Cation Distribution Assisted Tuning of Magnetization in Nanosized Magnesium Ferrite

Article abstract of DOI:10.1002/pssa.201700397

The MgFe₂O₄ nanoparticles are synthesized by combustion method and annealed at different temperatures from 500 to 1000 °C. Magnetic properties, morphology, valence states of iron, crystal structure, and microstructure of the samples

Full text of DOI:10.1002/pssa.201700397

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ORIGINAL PAPER
Magnesium Ferrite
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Cation Distribution Assisted Tuning of Magnetization in
Nanosized Magnesium Ferrite
Nguyen Kim Thanh, To Thanh Loan,* Nguyen Phuc Duong, Luong Ngoc Anh,
Dao Thi Thuy Nguyet, Nguyen Huu Nam, Siriwat Soontaranon, Wantana Klysubun,
and Than Duc Hien
spinel-type structure. The fraction of Fe3þ
The MgFe2O4 nanoparticles are synthesized by combustion method and
cations occupied in tetrahedral site (1ꢁx) is
the so-called inversion parameter.[5] The
magnetic couplings in MgFe2O4 solely
originate from the magnetic moment of
iron ions as Mg2þ ion is non-magnetic.
The distribution of Fe3þ and Mg2þ ions
between (A) and [B] sites depends strongly
on preparation methods as well as heat-
treatment conditions and greatly affects the
magnetic properties. In the bulk MgFe2O4
material the inversion parameter was
found to be about 0.9 corresponding to
magnetic moment at 0 K close to 1 mB and
Curie temperature TC ¼ 713 K.[6] Mean-
while, it was observed by O’Neill et al. in
crystalline magnesium ferrite quenched
from high temperatures that the inversion
degree can reduce to a value of 0.732,
which induces to a decrease of TC down to
565 K.[7]
annealed at different temperatures from 500 to 1000 ꢀC. Magnetic properties,
morphology, valence states of iron, crystal structure, and microstructure of
the samples are investigated systematically by vibrating sample magnetome-
ter, field emission scanning electron microscope, transmission electron
microscopy, X-ray absorption spectroscopy, and synchrotron X-ray diffraction.
Cation distribution is determined from synchrotron X-ray diffraction data
using Rietveld refinement combined with extended X-ray absorption fine
structure spectroscopy. The results indicates that all the samples are phase-
pure with crystallite size ranging from 11 to 41 nm. By adjusting the
annealing temperature, cation distribution and particle size can be changed,
and consequently leading to the change in structure and magnetic properties.
The saturation magnetization of the samples are enhanced significantly
compared to that of the bulk material. The variation of magnetic properties is
discussed based on cation distribution, particle size, valence state, surface
effect, and spin canting.
In nanocrystalline Mg-ferrite, it was
reported that the inversion parameter can
vary significantly and can reach to a value
of 0.64, and consequently magnetization
1. Introduction
Magnesium ferrite is one of the most important spinel ferrites
with wide applications in many fields including microwave
devices, electromagnets, hyperthermia, heterogeneous catalysis,
sensor technology, photocatalyst. . ..[1–4] MgFe2O4 is known to be
a partially inverse spinel that can be written as (MgxFe1ꢁx)A[Mg1-
was enhanced.[5] However, many reports on MgFe2O4 nano-
particles indicated
a reduced magnetization which was
attributed to enhanced surface effects as a result of the
decrease of particle size.[8–12] Improving magnetization of
nanosized MgFe2O4, therefore, still remains a challenge.
