Effect of yttrium doping on structure, magnetic and electrical properties of nanocrystalline cobalt ferrite

Article abstract of DOI:10.1016/j.jmmm.2018.04.051

Tailoring of properties by changing morphology or by doping is very much required for the suitable application of any materials. Here we report the effect of yttrium doping on microstructure, magnetic and electrical properties of cobalt ferrite nanoparticles prepared through citrate auto-ignition method. Rietveld refinement analysis of X-ray diffraction pattern confirms the growth of pure and single phase cobalt ferrite nanoparticles which corroborates with transmission electron microscopy (TEM) study. Microstructural parameters, obtained from Rietveld analysis showed that oxygen vacancy is maximum and inter-ionic bond lengths and bond angles attain optimum values for 15 mol% yttrium doped sample. An observed value of saturation magnetization indicates the existence of spin canting phenomenon which was explained by Yafet-Kittel model. Magnetic parameters such as anisotropy constant, anisotropy field have been estimated using Law of Approach (L.A.) formalism. Existence of interparticle dipolar interaction (IPDI) in the system was established with the help of M_r/M_s ratio around room temperature. Maximum electrical conductivity has been observed for the 15 mol% doped sample as estimated from Mott's 3-D V.R.H. model, which can be attributed to the optimum values of microstructural parameters at this composition.

Full text of DOI:10.1016/j.jmmm.2018.04.051

Journal of Magnetism and Magnetic Materials 461 (2018) 69–75
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Journal of Magnetism and Magnetic Materials
journal homepage: www.elsevier.com/locate/jmmm
Research articles
Effect of yttrium doping on structure, magnetic and electrical properties
of nanocrystalline cobalt ferrite
S. Chakrabarty a, A. Dutta a, M. Pal b,
⇑
a Department of Physics, The University of Burdwan, Burdwan 713 104, India
b CSIR-Central Glass and Ceramic Research Institute, Kolkata 700 032, India
a r t i c l e i n f o
a b s t r a c t
Article history:
Tailoring of properties by changing morphology or by doping is very much required for the suitable appli-
cation of any materials. Here we report the effect of yttrium doping on microstructure, magnetic and
electrical properties of cobalt ferrite nanoparticles prepared through citrate auto-ignition method.
Rietveld refinement analysis of X-ray diffraction pattern confirms the growth of pure and single phase
cobalt ferrite nanoparticles which corroborates with transmission electron microscopy (TEM) study.
Microstructural parameters, obtained from Rietveld analysis showed that oxygen vacancy is maximum
and inter-ionic bond lengths and bond angles attain optimum values for 15 mol% yttrium doped sample.
An observed value of saturation magnetization indicates the existence of spin canting phenomenon
which was explained by Yafet-Kittel model. Magnetic parameters such as anisotropy constant, anisotropy
field have been estimated using Law of Approach (L.A.) formalism. Existence of interparticle dipolar inter-
action (IPDI) in the system was established with the help of Mr/Ms ratio around room temperature.
Maximum electrical conductivity has been observed for the 15 mol% doped sample as estimated from
Mott’s 3-D V.R.H. model, which can be attributed to the optimum values of microstructural parameters
at this composition.
Received 18 January 2018
Received in revised form 23 March 2018
Accepted 23 April 2018
Available online 25 April 2018
Keywords:
Nanostructures
Rietveld analysis
Infrared spectroscopy
Crystal structure and microstructure
Ionic conductivity
Ó 2018 Elsevier B.V. All rights reserved.
1. Introduction
spheres [4]. Influence of cobalt ferrite nanoparticles in cell tran-
scription and alteration of cell phenotype was reported by Gharib-
Tremendous interest on science and technology of nanomateri-
als is strongly motivated by the idea that it can change all most all
the physical and chemical properties drastically while comparing
with bulk their counterpart. Nanocrystalline spinel ferrites are
being largely explored for their application in various devices. In
particular, cobalt ferrite nanoparticles have attracted increasing
interest due to their applicability in high density magnetic record-
ing, magnetic resonance imaging (MRI), drug deliver, gas sensing
and various other fields.
Efforts have been made to tailor the properties of nanocrys-
talline cobalt ferrites either by doping or making composites.
