Spin glass and exchange bias behavior in magnetically frustrated Ni1?xMgxCr2O4 (x = 0.0–0.50)

Article abstract of DOI:10.1016/j.jmmm.2020.166550

Single-phase polycrystalline samples of Ni_1?xMg_xCr₂O₄ (x = 0.0–0.50) were prepared by sol gel route and their structural and magnetic properties were studied. Structural transformation from tetragonal (I4₁/amd) to cubic (Fd3-m) phase is observed at room temperature due to Mg substitution. Mg substitution gives rise to reduction in ferrimagnetic and antiferromagnetic transition temperatures along with a signature of spin glass like phase in samples of intermediate compositions, i.e., for x = 0.10, 0.20 and 0.30. The observed stretched exponential type relaxation of thermoremanent magnetization and the highly frustrated magnetic behavior confirm the glassy magnetic phase. Significant increase in exchange bias field under field cooled condition for the Mg substituted samples is observed. The origin of exchange bias in theses samples is explained by considering exchange anisotropy between the ferrimagnetic and antiferromagnetic components of canted spin. The training effect of exchange bias field is also observed.

Full text of DOI:10.1016/j.jmmm.2020.166550

Journal Pre-proofs
Spin glass and exchange bias behavior in magnetically frustrated Ni1-
Mg Cr O (x = 0.0 - 0.50)
x
x
2
4
Ritupan Borah, S. Ravi
PII:
S0304-8853(19)33474-2
DOI:
https://doi.org/10.1016/j.jmmm.2020.166550
MAGMA 166550
Reference:
To appear in:
Journal of Magnetism and Magnetic Materials
Received Date:
Revised Date:
Accepted Date:
11 October 2019
7 January 2020
1 February 2020
Please cite this article as: R. Borah, S. Ravi, Spin glass and exchange bias behavior in magnetically frustrated Ni1-
Mg Cr O (x = 0.0 - 0.50), Journal of Magnetism and Magnetic Materials (2020), doi: https://doi.org/10.1016/
x
x
2
4
j.jmmm.2020.166550
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover
page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will
undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing
this version to give early visibility of the article. Please note that, during the production process, errors may be
discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
©
2020 Published by Elsevier B.V.

1
Spin glass and exchange bias behavior in magnetically frustrated
2
3
Ni Mg Cr O (x = 0.0 - 0.50)
1
-x
x
2
4
Ritupan Borah and S. Ravi*
4
5
6
Department of Physics, Indian Institute of Technology Guwahati, Guwahati-781039, India.
7
8
9
0
1
2
3
4
5
6
7
8
Abstract: Single-phase polycrystalline samples of Ni Mg Cr O (x = 0.0 - 0.50) were prepared
1
-x
x
2
4
by sol gel route and their structural and magnetic properties were studied. Structural
transformation from tetragonal (퐼4 /푎푚푑) to cubic (퐹푑3푚) phase is observed at room
1
1
1
1
1
1
1
1
1
1
temperature due to Mg substitution. Mg substitution gives rise to reduction in ferrimagnetic and
antiferromagnetic transition temperatures along with a signature of spin glass like phase in
samples of intermediate compositions, i.e., for x = 0.10, 0.20 and 0.30. The observed stretched
exponential type relaxation of thermoremanent magnetization and the highly frustrated
magnetic behavior confirm the glassy magnetic phase. Significant increase in exchange bias
field under field cooled condition for the Mg substituted samples is observed. The origin of
exchange bias in theses samples is explained by considering exchange anisotropy between the
ferrimagnetic and antiferromagnetic components of canted spin. The training effect of exchange
bias field is also observed.
1
2
2
2
2
2
2
2
9
0
1
2
3
4
5
6
Keywords: Spinel chromite; frustrated magnetism; spin glass; exchange bias.
*Corresponding author.
E-mail: sravi@iitg.ac.in (S. Ravi)
1