Numerous studies have been carried out on varying cation
distribution by using chemical preparation methods combined
with heat treatment in order to enhance magnetization of
MgFe2O4 nanoparticles.[13–16] In a highlighted work,[17] Franco
et al. showed an enhancement of the saturation magnetization
Ms of about 50 % (compared to the bulk counterpart) in 44 nm-
MgFe2O4 prepared by using combustion reaction method. The
authors obtained Ms ¼ 48.3 emu gꢁ1 at 4 K but did not
determine cation distribution in their sample. In general,
reported studies on magnetic properties together with
determination of cation distribution are still limited, and
hence the change in magnetic properties of nanostructured
MgFe2O4 was not yet clearly explained. Obviously, better
understanding of the magnetic properties requires detailed
knowledge of its structure including crystal structure, cation
distribution and valence state of iron ions. Such detailed
xFe1þx]BO4, where (MgxFe1ꢁx)A and [Mg1ꢁxFe1þx]B represent,
respectively, the tetrahedral (A) and octahedral [B] sites of the
N. K. Thanh, Dr. T. T. Loan, N. P. Duong, Dr. L. N. Anh,
Dr. D. T. T. Nguyet, N. H. Nam, Prof. T. D. Hien
International Training Institute for Materials Science (ITIMS)
Hanoi University of Science and Technology
Dai Co Viet 1, Hanoi 100000, Vietnam
E-mail: totloan@itims.edu.vn
N. K. Thanh
Le Quy Don University of Science and Technology
Hoang Quoc Viet 236, Hanoi 100000, Vietnam
Dr. S. Soontaranon, Dr. W. Klysubun
Synchrotron Light Research Institute
University Avenue 111, Nakhon Ratchasima 30000, Thailand
DOI: 10.1002/pssa.201700397
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structural information can be obtained by a combination of
synchrotron X-ray diffraction and X-absorption techniques.
This paper reports the study on cation distribution and its
influence on the magnetic properties of the MgFe2O4 nano-
particles prepared by combustion method with different
annealing conditions. The cation distribution was determined
from synchrotron X-ray diffraction (SXRD) data using Rietveld
refinement method combined with extended X-ray absorption
fine structure (EXAFS) spectroscopy. In addition the morphol-
ogy, valence states of iron ions, crystal structure, and
magnetization characterizations have also been investigated.
The cation distribution, surface effect and spin canting were
taken into consideration to explain the magnetic properties of
the samples.
in applied magnetic fields up to 10 kOe and in temperature range
88–600 K.
3. Result and Discussion
3.1. SXRD Analysis
Figure 1 shows the SXRD patterns of the MgFe2O4 samples
annealed at different temperatures. All the diffraction peaks
correspond to the cubic spinel structure confirming the
formation of phase-pure spinel ferrite in the samples. The
structural parameters of the samples were well refined using the
standard model of spinel ferrite within the cubic symmetry
(space group Fd3m) with atoms in positions (A)-site in 8a (1/8,
1/8, 1/8), [B]-site in 16d (1/2, 1/2, 1/2) and O in 32e (x, x, x). The
cation site occupancies of Fe3þ and Mg2þ ions in 8a and 16d sites
were estimated by Rietveld analysis of the SXRD data along with
lattice parameter and oxygen coordinate. The refinement fitting
quality was checked by goodness of fit (χ2) and weighted profile
R-factor (Rwp).[21] One of the synchrotron diffraction patterns
and its Rietveld refinement are shown in Figure 2.
2. Experimental Section
The MgFe2O4 nanoparticles were synthesized in the following
steps. Solution of NaOH 0.8 M was heated up to 70 ꢀC with
vigorously stirring. Stearic acid was added to the hot alkaline
solution to make saponification reaction. The solution of
prepared sodium stearate was kept in 70 ꢀC with continuously
stirring to avoid condensation. The mixed solution of Mg(NO3)2
0.1 M and Fe(NO3)3 0.2 M was prepared from the salts
Mg(NO3)2.6H2O and Fe(NO3)3.9H2O, then added to the sodium
stearate solution. A reddish-brown precipitate in the colloidal
form was obtained from this reaction. Precipitate was washed by
deionized water until pH ¼ 7. The washed product was collected
and dried at 100 ꢀC for 24 h. The as-synthesized powders were
combusted of at 400 ꢀC and annealed at various temperatures
(500, 750, 900, and 1000 ꢀC) during 5 h. After that, the as-
prepared samples were immediately quenched from high
temperature into ice-melting water. Nanoparticles were obtained
by a permanent magnet and drying at 60 ꢀC for 5 h.
The refined values of structural parameters including lattice
constant (a), oxygen positional parameter (x) and cation
distribution are given in Table 1. The lattice parameter values
of the samples are higher than the value of bulk MgFe2O4
(abulk ¼ 8.367 A[22]) but comparable to those reported previously
̊
for MgFe2O4 nanoparticles.[23,24] The lattice parameter was
found to increase with increasing annealing temperature. This
result is in good agreement with previous studies on quenched
magnesium ferrite[7,25] and can be explained by the distribution
of Mg2þ and Fe3þ ions over tetrahedral and octahedral sites.