Cr3+ substituted cobalt ferrite nanoparticles have been explored
to increase the coercivity for effective use in high density magnetic
recording [1]. Cobalt ferrite-Graphene oxide nanocomposite was
investigated successfully for the use of MRI and controlled drug
delivery purposes [2,3]. Talukdar et al. has reported photolumines-
cence and photocatalytic activities for cobalt ferrite nano-hollow
shahian [5]. Gas sensing properties of cobalt ferrite nanoparticles
has been demonstrated by Joshi et al. [6]. In addition, environmen-
tal applications of cobalt ferrite nanoparticles were also enlight-
ened successfully by Hu et al. [7]. Altogether, cobalt ferrite is an
important material which has application potential in various
fields.
Crystallographic structure plays an important role in controlling
the chemical and physical properties of any materials. So, detail
investigations on the structure of materials are quite meaningful
to interpret different changes in the properties of the material. Spi-
nel ferrites contain two sub-lattices which are called tetrahedral
[A] and octahedral [B] site respectively [8,9]. Normally cobalt fer-
rite exhibits inverse spinel structure in its bulk form. Reduction
of grain size to nanometer range promotes the formation of mixed
spinel structure due to the change in distribution of cations over
two interstitial sites. Co and Fe, both are being 3d block element,
can reside in multivalent states and can be easily doped with other
cations to made changes in the ultimate electronic configuration,
magnetic, transport and other properties of the material [10–12].
Also change in preparatory conditions and different growth
techniques can create various kinds of defects in crystals, can affect
⇑
Corresponding author.
E-mail addresses: adutta@phys.buruniv.ac.in (A. Dutta), palm@cgcri.res.in
(M. Pal).
https://doi.org/10.1016/j.jmmm.2018.04.051
0304-8853/Ó 2018 Elsevier B.V. All rights reserved.

70
S. Chakrabarty et al. / Journal of Magnetism and Magnetic Materials 461 (2018) 69–75
Table 1
Sample code names.
Microstructural analysis have been performed and a structure-
property correlation is established to accommodate the effect of
Y3+doping on magnetic and ionic properties of system.
Sample abbreviation
Sample formulation
Y0
CoFe2O4
Y10
Y15
Y20
Y30
CoFe1.9Y0.1O4
CoFe1.85Y0.15O4
CoFe1.8Y0.2O4
CoFe1.7Y0.3O4
2. Experimental
2.1. Sample preparation
Nanocrystalline CoYxFe1ꢀxO4 d(x = 0, 0.1, 0.15, 0.2, 0.3) were
prepared through the low temperature citrate auto-ignition
method. Co(NO3)2, Y2O3, Fe(NO3)2 and citric acid monohydrate
(C6H8O7ꢁH2O) were used as precursors for the preparation. All
materials were purchased from Sigma-Aldrich and utilized without
further purification. Y2O3 was mixed with de-ionized water and
nitric acid and stirred at 60–65 °C using magnetic stirrer for 2 h
to prepare yttrium nitrate. Then stoichiometric amounts of Co
(NO3)2 and Fe(NO3)2 were mixed with the solution. Citric acid
was added at 3:1 M ratio. The entire solution was stirred for 8 h
at temperature 80–85 °C. When the gel was formed, whole beaker
was taken into a furnace and heated around 120 °C to complete the
auto-ignition process. Ashes thus formed, grounded in an agate
mortar to get the powder sample. Powder samples was then
sintered at 800 °C for 2 h for further experiments.
the size of grain and grain boundaries which in turn will be
reflected on the properties of the material.
Changes in different physical and chemical properties by doping
with various rare earth ions in cobalt ferrite nanoparticles has
recently been studied by several research groups [8,13–18].
Different synthesis procedures have been adopted to prepare
single phase RE doped cobalt ferrite nanoparticles. The increase
in coercive force by doping with Gd3+, Tb3+ and Dy3+ ions [13],
Nd ion [14], increase of anisotropy properties due doping by Dy
ion [8] in cobalt ferrite has been reported earlier. Again decrease
in saturation magnetization and coercivity of cobalt ferrite
nanoparticles by Dy substitution was reported by Kambale et al.
[15]. Strong L–S coupling from the Co2+ ions in the octahedral lat-
tice [16], appearance of secondary phases at higher sintering tem-
perature and their influence on magnetic properties have also been
reported [17,18].
Series of samples of different yttrium concentration have been
prepared and listed in Table 1 with their code names and
corresponding formulae.
