whereas B-site doping affects the optical,
electrical, and dielectric properties of the SFO
nanostructures, we expect that doping of rare-earth
ions at A-site and transition metal ions on B-site
simultaneously in SFO crystal lattice can favour the
onset of random magnetic interactions and structural
distortion, thereby modifying the structural, electri-
cal, dielectric, and magnetic behaviour of SFO
nanoparticles. These factors motivated us to partially
substitute the nonmagnetic Sm
3?
ions with magnetic
Ce
3?
ions and Fe
3?
ions with Ni
?3
ions simultane-
ously with the intention to improve the multiferroic
properties of the SmFeO
3
system.
It made us curious to synthesise ultra-fine Sm
0.96-
Ce
0.04
Fe
1-x
Ni
x
O
3
(0 BxB0.3; step size =0.1) nano-
crystalline powder samples to determine the mag-
netic, optical, and electrical transport anomalies in
the context of their potential technological applica-
tions. In as-prepared samples, doping of cerium (Ce)
at A-site was kept fixed at 0.04 and nickel (Ni) doping
is varied at B-site in the steps of 0.1. The concentra-
tion of Ce
3?
ions was fixed at 0.04, as above this
concentration appearance of secondary phase of
CeO
2
starts perhaps due to the larger cationic size of
Ce
3?
(1.18 A
˚) ions in comparison to the Sm
3?
(1.09 A
˚)
476 Page 2 of 25 J Mater Sci: Mater Electron (2023) 34:476
ions [15]. To the best of our knowledge, no such work
has been reported till now.
2 Experimental
In the present study, we have used the sol-gel auto-
combustion method to synthesise
Sm0.96Ce0.04Fe
1-x
NixO(0BxB0.3; step
size =0.1) NPs. AR (Analytical reagent) grade R
(NO
3
)
3
6H
2
O(R=Sm, Ce, and Ni) and Fe (NO
3
)
3-
9H
2
O acquired from CDH were used as initial pre-
cursor materials. In this technique, stoichiometric
amounts of initial precursors were weighed and
dissolved in double distilled water. The resulting
precursor solution was transferred to the magnetic
stirrer to get a homogeneous primary solution. Now,
in a separate beaker, ethylene glycol and citric acid
were mixed in double distilled water. This solution
was then added drop by drop to the precursor solu-
tion. The stirring of the resultant solution was done
for 6 h at 70 °C until the solution was transformed
into a homogeneous dry porous gel and then placed
into an oven at 150 °C for 8 h to go through a self-
propagating combustion process. Consequently, the
gel is entirely burnt into an amorphous loose powder
and finally calcined at 800 °C for 2 h in an alumina
crucible with intermediate grinding for 1 h each,
resulting in the formation of nano-crystalline powder
samples.
The crystallinity and phase purity of as-prepared
samples were deliberated using X-ray diffraction
(XRD) measurements carried on XRD-6100, Shi-
madzu advance X-ray diffractometer with an oper-
ating voltage and current of 40 kV and 30 mA,
respectively. Fourier Transform Infrared (FTIR)
spectra were recorded by utilising Bruker Tensor-37
IR spectrometer in the transmission mode with a
wavenumber range varying from 400 to 4000 cm
-1
.
Transmission electron microscopy (TEM) and selec-
ted area electron diffraction pattern (SAED) images
were captured using a JSM-2100 JEOL microscope to
have a glimpse of the particle size and morphology of
each specimen. To investigate the optical properties,
UV–Visible Diffuse Reflectance spectra were probed
using Lambda 850, Perkin-Elmer spectrophotometer
in the wavelength range 250–800 nm. The magnetic
ordering of as-synthesised powder sample at 300 K
was studied by a Vibrating Sample Magnetometer
(VSM, Micro Sense EZ9) in the magnetic field range
of ±20 kOe. The dc resistivity variation with tem-
perature was investigated using a conventional two-
probe technique with the help of a Keithley elec-
trometer (Model No. 6517B) within the temperature
range of 320–473 K. The dielectric measurements
were carried out by making thin pellets of the pow-
dered samples and then coated with silver paste on
both sides to achieve parallel plate capacitor geome-
try followed using Hioki (3532-50) LCR meter in the
broad frequency range (42 Hz–5 MHz).
3 Results and discussion
3.1 Structural analysis
The room-temperature X-ray diffraction (RT-XRD)
patterns of Sm
0.96
Ce
0.04
Fe
1-x
Ni
x
O
3
(0 BxB0.3; step
size =0.1) NPs in the 20°B2hB80°range are
illustrated in Fig. 1a. The obtained Bragg diffraction
peaks are well resolved and turned out to be con-
comitant with the Standard Powder Diffraction
Database (JCPDS card number #74-1474). RT-XRD
patterns divulge that all the as-synthesised co-doped
SmFeO
3
(SFO) samples are formed in an orthorhom-
bic structure having Pbnm - D16
2hspace group,
respectively. Sharp and well-defined diffraction
peaks are an indication of a high degree of crys-
tallinity in all the samples. It is very much evident
from the RT-XRD patterns that all the synthesised
samples have polycrystalline nature with distin-
guishable crystallographic planes analogous to the
SFO matrix. No detectable trace of impurity/sec-
ondary phases is observed. This validates the suc-
cessful incorporation of Ce and Ni ions in SFO lattice
sites.
The influence of Ni doping on the crystal structure
of Sm0.96Ce0.04Fe1-xNixO3 (0 BxB0.3) is also
explored using Rietveld refinement analysis of
diffraction patterns using FULLPROF software and
the fitted data are represented in Fig. 2. The observed
crystallographic Wyckoff positions are as follows:
Sm/Ce atoms at 4c, Fe/Ni atoms at 4b, axial O (1)
atoms at 4c and equatorial O (2) atoms at 8d,
respectively, for all the samples. In the refinement
process, the Bragg (experimental) profile has been
fitted through the pseudo-Voigt profile and the
background has been minimised by utilising the
Twelve Coefficient Fourier Cosine series. Profile fit-
ting was varied in accordance to reach the lower v
2
J Mater Sci: Mater Electron (2023) 34:476 Page 3 of 25 476
Fig. 1 aX-ray diffraction patterns for Sm
0.96
Ce
0.04
Fe
1-x
Ni
x
O
3
(0 BxB0.3) samples, bmagnified view of most intense peak showing
phase shift, and cstructure of Sm
0.96
Ce
0.04
Fe
0.7
Ni
0.3
O
3
sample drawn using vista
Fig. 2 Rietveld-refined XRD patterns for Sm
0.96
Ce
0
.
04
Fe
1-x
Ni
x
O
3
(0 BxB0.3) samples
476 Page 4 of 25 J Mater Sci: Mater Electron (2023) 34:476
value, indicative of relatively good profile fitting
amongst the observed and simulated XRD spectra.
The refined structural parameters are tabulated in
Table 1.
Structural stability and tolerance of perovskite-type
Sm
0.96
Ce
0.04
Fe
1-x
Ni
x
O
3
(0 BxB0.3) are evaluated
using Goldschmidt’s tolerance factor (s) that repre-
sents the degree of distortion from ideal perovskite
structure and can be expressed as [2] follows:
s¼ðrSm=Ce þrOÞ=pð2ðrFe=Ni þrOÞ;ð1Þ
where r
Sm/Ce
,r
Fe/Ni
and r
O
are the ionic radii of
Sm
3?
/Ce
3?
,Fe
3?