O’Neill et al.[7,26] indicated that due to larger ionic radii of Mg2þ
2þ
3þ
ion compared to that of Fe3þ (rMg ¼ 0.71 A, rFe ¼ 0.63 A for
̊
̊
2þ
3þ
̊
̊
tetrahedral site and rMg ¼ 0.86 A, rFe ¼ 0.785 A for octahe-
dral site), the increase of Mg2þ ions fraction in (A) site leads to an
increase of lattice parameter. In other words, large lattice
parameter corresponds to a more disordered cation distribution.
Synchrotron X-ray powder diffraction (SXRD) experiments
were carried out at beamline Small/Wide Angle X-rayScattering
(SAXS/WAXS) of the Synchrotron Light Research Institute,
̊
Thailand (λ ¼ 1.55 A) to identify the crystal structure of the
samples at room temperature. The diffraction data were
analyzed using the Rietveld method with the help of FullProf
program.[18] The diffraction peaks were modeled by pseudo-
Voight function. A standard of LaB6 was used to determine
instrument broadening.
Field emission scanning electron microscope FESEM (JEOL
JSM-7600) and transmission electron microscopy TEM (JEOL
1010) were used to investigate particle size and morphology of
the samples.
X-ray absorption spectroscopy (XAS) measurements were
performed at BL8 of the Synchrotron Light Research Institute
(Thailand).[19] X-ray absorption near-edge spectroscopy (XANES)
and extended X-ray absorption fine structure (EXAFS) spectra of
the samples were measured at the Fe K-edge in transmission
mode at room temperature. A double crystal monochromator Ge
(220) was used to scan the energy of the synchrotron X-ray beam.
The XAS spectra were base line subtracted and normalized using
the software package ATHENA.[20]
Magnetization curves were measured using a vibrating
sample magnetometer VSM (ADE Technology ꢁ DMS 5000)
Figure 1. Synchrotron X-ray diffraction patterns of the MgFe2O4 samples
annealed at different temperatures.
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3.2. SEM, TEM, XANES, and EXAFS analyses
The morphology and particle size of the MgFe2O4 samples were
characterized by FESEM and TEM measurements which are
exhibited in Figures 3 and 4. FESEM (Figure 3a) and TEM
(Figure 4) images show that the MgFe2O4 sample annealed at
lowest temperature (500 ꢀC) composes of grains which are nearly
spherical and their diameter distribute in range of 10–30 nm.
Meanwhile, for the sample annealed at 750 ꢀC the grains are
inter-diffused to form particles (Figure 3b) under promotion of
higher thermal energy. Grain sizes of the sample can be seen to
distribute in range of 20–40 nm. With further increasing Ta small
grains are merged into bigger particles with sizes of about
100 nm for the sample annealed at 900 ꢀC and up to submicron
for the sample annealed at 1000 ꢀC.
The XANES spectra at Fe K-edge and their first derivative for
the MgFe2O4 samples and the standards (iron foil, ferrous oxide
and hematite) are shown in Figure 5. Oxidation state of iron in
the samples was determined by comparing the absorption edge
energy with those of the standards. It is known that at higher
oxidation state of elements, the corresponding absorption edge
shifts to higher energy. The absorption edge energy was defined
as the inflection point in the first derivative of the XANES
spectrum and was determined by using the software package
ATHENA (Figure 5a). The obtained edge energy values of the
MgFe2O4 samples correspond to that of the Fe2O3 standard.
Quantitative analysis on these results indicates that the [Fe2þ]/
[Fe3þ] fraction of all the samples is lower than statistical errors of
spectroscopy (3%[19]), therefore we can conclude that the
samples contain only Fe3þ ion and exhibit themselves as
stoichiometric magnesium ferrite.
Figure 2. Synchrotron diffraction pattern of the MgFe2O4 sample
annealed at 1000 ꢀC and processed by the Rietveld method. The
experimental points as well as calculated and difference functions are
indicated.
As seen in Table 1, when temperature of annealing increases
from 500 to 1000 ꢀC, the inversion parameter of the samples
decreases significantly from 0.841 down to 0.766 resulting in the
increase of lattice parameter.
The microstructural parameters including the average size
of coherent scattering region D (usually called the crystallite
size) and lattice microstrain Δa/a were obtained by analysis of
the peak broadening on applying Rietveld method using
FullProf program with the instrumental resolution function
identified by SXRD analysis of the LaB6 standard. The obtained
values of the microstructural parameters are listed in Table 1.
