Structure and magnetic phase transitions in (Ni1? xCox)Cr2O4 spinel nanoparticles

Article abstract of DOI:10.1016/j.jmmm.2019.166217

NiCr₂O₄ and CoCr₂O₄ are two distinct members of the chromite family (ACr₂O₄) having unique structural and magnetic properties. This paper is a continuation of previous work [Mohanty et al., J. Magn. Magn. Mater. 451(2018)20] and is focused on the modification of ferrimagnetic properties in NiCr₂O₄ by substituting Co ions at Ni sites. In order to do so (Ni_{1? x}Co_x)Cr₂O₄ (x = 0, 0.50, 0.75, 1.00) powder samples were synthesized using chemical co-precipitation techniques. Interest is primarily on (Ni_0.5Co_0.5)Cr₂O₄ and (Ni_0.25Co_0.75)Cr₂O₄ as characterization results on the end members have been reported. It was determined with in-situ temperature dependent X-ray diffraction measurements that these compositions become fully crystallized cubic spinels with space group Fd3-m above 700 °C. All samples were subsequently calcined at 900 °C to ensure phase purity and uniform crystallinity. Transmission electron microscopy showed non-uniform distribution of particle sizes with the majority of the particles having bi-pyramidal structures with flat tops for both samples. A comparative account of different ferrimagnetic Curie temperature, θ_f or T_C, estimations are presented as determined from measured temperature dependences of the following techniques: Fits of the magnetic susceptibility data indicated a minimum value for the (Ni_0.5Co_0.5)Cr₂O₄ sample at 56.1 ± 0.9 K, followed by an increase to 76.8 ± 0.4 K for the (Ni_0.25Co_0.75)Cr₂O₄ sample; Neutron diffraction measurements gave values of 80 ± 1 K and 87 ± 1 K; Their paramagnetic Curie points, θ_p, were determined to be 73.3 and 84.9 K, respectively. The magnetic frustration index f = Θ_CW/T_C was found to decrease continuously over the series from 11.9 for NiCr₂O₄ to 7.1 and 6.5 for x = 0.5 and 0.75 respectively with (Ni_0.5Co_0.5)Cr₂O₄ being more frustrated than (Ni_0.25Co_0.75)Cr₂O₄. Magnetization as a function of applied magnetic field measured at 3 K demonstrates unusually high coercivity for (Ni_0.5Co_0.5)Cr₂O₄, supporting the notion for the higher degree of magnetic frustration in this sample. No exchange bias was observed for M (μ₀H) in the (Ni_0.25Co_0.75)Cr₂O₄ sample measured at 3 K, but did however show a significant anomaly in its hysteresis loop at this temperature. The anomaly in hysteresis behaviour disappeared when measured at 1.7 K and also at higher temperatures. Frequency dependent ac-susceptibility measurements revealed no shift in the peak position with frequency refuting the existence of spin-glass like behavior in both these samples.

Full text of DOI:10.1016/j.jmmm.2019.166217

JournalofMagnetismandMagneticMaterialsxxx(xxxx)xxxx
Contents lists available at ScienceDirect
Journal of Magnetism and Magnetic Materials
journal homepage: www.elsevier.com/locate/jmmm
Research articles
Structure and magnetic phase transitions in (Ni1−xCox)Cr2O4 spinel
nanoparticles
⁎
P. Mohantya,b, , A.M. Venterc, C.J. Sheppardb, A.R.E. Prinsloob
a Spectrum Analytical Centre, Faculty of Science, University of Johannesburg, PO Box 524, Auckland Park, Johannesburg, South Africa
b Cr Research Group, Department of Physics, University of Johannesburg, PO Box 524, Auckland Park, Johannesburg, South Africa
c Research and Technology Development Division, Necsa SOC Limited, P.O. Box 582, Pretoria 0001, South Africa
A R T I C L E I N F O
A B S T R A C T
Keywords:
NiCr2O4 and CoCr2O4 are two distinct members of the chromite family (ACr2O4) having unique structural and
magnetic properties. This paper is a continuation of previous work [Mohanty et al., J. Magn. Magn. Mater.
451(2018)20] and is focused on the modification of ferrimagnetic properties in NiCr2O4 by substituting Co ions
at Ni sites. In order to do so (Ni1−xCox)Cr2O4 (x = 0, 0.50, 0.75, 1.00) powder samples were synthesized using
chemical co-precipitation techniques. Interest is primarily on (Ni0.5Co0.5)Cr2O4 and (Ni0.25Co0.75)Cr2O4 as
characterization results on the end members have been reported. It was determined with in-situ temperature
dependent X-ray diffraction measurements that these compositions become fully crystallized cubic spinels with
Chromites
Exchange bias
Magnetic frustration
Neutron diffraction
space group Fd m above 700 °C. All samples were subsequently calcined at 900 °C to ensure phase purity and
3
uniform crystallinity. Transmission electron microscopy showed non-uniform distribution of particle sizes with
the majority of the particles having bi-pyramidal structures with flat tops for both samples. A comparative
account of different ferrimagnetic Curie temperature,
or TC, estimations are presented as determined from
f
measured temperature dependences of the following techniques: Fits of the magnetic susceptibility data in-
dicated a minimum value for the (Ni0.5Co0.5)Cr2O4 sample at 56.1
0.9 K, followed by an increase to
76.8
0.4 K for the (Ni0.25Co0.75)Cr2O4 sample; Neutron diffraction measurements gave values of 80
1 K
and 87
1 K; Their paramagnetic Curie points, p, were determined to be 73.3 and 84.9 K, respectively. The
magnetic frustration index f = ΘCW/TC was found to decrease continuously over the series from 11.9 for NiCr2O4
to 7.1 and 6.5 for
x = 0.5 and 0.75 respectively with (Ni0.5Co0.5)Cr2O4 being more frustrated than
(Ni0.25Co0.75)Cr2O4. Magnetization as a function of applied magnetic field measured at 3 K demonstrates unu-
sually high coercivity for (Ni0.5Co0.5)Cr2O4, supporting the notion for the higher degree of magnetic frustration
in this sample. No exchange bias was observed for M (μ0H) in the (Ni0.25Co0.75)Cr2O4 sample measured at 3 K,
but did however show a significant anomaly in its hysteresis loop at this temperature. The anomaly in hysteresis
behaviour disappeared when measured at 1.7 K and also at higher temperatures. Frequency dependent ac-
susceptibility measurements revealed no shift in the peak position with frequency refuting the existence of spin-
glass like behavior in both these samples.