/Ni
3?
cations, and O
2-
anion,
respectively. By employing the above Eq. (1), it is
observed that the value of sincreases with the
increasing Ni content from 0.8794 to 0.8856 and
therefore a decline in the stability limit ranges
0.71–0.90, affirming the enhanced structural stability
of distorted perovskite crystal symmetry [3]. The
gradual transformation of the SFO crystal structure
from central symmetric to off-central symmetric
configuration manifested in the form of an increment
in the tolerance factor. This is consistent with the
term reported by Praveena et al. [10]. In addition, the
Octahedral factor (O
f
) is also equally important for
the formability of stable perovskite structure and can
be defined as r
B
/r
O
, where r
B
(Fe
3?
=0.645 A
˚,
Ni
3?
=0.60 A
˚) and r
O
(1.459 A
˚) stand for ionic radii
of Fe
3?
/Ni
3?
cations at B-site and O
2-
anion, respec-
tively. The suitable octahedral factor ratio lies
between 0.442 and 0.895 for stable perovskite for-
mation [17]. Values of octahedral factor fits well
within the octahedral factor limit as depicted in
Table 2. Using both factors, the formability of cubic
perovskites can be predicted reliably. Thereby mod-
ifying the properties Sm0.96Ce0.04Fe1-xNixO3
(0 BxB0.3) system due to the internal stresses
introduced as a result of incongruity between Sm–O/
Table 1 Rietveld-refined
structural parameters of
Sm
0.96
Ce
0.04
Fe
1-x
Ni
x
O
3
(0 BxB0.3) samples using
orthorhombic crystal structure
with Pbnm space group
Structural parameters x= 0.0 x= 0.1 x= 0.2 x= 0.3
Sm/Ce (x,y, 0.25) 4c X0.99173 0.99543 0.99804 0.99969
Y0.05313 0.05470 0.05497 0.05312
Fe/Ni (0.5, 0.0, 0.0) 4b
O (1) (x,y,z)4c X0.74652 0.73836 0.67846 0.69378
Y0.20869 0.29534 0.24892 0.26583
Z0.00377 0.04891 0.03713 0.05325
O (2) ( x,y,z)8d X0.10445 0.12217 0.09629 0.09530
Y0.45783 0.47448 0.46742 0.45705
Z0.25000 0.25000 0.25000 0.25000
u=-0.04137 -0.29118 -0.50159 -0.15728
v=-0.01393 -0.00108 -0.01863 -0.02643
z= 0.00884 0.01108 0.01019 0.09756
Residuals (%) R
P
4.22 4.29 4.43 4.74
R
wp
5.35 5.42 5.62 5.96
R
exp
4.89 4.84 5.00 5.20
Goodness of fit (v
2
)R
exp
/R
wp
1.20 1.25 1.26 1.31
X-ray density, gm/cm
3
d
x
6.886 6.919 6.988 7.040
Bond length (A
˚) Sm/Ce–O
1
2.7473(8) 2.7381(4) 2.6459(8) 2.4730(6)
Sm/Ce–O
2
2.5412(3) 2.4655(3) 2.4443(3) 2.2892(5)
Bridging angle (°) Fe–O
1
–Fe 141.456(5) 144.798(6) 147.204(4) 148.131(5)
Fe–O
2
–Fe 151.159(5) 154.518(4) 156.531(3) 161.110(3)
\Fe–O–Fe[146.3074 149.6583 151.8676 154.6207
Tilt angle (°)u1 19.272 17.601 16.398 15.934
u2 14.420 12.740 11.734 9.445
\u[16.846 15.171 14.066 12.689
Lattice parameters (A
˚)a= 5.4010(6) 5.3808(5) 5.3800(7) 5.3778(4)
b= 5.5937(6) 5.5886(6) 5.5852(8) 5.5795(8)
c= 7.7091(7) 7.6944(7) 7.6904(9) 7.6797(5)
Unit cell volume (A
˚
3
)V= 232.933(4) 231.366(4) 231.217(5) 230.719(4)
J Mater Sci: Mater Electron (2023) 34:476 Page 5 of 25 476
Ce–O and Fe–O/Ni–O bond lengths, alleviated by
cooperative rotation of FeO
6
octahedral and in turn
position switching of Sm
3?
cation as summarised in
Tables 1and 3.
One of the major contributors to structural vari-
ability in the case of perovskites is the octahedral tilt
angle (u) which is defined as tilting of the FeO
6
octahedra with respect to one or more symmetry axis,
sustaining both symmetry of the octahedral (approx.)
as well as their corner connectivity (strictly). That
tilting enables pronounced flexibility in the coordi-
nation of the A-site cation, whereas leaving the
matrix of B-site cation is necessarily unaltered, lead-
ing to alteration in the A–X bond angle. As illustrated
in Table 2, an increase in tolerance factor (s) and a
decrease in octahedral tilt angle (u) with Ni doping
are corroborated. The variation of octahedral tilt
angle and super-exchange angle with Ni doping is
also depicted in Fig. 3a. The distortion and tilting of
FeO
6
octahedra in the co-doped (Ce–Ni) SmFeO
3
crystal structure are also illustrated in Fig. 1c.
A decrement in the lattice parameters with the
increase in Ni concentration is observed from XRD
spectra. This may be responsible for the lattice con-
traction with increasing Ni content corresponding to
the shifting of XRD peaks towards a higher 2hvalue,
as shown in the magnified version in Fig. 1b of the
main diffraction peak (112). This is also implying that
the growth of lattice strain that arise by slight atomic
displacements (translations) from their original lattice
positions, which are usually prompted by crystalline
defects, such as stacking faults, sinter/contact stres-
ses, interstitial impurity atoms, coherency stresses,
dislocations, and grain boundary triple-junction [18].
Thus, the reduction in the lattice parameters is solely
due to the smaller ionic radii of Ni
3?
(0.60 A
˚) ion in
comparison to Fe
3?
(0.645 A
˚) ion.
The average crystallite sizes (d
s
) of each synthe-
sised powder sample were estimated from the size-
induced line broadening of (110), (111), (020), (112),
(200), (021), (022), 202), (113), (220), (004), (131), (312),
(411), and (116) diffraction peaks using Scherrer’s
formula:
dS¼0:9k
bhklcosh;ð2Þ
where b
hkl
represents FWHM, hrepresents Bragg’s
glancing angle, d
s
denotes crystallite size, and 0.9 is
the shape factor constant. The average values of
crystallite sizes estimated by taking abovementioned
diffraction peaks for each sample are tabulated in
Table 2.
Furthermore, Scherrer’s equation is corrected by
employing Williamson–Hall (W–H) analysis in which
both size- and strain-induced broadening have been
taken into account to obtain both crystallite sizes and
micro-strain associated with each specimen. Since
Table 2 Tolerance factor,
Octahedral factor, and
crystallite size calculated using
Scherrer’s equation and
Williamson–Hall analysis for
Sm
0.96
Ce
0.04
Fe
1-x
Ni
x
O
3
(0 BxB0.3) samples
Parameters x= 0.0 x= 0.1 x= 0.2 x= 0.3
Tolerance factor, (s) 0.8794 0.8814 0.8835 0.8856
Octahedral factor, (O
f
) 0.5039 0.5003 0.4969 0.4934
Crystallite size, nm dS37 34 32 31
dw52 49 46 40
Micro-strain, (e) 4.24 910
–4
5.38 910
–4
6.11 910
–4
6.40 910
–4
Table 3 Effective mass, force constant, bond length, and vibrational modes of Sm
0.96
Ce
0.04
Fe
1-x
Ni
x
O
3
samples
Concentration (x) Wavenumber (cm
-1
) From FTIR
Fe–O (1) Fe–O (2)
Effective mass,ðlÞ
(amu)
Force constant, k
(N/cm)
From FTIR
Fe–O (1) Fe–O (2)
Bond length,
Fe–O (1) (A
˚)
FTIR Rietveld
Bond length,
Fe–O (2) (A
˚)
FTIR_Rietveld
0.0 418_555 12.437 1.274_1.729 2.372_1.777(6) 2.142_1.953(6)
0.1 420_556 12.451 1.294_1.742 2.359_1.852(8) 2.137_1.982(3)
0.2 430 _558 12.464 1.358_1.755 2.322 _2.142(8) 2.132_2.016(3)
0.3 432_559 12.478 1.372_1.761 2.314 _2.245(9) 2.129_2.032(3)
476 Page 6 of 25 J Mater Sci: Mater Electron (2023) 34:476
size and strain broadening are independent of each
other, the W–H equation can be expressed as follows:
bhklcosh¼0:9k
dwþ4esinh;ð3Þ
where d
w
denotes average crystallite size and esig-
nifies micro-strain. Eq. (3) is based on the uniform
deformation model (UDM) in which strain is con-
sidered to be uniform in all three directions, thus
corroborating the isotropic nature of the crystal. A
plot of 4 sinhversus b
hkl
coshfor Sm
0.96
Ce
0.04
Fe
1-x-
Ni
x
O
3
(0 BxB0.3) samples as presented in Fig. 3b.