The mean crystallite size increases from 11 to 41 nm with
increasing annealing temperature. This increase in crystallite
size can be explained by the improved crystallinity and
promoted particles size of the samples at higher annealing
temperatures. This phenomenon was often observed in spinel
ferrite nanoparticles prepared by wet chemical routes.[27,28] In
addition, the lattice microstrain allows us to characterize the
structure disorder of the samples. Here we observe that with
increasing Ta the lattice microstrain increases (Table 1). This
result reveals the influence of quenching process on the
structure ordering since the samples were quenched from
higher annealing temperature corresponds to more disordered
structure.
Figure 6 shows the Fourier transforms (FTs) of EXAFS data
for the MgFe2O4 samples at the Fe K-edge. The modulus of the
FTs gives the pseudo-partial radial distribution around iron. In
this form the data directly reflect the average local environment
around the absorbing atoms where the peaks in the FTs typically
represent shells of atoms around the absorber. The range of wave
number k for Fourier transformation was 1 < k < 9 Aꢁ1. The first
̊
̊
peak in the FTs at about 0.9 A corresponds to iron coordinated to
oxygens in (A) site, the second peak at about 1.4 A corresponds to
̊
iron coordinated to oxygens in [B] site, the third one at about
̊
2.6 A corresponds to the iron-metal distance between neighbor-
̊
ing octahedral sites and the fourth peak at about 3.1 A is due to
the iron-metal distance between neighbouring octahedral and
tetrahedral sites.[29]
The obtained FTprofiles of the samples are similar to those of
the mixed spinel structures as reported for MgFe2O4.[29,30]
Table 1. Refinement result from SXRD analysis: Lattice parameter (a), average crystallite size (D), average value of microstrain (4a/a), cation
distribution, and the refinement fitting quality of the MgFe2O4 samples. Statistical errors are indicated in the last significant digit.
Cation distribution
̊
2
Ta, ꢀC
a, A
x
D, nm
4a/a
Site
[B] site
χ
Rwp, %
500
750
900
1000
8.3953(9)
8.4044(9)
8.4206(9)
8.4209(8)
0.2522(9)
0.2548(8)
0.2529(8)
0.2538(7)
11.2(1)
14.3(1)
31.2(1)
40.9(1)
0.0015(1)
0.0036(2)
0.0037(2)
0.0039(1)
Mg0.159Fe0.841
Mg0.165Fe0.835
Mg0.191Fe0.809
Mg0.234Fe0.766
Mg0.841Fe1.159
Mg0.835Fe1.165
Mg0.809Fe1.191
Mg0.766Fe1.234
1.28
1.31
1.49
1.57
10.1
13.2
16.1
15.2
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to well above the magnetic ordering tempera-
ture. For examples, Figure 7 shows the M–H
curves of the samples measured at 88 and
293 K.
At lowest measuring temperature (88 K),
magnetization of the samples was observed to
increase with increasing annealing tempera-
ture. A common feature of the M–H curves at
different temperatures is that the magnetiza-
tion for the most samples is not saturated
completely up to highest investigated mag-
netic field. This behavior is attributed to
random distribution of the magnetization
directions of nanoparticles in the samples
and the interactions between them.
In these cases, the law of approach to
saturation can be applied to estimate the
saturation magnetization Ms of the samples at
each measuring temperature, by which the
magnetization is expressed as a function of the
magnetic field as follows[31]
:
ꢀ
ꢁ
Figure 3. FESEM images of the MgFe2O4 samples annealed at 500 ꢀC (a), 750 ꢀC (b), 900 ꢀC
M ¼ Ms 1 ꢁ a=H1=2 ꢁ b=H2
ð1Þ
(c), and 1000ꢀC (d).
where the term a/H1/2 arises from defects in
the particles and the term b/H2 is attributed to the effec
tive anisotropy energy of the samples. The saturation
magnetization values calculated from Eq. (1) are plotted as a
function of temperature and shown in Figure 8. The Ms values
of the MgFe2O4 samples at room temperature are given in
Table 2. The saturation magnetization of the samples was
Besides it was observed that the first FT peak shifts to higher
radial coordinate R, which corresponds to higher iron–oxygen
distance in tetrahedral site with increasing Ta. The increase of
Fe–O distance in (A) site demonstrates the increase of Mg2þ ions
fraction in the site. This is additional evidence to confirm the
result of cation distribution as estimated via Rietveld analysis
(see section 3.1).