1. Introduction
a collinear antiferromagnetic component appears below 31 K, whereas
in the case of CoCr2O4, a short-range-ordered (SRO) spiral component
NiCr2O4 and CoCr2O4 are ferrimagnetic materials that crystalize
into the normal spinel structure having a general formula ACr2O4 [1,2],
where A refers to the tetrahedral site occupied by the magnetic Ni2+
and Co2+ ions, whilst the Cr ions are found in the octahedral (B) site of
the crystal lattice [1]. The interactions between the magnetic cations
result in a complex magnetic phase diagram at low temperature [2].
NiCr2O4 and CoCr2O4 both have distinct ferrimagnetic Curie tempera-
tures, TC = 74 K [1] and 93 K [3], respectively. In the case of NiCr2O4,
evolves that provides a conical magnetic structure below 24 K [4,5].
The conical spin structure contains a uniform and transverse spiral spin
state that has an incommensurate propagation vector [qq0] with q
0.63 [5] that lead to ferroelectric properties in CoCr2O4 [3]. A further
lock-in-transition appears below 15 K at a slightly smaller q value [6].
Structurally, NiCr2O4 crystallizes as cubic spinel with space group
Fd3m, shown in Fig. 1 at temperatures above 310 K [7]. At temperatures
below 310 K, orbital degeneracy on tetrahedral Ni2+ leads to
⁎ Corresponding author at: Spectrum Analytical Centre, Faculty of Science, University of Johannesburg, PO Box 524, Auckland Park, Johannesburg, South Africa.
E-mail address: pankajm@uj.ac.za (P. Mohanty).
https://doi.org/10.1016/j.jmmm.2019.166217
Received 27 July 2019; Received in revised form 14 October 2019; Accepted 26 November 2019
Availableonline30November2019
0304-8853/©2019ElsevierB.V.Allrightsreserved.
Pleasecitethisarticleas:P.Mohanty,etal.,JournalofMagnetismandMagneticMaterials,https://doi.org/10.1016/j.jmmm.2019.166217

P. Mohanty, et al.
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Fig. 1. Crystal structure of a normal cubic spinel with Fd3m space group, ob-
tained using VESTA software [13]. Tetrahedral A sites are occupied with di-
valent cations and octahedral B sites are occupied with trivalent cations.
Oxygen atoms are shown as red balls at the corners. (For interpretation of the
references to colour in this figure legend, the reader is referred to the web
version of this article.)
cooperative Jahn-Teller distortion that lowers the structural symmetry
from cubic to tetragonal (I41/amd) with elongated NiO4 tetrahedra [7].
Further distortion in the tetragonal structure observed in thermo-
dynamic and magnetization measurements [8,9] and leads to an or-
thorhombic (Fddd) phase at 65 K. The TC is found to increase above
room temperature with Fe substitution at the Cr site indicating the
properties follow the characteristics of CoFe2O4 [10]. However,
CoCr2O4 displays no such structural phase transition associated with
the low temperature magnetic phase transitions [2].
Since Co and Ni have similar ionic radii and oxidation states, it is thus
interesting to study the effect that Co substitution at the Ni site has on
both the crystal structure and magnetic phase transitions. This is done by
experimental measurements of the low temperature magnetic properties
of (Ni1−xCox)Cr2O4 (x = 0, 0.50, 0.75 and 1) along with the a com-
parative study of the estimation of TC values using different approaches.
Fig. 2. In-situ temperature dependent XRD patterns of the (a) (Ni0.5Co0.5)Cr2O4,
(b) (Ni0.25Co0.75)Cr2O4 powders synthesized at pH = 9.8 showing the evolution of
crystal structure. ‘*’ denotes the peak associated with the Cr2O3 impurity phase.
2. Experimental
2.1. Sample preparation
utilizing Cu-Kα radiation (λ = 1.54056 Å). Temperature dependent
XRD studies were carried out in-situ in a non-ambient Anton Parr HTK
1200 Oven-Chamber attachment capable of temperatures from room
temperature to 1200 °C under He or air atmospheres. Data were ac-
quired in a 2θ range of 10° ≤ 2θ ≤ 80°, with a hold time of 10 min
before each measurement carried out under He atmosphere. The in-
strument is equipped with an incident beam hybrid monochromator
that delivers a quasi-parallel X-ray beam to minimize effects associated
with possible sample height deviations during the course of heating. A
JEM-2100 transmission electron microscope (TEM) was employed to
investigate the microstructure of the calcined powders. Magnetic
measurements were performed using a 14T Cryogen Free Physical and
Magnetic Measurement System (CRYOGENIC Ltd., UK) with a vibrating
sample magnetometer (VSM) insert [11], under zero-field cooled (ZFC)
and field cooled (FC) protocols. In the ZFC protocol, the sample was
initially cooled to 2 K where the probing field was applied and the
measurements commenced during the heating cycle. In the FC protocol,
the sample was cooled to 2 K in an applied probing magnetic field and
measurements performed during heating the sample in this field.
Temperature dependent neutron diffraction measurements were carried
(Ni1−xCox)Cr2O4 (x = 0, 0.50, 0.75 and 1) powders were synthe-
sized by chemical co-precipitation techniques. In this technique stock
solutions of 0.5 M of nickel nitrate (Ni(NO3)2·6H2O), cobalt nitrate (Co
(NO3)2·6H2O) and chromium nitrate (Cr(NO3)3·9H2O) were mixed to
the desired amounts in a beaker and stirred continuously for 1 h using a
magnetic stirrer to ensure homogeneous mixing. Diluted aqueous am-
monia (30%) solution was then added to maintain the pH level at 9.8.