The crystallite size and micro-strain of each sample
are obtained from the linear fit of these plots. The
crystallite size obtained from W–H analysis is much
greater in comparison to that obtained from Scher-
rer’s formula. The reason is that in Scherrer’s formula
entire broadening of the diffraction peaks is analo-
gous to the size of crystallites, whereas in the W–H
formulation broadening occurs both due to crystallite
size and strain induced within the crystal lattice. The
values of average crystallite size (d
w
) and micro-
strain (e) evaluated using W–H analysis are also lis-
ted in Table 2. It is realised that Sm
0.96
Ce
0.04
Fe
1-x-
Ni
x
O
3
(0 BxB0.3) on Ni doping produces several
types of crystal defects and oxygen vacancies within
the crystal lattice which impute reduction in the
crystallite size and shrinkage in the unit cell volume.
Thus, in turn, the strain associated with the samples
increases as a function of Ni concentration which can
also be correlated with structural distortions induced
in the crystal lattice with the incorporation of Ni.
3.2 Fourier Transform Infrared (FTIR)
spectroscopy analysis
FTIR spectroscopy proves to be the most fundamen-
tal approach used to probe numerous functional
groups and vibrational interactions prevailing within
the system. The FTIR spectra of Sm
0.96
Ce
0.04
Fe
1-x-
Ni
x
O
3
(0 BxB0.3) samples are recorded in the
wavenumber range 400–4000 cm
-1
and illustrated in
Fig. 4. We noticed two strong and significant vibra-
tional bands at 555 cm
-1
and 418 cm
-1
, respectively,
which validates the formation of SmFeO
3
(orthorhombic perovskite) crystal structure. The fin-
gerprint bands attained at 418 cm
-1
are assigned to
the O–Fe–O bending mode of vibration, whilst
555 cm
-1
corresponds to the Fe–O stretching mode of
vibration [19]. Both bands are indicative of the alter-
ations in the Fe–O–Fe bridging angle. The FTIR
spectra of the doped samples reveal a significant
change in the position of these bands. Doping trans-
lates these bands towards higher wavenumbers for
the doped samples as shown in Fig. 4, wherein the
bands at 555 cm
-1
and 418 cm
-1
for the pristine
Fig. 3 aVariation of Fe–O–Fe (bridging angle) and FeO
6
tilt angle as a function of Ni concentration for Sm
0.96
Ce
0.04
Fe
1-x
Ni
x
O
3
(0 BxB0.3) samples and bWilliamson–Hall plots for Sm
0.96
Ce
0.04
Fe
1-x
Ni
x
O
3
(0 BxB0.3) samples
J Mater Sci: Mater Electron (2023) 34:476 Page 7 of 25 476
sample are relocated to 559 cm
-1
and 432 cm
-1
for the
30% Ni-doped sample. Since the replacement of
higher ionic radii Fe
3?
ions (0.645 A
˚) with the lower
ionic radii Ni
3?
ions (0.60 A
˚) leads to the shrinkage of
the unit cell volume and densification in the Sm
0.96-
Ce
0.04
Fe
1-x
Ni
x
O
3
(0 BxB0.3) samples, this may be
responsible for the relocation of the vibrational bands
towards higher wavenumber side (blue shift). Also,
this shifting can be explicated on the ground of
oxygen vacancies created with the incorporation of
Ni
3?
ions in the crystal lattice and leads to distortion
of FeO
6
octahedron. Also, this structural modification
leads to the increase in the force constant (K) of the
respective constituted bonds [20] which is listed in
Table 3. The absorption peaks around 2696 and
2827 cm
-1
are attributed to C–H vibration (deforma-
tion) modes. However, the bands around 1028 cm
-1
and 2332 cm
-1
correspond to C–O and O=C=O bonds,
respectively, originating from the surface adsorbed
carbonate species due to exposure to the ambient
environment. Besides, the surface of the Sm
0.96-
Ce
0.04
Fe
1-x
Ni
x
O
3
(0 BxB0.3) nanoparticles
obtained via decomposition of the heteronuclear
compound being more reactive towards adsorption
of atmospheric gases such as CO
2
in ambient air,
resulting in the formation of carbonate ions (CO
32-
)
that is accountable for the vibration at 1572–1287 cm
-1
[21]. However, XRD spectra do not detect any trace of
organic species such as carbonate or nitrate groups in
any of the specimens as these species do not fall
under the detectable XRD limit. The bands near
3400 cm
-1
and 1648 cm
-1
are assigned to the O–H
stretching and H–O–H bending vibrations in the
sample due to moisture adsorbed on the surface of
the material [22].
Further, the vibrational wavenumber of the Fe–O
(metal oxide) bond can be analysed using the fol-
lowing relation [23]:
t¼1
2pcffiffiffi
k
l
s
!
:ð4Þ
In the above relation, trefers to the wavenumber, c
refers to the speed of light in a vacuum, kdenotes the
force constant (average) of the molecule, and lrefers
to the effective mass (amu) corresponding to the
system that can be calculated using the following
equation [23]:
l¼Mo½1xðÞMFe þxMNi
Moþ½1xðÞMFe þxMNi:ð5Þ
Here, M
o
,M
Fe
and M
Ni
denote atomic weights
associated with the oxygen ions, Fe ions, and Ni ions,
respectively. The force constant can directly be
interrelated to Fe–O bond length by the following
relation [23]:
k¼17
r3N=cm:ð6Þ
Estimated values of l,r, and kare summarised in
Table 3. Thus, bond lengths calculated from the FTIR
spectrum is in close agreement with the XRD results.
Fig. 4 FTIR spectra of
Sm
0.96
Ce
0.04
Fe
1-x
Ni
x
O
3
(0 BxB0.3) samples
476 Page 8 of 25 J Mater Sci: Mater Electron (2023) 34:476
3.3 Transmission electron microscopy
(TEM) analysis
Transmission electron microscopy (TEM) and high-
resolution TEM (HRTEM) with SAED pattern are
influential techniques that provide crystallographic
information regarding the particle/grain size,
defects, miller indices of the diffraction planes, and
morphology of the diffraction patterns of prepared
NPs. Figs. 5a and 6a display that the TEM micro-
graphs of Sm
0.96
Ce
0.04
FeO
3
(pristine) and Sm
0.96-
Ce
0.04
Fe
0.7
Ni
0.3
O
3
samples recorded at 50,0009
magnification reveal that the particles are dispersive
in nature and formation of fairly large agglomerates
in the pristine samples than in 30% Ni-doped sample.