enhanced significantly in comparison with that of bulk
bulk
MgFe2O4 (at room temperature Ms
¼ 27 emu gꢁ1[22]) and
those reported for the MgFe2O4 nanoparticles prepared by other
methods including sol–gel route,[8] thermal decomposition,[9]
combustion,[17] hydrothermal,[32] and solid state reaction
technique.[33]
3.3. Magnetic Characterization
The magnetization as a function of external magnetic field for all
the samples was measured at different temperatures from 88 K
From the Ms–T curves presented in Figure 8, the Curie
temperature values (TC) of the samples were determined and
taken as temperature at which Ms vanishes. The Curie
temperature is given in Table 2. The TC values of all the
MgFe2O4 samples are much lower than that of bulk
counterpart. The reduction of Curie temperature in nano-
sized spinel ferrites in comparison with TC for bulk materials
has been recorded previously[11,27] and can be explained
firstly by finite-size effect. Das with co-workers found that the
Curie temperature of the MgFe2O4 nanoparticles synthesized
by ultrasonic spray pyrolysis technique decreases from 643 to
563 K with decreasing particle size.[11] The shift of TC in their
study is well described by the finite-size scaling formula. The
reported studies on nanosized magnetic materials pointed
out that the finite-size effect influences significantly on the
ordering temperature when particle diameter decreases
down to roughly 10 nm.[34,35] Nevertheless, most of the
particles of the MgFe2O4 samples in this work are larger than
10 nm. Moreover an increase of Curie temperature with
decreasing particle size was observed. The change in TC is
supposed to be less influenced by the finite-size effect but
Figure 4. TEM images of the MgFe2O4 sample annealed at 500 ꢀC.
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Figure 6. Fourier transform profiles of the k-weighted EXAFS spectra of
the MgFe2O4 samples at Fe K-edge.
where B and α are the Bloch constant and the Bloch exponent,
respectively. The Ms(0) values calculated from Eq. (2) are listed
in Table 2. The saturation magnetization values at 0 K of all
the MgFe2O4 samples were found to be higher than that of
Figure 5. (a) Normalized Fe K-edge XANES spectra of the MgFe2O4
samples together with those of Fe2O3, FeO, and Fe foil standards. (b)
First-derivative normalized Fe K-edge XANES spectra of the samples and
the standards.
mainly depends on cation distribution. As seen in the inset of
Figure 8, Curie temperature of the samples decreases with
decreasing
inversion parameter. Similar behavior has also been observed
previously in magnesium ferrite with low inversion parame-
ter, in which the Curie temperature has been shown as a
sensitive function of cation distribution.[5,7,25] The Curie
temperature of 633 K was observed in crystalline MgFe2O4
with inversion parameter of 0.84.[25] O’Neill et al. revealed a
TC reduction from 639 to 565 K in magnesium ferrite with
decreasing inversion degree from 0.883 down to 0.732.[7]
Obviously, the increase of concentration of nonmagnetic
Mg2þ ion in tetrahedral site should lead to a decrease of the
intersublattice exchange coupling between (A) and [B] sites,
and hence a decrease in TC.
In order to determine the saturation magnetization at
zero Kelvin Ms(0), the Ms data in temperature region below
300 K (Figure 8) were fitted using the modified Bloch’s
function[34]
:
Figure 7. M–H curves measured at 88 and 293 K of the MgFe2O4
samples.
MsðTÞ ¼ Msð0Þ½1 ꢁ BTαꢂ
ð2Þ
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(nBtheo(0)) are presented in Table 2. It can be seen that the
experimental values are lower than the theoretical ones. For the
samples annealed at low temperature 500 and 750 ꢀC, which have
small particle size of about 10–30 nm and 20–40 nm respectively,
this observation can be explained reasonably based on the spin
disorder in surface shell regions. Namely, in nanoparticles the
contribution of the disordered spins in the surface regions to the
total magnetic moments of the particles becomes significant
resulting in the decrease of net magnetization.[36] In this case, the
core-shell model can be assumed for the magnetic nanoparticles
where the core orders ferrimagnetically and the shell contains
exp
theo
disordered spins. The experimental nB and nB
values are
related via the expression[38]: nB ¼ nBtheo[(D/2 ꢁt)/D/2]3, where
exp
D is the diameterof the particleandt is the thicknessof the surface
shell. With the assumption that the shell thickness t is about a unit
theo
cell length (ꢄ 1 nm), the nBexp/nB
fraction calculated for the
samples with particle size 30 and 40 nm will be 81 and 86%,
respectively. As seen in Table 2, the obtained nBexp(0)/nBtheo(0)
ratios for the samples are in fair agreement with that calculated on
applying core-shell model. However, this model cannot be applied
forthesamplesannealedathighertemperatures(900and1000 ꢀC)
since their particles are much bigger with diameters of about
100 nm to submicron. In these samples, the lower values of the
experimental magnetic moment in comparison with ones
Figure 8. Temperature dependence of saturation magnetization of the
MgFe2O4 samples. Inset: Dependences of Curie temperature and the
saturation magnetization at 0 K on inversion parameter.