1
Introduction:
Frustration in a magnetic system can leads to unique state of magnetic phases [1, 2]. It is
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
interesting to study such magnetic system as it is difficult to predict their behavior. Magneto-
elastic coupling and spin disorder are the two most important phenomena that can take place in a
frustrated magnet [3]. If the frustration is strongly connected to atomic lattice, magneto-elastic
coupling occurs in order to remove the ground state degeneracy [4]. Chromium based spinels are
an important class of magnetic materials that show glassy spin structure and several low
temperature transitions due to the presence of frustration [5 - 7]. In addition, the investigation of
exchange bias (EB) behavior in spinel chromite has drawn considerable research interest due its
relevance in applications such as magnetic read head and spintronic devices [8 - 10]. In normal
1
1
1
1
1
1
1
1
1
1
2
+
2+
2+
2+
spinels with general chemical formula AB O the A (Co , Ni , Fe etc.) cations occupy the
2
4
3
+
3+
3+
3+
tetrahedral sites, while the B (Cr , Fe , Al etc.) cations occupy the octahedral sites [11 - 13].
Spinel chromite ACr O with magnetic or non-magnetic A site ion is one of the interesting class
2
4
of magnetic materials due to several applications in light or heat sensitive micromechanical
devices, catalytic material or gas sensors and also due to their interesting magneto-dielectric,
magneto-elastic, magneto-resistive and multiferroic properties [14 - 17]. In general, these
chromites crystallize in cubic crystal structure with space group 퐹푑3푚. However, Jahn –Teller
2
+
2+
2+
(JT) active ions such as A = Ni , Cu , and Fe at tetrahedral sites induce a structural transition
from cubic to tetragonal structure [17, 18].
2
2
2
2
2
2
2
2
2
2
3
0
1
2
3
4
5
6
7
8
9
0
Normal spinel nickel chromite (NiCr O ), which crystallizes in tetragonal crystal
2
4
structure attracts much attention for its rich physical and chemical properties. It is ferrimagnetic
(FIM) in nature with Curie temperature T = 70 K [19]. An additional transition occurring at T
C
N
= 31 K is due the antiferromagnetic (AFM) ordering of the transverse components of magnetic
moment [20]. This compound crystallizes in cubic phase at high temperature with space group
퐹푑3푚. When lowering the temperature, the symmetry of the nickel chromite decreases to
2
+
tetragonal at 320 K driven by the cooperative JT effect associated with the Ni cations in the
tetrahedral position [21, 22]. As a result, despite the presence of pyrochlore lattice formed by
3
+
Cr ions the possibility of frustration is canceled out by the JT distortion. However, with non-JT
2
+
2+
2+
magnetic A (Mn , Co ) ions the system can survive frustration and can lead to spin glass like
2
+
2+
2+
spiral ordering [13]. ACr O (A = Zn , Mg ), with a non-magnetic A cations can give rise to
2
4
2

1
2
3
4
5
6
7
8
frustrated AFM [23]. Recently in Ni Zn Cr O short-range glassy behavior, multiferroic
.95 0.05 2 4
properties and magnetostructural coupling have been reported [3]. So, the choice of A site cation
and the substitution at A site can result in interesting magnetic properties due to the modulation
of different exchange interactions between the sublattices. The magnetic structure of NiCr O4
2
contains two magnetic sublattices at tetrahedral (A) and octahedral (B) sites respectively. Two A
sites are grouped into a single sublattice while four B sites are grouped into two sublattices with
each sublattice having both longitudinal and transverse components of magnetic moment [20].
The AFM exchange interaction among B sites results in magnetic frustration in the system [24].
9
0
1
2
3
In this study, we have investigated the evolution of structural and magnetic properties of
NiCr O upon Mg substitution. The observed glassy magnetic phase in the Mg substituted
1
1
1
1
2
4
NiCr O single phase polycrystalline compound can be explained by the presence of magnetic
2
4
frustration and relaxation mechanism, while the field cooled exchange bias (FC EB) behavior
can be explained by considering competing AFM and FIM components of magnetic moments.
1
4
Experimental Details:
1
1
1
1
1
2
2
2
2
2
2
2
5
6
7
8
9
0
1
2
3
4
5
6
Polycrystalline samples of Ni Mg Cr O (x = 0.0 – 0.50) were synthesized by using sol-
1
-x
x
2
4
gel method. Stoichiometric ratio of Ni(NO ) ∙ 6H O, Mg(NO ) ∙ 6H O and Cr(NO ) ∙ 9H O of
3
2
2
3 2
2
3 3
2
99% purity were weighed, dissolved in distilled water and mixed in a beaker. Citric acid and
ethylene glycol were added to the solution and the solution was heated slowly to evaporate the
0
solvent, leaving a precipitate. The precipitate was grinded and pre-sintered at 600 C followed by
0
0
an intermediate sintering at 800 C. Final sintering was performed at 1100 C for 24h. For phase
identification powder X-ray diffraction pattern was recorded at room temperature using a Rigaku
X-ray diffractometer (XRD) (TTRAX III) using Cu-Kα (λ = 1.5406Å) radiation. The particle
size and microstructure of samples were analyzed by recording microstructural images using
ZEISS make FESEM (ΣIGMA). The magnetization data were recorded by using Vibrating
Sample Magnetometer (VSM) probe installed in Quantum Design Physical Property
Measurement System (PPMS) fitted with a superconducting magnet of 9T capacity.
2
2
2
7
8
9
3