The agglomeration supports strong indication of high
surface activity as well as presence of magnetism. As
depicted in the micrographs porous characteristic of
agglomerates may be associated with various organic
gases released during the combustion process of the
synthesis. In addition, particles are irregular in size
and shape having smooth surfaces. This is the char-
acteristic feature of the nanoparticle, deduced during
the auto-combustion method [20,24]. Average parti-
cle size has been elucidated by the Gaussian fit of the
histograms using ImageJ software which is shown in
Figs. 5b and 6b. Easily distinguishable particles have
been taken into consideration for grain/particle size
determination. In the case of the pristine sample the
average particle size comes out to be *55 nm,
whereas, in the case of the 30% Ni-doped sample, the
average particle size found to be *46 nm. This
reduction in average particle size is due to the fact
that particles of Fe
3?
ions (0.645A
˚) are replaced by the
particles of Ni
3?
ions (0.60 A
˚) ensuring in a decre-
ment in the average particle size. Thus, this result is
concomitant with that obtained using Williamson–
Hall analysis of the XRD data. High-resolution
transmission electron microscopy (HRTEM) micro-
graphs with 500,0009magnification, shown in
Figs. 5c and 6c, convey the single crystalline nature of
each NP. The lattice fringes in these micrographs
interpret the interplanar spacing (d) to be 2.21 A
˚
(pristine) and 1.34 A
˚(30% Ni doped). The interplanar
spacings, d=2.21 A
˚and d= 1.34 A
˚correspond to
(202) and (004) Bragg planes for pristine and 30% Ni-
doped sample, respectively, as marked in Figs. 5c and
6c. In addition, HRTEM micrographs may be utilised
for the detection of vacancies and defects created in
the specimen. A single vacancy or defect is mainly
undetectable under TEM images, whereas an array of
Fig. 5 aTEM micrograph, bParticle size distribution, cHRTEM micrograph, and dSAED micrograph of Sm
0.96
Ce
0.04
FeO
3
sample
J Mater Sci: Mater Electron (2023) 34:476 Page 9 of 25 476
defects can be detected by a peculiar dark or bright
diffraction contrast that are responsible for the strain
induced within the system [25]. This suggests that the
pristine sample consists of some oxygen vacancies,
whereas Ni dopant leads to escalation in the number
of oxygen vacancies that can be visualised through
dark blotches obtained in the HRTEM micrographs.
Likewise, selected area electron diffraction (SAED)
images of pristine and 30% Ni-substituted samples
are presented in Figs. 5c and 6c, respectively. SAED
images reveal the polycrystalline nature of both
samples. On careful examination the images disclose
that each circular ring is composed of bright spots
that originate out of Bragg reflection through an
individual crystallite depicts allowed Bragg diffrac-
tion planes of the perovskite-based orthorhombic
system. The interplanar spacing (d) obtained from
XRD data in combination with the SAED pattern
implies a bright circular spotty ring corresponding to
(112) Bragg plane for both the samples.
3.4 Magnetic analysis
For the investigation of magnetic order in Sm
0.96-
Ce
0.04
Fe
1-x
Ni
x
O
3
(0 BxB0.3) powder samples, M–
H loops have been recorded at room temperature on
a Vibrating Sample Magnetometer (VSM) with a
maximum applied field of 20 kOe for all the prepared
samples as illustrated in Fig. 7. The values of rema-
nent magnetisation, coercive field, squareness, and
maximum magnetisation are tabulated in Table 4.
SmFeO
3
is an antiferromagnetic insulator. However,
the nanoparticles of SmFeO
3
display magnetic
moments due to canted (Fe
3?
–Fe
3?
) antiferromag-
netic ordering and also due to uncompensated spin at
the surface originating via super-exchange interac-
tion which in turn gives rise to weak ferromagnetism.
In order to have a deeper understanding of mag-
netism in SmFeO
3
NPs, we have to include the con-
tribution of three different magnetic interactions,
such as Fe
3?
–O–Fe
3?
,Fe
3?
–O–Sm
3?
and Sm
3?
–O–
Sm
3?
. The magnetic properties evolved mainly as a
result of Fe
3?
–Fe
3?
interaction, since Sm
3?
ions
remain in the paramagnetic state according to the
electronic configuration, thus inducing long-range
AFM ordering below 5 K and in turn exhibiting
spontaneous magnetisation reversal [3]. Therefore,
the resultant contribution of Sm
3?
–Sm
3?
is negligible
at higher temperatures, whereas the role of Fe
3?
–
Sm
3?
interaction comes into the picture around
135 K. At this particular temperature, the magnetic
moment of Sm
3?
ions are anti-parallel to Fe
3?
ions
Fig. 6 aTEM micrograph, bParticle size distribution, cHRTEM micrograph, and dSAED micrograph of Sm
0.96
Ce
0.04
Fe
0.7
Ni
0.3
O
3
sample
476 Page 10 of 25 J Mater Sci: Mater Electron (2023) 34:476
(canted) magnetic moment. In addition, the magnetic
moment value for Sm
3?
ions is greater in comparison
to Fe
3?
ions. Therefore, 4f orbital electrons of Sm
3?
ions interact actively with the 2p orbital electrons of
O
2-
ions, this in turn eventuates Sm
3?
–O
2-
–Fe
3?
interaction [26]. In this framework, there are only two
possibilities for the occurrence of weak ferromag-
netism at room temperature listed as follows: Firstly,
the super-exchange interaction between Fe
3?
and
Fe
3?
ions mediated by O
2-
ions induces AFM beha-
viour. However, at 300 K the relative stability of
Fe
3?
–O
2-
–Fe
3?
hybridisation is more in comparison
to Sm
3?
and O
2-
ions hybridisation. Although the
main reason behind the weak ferromagnetic beha-
viour of SFO is the weak AFM exchange interaction
amongst Fe
3?
–O
2--
–Sm
3?
that promotes spin reori-
entation (SR) of the Fe
3?
ions. Secondly, antisym-
metric Dzyaloshinskii–Moriya (D–M) exchange
interaction in which the magnetic moment of Fe
3?
ion
spins are not perfectly collinear with the surrounding
neighbours of Fe
3?
ion spins and generally, Fe
3?
ion
spins are canted in a small angle, resulting in the
weak ferromagnetic behaviour [26]. The magnetic
properties of orthoferrites are strongly dependent on
the extrinsic factors, namely particle size, density,
and porosity as well as on the intrinsic factors. The
Fig. 7 M–H curve for Sm
0.96
Ce
0.04
Fe
1-x
Ni
x
O
3
(0 BxB0.3) samples at room temperature
Table 4 Magnetic parameters
of Sm
0.96
Ce
0.04
Fe
1-x
Ni
x
O
3
(0 BxB0.3) samples
Physical parameters x= 0.0 x= 0.1 x= 0.2 x= 0.3
Coercive field, Hc(Oe) 433.060 1233.380 1766.680 3050.730
Maximum magnetization, Mmax (emu/g) 0.337 0.362 0.371 0.580
Remanent magnetization, Mr(emu/g)
Average magnetic moment
0.092 0.264 0.317 0.923
Per formula unit, lB0.153 0.165 0.169 0.264
Squareness, S (Mr=Mmax) 0.027 0.073 0.085 0.159
J Mater Sci: Mater Electron (2023) 34:476 Page 11 of 25 476
observed magnetic hysteresis (M–H) loops for all the
prepared samples depict antiferromagnetic beha-
viour with weak ferromagnetism associated with the
internal spin canting along the c-direction as well as
by uncompensated spin at the surface.
The maximum magnetisation value is elevated
from 0.337 (pristine) to 0.580 emu/g (30% Ni doped).
The enhancement in the maximum magnetisation is
observed on account of the incorporation of Ni
3?
ions
as compared to Sm
0.96
Ce
0.04
FeO
3
. It may be due to the
following reasons: (1) Doping of Ni
3?
ions at the B-
site can lead to the generation of oxygen vacancies,
crystal defects, and distortion in the Sm
0.96
Ce
0.04
FeO
3
(pristine) system that alters the bridging angles Fe–
O
2
–Fe and Fe–O
1
–Fe from 151.159°to 161.110°and
141.456 to 154.621 degree, respectively, as illustrated
in Table 1. (2) When Ni
3?
ions are doped at Fe site, it
develops oxygen non-stoichiometry within the sys-
tem by charge anisotropy, which changes the valence
state of Fe from Fe
3?