bulk magnesium ferrite (Ms(0)bulk ¼ 33.4 emu gꢁ1[36]). Ms(0)
increases with increasing annealing temperature and reaches
to a value of 58.82 emu gꢁ1 for the sample annealed at 1000ꢀC.
To the best of our knowledge, such Ms(0) value is the highest
ever found in MgFe2O4 nanoparticle prepared by using
combustion method.
As shown in the inset of Figure 8, the saturation magnetiza-
tion at 0 K increases with decreasing the inversion parameter
indicating the effect of cation distribution on the magnetization.
From the extrapolated Ms(0) determined from Eq. (2), the
magnetic moment values nBexp(0) of the samples described as
number of Bohr magnetons per formula unit were determined
ꢀ
calculated by collinear Neel model in Eq. (3) can be attributed to
a non-collinear ordering of magnetic moments of Fe3þ ions
(known as spin canting). The effect has been found in nano-
[39,40]
crystalline MgFe2O4
and in others nanostructured spinel
ferrite.[41,42] Itwasindicatedinspinelferritethatthespincantingis
caused by cationic inversion due to chemical disorder which
modifies super-exchange interactions.[42] When the tetrahedral
site was diluted by non-magnetic ions, competition between the
[B]-O-[B] intersublattice interaction and the strongly reduced (A)-
O-[B] intersublattice interaction induces the canting of the
moment in [B] site. Corliss et al.[43] demonstrated that in MgFe2O4
withhighdegreeofinversion,magneticmomentisconsistentwith
exp
using the relation[37]: nB ð0Þ ¼
, where MW is the
MsꢃMW
5585
molecular weight of the sample and Ms is the saturation
magnetization in emu gꢁ1. The results are presented in Table 2.
On the other hand, the cation distribution for MgFe2O4
composition was written as (MgxFe1ꢁx)A[Mg1ꢁxFe1þx]BO4. Then
the theoretical magnetic moment (nBtheo(0)) per one formula
unit can be calculated based on cation distribution results
derived from Rietveld analysis (see Table 1) and with assumption
ꢀ
the collinear Neel model. Nevertheless, the spin canting will take
place with the inversion parameter lower about 0.805[44] which is
the case of our samples annealed at 900 and 1000 ꢀC.
4. Conclusions
ꢀ
of the Neel model:
By using combustion method and adjusting the annealing
temperature we have successfully synthesized phase-pure nano-
structured magnesium ferrite and simultaneously changed their
cation distribution. With increasing the annealing temperature
from 500 to 1000 ꢀC, it was found that the inversion parameter
ntBheoð0Þ ¼ 5ð1 þ xÞ ꢁ 5ð1 ꢁ xÞ ¼ 10x
ð3Þ
In the calculation, the spin value of Fe3þ (S ¼ 5/2, g ¼ 2) was
taken into account. The theoretical magnetic moment values
Table 2. Magnetic parameters of the MgFe2O4 samples including saturation magnetization at room temperature, extrapolated magnetization at
zero temperature Ms(0), magnetic moment values nB, and Curie temperature TC.