1
2
3
4
5
6
7
8
9
0
1
Results and Discussion:
Room temperature XRD patterns along with Rietveld refinements are shown in Fig. 1(a-
d). All the samples are in single-phase form with tetragonal structure (퐼4 /푎푚푑) for x = 0 and
1
cubic structure (퐹푑3푚) in Mg doped samples. For x = 0 the lattice parameters are found to be a
= b = 5.8299 Å and c = 8.4363 Å and they are comparable to earlier reports [22, 25]. All Mg
substituted samples exhibit cubic structure with lattice constant varying from a = 8.3186 Å for
x = 0.05 to a = 8.3252 Å for x = 0.50 as given in Table 1. The increase in lattice parameters in
2
+
the Mg substituted cubic systems can be understood in terms of replacement of smaller Ni (0.55
2
+
Å) ions by Mg (0.57 Å) ions [26]. The structural transformation confirms that some of the JT
2
+
2+
1
1
active Ni ions are replaced by JT inactive Mg ions such that it drives the system into higher-
symmetric cubic structure at room temperature.
1
1
2
3
Fig. 1. (a) Room temperature XRD patterns of Ni Mg Cr O (x = 0.0 - 0.50) along with
1
-x
x
2
4
1
4
Rietveld refinement for (b) x = 0.0, (c) x = 0.50 and (d) magnified view of (113) and (311) peaks.
1
1
1
1
1
2
2
5
6
7
8
9
0
1
The FESEM micrographs of the samples are shown in Fig. 2(a - g) and the variation
of average particle size with Mg substitution is shown in Fig. 2(h). FESEM micrographs
reveal that they exhibit broad particle size distribution over a scale of 50 nm to 850 nm. We
have observed a decrease in average particle size with increase in Mg concentration in the
present series. The elemental mapping for x = 0.0 and 0.05 (Fig. 3.) confirms the uniform
distribution of various elements in the samples. All samples show similar kind of morphology
with most of the particles having bi-pyramidal shape.
4

1
2
3
4
5
6
Susceptibility (χ = M/H) as a function of temperature measured under zero field cooled
(ZFC) and field cooled (FC) conditions for an applied field of H = 200 Oe are shown in Fig. 4 &
5. Samples with x = 0.0, 0.05 and 0.10 show typical FIM behavior while the rest of the samples
i.e., for 0.20 ≤ x ≤ 0.50 behave antiferromagnetically. For T < T , significant irreversibility
C
between ZFC and FC curves appears indicating the presence of non-collinear ferrimagnetism and
canted magnetic moment in x = 0.0 - 0.10 samples. At 10 K for H = 200 Oe, the value of
∆
푀
(
푀 ― 푀
)
7
8
9
0
1
2
3
4
5
6
irreversibility in magnetization is found to be
푀푍퐹퐶
=
퐹퐶
푍퐹퐶 푀
= 9.72, for x =
푍퐹퐶
0.0 sample. These values for x = 0.05 and 0.10 samples are found to be 11.41 and 22.08
respectively. The FIM transition temperature (T ) values for the samples x = 0.0, 0.05 and 0.10
C
1
1
1
1
1
1
1
are found to be 70 K, 57 K and 42 K respectively. The T value for the parent compound is
C
comparable to that reported in literature [27, 28]. We observed a clear inflection in the χ – T
plots of x = 0.0, 0.05, 0.10 samples at 29 K, 27 K and 22 K respectively due to the ordering of
AFM component (T ) of spin structure. In addition to the observed FIM and AFM transitions in
N
x = 0.10 sample, we have observed a step like transition around T = 34 K as shown in Fig.4 (d)
f
in an expanded scale. This may be due to the short-range glassy magnetic phase as a result of
enhancement of frustration triggered by the substitution of nonmagnetic Mg.
1
1
1
2
2
2
2
7
8
9
0
1
2
3
From the ZFC and FC susceptibility (χ) curves of x = 0.20 and 0.30 samples, a fall in
magnetization value starting from 34 K followed by an enhancement in its value for T  22 K
have been observed as shown in Fig. 5. Recently, similar type of complex magnetic transition
has been reported in FIM Ni0.95Zn0.05Cr O compound and is explained in terms of short-range
2
4
glass like magnetic structure due to the canting nature of magnetic moments [3]. However, in our
system magnetic behaviors in both x = 0.20 and x = 0.30 samples are dominated by the strong
AFM interaction.
2
4
5

1
2
Fig. 2: FESEM images of Ni Mg Cr O (x = 0.0 – 0.50).
1
-x
x
2
4
6

1
2
Fig 3: Elemental mapping for x = 0.0 and 0.05 samples.
3
Table 1: Structural and Magnetic parameters of Ni Mg Cr O .
1
-x
x
2
4
Samples
x = 0
x = 0.05
x = 0.10
x = 0.20
x = 0.30
x = 0.40
x = 0.50
Parameters
Lattice
Parameters (Å)
a = b = 5.8299 a = 8.3186 a =8.3206 a = 8.3214 a = 8.3222 a = 8.3248 a = 8.3252
c = 8.4363
M (emu/mol)
-
-
349.93
8.40
750 ± 4
0.41
42
1.46
1.27
-
-
0
M (emu/mol)
sg
-
-
0.45
0.26
-
-
τ (Sec)
n
-
-
1460 ± 10 685 ± 18
-
-
-
-
0.37
-
0.42
-
-
-
TC (K)
TN (K)
Tf (K)
70
29
-
57
27
-
-
-
22
19
30
20
29
18
-
17
-
34
4
5
7