Here we have systematically studied the effect of yttirum dop-
ing on the structure, electrical and magnetic properties of
nanocrystalline cobalt ferrite. Single phase Y doped cobalt ferrite,
2.2. Sample characterization
CoYxFe1ꢀxO4 NPs were prepared up to 30 mol% (x = 0, 0.1, 0.15,
d
0.2, 0.3) while to the best of our knowledge, previous report
claimed it can go up to maximum 20 mol% [18]. Rietveld analysis
of XRD data also confirmed the absence of any impurity.
Powder diffraction pattern of the prepared samples in 2h range
from 20° to 90° was record with X-Pert Pro X-ray diffractometer
(PANLYTICAL, Almelo, The Netherlands) fitted with nickel filter
Fig. 1. (a) TEM micrograph, (b) particle size distribution with log-normal fitting of the micrograph of Fig. 2(a), (c) selected area diffraction (SAD) pattern, (d) HRTEM lattice
fringes of Y15 sample.

S. Chakrabarty et al. / Journal of Magnetism and Magnetic Materials 461 (2018) 69–75
3. Results and discussion
71
3.1. Transmission electron microscopy
Typical TEM micrograph of Y15 sample is shown in Fig. 1(a)
where we can see the particles which are nearly spherical in shape.
Average particle size was estimated by fitting experimental values
with standard log-normal size distribution. This reveals the forma-
tion of nanoparticles having average sizes around 40 nm and the
corresponding histogram is presented in Fig. 1(b). Highly crys-
talline nature of the nanoparticles was confirmed from the rings
of SAD pattern of the sample that are made up of discrete spots
(Fig. 1(c)). By measuring the diameters for each circle lattice plane
has been identified and comparing them with JCPDS (card no #
221086) data we can reconfirm the precipitation of cobalt ferrite
phase. In addition, distance estimated from the lattice fringes of
high resolution image (HR-TEM) presented in Fig. 1(d) confirmed
the formation of the planes (2 2 0), (3 1 1) of cobalt ferrite.
Fig. 2. XRD patterns of different samples with Reitveld fitting.
3.2. XRD analysis
and Cu K radiation (k = 1.5414 Å). Transmission electron micro-
a
Fig. 2 delineates the experimental X-ray diffraction data of all
the prepared samples along with their corresponding Rietveld
refinement pattern. Peaks can be indexed of spinel cobalt ferrite
phase (JCPDS Card no #221086). To get an estimation about the
cation distribution of the present system and related microstruc-
tural parameters, we have used XRD analysis along with Rietveld
refinement of all the samples.
scopy (TEM) images were taken by JEOL-200FX microscope oper-
ated at 200 kV. Room temperature FT-IR study was carried out
using Nicolet Magma-IR (750, Series II) spectrophotometer in the
range 400–4000 cm–1. Magnetic measurements at room tempera-
ture were carried out using a Lake Shore (Model 7410) vibrating
sample magnetometer (VSM). DC electrical measurements were
carried out at various temperatures starting from 303 K up to
573 K by Keithley electrometer (Model 6517A) in air atmosphere
using standard two probe method. Electroding of prepared pellets
were done using graphite paste to ensure good electrical contacts
on either side.
Though the estimation of cation distribution with Rietveld anal-
ysis for such a material with ions of closer atomic weights is not
very accurate, still it is a tool that can give an idea about most
probable cation distribution in spinel ferrites, if handled with care
[22,23]. In the Reitveld refinement, first the occupancy of the sites
taken from the standard values as described in the experimental
section. Keeping the occupancies fixed, the global parameters
(such as 2h–zero and background) and all other structural param-
eters (lattice parameter, atomic coordinates etc.) are refined. Then
the site occupancies of all the ions in all possible manners were
determined with stoichiometric sensitivity 0.01 for each site main-
taining site occupancy constraints (MAUD has an inbuilt option to
maintain occupancy constraints). Then keeping these values fixed,
oxygen parameter u and oxygen occupancy were refined. Oxygen
positional parameter was initially taken 0.375 which is the ideal
value for spinel structure, however after refinement, it was
deviated slightly from the standard value defined by the relation
/ = u - uideal. Most probable cation distribution of the system is
Rietveld refinement analysis was carried out using MAUD soft-
ware (Version: 2.33) was used [19]. Various microstructural
parameters such as effective crystallite size (dc), root mean square
microstrain (<e2 1/2), different inter ionic bond lengths, bond
>
angles etc can be estimated from this analysis. Microstructural
parameters were evaluated using the Popa model [20] and the
background correction was done using 5th degree polynomial.