Ta, ꢀC
Ms at room temperature, emu gꢁ1
Ms(0), emu gꢁ1
nBexp(0), μ /f.u.
nBtheo(0), μ /f.u.
nBexp(0)/nBtheo(0), %
TC, K
B
B
500
750
900
1000
24.3
29.1
31.4
38.8
34.74
39.51
47.58
58.82
1.24
1.41
1.7
1.59
1.65
1.91
2.34
78
85
89
90
600
575
570
569
2.1
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reduced from 0.841 down to 0.766, meanwhile the particle size
increased. The decrease of inversion parameter was confirmed to
bethemainreasonthatleadstotheincreasesoflatticeparameteras
well as saturation magnetization and a reduction of the Curie
temperature. The saturation magnetization of the samples was
enhancedsignificantlycomparedtothatofthebulkmaterial, thatis
Ms ¼ 38.8 emu gꢁ1 atroomtemperatureforthesampleannealedat
1000ꢀC which is the highest value obtained so far for magnesium
ferrites prepared by using combustion method. The magnetic
moment values of the samples inthe ground statewerefound tobe
lower than the calculated values using the cation distribution data
[11] H. Das, N. Sakamoto, H. Aono, K. Shinozaki, H. Suzuki, N. Wakiya,
J. Magn. Magn. Mater. 2015, 392, 91.
[12] M. Goodarz Naseri, M. H. M. Ara, E. B. Saion, A. H. Shaari, J. Magn.
Magn. Mater. 2014, 350, 141.
ꢁ
[13] V. Sepelák, I. Bergmann, D. Menzel, A. Feldhoff, P. Heitjans,
F. J. Litterst, K. D. Becker, J. Magn. Magn. Mater. 2007, 316, 4.
[14] B. Antic, N. Jovic, M. B. Pavlovic, A. Kremenovic, D. Manojlovic,
M. Vucinic-Vasic, A. S. Nikolic, J. Appl. Phys. 2010, 107, 1.
[15] D. Chen, Y. Zhang, C. Tu, Mater. Lett. 2012, 82, 10.
[16] T. P. Sumangala, C. Mahender, N. Venkataramani, S. Prasad, J. Magn.
Magn. Mater. 2015, 382, 225.
[17] A. Franco, T. E. Pereira Alves, E. C. De Oliveira Lima, E. Da Silva
Nunes, V. Zapf, Appl. Phys. A Mater. Sci. Process. 2009, 94, 131.
[18] J. Rodriguez-Carvajal, Phys. B 1993, 192, 55.
[19] W. Klysubun, P. Sombunchoo, W. Deenan, C. Kongmark, J.
Synchrotron Radiat. 2012, 19, 930.
[20] B. Ravel, M. Newville, J. Synchrotron Radiat. 2005, 12, 537.
[21] L. B. McCusker, R. B. Von Dreele, D. E. Cox, D. Louër, P. Scardi,
J. Appl. Crystallogr. 1999, 32, 36.
ꢀ
under the assumption of collinear Neel model. For the samples
withhighdegreeofinversion(withTa ¼ 500and750 ꢀC), thesedata
can be explained by surface effect on applying of core-shell model.
Meanwhile forthe restsampleswith lowinversionparameter (with
Ta ¼ 900 and 1000ꢀC), the effect is attributed to spin canting.
[22] R. G. Kulkarni, H. H. Joshi, J. Solid State Chem. 1986, 64, 141.
[23] Y. Ichiyanagi, M. Kubota, S. Moritake, Y. Kanazawa, T. Yamada,
T. Uehashi, J. Magn. Magn. Mater. 2007, 310, 2378.
[24] C. Liu, B. Zou, A. J. Rondinone, Z. J. Zhang, J. Am. Chem. Soc. 2000,
122, 6263.
Supporting Information
Supporting Information is available from the Wiley Online Library or from
the author.
[25] S. M. Antao, I. Hassan, J. B. Parise, Am. Mineral. 2005, 90, 219.
[26] H. S. C. O’Neill, A. Navrotsky, Am. Mineral. 1983, 68, 181.
[27] N. K. Thanh, N. P. Duong, D. Q. Hung, T. T. Loan, T. D. Hien,
J. Nanosci. Nanotechnol. 2016, 16, 7949.
[28] P. Hu, H. Yang, D. Pan, H. Wang, J. Tian, S. Zhang, X. Wang,
A. A. Volinsky, J. Magn. Magn. Mater. 2010, 322, 173.
[29] C. M. B. Henderson, J. M. Charnock, D. a Plant, J. Phys. Condens.
Matter 2007, 19, 76214.
Acknowledgement
This research is funded by the Hanoi University of Science and
Technology (HUST) under project number T2016-LN-17.
Conflict of Interest
[30] J. P. Singh, S. O. Won, W. C. Lim, I. J. Lee, K. H. Chae, J. Mol. Struct.
2016, 1108, 444.
The authors declare no conflict of interest.