1
2
3
4
Fig. 4: Temperature dependent susceptibility (χ) under zero field cooled (ZFC) and field cooled
(FC) conditions for (a) x = 0.0, (b) x = 0.05 and x = 0.10 samples. (d) χ – T plots in the expanded
scale in the low temperature region.
5
6
7
8
9
0
1
2
3
In order to justify and investigate the nature of glassy magnetic phase in x =
0.10, 0.20 and 0.30 samples we have studied the relaxation of thermoremanent magnetization
at T = 25 K, i.e., below the spin glass transition temperature (Fig. 6). For this study, the
samples were first ZFC to T = 25 K and then a magnetic field of 6 T was applied. After reducing
the applied field to zero, the remanent magnetization M(t) was measured as a function of time
upto t = 10000 s. Glassy magnetic system shows long-lasting magnetization relaxation. Fig. 6
1
1
1
1
(a) & (b) show the normalized magnetization decay (M(t)/M(t )) for the FIM and AFM
0
samples respectively. Where M(t ) stands for initial magnetic moment at t = 0 s. It can be
0
noted, M(t)/M(t ) rapidly drops to a nearly constant value for non-spin glass sample, while it
0
8

1
2
3
Fig. 5: Temperature dependent susceptibility (χ) under zero field cooled (ZFC) and field cooled
(FC) conditions for x = 0.20, 0.30, 0.40, and 0.50.
4
5
6
keeps continuously decreasing for spin glass system [29]. From Fig. 6 it is clear that among
all the samples, only x = 0.10, 0.20 and 0.30 samples are showing such kind of glass like
relaxation.
7
8
9
0
1
2
3
4
5
The time dependent thermoremanent magnetization curve can be well explained by a
― (푡/휏)1 ― 푛
stretched exponential function 푀(푡) = 푀 + 푀 exp [30]. Here 푀 is related to
( )
0
0
푠푔
the intrinsic FIM component and 푀푠푔 is attributed to the contribution from glassy magnetic
phase. The rate of relaxation is defined by the parameters τ and n, where n lies in the range of
0 to 1. The values of all the fitted parameters are presented in Table 1. The fitted values of 푛 are
considerably smaller than one which indicates that relaxation is due to the activation against
multiple anisotropy barriers as observed in spin glass system [31]. The relaxation in
thermoremanent magnetization suggests that the competition between FIM and AFM coupling
leads to the spin glass state due to the significant frustration in magnetic system.
1
1
1
1
1
1
9

1
2
Fig. 6: Normalized relaxation of thermoremanent magnetization of (a) x = 0.0 - 0.10 (b) x = 0.20
3
- 0.50 along with fitted data for (c) x = 0.10, (d) x = 0.20 and x = 0.30.
4
5
6
7
Studying the temperature dependence of inverse susceptibility by using molecular field
theory is an excellent approach to understand the magnetic properties. According to molecular
field theory of ferrimagnetism for T > T the hyperbolic nature of inverse susceptibility can be
C
characterized by the following expression [32, 33],
(
T ― Θ)
ξ
χ ―1
=
) ― ((T ― Θ′))
8
(1)
(
C
9
0
1
2
3
Here, the first term is the hyperbolic asymptote in the high temperature region and has a Curie-
Weiss form and the second term stands for hyperbolic behavior near the FIM transition
temperature. We fitted our experimental data to Eq. (1) as shown in Fig. 7 and the fitted
parameters are presented in Table 2. A clear kink at T = 232 K observed in the inverse
susceptibility curve of x = 0.05 (Fig. 7 b), can be attributed to the decreased JT transition
1
1
1
1
1
0