?Fe
2?
to maintain the charge
neutrality in the system. This in turn produces a
resultant magnetic moment and effectuates an
increase in the existing magnetic moment of the
pristine sample. This increase in the magnetic
moment is higher in the 30% Ni-doped sample as
listed in Table 4. The average magnetic moment per
formula unit in terms of Bohr magnetons is estimated
using the following relation [27]:
nB¼MwMmax
5585 ;ð7Þ
where M
max
denotes the value of maximum mag-
netisation and Mwdenotes the molecular weight of
the samples. The coercive field (H
c
) and remanent
magnetisation (M
r
) values show a remarkable
increase for the 30% Ni-doped sample, as tabulated in
Table 4. The Ni
3?
substitution weakens the Fe
3?
–Fe
3?
antiferromagnetic interaction, which in turn sub-
sidises the enhanced ferromagnetic coupling. Fur-
thermore, the reason being that Fe
3?
spins couple
more actively to the neighbouring spins than do the
Ni
3?
spins. It is also realised that the hysteresis (M–
H) loops are shifted in the negative direction with
respect to H = 0 in the doped samples, which is
attributed to the phenomenon of exchange bias (EB)
effect established on account of exchange anisotropy
amongst Sm and Fe sublattices at the surface of these
samples. EB effect suggests the evolution of ‘‘cluster
glass states’’ within the system [28]. Therefore, the M–
H loop for 30% Ni doping exhibits prominent
‘‘butterfly’’-shaped hysteresis that elucidates the most
prominent ferromagnetic behaviour with surpris-
ingly larger values of maximum magnetisation,
remanent magnetisation, and coercive field. This
intriguing behaviour is associated with the complex
magnetic interaction amongst Fe
3?
and Ni
3?
ions
within the system. All the magnetic parameters are
tabulated in Table 4as determined through magnetic
measurements.
3.5 Optical analysis
Several methods have been adopted to deduce band-
gap, including photoluminescence (PL), optical
ellipsometry, and UV–Visible spectroscopy. Amongst
all of them, UV–Vis. diffuse reflectance spectroscopy
(DRS) serves as one of the most helpful and reliable
technique to examine the electronic band structure,
particularly charge transfer transitions, optical
energy band-gap (E
g
), and various other optical
parameters. When a material composed of NPs is
exposed to electromagnetic radiation, it penetrates
within the sample consisting of scattered and trans-
mitted components of radiation and some part of it
gets reflected. Thus, the reflected component gives
rise to diffuse reflectance spectra.
The absorbance spectra of Sm
0.96
Ce
0.04
Fe
1-x
Ni
x
O
3
(0 BxB0.3; step size =0.1) are shown in Fig. 8a.
The optical behaviour of rare-earth orthoferrites
(RFeO
3
) is attributed to its distorted FeO
6
octahedral
configuration. As illustrated in Fig. 8a, the system
manifests incredible absorption in the Ultraviolet and
Visible regions. In the case of the pristine sample, the
two most prominent peaks appear around 312 nm
and 380 nm in the ultraviolet region attributed to the
charge transfer transition between O
2-
and Fe
3?
ions
from non-bonding level (O (2p)) to e
g
orbital of Cr
3?
ions. However, absorption peaks around 520 nm and
700 nm in the visible region are responsible for
ligand field transitions amongst non-bonding orbital
(O (2p)) and the slowest vacant orbital (t
2
)[29]. The
absorption peak around 700 nm (Fe 3d (t
2g
)toFe3d
(e
g
) transitions) is a typical characteristic feature of
iso-structural orthoferrites. We observed that absor-
bance decreases with the Ni substitution as compared
to the pristine sample. This may be associated with
augmented conductivity value for the Ni-doped
samples, forging the system to be more transparent.
All the calcined samples elucidate wider absorption
bands in the visible region which is of vital
476 Page 12 of 25 J Mater Sci: Mater Electron (2023) 34:476
importance as this intriguing behaviour plays a sig-
nificant role in photo-catalysts and optoelectronic-
based device applications.
The diffuse reflectance data have been transformed
into absorbance data using the following relation:
A¼logRd;ð8Þ
where symbols have their usual meanings. Using the
absorbance data, the absorption coefficient
(a) can directly be correlated from the relation:
a¼2:303 A=dðÞ;ð9Þ
where, drepresents cuvette length. Furthermore, the
band-gap energy (E
g
) of the samples can be deter-
mined from the absorbance data using Tauc’s
relation:
aht¼BðhtEgÞn;ð10Þ
where Bis a constant and n signifies inter-band
transition depending on photon transition and the
type of material whether amorphous or crystalline.
According to McLean analysis [30], we can identify
the type of transition, depending on the values of
nsuch that direct, direct-forbidden, indirect, and
indirect-forbidden transitions are given by 1/2, 3/2,
2, and 3, respectively.
To determine the optical energy band-gap, graphs
have been plotted between (ahm)
1/n
and (hm) for
n=1/2 (direct transition) and n=2 (indirect tran-
sition) for all the samples. Plotting graphs between
(ahm)
2
versus (hm) corroborate the direct allowed
band-gap transition occurring within the system
which is concomitant with the previously reported
data [27] and is shown in Fig. 8b. Hence, accordingly
the Tauc’s relation will be transformed further for the
n=1/2 value such that
ðahtÞ2¼BðhtEgÞ:ð11Þ
On extrapolating the linear portion of the plots
(Fig. 8b) towards a= 0 (zero absorption coefficient)
gives optical energy band-gap (E
g
) for all the
nanoparticles under investigation are listed in
Table 5. The maximum absorption peak of co-doped
(Ce–Ni) SmFeO
3
samples exhibits a red shift that may
be attributed to the successful incorporation of Ce–Ni
ions within the SFO system. The band-gap energy is
found to be 2.51 eV for the pristine sample and
decreases monotonically to 1.97 eV for the 30% Ni-
doped sample. This reduction may be linked with the
creation of additional energy levels near the con-
duction band (CB). In particular, anions play a sig-
nificant role in manipulating the band-gap of rare-
earth-based perovskites. Substitution of Ni ions leads
to charge imbalance within the system and to main-
tain the charge neutrality within the system oxygen
vacancies are developed, resulting in the alteration of
the electronic band structure which is proportional to
the energy band-gap. Furthermore, the crystal field
varies near the oxygen ions due to the reduction in
Fig. 8 aAbsorbance spectra for Sm
0.96
Ce
0.04
Fe
1-x
Ni
x
O
3
(0 BxB0.3) samples and bTauc plots for Sm
0.96
Ce
0.04
Fe
1-x
Ni
x
O
3
(0 BxB0.3) samples
J Mater Sci: Mater Electron (2023) 34:476 Page 13 of 25 476
the coordination number of B-site ions. In addition,
the presence of oxygen vacancies advances defects/
localised electronic states and pores within the band-
gap of the specimen system. The number of oxygen
vacancies also enhances the concentration of elec-
trons depicting distortion in the crystal lattice and in
turn, leads to a reduction in the optical energy band-
gap. Sajad Ahmad Mir et al. [1] reported contraction
in the unit cell volume and reduction in the energy
band-gap on the incorporation of Ni content which
has been attributed to variation in the crystal field
potential of the SmFeO
3
system. Ritwik Maity et al.