XRD theoretical pattern was generated by considering ideal spinel
phase with space group Fd-3 m (2 2 7). Not only the goodness of fit
(GoF), but other global parameters such as weighted pattern (Rwp),
expected factor (Rexp) was also monitored at each step to under-
stand the fitting of experimental data with the theoretical pattern
[21].
Table 2
Amounts of different cations in A and B site for different compositions along with detailed Rietveld parameters and calculated values of defined deviation factor ɸ.
CoYxFe1ꢀxO4
x = 0
x = 0.1
x = 0.15
x = 0.2
x = 0.3
d
Co (8a) occupancy
Fe (8a) occupancy
Co (16d) occupancy
Fe (16d) occupancy
Y (16d) occupancy
(x = y = z)
0.325
0.675
0.675
1.325
─
0.3739
0.9727
0.0011
8.4011
44
0.301
0.699
0.699
1.201
0.100
0.3731
0.9463
0.0019
8.4026
39
0.273
0.727
0.727
1.123
0.150
0.3684
0.8948
0.0066
8.4073
38
0.294
0.706
0.706
1.094
0.200
0.3689
0.9525
0.0061
8.4119
33
0.316
0.684
0.684
1.016
0.300
0.3700
1.0747
0.0050
8.4145
40
O2– (32e) occupancy
ɸ
Lattice parameter (Å)
DTEM
DXRD
38
4.86
5.08
40
5.13
5.11
43
5.25
5.15
37
5.36
5.19
41
5.57
5.23
R.M.S. strain (ꢂ10ꢀ4
)
Density (gm cmꢀ3
)
R
R
wp(%)
exp(%)
1.87
1.48
1.71
1.48
1.56
1.42
1.56
1.42
2.46
1.76
G.O.F.
1.27
1.16
1.10
1.10
1.39

72
S. Chakrabarty et al. / Journal of Magnetism and Magnetic Materials 461 (2018) 69–75
Table 3
Calculated values of different ion pair distance parameters (in Å) and bond angles (in
degrees).
CoYxFe1ꢀxO4
x = 0.0
x = 0.1
x = 0.15
x = 0.2
x = 0.3
d
Edt
Edso
Eduo
MA–MA
MB–MB
MA–MB
MA–O
2.9351
2.9871
2.9702
3.6537
2.9613
3.4829
1.8348
2.0910
124.91
90.162
74.942
2.9163
3.0067
2.9709
3.6660
2.9619
3.4835
1.8468
2.0848
124.64
90.527
74.527
2.8076
3.1203
2.9745
3.7365
2.9635
3.4854
1.9163
2.0478
123.06
92.701
72.180
2.8205
3.1095
2.9758
3.7313
2.9651
3.4873
1.9101
2.0529
123.23
92.468
72.420
2.8470
3.0842
2.9761
3.7164
2.9661
3.4884
1.8946
2.0624
123.61
91.958
72.961
MB–O
<MA–O–MB
<MB–O–MB
<MA–O–MA
Increase in density with Y doping was observed due to the
increase of lattice parameter and increase in the molecular weight
(M) of the samples as the atomic weight of Y (88 u) is greater than
that of Fe (55 u).
Fig. 3. Variations of oxygen concentration and lattice parameter with the doping
percentage. (Lines are for the guidance of the eyes).
We have calculated the tetrahedral (rA), octahedral radii (rB),
tetrahedral edge (Edt), shared octahedral edge (Edso) and unshared
octahedral edge (Eduo) using the standard relations described else-
where [10].
Also the values of metal-metal (MeꢀMe) and metal-oxygen (Me-
ꢀO) bond length parameters and different bond angles were calcu-
lated using the simple geometric and trigonometric relations [27].
Variations of calculated tetrahedral and octahedral bond
lengths rA and rB with doping concentration are presented in
Fig. 4. Octahedral bond length rB shows maximum and tetrahedral
bond length rA shows minimum at Y15 sample. Calculated compo-
sition wise results are shown in Table 3. Calculated results shows
that <MB–O–MB angle increases up to Y15 and then decreases. So
B site–B site interaction is minimum for Y15 sample whereas
<MA–O–MB and <MA–O–MA angles attains minimum values for this
doping percentage indicating the strongest A site–B site and A site–
A site interactions [23,28].
Fig. 4. Variations of rA and rB with doping concentration for different samples.