1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
temperature from 320 K for x = 0 sample due to the substitution of JT inactive Mg2+ ions.
However, we did not observe any such kink for x = 0.10 sample in the paramagnetic (PM)
region. Thus, the Mg substituted samples are more stable in the cubic crystal structure at room
temperature due to the shifting of JT distortion below the room temperature. In order to fit the
inverse susceptibility of x = 0.05 sample we consider the PM region below the onset of JT
distortion i.e. for T < 232 K. Here the parameter Θ, is known as the asymptotic Curie
2
+
3+
temperature and it represents the strength of AFM exchange interaction between Ni and Cr .
The characteristic temperature Θ' should be close to T [34], which can be seen in our case. The
C
closeness of Θ' and T confirms the long-range FIM ordering in these samples. The difference
C
1
1
1
1
1
1
1
1
1
1
2
2
between Θ' and T generally gives an idea of broadening of magnetization about FIM
C
transition temperature. With increase in broadening, the magnetic disorder increases and the
FIM state changes from long-range to short-range order [35]. Although there is an overall
FIM ordering in the sample but considerable short-range order can produce spin glass like
dynamics below T . From earlier reports it is confirmed that magnetic interaction in bulk
C
NiCr O is long range FIM in nature [36], so closeness of Θ' and T is expected. However, for
2
4
C
x = 0.10, the difference between these two temperatures is distinguishable. The difference can be
attributed to the increase in magnetic disorder in the sample. The parameter ξ, in the hyperbolic
term represents the curvature in the inverse susceptibility plot. If ξ→0, Eq. 1 takes the form of a
straight line i.e. the typical Curie-Weiss law. The ξ value is found to decrease with Mg
substitution as given in Table 2 and it confirms domination of Curie-Weiss law term. The spin
only effective magnetic moment per formula unit of NiCr O is 6.16 µ which is small as
2
4
B
µ
2
2
2
2
2
2
2
2
3
3
2
3
4
5
6
7
8
9
0
1
compared to the value obtained from the molecular field theory fitting (6.6 B 푓.푢.). Though, the
angular momentum of the system is largely quenched by the JT distortion at T = 320 K, but some
contribution from partially quenched orbital magnetic moment cannot be neglected [28, 37]. We
have observed a larger effective magnetic moment for x = 0.10 compared to the expected value
of μ = 6.10  per formula unit, which further confirms the unquenched orbital magnetic
eff
B
2
+
moment of Ni in the tetrahedral sites of cubic structure due to considerable suppression of JT
distortion by Mg2+ substitution. The electronic configuration of Ni2+ in the tetrahedral
4
4
environment is 푒 푡 . Due to the triply degenerate energy levels of t caused by the similar
푔 2푔
2g
0
shape of orbitals d , d and d one orbital can be transformed into another orbital by simple 90
xy
yz
zx,
rotation about proper axis. This orbital motion of electron gives rise the orbital magnetic moment
1
1

1
2
3
4
5
6
7
8
9
and contribute to the total magnetic moment of the system. In NiCr O , t energy levels split into
2 4 2g
two energy levels due to the JT distortion taking place just above the room temperature.
Therefore, the orbital magnetic moment is partially quenched. But with Mg substitution the JT
distortion decreases and contribution from the orbital magnetic moment is higher compared to
that of NiCr O .This is one of major possible reasons behind the high value of experimental
2
4
effective magnetic moment of x = 0.10. In case of x = 0.05, we have fitted the inverse
susceptibility data below (T < 232 K) the onset of JT distortion transition temperature and the
experimental effective magnetic moment is close to the theoretical spin only magnetic moment
(6.13 µ ). Considering spin- orbital coupling in the system the effective magnetic moment of
B
1
1
1
1
0
1
2
3
ions can be expressed as µ푒푓푓 = 푔 퐽(퐽 + 1) in the unit of µ . With L = 3, S = 1 and g = 5/4 for
B
2
+
3+
Ni the effective magnetic moment is 5.59 µ , while that is for Cr is 3.87 µ (spin only ).
B
B
Hence, the resultant effective theoretical magnetic moment for x = 0.10 compound is found to be
µ
µ
7.62 B 푓.푢. and is close to our experimental value of 7.5 B 푓.푢..
1
1
1
4
5
6
From the fitting of inverse susceptibility, we can see the frustration index (f = 16) for x =
0.10 compound is much higher than those of other two FIM samples. So it is possible that such a
frustrated magnetic behavior gives rise to glassy state below the transition temperature T = 34 K
f
.
1
7
Table 2: Parameters obtained from fitting of inverse susceptibility.
µ
Sample
Θ (K)
C
ξ
Θ' (K)
μ ( B 푓.푢.)

eff
푓 =
(
emu K/Oe (Oe mol
mol)
| |
T
C
K/emu)
1058
x = 0.0
-720
5.56
72
6.6
10
x = 0.05
x = 0.10
-403
-670
4.63
7.14
602
460
61
56
6.1
7.5
7
16
1
8
1
2
2
2
2
2
9
0
1
2
3
4
Magnetization as a function of applied magnetic field was recorded for all the samples at
T = 5 K as shown in Fig. 8(a & b). The unsaturated hysteresis loops for x ≤ 0.10 samples indicate
the presence of non-collinear magnetic structure of these compounds. For NiCr O the value of
2
4
µ
spontaneous magnetization (Table 3) is found to be 0.257 B 푓.푢. at T = 5 K by linearly
extrapolating the high field magnetization to zero field and is comparable to earlier report [38].
The appearance of similar hysteresis loop and comparable coercivity values for x = 0.05 and 0.10
1
2

1
2
3
4
5
samples confirm the FIM nature of these samples. The observed large value of coercivity
indicates the existence of competing AFM component along with a long- range FIM interaction.
For x ≥ 0.20 the predominant linear behavior of M-H curves confirms the strong AFM
interaction in these samples. The complete magnetic phase diagram of our system is shown in
Fig. 9.
6
7
Fig. 7: Fitting of inverse susceptibility with Molecular field theory.
1
3