[4] also reported the reduction in the energy band-
gap for the Mn-doped SmFeO
3
system, which is
consistent with the results obtained in the present
case. The obtained values of energy band-gap are
strongly correlated with average crystallite size as
obtained using Scherrer’s equation and Williamson–
Hall methods.
3.5.1 Urbach energy (absorption band tail)
The absorption spectra of Sm
0.96
Ce
0.04
Fe
1-x
Ni
x
O
3
(0 BxB0.3) samples can be divided into three
principal regimes: the active absorption region,
which influences the energy band-gap, the absorption
edge region that occurs due to disorder (or low
crystallinity) of the material, and the weak absorption
region resulted on account of defects created in the
material [31]. The exponential portion together with
the absorption plot near the optical band edge region
is identified by the parameter known as Absorption
band tail (or Urbach tail) and is suggestive of defor-
mities and crystallinity associated with the material.
According to Urbach’s empirical formula [32]:
lna¼lna0þðht=EuÞ;ð12Þ
where a
0
,hmand E
u
denote proportionality constant,
incident photon energy, and Urbach energy (or band
tail width), respectively [33]. The behaviour of the ln
(a) versus (hm) plot exhibits linear dependence as
presented in Fig. 9. We noticed that Ni substitution
augments the value of E
u
, interrelated with available
localised states near CB by the defects and disordered
atoms in the structural bonding [31,34]. The obtained
values of Urbach energy are tabulated in Table 5. The
inverse behaviour of Urbach energy of the optical
energy band-gap as a function of Ni concentration is
depicted in Fig. 10a. It has been perceived that the
incorporation of Ni ions in the pristine crystal lattice
escalates disorder within the crystal lattice, generat-
ing extra number of localised levels in the band-gap
region, leading to enhancement in E
u
and reduction
in the optical energy band-gap.
Furthermore, there is a decrease in steepness
parameter (s) as a function of Ni concentration
(Table 5) associated with the increment in electron–
phonon interaction due to the tensile strain effect
induced within the crystal lattice with doping which
in turn leads to enlargement of Fermi surface.
3.5.2 Extinction coefficient (K)
When electromagnetic radiation is incident on a
material composed of NPs, it penetrates the material
medium and hence, the absorption per unit distance
is known as the extinction (attenuation) coefficient of
participating material. Hence, the extinction coeffi-
cient (K) is a measure of the extent of losses as it
passes through the medium. It can be determined by
the following relation [35]:
K¼ak
4p;ð13Þ
where symbols have their usual meanings. It is
strongly interrelated with the local field and elec-
tronic polarisation existing within optical materials.
The spectral distribution K as a function of the energy
of incident electromagnetic radiation is presented in
Fig. 10b. The figure reveals the oscillatory behaviour
of extinction coefficient in the lower wavelength
range. The value of ‘‘K’’ increases with the increase in
Ni doping this may be elucidated by taking into
account the effect of electron excitation based on the
underlying definition of extinction coefficient (K).
The incorporation of Ni
3?
ions in place of Fe
3?
ions
Table 5 Threshold
wavelength, Band-gap energy,
Urbach energy, Steepness
parameter, and Activation
energy values of
Sm
0.96
Ce
0.04
Fe
1-x
Ni
x
O
3
(0 BxB0.3) samples
Concentration (x)kc(nm) Eg(eV) Eu(meV) sE
a(eV)
0.0 606 2.51 406.32 63.68 910
–3
0.742
0.1 654 2.47 542.15 47.73 910
–3
0.504
0.2 699 2.03 706.56 36.62 910
–3
0.418
0.3 730 1.90 1251.2 25.45 910
–3
0.308
476 Page 14 of 25 J Mater Sci: Mater Electron (2023) 34:476
result in the generation of oxygen vacancies. The
motion of oxygen vacancies and hopping of charge
carriers advance the system towards conductive
nature and thus in turn become more transparent.
More energy is utilised for the excitation to occur
because Ni-doped samples have a larger concentra-
tion of charge carriers. At longer wavelengths scat-
tering losses are escalated which can be associated
with the inadequate energy available for the hopping
phenomenon to occur.
3.5.3 Skin depth
The exponential decay of the electromagnetic waves
as they penetrate inside the conducting medium is
represented by penetration depth or skin depth. At
the surface of the conductor, photon current density
is maximum and it decays exponentially inside it.
This reduction in the photon current density may be
associated with the refractive index, surface mor-
phology or microstructure of the samples. The
thickness at which the optical photon density reduces
to 1/e times the value at the surface is called skin
depth. Skin depth is related to the absorption coeffi-
cient by the following relation:
d¼1=a:ð14Þ
Figure 10c represents the dependence of skin depth
(d) upon incident energy of the photon (hm) for all the
samples. From the graphs, it is observed that as the
frequency increases the skin depth decreases, cor-
roborating that penetration becomes difficult at a
higher frequency. Hence, high energy waves cannot
travel through these conducting samples. In addition,
the skin depth has been found to decrease with the Ni
doping as illustrated in Fig. 10c, which affirms that
Ni-doped samples are more conducting as compared
to the pristine sample.
3.5.4 Threshold wavelength
The maximum wavelength of electromagnetic radia-
tion required for the ejection of electrons from the
surface of the material is termed as threshold wave-
length. To determine the threshold wavelength or
cut-off wavelength (k
c
) of incident wavelength, UV–
Fig. 9 lnðaÞversus energy plots of Sm
0.96
Ce
0.04
Fe
1-x
Ni
x
O
3
(0 BxB0.3) samples
J Mater Sci: Mater Electron (2023) 34:476 Page 15 of 25 476
Visible absorption data are analysed using the rela-
tion as follows:
ðA=kÞ2¼G1
k1
kc
;ð15Þ
where Asignifies absorbance, kdenotes the wave-
length of incident radiation, k
c
denotes threshold
wavelength, and Gdenotes an empirical constant. To
evaluate the value of threshold wavelength. The
graphs for (A/k)
2
versus 1/khave been plotted for all
the samples as depicted in Fig. 11. We observe an
increase in the value of threshold wavelength with Ni
substitution (Table 5) can be correlated with the
increment in optical conductivity of all prepared
samples. The incorporation of Ni ions at the Fe site
prompts the hopping motion, oxygen vacancies, as
well as concentration of electrons; this in turn
responsible for an increase in threshold wavelength.
Thus, we can correlate the increase in threshold
wavelength with an increase in the magnetic moment
(discussed previously), as penetration depth (skin
depth) is dependent on the permeability of the
material.
3.5.5 Optical conductivity (rop)
According to the linear response theory, the dynam-
ical conductivity is represented as r
op
(q,x). Under
the limit of q?0, dynamical conductivity (r
op
(q,x))
is represented as optical conductivity (r
op
(x)),
depicts the behaviour of the system in response to the
transverse electric field, and under the limit x?0, it
is referred as DC electrical conductivity, refers to the
longitudinal electric field. The real part (r
op1
(x))
signifies the dissipation of electromagnetic energy
density associated with the medium, whereas the
imaginary part (r
op2
(x)) signifies the screening effect
of the applied electric field. Optical conductivity is
analogous to diffusion current associated with the
medium and its value being sensitive to various
optical parameters. The real part of optical conduc-
tivity ðropÞis determined using the following relation
[36]:
rop ¼anc=4pK;ð16Þ
where symbols have their usual meanings. Fig. 12
elucidates the variation of optical conductivity versus
incident wavelength of photon for all the samples.