The precipitates were filtered, then washed several times – firstly with
distilled water, followed by acetone and then with ethanol to evaporate
the volatile impurities. Finally, the precipitated powders were dried at
100 °C and the conglomerate crushed to a powder. In order to obtain
good crystallinity and crystallographic phase purity the samples were
calcined at 900 °C for 2 h in a tubular furnace at ambient atmosphere.
2.2. Characterization techniques
Structural characterizations of these samples were carried out using
a
Phillips PAN analytical X-pert Pro X-ray diffractometer (XRD)
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out on the PITSI instrument at a wavelength of 1.76 Å and equipped
with a closed cycle cryogenic system, at Necsa, South Africa [12].
3. Results and discussion
Fig. 1 shows the crystal structure of a normal cubic spinel as gen-
erated using the VESTA software [13]. In order to study the phase
formation during calcination, in-situ high temperature powder XRD
measurements were performed on the (Ni1−xCox)Cr2O4 (x = 0.50,
0.75) samples for temperatures between 35 and 1100 °C (Fig. 2). At
35 °C no distinct peaks are observed indicating the amorphous nature of
the starting phases. With increased temperature, crystalline phase for-
mation develops at 500 °C as observed by the appearance of diffraction
peaks corresponding to the major (2 2 0), (3 1 1), (4 0 0), (5 1 1) and
(4 4 0) reflections of the (Ni1−xCox)Cr2O4 phase [4]. The broadness of
the peaks is attributed to the size of the particles [14]. Also, the ap-
pearance of the Cr2O3 phase, indicated with an asterisk (*) in Fig. 2, is
observed in both samples as an intermediate phase. Upon further
heating to 700 °C, the Cr2O3 phase disappeared and the structure re-
mained cubic up to the highest measurement temperature of 1100 °C.
Thus, considering this data confirming the phase formation tempera-
ture, it was decided to calcine the samples at 900 °C to avoid the pre-
sence of any Cr2O3 phase and to retain the nanometric crystallite size.
The preliminary results for these samples were reported in Ref. 15
and compared with both the end products CoCr2O4 and NiCr2O4. Co
and Ni were found to be in 2+ and Cr in 3+ oxidation states, as
confirmed by X-ray photoelectron spectroscopy. Variations of the
coercivity (HC), remanent magnetization (MR), saturation magnetiza-
tion (MS) with compositions x = 0.5 and 0.75 indicated TC values
89.2
0.7 K and 90.6
0.9 K at a probing field of 0.5 T respectively
using a knee-point method. Unusually high coercivity of 3.6
0.7 T
was observed for the x = 0.5 sample.
The present work reports on additional M (T) measurements carried
out with different probing fields to obtain deeper insight into the
magnetic properties and theoretical simulation of the magnetic frus-
tration. To understand the anomalous kink in M (µ0 H) data observed at
3 K, additional measurements were performed using different cooling
fields and temperatures. Possible spin-glass like behaviour was probed
utilizing frequency dependent ac-susceptibility measurements.
Furthermore, low temperature neutron diffraction measurements were
carried out to unambiguously locate the TC’s.
Fig. 3 (a) and (b) show XRD data at 300 K, as well as Rietveld re-
finement simulations for the (Ni1−xCox)Cr2O4, x = 0.50, 0.75, samples
calcined at 900 °C. For comparison, result from the CoCr2O4 sample is
shown in Fig. 3 (c). The structural parameters obtained from the Riet-
veld refinement process are given in Table 1. This indicates that all
three samples crystallize in the Fd m cubic phase in contrast to the
3
known tetragonal phase of NiCr2O4 [15] at 300 K. It is obvious that the
substitution of Ni by Co on the Ni site stabilizes the formation of the
cubic structure [15]. This in addition leads to an expansion in the lattice
parameters from 8.322 Å to 8.326 Å for x = 0.5 to x = 0.75 Co, re-
spectively, that is attributed to the larger ionic radius of Co compared to
the Ni ion [15]. On the diffraction patterns of Fig. 3 this is observed by
slight shifts in the Bragg peak positions towards lower 2θ values, as was
reported earlier [15]. It is known that stress in bulk samples also in-
fluences the peak positions, but such macro stresses cannot be sustained
in powders and thus not a contributing factor. The average crystallite
size determined using Scherer’s formula is about 45(2) nm for x = 0.5
and about 50 (1) nm for x = 0.75.
In Fig. 4 TEM micrographs of (Ni1−xCox)Cr2O4, with x = 0.50 (a)
and 0.75 (b) samples calcined at 900 °C, are given. It is clear that both
the samples have non-uniform particle shapes and sizes. Particle size
histogram analyses shown in Fig. 5 indicate that the average particle
Fig. 3. Rietveld refinement of XRD patterns of the (a) (Ni0.5Co0.5)Cr2O4 and (b)
(Ni0.25Co0.75)Cr2O4 and (c) CoCr2O4 powders synthesized at pH ~ 9.8 and
calcined at 900 °C for 3 h. Measured data are indicated with the open symbols
with Rietveld refinements indicated with red solid lines. The plots in blue show
the difference curves between measured and refined data. (For interpretation of
the references to colour in this figure legend, the reader is referred to the web
version of this article.)
size initially increase from 72
maximum of 115
5 nm for the x = 0 sample, to a
4 nm for x = 0.5, where after it decreased to
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Table 1
Structural parameters obtained from Reitveld refinement of (Ni0.5Co0.5)Cr2O4, (Ni0.25Co0.75)Cr2O4 and CoCr2O4.