1
2
3
Fig. 8: (a) ZFC M-H curves at 5 K and (b) the magnified M-H loops near coercive field for x ≥
20.
4
5
Fig. 9: Magnetic phase diagram of Ni Mg Cr O series.
1
-x
x
2
4
6
7
8
9
In order to investigate EB effect in these FIM compounds, the magnetic hysteresis loops
were recorded at T = 5 K after FC the samples at an applied field of 0.5 T from room
temperature. We have observed a shifting of M-H loop for all the samples along the negative H
axis as shown in Fig. 10. However, the shifting in the M-H loop for the parent compound is
1
4

1
2
3
small as compared to the Mg substituted samples. It is noted that the value of EB field also
depends on measuring field and FC field. The values of EB field for the samples are presented in
Table 3.
4
5
6
7
8
9
0
The shifting of hysteresis loop can be attributed to the presence of competing FIM and
AFM moments in the system and can be explained by the model proposed by Tomiyasu and
Kagomiya [20]. According to this model A sublattices are classified in to A1 - A2 pairs and B
sublattices are classified into B1 - B3 and B2 - B4 pairs for FIM (longitudinal) ordering along
[100] and AFM (transverse) ordering along [001].
1
Table 3: Magnetic Parameters obtained from M-H loops recorded at 5 K.
µ
Sample
H (Oe)
C
M ( B f.u.)
H (Oe)
EB
S
x = 0.00
x = 0.05
x = 0.10
7384
8486
7855
0.26
0.24
0.23
91
590
747
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
In spinel chromite uncompensated magnetic moment can exist due to the magnetic
frustration occurring in the octahedral (B) pyrochlore sublattice [39]. In NiCr O , for T < T A
2
4
C,
sublattices moment A (= A1-A2) is aligned along the field direction and dominates over the net
B sublattices moment B (= B1-B3 - B2-B4). So, under FC condition far above from the Curie
temperature, the net magnetic moment of the sublattices is oriented along the field direction.
Therefore, in the first quadrant of the hysteresis loop (initial curve) at a particular temperature,
the uncompensated magnetic moment contributes to the total magnetic moment in the positive
direction. As the direction of magnetic field is gradually reversed (second quadrant), it is quite
difficult to align A along the field direction due to the strong AFM interaction with B. The
2
+
substitution of nonmagnetic Mg ions in the A sites further decreases A and hence the value of
B component becomes quite dominant. As the B component exerts a torque on the A of ions,
a relatively larger negative magnetic field is required to align the magnetic moment in the
reverse direction. This asymmetric behavior in the ascending and descending branches of M-H
loop gives rise to shift in hysteresis loop towards the negative field axis. With decrease in
temperature the AFM interaction is strengthened and it gives rise to larger exchange bias field
(H ).
EB
1
5

1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
Temperature variation of HEB and coercive field (H ) is studied for x = 0.10 sample
C
with a maximum field of ± 6 T. As shown in Fig. 11 (a), the exponential rise in magnitude of
HEB with decrease in temperature can be fitted to the exponential function of the form H =
EB
HEB (0) exp (-T/T ). Where, H (0) is the value of HEB, at T = 0 K and T is a constant. The
1
EB
1
best fitted parameters are found to be HEB (0) = 2241 ± 5 Oe and T = 4.99 ± 0.09 K. The
1
exponential rise of HEB with decrease in temperature can be undestood by growth of long
range AFM ordering and corresponding increase in exchange anisotropy between FIM and
AFM components at low temprature. The temperature dependance of coercive field (H ) is
C

found to follow modified Kneller’s law [40], H (T) = H (0)[1-(T/T ) ]. Where, H (0) is the
C
C
B
C
1
1
1
1
1
1
coercivity at T = 0 K, T is the blocking temperature and  is a constant. In case of
B
nanoparticles (single domain), T represent the superparamagnetic blocking temperature and
B
 = 0.5. Since, we are dealing with polycrystalline (multi domain) particles, therefore a
deviation from original Kneller’s law can be expected. From the fitted data as shown in Fig.
11 (b), the value of H (0) is found to be 10554 Oe. The estimated values of T and  are
C
B
found to be 41.2 K and 0.64 respectively.
1
1
1
1
2
2
2
2
2
2
2
2
2
2
3
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
EB behavior depends on both cooling field (H ) and maximum measuring field
FC
(Hmax). Fig. 12 (a) & (b) show the variation of HEB for x = 0.10 sample with respect to HFC and
Hmax respectively. In order to study the effect of HFC on H , we recorded M-H data after
EB
cooling the sample at 0.05, 0.1, 0.5, 1, 3 and 5 T respectively. As shown in the inset of Fig. 12
(a), the initial increase in HEB for HFC upto 1 T can be atributed to the consolidation of
magnetic domains due to applied higher cooling magnetic field. However, for cooling field
HFC > 1T the HEB value decreases due to possible permanent allignment of some of the
components of magnetic moment along the field direction, thereby reducing the anisotropic
exchange interaction between FM and AFM components. Fig. 12 (b) shows hysteresis loops
recorded at various maximum measuring field . For each loop, the sample was cooled down to
5 K from room temperature at a field 0.5 T and measurements were carried out in the field
ranges Hmax = ± 1, ± 2, ± 3, ± 6 and ± 9 T. To avoid the training effect, each hystersis loop was
recorded after demagnetizing the sample by warming to room tempearture, removing of the
stray magnetic field in oscillating mode and field cooling to 5 K again. We have observed a
monotonic decrease in HEB with increase in measuring field. For Hmax ≤ 3 T, mostly minor
1
6