(Lines are for the guidance of the eyes).
3.3. FT-IR analysis
FT-IR spectra of the synthesized nanocrystals are shown in
Fig. 5. The bands around 3679 cmꢀ1 and 1410 cmꢀ1 are due to
the presence of hydroxyl groups in the samples. The band at
1275 cmꢀ1 is attributed to the C = O stretching vibration of the car-
boxylate group (CO2–), and the band around 1060 cmꢀ1 is associ-
ated with nitrate group [29]. Around 550 cmꢀ1 vibration of the
tetrahedral metal–oxygen bond is observed, and the absorption
band around 350 cmꢀ1 is due to the octahedral metal–oxygen
bond. The force constant of the interatomic bonding strength (Kt)
has been estimated by [30]:
tabulated in Table 2. Rietveld refinement parameters along with
crystallite sizes (DXRD) and TEM (DTEM) analysis are enlisted in
Table 2. G.O.F. remains around 1.10–1.27. Crystallite and particle
sizes estimated from Rietveld analysis and TEM measurement gave
almost identical results. Oxygen vacancies in the prepared samples
increases up to Y15 sample and with further addition of Y ion, it
again decreases.
Table 2 also includes the cell parameter, cell volume, micros-
train (<e2>1/2) and X-ray density of the compositions (dX). Cell
parameter was increased due to the inclusion of smaller Fe3+
(0.64 Å) ion in the B site in place of larger Y3+ (0.9 Å) ion. Variations
of oxygen concentration and lattice parameter with doping con-
centration are depicted in Fig. 3.
Kt ¼ 7:62 ꢂ M ꢂ m2 ꢂ 10ꢀ7
ð1Þ
where M and
m are the tetrahedral mass and frequency respec-
tively. In the inset of Fig. 5 the variation of interatomic force con-
It seemed that change in lattice parameter does not obey
Vegard’s law. There are possibilities of non-linear behavior i.e. pos-
itive and negative deviations from linearity of the lattice parameter
for spinel structures, particularly for mixed spinel structures [24].
Distribution of cations inside the present system shows the mixed
spinel structure. Random distribution of cations over the two inter-
stitial sites causes in-homogeneities inside the crystal. These in-
homogeneities and also the size mismatch between host and
dopant cations are found to be responsible for the deviations from
Vegard’s law for the present system [25,26]. Increase in lattice
strain was observed in the doped samples which also arise due
to different ionic radii in the lattice sites.
stant with Y content is depicted.
Inter-atomic force constant Kt along with corresponding fre-
quency (m) and mass (M) are presented in Table 4. Tetrahedral mass
is minimum for Y15 sample and hence the tetrahedral frequency is
maximum for Y15 sample. Also the force constant calculated by
using Eq. (1) is maximum for Y15 sample. This is consistent with
our calculated cation distribution as discussed earlier.
3.4. Room temperature magnetic study
Room temperature magnetic study (M-H curves) were carried
out for all the prepared samples and shown in Fig. 6. M-H curve

S. Chakrabarty et al. / Journal of Magnetism and Magnetic Materials 461 (2018) 69–75
73
Fig. 6. M-H hysteresis loops of different samples at room temperature. Typical L.A
fit of Y15 sample [inset].
Fig. 5. FTIR spectra of the prepared samples. Variation of force constant with
doping concentration (inset).
Table 4
for collinear spin structure as nB = MA ꢀ MB where MB and MA are
Interatomic force constant Kt along with corresponding frequency (m) and mass (M).
the B and A sublattices magnetic moments in
lB, respectively.
Compositions
m
ꢂ 10ꢀ2 (mꢀ1
)
M ꢂ 10ꢀ3 (kg)
Kt ꢂ 102 (N/m)
We have considered, therefore, the non-collinear spin arrange-
ment, according to Yafet-Kittel (YK) model [31], where net magne-
tization for spinel structure is given by (in terms of Bohr
magneton) nB = coshY-K MB ꢀ MA where hY-K is the Y-K angle i.e.
the angle between the magnetic moments of A site and B site. Cal-
culated values of Y-K angle for different compositions are enlisted
in Table 5. Mixed spinel structure with defects and incorporation of
Y3+ in the ferrite lattice changes magnetic interactions and thereby
causes canting spin arrangements in the present system.