(Ni0.5Co0.5)Cr2O4
(Ni0.25Co0.75)Cr2O4
CoCr2O4
Refined Parameters (Structure Cubic, Space Group: Fd m)
3
a, b, c [Å]
χ2
8.322
8.326
8.326
1.08
1.76
1.39
Bragg R-factor
RF-factor
Ni (x, y, z)
Co (x, y, z)
Cr (x, y, z)
O (x, y, z)
1.75
1.83
2.65
2.49
2.52
3.92
(0.125, 0.125, 0.125)
(0.125, 0.125, 0.125)
(0.5, 0.5, 0.5)
(0.26, 0.26, 0.26)
(0.125, 0.125, 0.125)
(0.125, 0.125, 0.125)
(0.5, 0.5, 0.5)
–
(0.125,0.125,0.125)
(0.5,0.5,0.5)
(0.26035, 0.26035, 0.26035)
(0.25979, 0.25979, 0.25979)
Fig. 4. Transmission electron microscopy (TEM) images of (a) (Ni0.5Co0.5)Cr2O4 and (b) (Ni0.25Co0.75)Cr2O4 (Insets show the enlarged view of a single particle). High
resolution electron microscopy images of (c) (Ni0.5Co0.5)Cr2O4 and (d) (Ni0.25Co0.75)Cr2O4 (Insets show the selected area electron diffraction (SAED) patterns). Note:
Relevant scales are given by the bar lengths).
91
4 nm for x = 0.75, and 52
1 nm for x = 1. The average
x = 0.75 which are larger than the expected values. This may be related
to a possible lattice expansion observed in nanoparticles [18].
The temperature dependence of the magnetization, M (T), and ap-
plied magnetic field, M (µ0 H), were carried out in zero field cooled
particle sizes are in line with the values obtained by taking the mean
diameter of the particles [15]. These values are larger than the average
crystallite sizes calculated from the XRD, indicating polycrystalline
nature of the particles [16]. The insets of Fig. 4 (a) and (b) show
zoomed TEM views of isolated particles for each composition, in-
dicating similar morphologies and bi-pyramidal shapes with the tips of
the bi-pyramid being flat rather than sharp. This was previously re-
ported in NiCr2O4, as a characteristic structure for spinel compounds
[17] and is maintained on substituting Ni with Co in the lattice. The
(
MZFC) and field cooled (MZFC) conditions by applying probing magnetic
fields of magnitudes 0.1, 0.5, 1 and 2 T, respectively. M (T) data using
only 0.5 T probing field were previously reported [15]. MZFC and MFC
investigations were done as described in the experimental section. After
each measurement run of zero-field cooled (ZFC) and field cooled (FC)
experiments, the samples were heated to 300 K to ensure that the
sample regained the paramagnetic phase. Results are shown in Fig. 6 (a)
and (b) for (Ni0.5Co0.5)Cr2O4 and (Ni0.25Co0.75)Cr2O4 samples, respec-
tively, for the different probing magnetic fields indicated. In all mea-
surements MFC (T) does not follow the MZFC (T), indicating prominent
irreversibility at low temperatures. This is due to the magnetic frus-
tration typically observed in these chromite systems [19,20] as dis-
cussed in the next paragraphs. MZFC (T) curves show a hump at low
temperatures for the (Ni0.5Co0.5)Cr2O4 sample (Fig. 6 (a)), whereas
MFC (T) shows significant broadening of the hump and its expansion at
low temperatures. In the case of the (Ni0.25Co0.75)Cr2O4 sample, the
highly
crystalline
nature
of
the
(Ni0.5Co0.5)Cr2O4
and
(Ni0.25Co0.75)Cr2O4 particles is demonstrated by the distinct lattice
fringes observed in the high resolution transmission electron micro-
scopy (HRTEM) images shown in Fig. 4 (c) and (d), respectively. The
spotty ring patterns related to the (4 4 0), (4 4 4) and (6 4 2) planes
observed from the selected area electron diffraction (SAED: Insets)
images confirm the high level of crystallinity of the nanoparticles, in
correlation with the XRD results (Fig. 3) and the parameters shown in
Table 1. Determination of the d-spacing related to the (1 1 1) plane
from the lattice fringes gives 5.39 Å for x = 0.5 and 5. 53 Å for
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Fig. 5
Fig. 5. Particle size histograms obtained from the TEM images for (a) NiCr2O4, (b) (Ni0.5Co0.5)Cr2O4, (c) (Ni0.25Co0.75)Cr2O4 and (d) CoCr2O4. XC represents the
average particle sizes.
hump in magnetization is significant in both the MZFC (T)and MFC (T)
curves (Fig. 6 (b)). The MFC (T) behaviour also shows an increase in the
value of the magnetization at low temperatures (Fig. 6 (b)). For both
the samples, the slopes near TC in MZFC (T) and MFC (T) increases to-
wards higher temperature with increasing probing field strength. Si-
milar shifting of slopes towards higher temperature with increasing
field was also reported previously for the case of Fe doped CoCr2O4
[20]. The bifurcation in MZFC (T) and MFC (T) curves, represented by the
frustrated nature of the nanoparticles [19]. To demonstrate thispoint,
M = |MZFC MFC
|
as a function of temperature plots are shown in
Fig. 8 for the x = 0.5 and x = 0.75 samples at the different probing
magnetic fields. Overall, M decreases with increasing probing field up
to 2 T, except for the x = 0.5 sample where the difference at low
temperature exceeds that measured at 0.1 T (Fig. 8 (a) and (b)). For the
x = 0.75 sample (Fig. 6 (b)) the spiral ordering and lock-in-transitions,
at temperatures of approximately 26 K and 6.5 K, respectively, become
more prominent compared to the x = 0.5 sample (Fig. 6 (a)). The
MZFC (T) for (Ni0.25Co0.75)Cr2O4 shows negative magnetization values
when measured under a probing field of 0.5 T (Fig. 6 (b)). This type of
behaviour in ferrimagnets is often ascribed to the change in the direc-
tion of the magnetization in the ferromagnetic component at the com-
pensation temperature [15,21,22]. In the case of spinel compounds
having A and B sublattices with different magnetizations associated
with their crystallographic sites, the resultant magnetization changes
sign at a temperature known as the compensation temperature [21,22].