1
2
3
loop is observed with considerable vertical shift in magnetization. The decrease of HEB with
increase in measuring field can be understood in terms of dominant Zeeman energy which
overcomes the exchange anisotropy.
4
5
6
Fig. 10: Magnetic hysteresis loop recorded at 5 K under ZFC and FC conditions for (a) x = 0.0,
(b) x = 0.05 and (c) x = 0.10. Insets show the loop in expanded scale close to HC.
7
1
7

1
2
3
Fig. 11: Temperature dependence of (a) exchange bias (H ) and (b) coercivity (H ) for x =
EB C
0.10.
4
5
6
Fig. 12: (a) Cooling field (H ) dependence of exchange bias and (b) the maximum measuring
FC
field (Hmax) dependence of exchange bias for x = 0.10.
7
8
9
0
1
Training effect is an interesting characteristics of EB phenomena. The training effect
refers to the gradual and monotonous decrease of HEB when the sample is cycled through
consecutive hysteresis loops at a fixed temperature. In order to investigate training effect in x =
0.05 compound eight consecutive hysteresis loops (n = 8) have been recorded at 5 K after field
cooling through T with H = 0.5 T. Consecutive hysteresis loops are shown in Fig. 13 (a),
1
1
C
FC
1
8

1
2
3
where the inset shows the plot in the expanded scale close to M = 0. The observed training effect
may be due to relaxation of transverse component (AFM) along an equilibrium configuration by
each reversal process. It is found that the variation of H with n follows a power law for n ≥ 2 :
EB
1
n
4
H (n) ― H (∞) ∝
(2)
EB
EB
5
6
Where H (∞) is the EB field after infinite number of loops. The value of H (∞) is found to be
EB EB
448 Oe from the fitted data as shown in Fig. 13 (b).
7
8
9
0
Fig. 13: (a) Consecutive M-H loops recorded at T = 5 K for x = 0.05 with index n = 1 to n = 8.
Inset shows the loops in expanded scale (b) HEB as a function of n along with fitted data using
Eq. 2.
1
1
1
Conclusion:
1
1
1
1
1
1
1
1
2
2
3
4
5
6
7
8
9
0
Polycrystalline Ni Mg Cr O (x = 0.0 - 0.5) samples were synthesized by sol gel route. Rietveld
1
-x
x
2
4
refinement of XRD patterns at room temperature confirms the phase purity of the samples and
4
transformation from tetragonal (퐼 1 푎푚푑) to cubic (퐹푑3푚) crystal structure upon Mg
substitution. The magnetic structure of x = 0.10 compound is found to be complex showing
multiple magnetic transitions. In addition to the long-range FIM and AFM transitions, a spin
glass like behavior is observed around T = 34 K in x = 0.10 sample. No FIM transition is
f
observed for x ≥ 0.20, except the appearance of glassy magnetic phase for x = 0.20 and x = 0.30
samples due to the influence of strong AFM interaction. The stretched exponential type magnetic
relaxation supports the observed glassy phase in the samples. Exchange bias field is found to be
1
9