Fig. 10 aVariation of energy band-gap and Urbach energy as a
function of Ni concentration for Sm
0.96
Ce
0.04
Fe
1-x
Ni
x
O
3
(0 BxB0.3) samples, bvariation of extinction coefficient of
as a function of incident wavelength, and cthe variation of skin
depth versus energy for Sm
0.96
Ce
0.04
Fe
1-x
Ni
x
O
3
(0 BxB0.3)
samples
476 Page 16 of 25 J Mater Sci: Mater Electron (2023) 34:476
From the graphs, it can be noticed that the value of
optical conductivity for all the samples is found to be
of the order of 10
15
s
-1
. The optical conductivity has
relatively larger values at shorter wavelengths due to
the adequate electron excitation via photons of high
energy and may be due to the high absorbance in all
the prepared samples. However, the photons have
still lesser energy at higher photon wavelengths and
in turn incapable to stimulate the hopping mecha-
nism of either electrons or holes. Consequently,
dwindling the optical conductivity at higher wave-
lengths. It can be perceived that on the whole optical
conductivity escalates with Ni substitution in com-
parison to the pristine sample which can be associ-
ated with the hopping phenomenon of the charge
carriers amongst Fe
2?
and Fe
3?
ions. With the Ni
substitution, oxygen vacancies are originated thereby
improving the hopping mechanism and resulting in
the enhancement of optical conductivity.
3.6 Transport properties
3.6.1 DC electrical resistivity
The DC resistivity (qdc) variation as a function of
temperature of Sm
0.96
Ce
0.04
Fe
1-x
Ni
x
O
3
(0 BxB0.3;
step size = 0.1) NPs has been carried out as shown in
Fig. 13 using two probes. We noticed that the DC
resistivity of rare-earth orthoferrite samples falls
rapidly with rising temperature showing typical
semiconducting behaviour for all the calcined sam-
ples. This can be interpreted in terms of increased
hopping of charge carriers amongst Fe
3?
$Fe
2?
ions
on account of thermal activation. Thus, the behaviour
of dc resistivity can be elucidated according to the
hopping mechanism as a result of which the con-
duction takes place predominantly due to the polaron
hopping amongst Fe
3?
and Fe
2?
ions. The tempera-
ture variation of DC resistivity can be described by
the Arrhenius equation [37]:
qdc ¼q0Ea=KBTðÞ;ð17Þ
Fig. 11 ðA=kÞ2versus (1/ k) plots for Sm
0.96
Ce
0.04
Fe
1-x
Ni
x
O
3
(0 BxB0.3) samples
J Mater Sci: Mater Electron (2023) 34:476 Page 17 of 25 476
where K
B
,T,q
0
, and E
a
signify Boltzmann constant,
absolute value of temperature, pre-exponential term,
and activation energy associated with the conduction
mechanism, respectively. Previously, Zhao et al. [7]
synthesised SmFeO
3
via sol-gel technique and
reported 0.63 eV activation energy in the temperature
range of 300–600 K.
Using equation (18), the linear fit of the slope of
log
e
(q
dc
) versus (10
3
/T) plots (Fig. 14) gives the
values of activation energy for all the synthesised
NPs and turned out to be in the range 0.742–0.308 eV
as listed in Table 5. This is in good agreement with
the previously reported results as discussed above.
3.7 Dielectric properties
To explore the dipolar dynamic nature of any solid
specimen, ac electrical measurements such as
dielectric permittivity, dielectric loss, and impedance
analysis are widely used. This investigation com-
prises the conductive behaviour of grains, grain
boundaries, relaxation processes, and charge storage
capabilities over a wide range of frequencies.
The dielectric constant of an isotropic material is
always a complex quantity which can be expressed as
follows:
e¼e0je00;ð18Þ
where e0(energy stored) and e00 (energy dissipation)
denote the real part and the imaginary part of the
dielectric constant, respectively. The value of the real
part ðe0Þof the dielectric constant can be evaluated
using the relation:
e0¼Cpd
eoA;ð19Þ
where Cp,d,Aand eorepresent the capacitance,
thickness of the circular pellet, area of cross-section of
the circular pellet, and permittivity of free space,
respectively. Figure 15 illustrates the frequency
dependence of the real part e0of dielectric constant at
room temperature for Sm
0.96
Ce
0.04
Fe
1-x
Ni
x
O
3
(0 B
Fig. 12 The variation of optical conductivity (rop ) versus incident wavelength of photon (k) for Sm
0.96
Ce
0.04
Fe
1-x
Ni
x
O
3
(0 BxB0.3)
samples
476 Page 18 of 25 J Mater Sci: Mater Electron (2023) 34:476
Fig. 13 The DC resistivity variation with temperature for Sm
0.96
Ce
0.04
Fe
1-x
Ni
x
O
3
(0 BxB0.3) samples
Fig. 14 logeðqdc Þversus ð103/T) plots for Sm
0.96
Ce
0.04
Fe
1-x
Ni
x
O
3
(0 BxB0.3) samples
J Mater Sci: Mater Electron (2023) 34:476 Page 19 of 25 476
xB0.3) samples. It is evident from the figure that the
real part of the dielectric constant of all samples has
higher value at lower frequencies, whilst it decreases
rapidly with the increasing frequency and becomes
almost constant in the higher-frequency regime dis-
playing the phenomenon of dielectric dispersion for
all the samples. The plots make known that the
dielectric behaviour is in good agreement with those
reported earlier [38,39]. The origin of dielectric dis-
persion behaviour can be explained based on the
collective response of the many type of polarisation
of dipoles and conduction mechanism of charge
carriers that obey Koop’s phenomenological theory
and Maxwell–Wagner model [40]. Accordingly, at
lower frequencies, the space-charge/interfacial
polarisation is dominant. This leads to colossal values
of dielectric constant at low frequency. While, at
higher frequencies, dipolar polarisation of ion pairs
results in atomic/electronic polarisation [41]. Also,
the polarisation decreases with the increase in fre-
quency because the effective electric dipoles become
unable to track the rapid applied field reversal. As a
result, the dielectric constant decreases and finally
becomes constant [42].
It is also observed that the dielectric constant
increases as a function of Ni concentration; this may
be due to the increase in the number of hopping
charge carriers. Ni substitution results in the gener-
ation of Fe
2?
ions along with the creation of oxygen
vacancies. The enhanced number of Fe
2?
ions leads to
an increased Fe
3?
–Fe
2?
electron hopping mechanism
[1,18,43]. This is responsible for the decrease in the
grain resistance and therefore weakens the sub-lattice
interaction. As a result leads to oriental dipolar
polarisation and therefore increases the dielectric
constant.
The imaginary part of dielectric constant has been
obtained from the relation:
e00 ¼e0tand;ð20Þ
where tanddenotes the loss tangent factor and exhibit
the energy dissipation in a dielectric material. Fig-
ure 16a and b illustrates the frequency response of
tandin the frequency range of 42 Hz–5 MHz for
Sm
0.96
Ce
0.04
Fe
1-x
Ni
x
O
3
(0 BxB0.3) samples. The
creation of defects, oxygen vacancies, and other
structural abnormalities/deformities with doping
augments the energy losses in the doped samples in
comparison to the pristine sample and signifies that
doped samples attain larger number electrically
active defects. During the crystal growth, crystal
distortion occurs due to incongruity amongst the
ionic radii of Fe and Ni, this in turn responsible for
the creation of defects and oxygen vacancies in the
crystal structure due to change in the valence state of
cations involved and further capture the surface
electrons owing to reduce the mobility of charge
carriers [44]. Although the dielectric losses are
inversely proportional to the mobility of charge car-
riers, accordingly an increase in dielectric losses is
achieved in the doped samples as a function of Ni
concentration. In addition, Fig. 15b exhibits promi-
nent relaxation peak in the pristine sample which is
the typical characteristic feature of dielectric relax-
ation mechanism. This peak signifies the correlation
between the hopping frequency of charge carriers
and doping concentration.