The negative magnetization in these systems mostly arises due to the
presence of uncompensated spins [22–24]. The dM/dT for the NiCr2O4
and CoCr2O4 samples are shown in Fig. 7 (c) with the characteristic
transitions labeled.
difference in these curves, is higher for the
2 T field in the
(Ni0.5Co0.5)Cr2O4 sample when compared with the (Ni0.25Co0.75)Cr2O4
sample, suggesting an increase in the frustration in the former [19,20].
Further, considering the ZFC data, dM/dT as a function of temperature
plots are shown in Fig. 7 to facilitate in the determination of the
magnetic transitions. For the (Ni0.5Co0.5)Cr2O4 sample two transitions,
labeled as T1 and T2 corresponding to temperatures 20 and 32 K, re-
spectively below TC (Fig. 7 (a)) are observed which become more
prominent with increased field. Here T2 possibly corresponds to the
ordering of the antiferromagnetic component as seen in NiCr2O4 [4].
However, the origin of the transition at 20 K related to T1 is not clear.
Retention of bifurcation in MZFC (T) and MFC (T) up to a 2 T applied
field at low temperatures seen in Fig. 6 is usually associated with the
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Fig. 6. Temperature-dependent magnetization under zero field cooled (ZFC)
and field cooled (FC) protocols for the (a) (Ni0.5Co0.5)Cr2O4 and (b)
(Ni0.25Co0.75)Cr2O4 samples with different probing fields.
For a standard ferrimagnetic material, the theoretical variation of
reciprocal susceptibility with temperature in the paramagnetic region is
expressed as [25]:
T
C
1
b
1
=
+
T
(1)
are
0
1
where T is the temperature, C is the Curie constant, b , and
constants. The above equation represents a hyperbola containi0ng a
Curie-Weiss (ferrimagnetic) term and a Curie (paramagnetic) term [25].
The significance of the paramagnetic term is associated with the non-
saturation behaviour as demonstrated by certain chromites [20]. As the
studied materials are ferrimagnetic, equation (1) is used to fit the re-
ciprocal susceptibility as a function of temperature, as shown in Fig. 9.
The high temperature (paramagnetic) experimental data is well fit with
the equation with a deviation occurring near the Curie temperature.
Similar results have previously been reported where there is dis-
crepancy between experimental and theoretical fitting results [25]. The
fitting parameters are summarized in Table 2. By linear extrapolation of
the experimental data points below this Curie temperature to zero
susceptibility, the intercept with the temperature axis gives the tem-
Fig.7. dM/dT as a function of temperature measured under ZFC conditions for
(a) (Ni0.5Co0.5)Cr2O4, (b) (Ni0.25Co0.75)Cr2O4, and (c) NiCr2O4 and CoCr2O4.
Legends depict the probing fields.
susceptibility diverges at temperatures lower than this point due to the
appearance of spontaneous magnetization. The values of
for
0.9 K and
0.4 K respectively. The data fitted with equation (1) intersects
f
(Ni0.5Co0.5)Cr2O4 and (Ni0.25Co0.75)Cr2O4 are 56.2
76.8
perature
(or TC) called the ferrimagnetic Curie point (TC) [25]. The
f
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C
=
T + (C/
)
(2)
0
where C is the Curie constant, T is the temperature and
is a constant
[25]. Equation (2) represents a straight line, to which (1/0χ) as function
of T curves becomes asymptotic at high temperatures. There is a dis-
agreement between theoretical and experimental values for TC and this
is due to the short-range spin order (in the spin clusters) at temperature
[27]. The fitting parameters using equation (1) and the estimated
vfalues of the frustration index f = CW/T are calculated and listed in
C
Table 2 [28]. The frustration parameter f is highest for the NiCr2O4 and
decreases with Co substitution at the Ni site from 7.1 to 6.5 with in-
creasing x from 0.5 to 0.75, indicating that the Co addition stabilized
the structure, with CoCr2O4 having the least frustration index f. The
large value of f for NiCr2O4 possibly implies the occurrence of structural
changes at the onset of the magnetic transitions.
It has been reported that for CoCr2O4 nanoparticles with average
size ranging from 8 to 10 nm, the TC remains unaffected by reducing the
particle size to nano-scale range, or having a non-uniform distribution
of particles [19]. However, in similar spinel structures such as MnFe2O4
nanoparticle ferrites, a significant increase in TC has been reported
compared to the bulk value when the particle size is reduced to nano-
scale range (7.5–24.5 nm) [29,30]. The shift in Curie temperature was
described by a finite size scaling formula [TC(d) − TC( )]/TC( ) = (d/
d0)−1/ν [31]. Here, d is the size of the nanoparticles, TC( ) is the TC
related to the bulk value, d0 = 2.0 nm and ν = 0.71
0.071 [31].
However, the present work does not allow for the estimation of the
exponent values since the size dependence of TC is not known for the
material [32]. It is further noted that two different compositions having
different particle sizes are not comparable. In addition, an important
aspect to take note of is the average particle size. The scaling law is
valid for the sizes ranging from 7.5 to 24.4 nm in the case of MnFe2O4
[31]. However, in our case, the average particle size ranges from 50 to
102 nm. In the case of CoCr2O4 nanoparticels particle size had no de-
pendence on TC [19,32]. On the other hand Dutta et al. [22] reported
the reduction of TC from 98 to 84 K when the particles were reduced to
nanoscale (30–40 nm), contradicting the scaling feature reported by
Tanng et al. [31]. From the above findings it can be concluded that the
TC of these nanoparticles are evidently dependent on the particle size,
but the relation is difficult to predict.
M = |MFC MZFC
|
plots as
Fig. 8.
a function of temperature for (a)
(Ni0.5Co0.5)Cr2O4 and (b) (Ni0.25Co0.75)Cr2O4.
In order to investigate the magnetic behaviour further, magnetiza-
tion, M, as a function of applied magnetic field, B = μ0H, measurements
were done at different constant temperatures for both ZFC and FC
conditions. The results of these studies are shown in Fig. 10 and Fig. 11.