Y0
524
534
544
540
541
56.84
56.76
56.68
56.74
56.81
11.89
12.33
12.78
12.66
12.60
Y10
Y15
Y20
Y30
clearly indicates that saturation magnetization decreases gradually
from 72.19 emu/gm to 35.63 emu/gm when doping concentration
of yttrium varies from 0 to 30%.
In order to obtain anisotropy information of the samples, room
temperature hysteresis loop was fitted to ‘‘Law of Approach to sat-
uration’’ (L.A.S.) equation described by [32]:
Decrease of saturation magnetization with the Y3+ concentra-
tion depends upon the two factors. (1) Magnetic interactions
between A-A, B-B and A-B sites and interaction of magnetic ions
with the external applied field determines the net magnetic
moment of the material and (2) being a non-magnetic ion, Y3+ does
not take part in the exchange interaction to its nearest neighbors.
As a consequence, net magnetization is reduced with the increase
of Y3+ content. In the present system we have observed that the
effective metal ion bond lengths reach their optimum values and
calculated bond angles indicate strengthening of A–B and A–A
interactions and decrease in angle indicate weakening of B–B inter-
action. These factors ultimately leads to the decrease of saturation
magnetization in the present system.
ꢀ
ꢁ
A
H
B
H2
M ¼ Ms 1 ꢀ
ꢀ
þ
jH
ð2Þ
where M is the magnetization near the saturation magnetiza-
tion, H is the applied magnetic field, MS is the saturation magneti-
zation, l0 is the permeability of the free space.
The first term A/H is valid only for finite range of applied field
strength as inhomogeneities, crystal defects etc., if present in the
system, will be diminished as the applied field gets sufficiently
higher. The last term is applicable at higher temperatures and
higher fields. This term comes into effect due to the impurities con-
tained in the material, which are forced to align themselves along
the direction of the applied field at higher values. We, therefore fit-
Also the values of saturation magnetization are not in corre-
spondence with our cation distribution (Table 5). Observed values
are lower than what should be according to our cation distribution
in previous section if we consider Neel’s collinear spin structure
model. Magnetic moment per formula unit in lB can be estimated
ted Eq. (2) with B/ H2 term above 0.8 T. Here B is given by
8K21
B ¼
ð3Þ
105l
20M2s
Table 5
Calculated values of saturation magnetization estimated from XRD (MXRD), observed value from VSM (Msvsm), coercive field (Hc), anisotropy constant (K1), remnance
magnetization (Mr), remnance ratio (Mr/Ms), anisotropy field (Hk) and Yafet-Kittel angle (hY-K).
Composition
MXRD (in lB
)
Msvsm (in lB
)
Hc(Oe)
K1ꢂ105 (erg/cc)
Mr (emu/g)
Mr/Ms
Hk(KOe)
hY-K
Y0
4.30
3.70
3.34
3.17
2.76
3.03
2.29
2.22
2.08
1.55
684
500
346
486
679
6.14
5.11
4.82
4.56
3.20
27.41
18.24
17.37
16.78
12.89
0.36
0.34
0.33
0.34
0.36
16.8
18.1
19.7
18.7
18.0
31.44
34.36
31.12
31.17
33.92
Y10
Y15
Y20
Y30

74
S. Chakrabarty et al. / Journal of Magnetism and Magnetic Materials 461 (2018) 69–75
Fig. 7. Variations of particle sizes obtained from TEM and XRD analyses and
magnetic grain diameter with doping concentration for different samples. (Lines are
for the guidance of the eyes).
Fig. 8. Room temperature dM/dH versus
Variation of Hc with doping concentration (inset). (Lines are for the guide of eyes
only).
H curves for the prepared samples.
Numerical coefficient 8/105 applies to cubic anisotropy of ran-
dom polycrystalline materials. Typical L.A.S. fit for Y15 sample is
shown in inset of Fig. 6. Anisotropy field (Hk) for the materials
was estimated using the formula:
2k1
l0Ms
Hj
¼
ð4Þ
K1 is the first anisotropy constant.
Inter grain group exchange mechanism can be understood by
the values of remanence ratio R = Mr/Ms [33]. When the particles
interact by magnetostatic interaction, the value of R is less than
0.5. Lower values of remanence ratio suggests the decrease of
exchange interactions i.e. existence of magnetic dipole interaction
with random orientation [34].