[31] Z.-Q.Jin,W.Tang,J.-R.Zhang,H.-X.Qin,Y.-W.Du,Eur.Phys.J.B1998,3,41.
[32] T. Sasaki, S. Ohara, T. Naka, J. Vejpravova, V. Sechovsky, M. Umetsu,
S. Takami, B. Jeyadevan, T. Adschiri, J. Supercrit. Fluids 2010, 53, 92.
[33] K. K. Bamzai, G. Kour, B. Kaur, S. D. Kulkarni, J. Magn. Magn. Mater.
2013, 327, 159.
Keywords
cation distributions, magnesium ferrite, magnetic properties, oxidation
state, synchrotron diffractions
[34] P. V. Hendriksen, S. Linderoth, P.-A. Lindgård, J. Magn. Magn. Mater.
1992, 104, 1577.
Received: June 21, 2017
Revised: November 3, 2017
Published online:
[35] L. N. Anh, T. T. Loan, N. P. Duong, S. Soontaranon, T. T. Viet Nga,
T. D. Hien, J. Alloys Compd. 2015, 647, 419.
ꢁ
[36] V. Sepelák, A. Feldhoff, P. Heitjans, F. Krumeich, D. Menzel,
F. J. Litterst, I. Bergmann, K. D. Becker, Chem. Mater. 2006, 18, 3057.
[37] M. A. Gabal, Y. M. Al Angari, S. S. Al-Juaid, J. Alloys Compd. 2010,
492, 411.
[1] W. Tang, Y. Su, Q. Li, S. Gao, J. K. Shang, RSC Adv. 2013, 3, 13961.
[2] V. M. Khot, a. B. Salunkhe, M. R. Phadatare, S. H. Pawar, Mater.
Chem. Phys. 2012, 132, 782.
[3] V. Jeseentharani, M. George, B. Jeyaraj, A. Dayalan, K. S. Nagaraja,
K. S. Nagaraja, J. Exp. Nanosci. 2013, 8, 358.
[4] Z. Y. Kong, N. X. Wong, S. W. Lum, S. Y. Tan, M. R. Khan,
C. K. Cheng, J. Eng. Sci. Technol. 2015, 10, 1.
[5] M. Gateshki, V. Petkov, S. K. Pradhan, T. Vogt, J. Appl. Crystallogr.
2005, 38, 772.
[38] A. Millan, A. Urtizberea, N. J. O. Silva, F. Palacio, V. S. Amaral,
E. Snoeck, V. Serin, J. Magn. Magn. Mater. 2007, 312, L5.
ꢁ
[39] V. Sepelák, D. Baabe, D. Mienert, F. J. Litterst, K. D. Becker, Scr.
Mater. 2003, 48, 961.
ꢁ
[40] V. Sepelák, D. Baabe, F. J. Litterst, K. D. Becker, J. Appl. Phys. 2000,
88, 5884.
[41] C. N. Chinnasamy, A. Narayanasamy, N. Ponpandian, K. Chattopadhyay,
ꢀ
H. Guerault, J.-M. M. Greneche, H. Guerault, J.-M. M. Greneche, J. Phys.
[6] B. D. Cullity, C. D. Graham, Introduction to Magnetic Materials, 2nd.
Wiley-IEEE Press, New Jersey 2009.
Condens. Matter 2000, 12, 7795.
[42] D. Peddis, N. Yaacoub, M. Ferretti, A. Martinelli, G. Piccaluga,
A. Musinu, C. Cannas, G. Navarra, J. M. Greneche, D. Fiorani, J. Phys.
Condens. Matter 2011, 23, 426004.
[7] H. S. C. O’Neill, H. Annersten, D. Virgo, Am. Mineral. 1992, 77, 725.
[8] A. Pradeep, P. Priyadharsini, G. Chandrasekaran, J. Magn. Magn.
Mater. 2008, 320, 2774.
[43] L. M. Corliss, J. M. Hastings, F. G. Brockman, Phys. Rev. 1953, 90,
1013.
[44] E. Wieser, H. Schroder, K. Kleinstuck, Phys. Status Solidi 1970, 1, 749.
[9] B. Aslibeiki, G. Varvaro, D. Peddis, P. Kameli, J. Magn. Magn. Mater.
2017, 422, 7.
[10] C.Murugesan, G. Chandrasekaran,J. Supercond. Nov. Magn.2015, 28, 3607.
Phys. Status Solidi A 2017, 1700397
1700397 (7 of 7)
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