The M (µ0 H) loop for (Ni0.5Co0.5)Cr2O4 shifts towards larger negative
values when measured under FC conditions with fields of 0.1 T and
0.5 T (Fig. 10 (a)), indicating the presence of exchange bias effects in
the system. The coercivity is found to be 3.6 T for the (Ni0.5Co0.5)Cr2O4
sample, which is higher compared to the conventional ferrimagnetic
materials [25]. In addition careful observation of the magnetization
indicated an anomalous change in the slope of the curve at about 5 T.
For clarity, a zoomed view is shown as Fig. 10 (b) within the low field
region. In the positive quadrant the behaviour of the magnetization for
the sample’s hysteresis loops measured at 3 K is found to be mostly
independent of the cooling field, but on the negative quadrant the
magnetization values shifts more when the sample is cooled under 0.5 T
field than compared to cooling in a 0.1 T field (Fig. 10 (b)). Upon in-
creasing the temperature to 56 K the exchange bias effect disappears
(Fig. 10 (c)). For both the measurements taken at 3 K and 56 K, the
magnetization is not saturated in an applied field of 12 T. Hence, the
true nature of the observed exchange bias is disputed [15]. The fact that
the M (µ0 H) does not saturate is an indication of the non-collinear
magnetic structure of these compounds and similar results have been
the temperature axis at p, which is called the paramagnetic Curie
point. The values of
found for (Ni0.5Co0.5)Cr2O4 and (Ni0.25Co0.75)
p
Cr2O4 are 73.3 and 84.9 K, respectively, (Fig. 9). The appearance of two
Curie temperatures which are not identical, termed as
and f , re-
spectively representing paramagnetic and ferrimagneticp Curie tem-
peratures is commonly observed in ferrimagnetic compounds [25]. The
temperature difference between
and
indicates that the ferrimag-
p
f
netic to paramagnetic phase transition is not strongly defined, but
smeared out, which is in line with the reported results for ferrimagnets
[25]. The smeared or diffused nature, of the transition is due to the
presence of spin clusters in the material [25]. These spin clusters are
small group of atoms having parallel spins over a small temperature
regime above p, giving rise to a short-range order. This temporal spin
order disappears with increasing temperature above p. Below a long
f
range order of spin persists even in the absence of external magnetic
field [25]. A careful analysis of the fits, as shown in Fig. 9, indicates that
the data for (Ni0.25Co0.75)Cr2O4 fits well to the equation when com-
pared to that of the other sample. It affirms the previous notion that the
(Ni0.5Co0.5)Cr2O4 is magnetically more frustrated at low temperatures,
which subsequently leads to the deviation from the expected theoretical
values [26]. At high temperatures the last term of equation (1) becomes
negligible and the equation reduces to a Curie-Weiss law [26]:
7

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Fig. 9. Reciprocal susceptibility as a function of temperature for (a) NiCr2O4, (b) (Ni0.5Co0.5)Cr2O4, (c) (Ni0.25Co0.75)Cr2O4 and (d) CoCr2O4 measured under a
probing field of 0.5 T. The solid line in the figure refers to equation (1) given in the text.
Table 2
Results from the fitting the inverse magnetic susceptibility data to the Curie-Weiss equation for the Ni1−xCoxCr2O4 samples.
Ni1−xCoxCr2O4 (x = 0, 0.50, 0.75, 1)
Fitting Parameters
ΘCW
f or TC
f = CW/T
p
c
1/χ0
b
θ
C
x = 0
167
140
160
175
2120
2540
4180
4800
55
55
59
68
69
−786 K
−399 K
−502 K
−520 K
67.5 K
73.3 K
84.9 K
95.6 K
65.6
56.1
76.8
93.7
0.5 K
0.9 K
0.4 K
0.5 K
11.9
7.1
x = 0.50
x = 0.75
x = 1
75
80
6.5
105
5.5
reported in Mn doped CoCr2O4 [28]. It was suggested [33] that the
linear increase in magnetization was the result of the distortion of the
lattice during the structural transition and suppression of ferromagnetic
interactions induced by Mn ions that created an increased frustration in
the system [33]. Though, in MnCr2S4 single crystals similar behaviour is
regarded as the coexistence of a ferrimagnetic and quasi-paramagnetic
contribution arising only because of the nonlinear spin structure of B
site Cr3+ ions [34]. For the (Ni0.25Co0.75)Cr2O4 sample, the M (µ0 H)
loop measured at 1.7 K does not show a kink (Fig. 11 (a)). The coer-
civity is found to be 2.2 T. However, the hysteresis loop measured at 3 K
shows an anomaly similar to the (Ni0.5Co0.5)Cr2O4 sample at an applied
magnetic field of about 2.3 T (Fig. 11 (c): zoomed in view of Fig. 11 (b))
both measured under ZFC and FC protocols. The anomaly suggests the
moments comprise of soft and hard magnetic components where the
soft component does not couple strongly to the hard-magnetic compo-
nent to cause a change in slope in the hysteresis loop [35]. Similar kinks
in the hysteresis loop are mostly observed in multilayered thin films due
to exchange-decoupling [36]. The hysteresis loop measured at a cooling
field of 0.5 T almost mimics the ZFC curve (Fig. 11 (c)). Similar
anomalies in M (µ0 H) plots were observed for manganite bilayers of
collinear ferromagnetic La0.7Sr0.3MnO4 and non-collinear multiferroic
TbMnO3 [34]. In that case the pronounced exchange bias and the en-
hancement of coercivity in the bilayer was because of the existence of
strong interfacial exchange coupling which is a consequence of the
presence of uncompensated spins at the interface between the anti-
ferromagnetic TbMnO3 and ferromagnetic La0.7Sr0.3MnO4 [37]. In the
present case the surface spins at the grain boundaries almost act like
different layers and the modification in the sub-lattice magnetization
8

P. Mohanty, et al.
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because of cationic substitution leads to an exchange bias as well as a
kink in the temperature dependent M (µ0 H) loop. However, this beha-
viour is only observed at 3 K and not in M (µ0 H) measured at tem-
peratures higher than 20 K, 40 and 70 K for (Ni0.25Co0.75)Cr2O4 sample
(Fig. 11 (d-e)) where no exchange bias is observed. The true nature of
exchange-bias in these systems is hard to claim because of the un-
saturated hysteresis loops, even seen up to a field of 12 T [15].