The AC conductivity of orthoferrites as a function
of frequency can be expressed at room temperature
using the following relation:
rac ¼e0e0xtand;ð21Þ
where symbols have their usual meanings. Based on
the type of polaron hopping, AC conductivity may
decline/enhance with the frequency. In the case of
large polaron hopping, it decreases as a function of
frequency and in the case of small polaron hopping it
increases as a function of frequency [45]. At lower
frequencies, the transport of charge carriers amongst
ions is quite less. In electrical conduction, the role of
charge carriers is more evident at grain boundaries
than within the grains. As the frequency increases,
Fig. 15 Variation of real part of dielectric constant (e0) with
frequency for Sm
0.96
Ce
0.04
Fe
1-x
Ni
x
O
3
(0 BxB0.3) samples
476 Page 20 of 25 J Mater Sci: Mater Electron (2023) 34:476
the grains become more viable by instigating the
hopping of charge carriers between Fe
2?
and Fe
3?
ions. The enhancement in the ac conductivity is
observed as a function of frequency for Sm
0.96
Ce
0.04-
Fe
1-x
Ni
x
O
3
(0 BxB0.3) samples as illustrated in
Fig. 17. This behaviour signifies that conduction
occurs via hopping of charge carriers between loca-
lised states and small polaron hopping being
responsible for this conduction phenomenon [19]. It
has been observed that the ac conductivity increases
with the increase in Ni concentration. This may be
due to the generation of oxygen vacancies within the
Fig. 16 aand bLoss tangent (tand) with frequency for Sm
0.96
Ce
0.04
Fe
1-x
Ni
x
O
3
(0 BxB0.3) samples
Fig. 17 Variation of AC conductivity (rac) with frequency for Sm
0.96
Ce
0.04
Fe
1-x
Ni
x
O
3
(0 BxB0.3) samples
J Mater Sci: Mater Electron (2023) 34:476 Page 21 of 25 476
system on account of Ni doping and consequently
promotes the hopping process.
The total conductivity at a particular frequency can
be expressed as follows:
rT¼rdc TðÞþrac x;TðÞ;ð22Þ
where the first part on the right-side represents the
DC electrical conductivity, which is related to the
mobility of charge carriers and is independent of
frequency but dependent on temperature. The second
part represents the AC conductivity, which is linked
with the hopping mechanism of bound charge carri-
ers and depends on both frequency and temperature.
The AC conductivity obeys the Jonscher power law,
rac x;TðÞ¼Bxs(here B is temperature-dependent
constant with units of conductivity, xis the angular
frequency and exponential ‘s’ represents the degree
of interaction amongst lattice and mobile charge
carriers, with values between 0 and 1). The conduc-
tion mechanism in a system is regulated by the ‘s’
parameter, for s= 0 the conductivity is DC and for
AC conductivity ‘s’ values are greater than 0 [46]. The
‘s’ values are determined for all the Ni concentrations
and in different frequency intervals by the linear fits
as shown in Fig. 18. The values of s for all the pre-
pared samples lie between 0 and 1 which are con-
comitant with the frequency-dependent behaviour of
AC conductivity and also validate the hopping
motion of charge carriers [47].
To understand the correlation between the struc-
tural and electrical transport properties of nanopar-
ticles, complex impedance analysis has been carried
out. The fact that nanoparticles are composed of
grains separated via grain boundaries, this technique
investigates the role of grain and grain boundaries in
the electrical properties of the as-synthesised sam-
ples. Figure 19 displays the complex impedance plots
commonly known as Nyquist plots for Sm
0.96
Ce
0.04-
Fe
1-x
Ni
x
O
3
(0 BxB0.3) samples. Generally, the Z00
versus Z0plot can display three semi-circles amongst
which the first semi-circle is attributed to lower fre-
quency, illustrating the total resistance of grains and
grain boundaries, whilst the second semi-circle,
which is usually observed at higher frequencies,
Fig. 18 Linear fits of different frequency intervals for log (rac ) versus log (x) plots of Sm
0.96
Ce
0.04
Fe
1-x
Ni
x
O
3
(0 BxB0.3) samples
476 Page 22 of 25 J Mater Sci: Mater Electron (2023) 34:476
indicates the resistance contribution only from the
grains. Finally, the third semi-circle might be due to
the electrode effect in few systems [48]. In addition,
the diameter of the semi-circle influenced by the
resistance and capacitance values, nature of dopants
and composition of the materials.
It is observed that the pristine sample shows nearly
linear behaviour; however, with the incorporation of
Ni in the system, the plots turned into nearly semi-
circular shape, stipulating relaxations within the
system. This implies that the samples under investi-
gation follows non-Debye type of relaxation beha-
viour. For the 10% Ni-doped sample there is only one
semi-circular arc which suggests that relaxation
phenomenon is associated with the grain boundaries.
At higher frequencies, the resistance of grains is low,
thus contributing to the relaxation phenomenon.
Whereas, two semi-circular arcs are perceived for
20% and 30% Ni-doped samples which implies that
both grains and grain boundaries are responsible for
the relaxation process. Since the semi-circle got dis-
torted appreciably at higher frequencies in the Ni-
doped samples, this signifies that the hopping of
charge carriers (Fe
2?
$Fe
3?
) is responsible for the
relaxation process. It can also be noticed that the
maximum relaxation time factor increases as a
function of Ni content due to the generation of oxy-
gen vacancies, creation of defects, and various other
lattice deformations in the samples under study.
4 Conclusion
The nano-crystalline powder samples of Sm
0.96-
Ce
0.04
Fe
1-x
Ni
x
O
3
(0 BxB0.3) are synthesised using
the sol–gel auto-combustion method. Rietveld
refinement of XRD patterns of all co-doped systems
validates the formation of orthorhombic perovskite
crystal structure having Pbnm space group. FTIR
spectra confirm the presence of significant molecular
vibrations and hence provide support to the forma-
tion of the desired phase. The average particle size
evaluated from Transmission electron microscopy
(TEM) is concomitant with the W–H findings. A
significant red shift in the energy band-gap, whereas
an increase in the Urbach energy is found with
increasing Ni concentration. The values of maximum
magnetisation, coercive field, and remanent mag-
netisation increase as a function of Ni content. DC
resistivity measurement divulges the typical semi-
conductor-like behaviour with a systematic reduction
in the activation energy with the increase in Ni
Fig. 19 Nyquist plots for Sm
0.96
Ce
0.04
Fe
1-x
Ni
x
O
3
(0 BxB0.3) samples
J Mater Sci: Mater Electron (2023) 34:476 Page 23 of 25 476
concentration. The usual dielectric dispersion beha-
viour is found in all samples. AC conductivity obeys
the Jonscher power law and affirms that small
polaron hopping is responsible for the conduction
phenomenon. Nyquist plots of all the prepared
samples predict the non-Debye type of relaxation
behaviour. These properties of nanoparticles under
investigation can be utilised in potential applications
in dynamic random access memories (DRAMs) and
dielectric resonators.
Acknowledgements
One of the authors, Surbhi Sharma gratefully
acknowledges the University Sophisticated Instru-
ment Facility (USIF) and Aligarh Muslim University
(AMU) Aligarh for providing TEM facilities and
Department of Chemistry, Aligarh Muslim Univer-
sity (AMU) Aligarh for the UV–Visible diffuse
reflectance and FTIR spectroscopy facilities.
Author contributions
The authors contribution to the research paper are as
follows: Concept and design: SS, NS, and SK. Syn-
thesis of materials and analysis of data: SS. Writing
and reviewing: SS, NS, and SK. Theory and expla-
nation: SS, NS, and SK. Supervision: SK.
Data availability
The data generated and analysed during the current
study are not publicly available but may be made
available from the corresponding author if request is
genuine.
Declarations
Conflict of interest No conflicts of interest amongst
the authors associated with this publication.
Ethical approval We declare that this manuscript is
original and has not been published before and is not
currently being considered for publication elsewhere.
All authors give their consent to submit this paper in
this esteemed journal.
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