A close correspondence between Mr/Ms ratio and interparticle
dipolar interaction (IPDI) around room temperature has been
established recently by few researcher groups [35,36]. Concentra-
tion of nanoparticles is reflected by dipolar field energy Hdip
/
ðMSꢂVm
Þ
where Ms is the saturation magnetization, Vm is the mag-
Fig. 9. Tꢀ1/4 dependence of dc resistivity (
qdc) with least square straight line fitting
d3
for different compositions. Variations of localized states at the Fermi level N(EF) and
activation energy W with different compositions [inset].
netic grain volume and d is the inter particle distance. Inverse log-
arithm of Hdip (1/lgHdip) can be estimated equating it to the Mr/Ms
ratio as these two values are very close to each other at room tem-
perature and differ only at lower temperatures [36]. Magnetic
grain volumes (Vm) can thus be estimated and hence the diameter
of a magnetic grain (Dm) calculated. Inter particle distances were
taken from TEM as well as XRD analyses earlier. A comparison of
particle size obtained from TEM and XRD with magnetic grain
diameter (Dm) is depicted in Fig. 7 where Dm is lower than DTEM
and DXRD. This is consistent with previous results where the critical
size of particle for single domain structure is well below than the
particle size [35]. Also Mr/Ms ratio for the present system is lower
than 0.5 which is the theoretical value for uniaxial anisotropy. This
phenomenon is attributed to the existence of interparticle dipole
interaction (IPDI) [37].
doping, the coercive field decreases and beyond that, it increases
again. Nature of the magnetic inter-grain interactions controls the
coercive field inside the material. From the structural analysis it
was observed that B site–B site interaction is minimum and A
site–B site and A site–A site interactions are maximum for this par-
ticular doping percentage. Also bond lengths attain optimum values
for this composition. These structural changes ultimately control the
soft-hard nature of the system and incorporate the changes
observed in the coercive field inside the material.
Calculated values of saturation magnetization from our cation
distribution (MXRD), observed from VSM (Msvsm), coercive field
(Hc), anisotropy constant (K1), remanence magnetization (Mr),
remanence ratio (Mr/Ms), anisotropy field (Hk) and YK angle (hY-K
)
Switching field distribution is depicted in Fig. 8 with the help of
room temperature dM/dH versus H curve [38]. Only one peak is
observed in the curve which indicates the single magnetic domain
type nature of the system. Narrow magnetic domain distribution
is confirmed by the narrow nature of the peak. Position of the peak
near the zero of the magnetic field proves the soft magnetic nature
of the nanocrystals. Variation of coercive field with doping concen-
tration is depicted in the inset of Fig. 8. We can see that up to 15 mol%
are summarized in Table 5.
3.5. Mott VRH analysis
DC conductivity has been analyzed employing variable range
hopping conduction mechanism (VRH) [39,40]. Temperature
dependence of the resistivity can be expressed by the relation:

S. Chakrabarty et al. / Journal of Magnetism and Magnetic Materials 461 (2018) 69–75
75
Table 6
him to do this work. S. Chakrabarty and A. Dutta thankfully
acknowledge The University of Burdwan for infrastructural sup-
port. One of the authors A. Dutta thankfully acknowledged the
financial assistance from Science and Engineering Research Board
(SERB), India, (Grant no: EMR/2017/000325) and the instrumental
and other supports from DST (Govt. of India) under departmental
FIST program (Grant no: SR/FST/PS-II-001/2011) & PURSE-Phase2
program (Grant no: SR/PURSE/Phase 2/34) and University Grants
Commission (UGC), India, for departmental CAS [Grant no.
F.530/5/CAS/2011 (SAP-I)] scheme. Also, all the authors are thank-
ful to DST-FIST scheme of the Department of Physics, University of
Kalyani for providing the instrumental facilities.
Various electrical parameters for different compositions estimated using Mott’s VRH
model.
Compositions
a
(Å)
N(EF) (Jꢀ1mꢀ3
ꢂ1046
)
T0(K)
ꢂ109
17.2
7.80
7.40
7.02
6.20
W ꢂ 10ꢀ21
R
(Å)
(J)
Y0
0.119 1.91
0.134 2.92
0.144 3.92
0.161 1.89
0.164 1.77
14
10
08
12
13
8.8
8.1
7.4
9.4
9.5
Y10
Y15
Y20
Y30
c
qdc
¼
q0expðT0=TÞ
ð5Þ
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Acknowledgements
One of the authors M. Pal is thankful to Director, CSIR-Central
Glass and Ceramic Research Institute (CSIR-CGCRI) for allowing