Neutron diffraction measurements were done to directly observe the
magnetic ordering for the determination of the phase transition and
lock-in temperatures, as well as the crystallographic structures at low
temperatures. In NiCr2O4 magnetic transitions are associated with
structural transitions [7]. The magnetic order is composed of a ferro-
magnetic component with a transition temperature of 74 K that man-
ifests at the (1 1 1) fundamental reflection, with the manifestation of
superlattice reflections below 31 K that are associated with anti-
ferromagnetic ordering observed as peaks at the (1 1 0) and (2 0 1)
positions [1]. This transition is related to additional lattice distortion in
the same space group that was confirmed with high-resolution syn-
chrotron based XRD measurements that obtained T = 30 K [7]. It was
found [5] that the magnetism in CoCr2O4 single crystals orders as a
combined ferrimagnetic spiral below TC = 93 K with the magnetic peak
manifesting at the (1 1 1) nuclear position. The presence of the ferro-
magnetic component for all temperatures below TC implies that it has
long-range order whilst the spiral component exhibits short-range order
(no major coherent magnetic contribution). The latter component
though transforms into long-range incommensurate order with propa-
gation vector (0.63, 0.63, 0) below approximately 24 K that was ob-
served as satellite reflections to (2 2 0) and (2 0 0). With further cooling
this magnetic order becomes commensurate below 15 K with a propa-
gation vector of (0.675, 0.675, 0) [38]. The stability of the cubic phase
of CoCr2O4 has been confirmed down to 11 K [7].
In Fig. 12, the results of the neutron diffraction measurements down
to about 4.2 K are shown for all the samples used in this study. These
figures show only the region where the dominant magnetic reflections
were observed using a wavelength of 1.76 Å. Fig. 12(a) summarizes the
temperature dependence of the diffraction patterns of NiCr2O4 with the
magnetic contributions associated with ferromagnetic ordering being
superimposed on the (1 1 1) nuclear reflection. The structural (2 2 0)
peak observed at 300 K systematically converts into (2 0 2) with de-
creasing temperature, indicating a structural change. The results are in
qualitative agreement with [1]. No evidence of the lower temperature
transition is though observed. The other graphs of Fig. 12 indicate that
with Co substitution the tetragonal crystal structure converts to an
Fd3m cubic structure for x ≥ 0.5. The ferromagnetic features are ob-
served superimposed on the (1 1 1) nuclear reflection. In order to es-
timate the TC values, the integrated intensities of the (1 1 1) peak as a
function of temperature are shown in Fig. 13 for all the samples. The
magnetization results were analyzed and correlated using the in-
tegrated intensities from the temperature dependent neutron diffraction
results for the (Ni0.5Co0.5)Cr2O4 and (Ni0.25Co0.75)Cr2O4 samples of
80
1 K and 87
1 K, respectively [Fig. 13].
Ferrimagnetic Curie temperature TC, spiral ordering temperature TS
and lock-in transition TL were determined from the magnetization
measurements [Fig. 6 (b)] for (Ni0.25Co0.75)Cr2O4 samples using dif-
ferent probing fields. Temperature dependence plots of the neutron
diffraction intensities related to the (1 1 1) peaks, [Fig. 13 (c)] show
anomalous behaviours below 30 K with Co addition which are attrib-
uted to TS. This anomaly is most prominent in CoCr2O4. In addition
careful observation of the (2 0 1) satellite peak, shown in Fig. 12 (c) for
sample (Ni0.25Co0.75)Cr2O4, starts to manifest below 24 K. This also
supports the claim for the TS. The (2 0 1) satellite intensities become
more prominent with Co content and is most prevalent in the CoCr2O4
compound, corroborating the transition related to TS [Fig. 12 (d)]. The
Fig. 10. Magnetic field dependent magnetization measurement, M (µ0 H), for
(Ni0.5Co0.5)Cr2O4 sample measured under zero field cooled (ZFC) and field
cooled (FC) protocols at (a) 3 K, (b) 3 K (zoomed in view) and (c) 56 K.
9

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Fig. 11. Magnetic field dependent magnetization measurements, M (µ H), for (Ni0.25Co0.75)Cr2O4 sample measured under zero field cooled (ZFC) and field cooled
(FC) protocols at (a) 1.7 K and (b) 3 K, (c) 3 K (zoomed in view), (d)020 K and (e) 40 K. Inset on latter shows the ZFC and FC magnetization at 70 K.
appearance of TS critically depends on the average particle size since
Ptak et al. [32] observed the incommensurate spiral magnetic structure
below TS = 24 K in particles with mean size of 23 nm, whereas the TS
was not prominent for the particles with average size 4.5 nm. Rath et al.
[19] observed TS = 23 K for the nanoparticles with average size
ranging from 8 to 12 nm. Dutta et al. [22] reported TS = 25 K for
nanoparticles with size ranging from 30 to 40 nm claiming that the
wavelength of the incommensurate magnetic structure is at least ten
times that of the chemical unit cell that would be longer than ~10 nm
for the CoCr2O4. Below this size, spiral ordering would not be possible.
10

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Fig. 12. Neutron diffraction patterns as function at fixed temperatures for the samples (a) NiCr2O4, (b) (Ni0.5Co0.5)Cr2O4, (c) (Ni0.25Co0.75)Cr2O4 and (d) CoCr2O4
within a selected 2θ range.
Hence, in the present case the transitions are evident both from the M
(T) and the temperature dependent neutron diffraction measurements.
The anomalies related to TS are indicated in the Fig. 13. A zoomed view
for the Fig. 13 (b) and (c) are shown as insets for clarity. Superlattice
peaks associated with the spiral component manifest at the (2 2 0)-sa-
tellite position for temperatures lower than 25 K and becomes more
prominent with increased Co substitution [5,38,39] suggesting the
onset of a larger magnetic moment as shown in Fig. 12.
However, for (Ni0.5Co0.5)Cr2O4 the peak splits into a doublet with
increasing frequency, whereas the peak for (Ni0.25Co0.75)Cr2O4 is
sharp compared to the previous (Fig. 14 (b)). The broader peak shape
of (Ni0.5Co0.5)Cr2O4 suggests a higher degree of frustration for this
sample, as calculated from the frustration index. Magnetization mea-
surements of CoCr2O4 nanoparticles with sizes ranging from 8 to
12 nm at a probing magnetic field of 10 Oe revealed that the TS was
absent [19]. However, an anomaly related to TS appeared when M(T)
was measured with an increased probing field of 500 Oe [19]. In ac-
susceptibility measurements with different frequencies and probing
field of 3 Oe the TS feature was absent in the real part of the ac-sus-
ceptibility [19]. From this it can be inferred that the transition related
to TS is sensitive to the probing field.
The TC values obtained by the M (T) (using knee-point method)
measurements [15], dM/dT, estimation of θf using equation (1), and
neutron diffraction results are collectively listed in Table 3. It is clear
that the estimated TC values for M (T) data using the knee-point method
overestimated the temperatures. The data obtained by neutron dif-
fractions are most acceptable as there is no external perturbing para-
meter influence, such as magnetic field.
4. Conclusions
In order to understand the spin-dynamics of the system, frequency
dependent ac-susceptibility measurements were performed for the
(Ni0.5Co0.5)Cr2O4 and (Ni0.25Co0.75)Cr2O4 samples as shown in Fig. 14.
The real part of the ac-susceptibility showed a cusp for both the
samples with significant dispersion with frequency, suggesting mag-
netic frustration in the system as predicted [35]. For spin-glass sys-
tems the peak of the ac-susceptibility shifts to lower temperature with
an increase in frequency [40]. In the current study the peak of the ac-
susceptibility did not shift with increased frequency (Fig. 10).
(Ni0.5Co0.5)Cr2O4 and (Ni0.25Co0.75)Cr2O4 powder samples were
synthesized using chemical co-precipitation techniques. The as-synthe-
sized samples were amorphous in nature. From in-situ temperature de-
pendent XRD measurements it was observed that the cubic phase had
fully crystalized around 700 °C with no further change in crystal-
lographic structure observed upon heating to 1100 °C. Samples calcined
at 900 °C were subsequently used for microstructural and magnetic
studies. TEM analyses showed non-uniform particle size distribution with
11

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Fig. 13. Integrated neutron intensities of (1 1 1) peak as a function of temperature for (a) NiCr2O4, (b) (Ni0.5Co0.5)Cr2O4, (c) (Ni0.25Co0.75)Cr2O4 and (d) CoCr2O4.
Insets (b) and (c) show the zoomed view of the low temperature data. The TC values were obtained using “knee-point method” similar to the results obtained for M (T)
data. The solid lines in the figure are guide to eyes.
Table 3
Comparison of TC values obtained using different methods.
Ni1−xCoxCr2O4 (x = 0, 0.50,
From M(T) data using the knee-point
From dM/dT versus T curves minimum point θf [25]
From integrated intensities using
neutron diffraction data
0.75, 1)
method Ref [15]
for 0.5 T probing field
x = 0
82.4
89.2
90.6
99.5
0.8 K
0.7 K
0.9 K
0.5 K
69.9
66.9
81.3
95.2
2 K
65.6
56.1
76.8
93.7
0.5 K 76
1 K
1 K
1 K
1 K
x = 0.50
x = 0.75
x = 1
0.5 K
0.1 K
0.2 K
0.9 K 80
0.4 K 87
0.5 K 95
particles having mostly bi-pyramidal structure with flat tops. MZFC (T)
utilizing other standard methods and found to be lower than the values
obtained from the knee-point method applied to M(T) data, whilst higher
than the results found from the dM/dT or f . The anomaly in tempera-
ture dependent hysteresis loops indicate that cationic substitution leads
to changes in magnetic exchange interactions. Frequency dependent ac-
susceptibility measurements refute the possibility of spin-glass like fea-
tures in these systems. These features are totally unique compared to
both the NiCr2O4 and CoCr2O4 samples. Hence, the magnetic properties
can be substantially modified by cationic substitution.
and MFC (T) measurements at low temperature showed significant irre-
versibility at low temperatures with the degree of irreversibility being
larger for (Ni0.5Co0.5)Cr2O4 compared to (Ni0.25Co0.75)Cr2O4, indicating
larger frustration. From fits of the susceptibility as a function of tem-
perature data the ferrimagnetic Curie temperature,
or TC of these
f
samples were found to be 56.2
0.9 and 76.8
0.4 K, respectively.
The paramagnetic Curie points were calculated to be 73.3 and 84.9 K,
p
respectively. The frustration index f = CW/T decreased from 7.1 to 6.5
C
with increasing
x from 0.5 to 0.75 that supports the claim of
As an extension of this study, film samples of these compositions
will be grown on single crystal substrates to further explore the prop-
erties dependent on composition and directional nature.
(Ni0.5Co0.5)Cr2O4 is magnetically more frustrated. The TC values ob-
tained using neutron diffraction data are compared with those obtained
12

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Appendix A. Supplementary data
Supplementary data to this article can be found online at https://
doi.org/10.1016/j.jmmm.2019.166217.
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Authors acknowledge the financial support from the South African
National Research Foundation (Grant No’s: 80928, 93551 and 88080)
and the UJ URC (Grant No: 282810) and UJ FRC (Grant No: 083135) of
University of Johannesburg (UJ), South Africa. PM acknowledges Dr.
W. Oldewage, University of Johannesburg for inspiration and support.
Authors thank the UJ Spectrum for the characterization facilities. Necsa
SOC Ltd. is acknowledged for facility access and assistance with the
neutron diffraction investigations.
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13