1
2
3
4
enhanced significantly with Mg substitution and is explained in terms of competing FIM and
AFM components of magnetic moment. Temperature variations of HEB and H were analyzed
C
based on exponential law and modified Kneller’s law respectively. Training effect of HEB
follows the typical power law behavior.
5
6
7
8
Acknowledgments: We acknowledge the Central Instrumentation Facility (CIF), IIT Guwahati,
India, for providing FE-SEM and EDS facility. The authors acknowledge the DST for granting
PPMS facility under FIST-II Program (SR/FST/PSII-037/2016) in the department of Physics, IIT
Guwahati.
9
References:
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
1. V. Tsurkan, S. Zherlitsyn, S. Yasin, V. Felea, Y. Skourski, J. Deisenhofer, H.-A. K. von
Nidda, J. Wosnitza, A. Loidl, Phys. Rev. Lett., 110 (2013), 115502.
2. S. H. Lee, C. Broholm, W. Ratcliff, G. Gasparovic, Q. Huang, T. H. Kim, S. W. Cheong,
Nature, 418 (2002), 856.
3. K. Devi Chandrasekhar, J. Krishna Murthy, J.-Y. Lin, H. C. Wu, W. J. Tseng, A.
Venimadhav, H. D. Yang, Phys. Rev. B, 94 (2016), 205143.
4. S. Bordács, D. Varjas, I. Kézsmárki, G. Mihály, L. Baldassarre, A. Abouelsayed, C. A.
Kuntscher, K. Ohgushi, and Y. Tokura, Phys. Rev. Lett., 103 (2009), 077205.
5. M. Nogues and J.L. Dormann, J. Magn. Magn. Mater., 54-57 (1986), 87-88.
6. T. G. Aminov, G. G. Shabunina, E. V. Busheva, V. M. Novotortsev, Inorg. Mater., 53
(2017), 11.
7. A. D. LaForge, S. H. Pulido, R. J. Cava, B. C. Chan, A. P. Ramirez, Phys. Rev. Lett., 110
(2013), 017203.
8. S. Guo, X.H. Liu, W.B. Cui, W. Liu, X.G. Zhao, D. Li, Z.D. Zhang, J. Appl. Phys., 105
(2009), 064702.
9. C. Tsang, R.E. Fontana, T. Lin, D.E. Heim, V.S. Speriosu, B.A. Gurney, M.L. Williams,
IEEE Trans. Magn., 30 (1994), 3801.
10. J. C. S. Kools, IEEE Trans. Magn., 32 (1996), 3165.
11. E. prince, J. Appl. Phys., 32 (1961), 685.
12. G. Ueno, S. Sato, Y. Kino, Acta Cryst. C, 55 (1999), 1963.
2
0

1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
13. K. Tomiyasu, J. Fukunaga, H. Suzuki, Phys. Rev. B, 70 (2004), 214434.
14. N. Mufti, G. R. Blake, T Palstra, J. Magn. Magn. Mater., 321 (2009), 11.
15. V. Kocsis, S. Bordacs, D. Varjas, K. Penc, A. Abouelsayed, C.A. Kuntscher, K. Ohgushi, Y.
Tokura, I. Kezsmarki, Phys. Rev. B, 87 (2013), 064416.
16. A. Maignan, C. Martin, K. Singh, C. Simon, O.I. Lebedev, S. Turner, J. Solid State Chem.,
195 (2012), 41.
17. K. Singh, A. Maignan, C. Simon, C. Martin, Appl. Phys. Lett., 99 (2011), 172903.
18. M. Reehuis, M. Tovar, D. M. Tobbens, P. Pattison, A. Hoser, B. Lake, Phys. Rev. B, 91
(2015), 024407.
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
3
3
19. S. Klemme, J. C. van Miltenburg, Phys. Chem. Miner., 29 (2002), 663.
20. K. Tomiyasu, I. Kagomiya, J. Phys. Soc. Jpn., 73 (2004), 2539.
21. K. Siratori, J. Phys. Soc. Jpn., 23 (1967), 948.
22. O. Crottaz, F. Kubel, H. Schmid, J. Mater. Chem., 7 (1997), 143–146.
23. M. C. Kemei, S. L. Moffitt, L. E. Darago, R. Seshadri, M. R. Suchomel, D. P. Shoemaker, K.
Page, J. Siewenie, Phys. Rev. B, 89 (2014), 174410.
24. B. C Melot, J. E. Drewes, R. Seshadri, E M Stoudenmire and A. P. Ramirez, J. Phys.
Condens. Matter 21 (2009), 216007.
25. J. Barman, T. Bora, S. Ravi J. Magn. Magn. Mater., 385 (2015), 93–98.
26. R. D. Shannon, Acta Cryst. A, 32 (1976), 751.
27. H. Ishibashi, T. Yasumi, J. Magn. Magn. Mater., 310 (2007), e610.
28. X. Liu, N. Yin, T. Thomas, M. Yang, J. Wang, Q. Shi, RSC Adv., 6 (2016), 112140.
29. L. T. Coutrim, E. M. Bittar, F. Garcia and L. Bufaiçal, Phys. Rev. B, 98 (2018), 064426.
30. D. Karmakar, S. K. Mandal, R. M. Kadam, P. L. Paulose, A. K. Rajarajan, T. K. Nath, A. K.
Das, I. Dasgupta, G. P. Das, Phys. Rev. B, 75 (2007), 144404.
31. K. Dey, S. Majumdar, S. Giri, Phys. Rev. B, 90 (2014), 184424.
32. L. Néel, Ann. Phys., 12 (1948), 137.
33. E. Winkler, S. B. Canosa, F. Rivadulla, M. A. López-Quintela, J. Rivas, A. Caneiro, M. T.
Causa, M. Tovar, Phys. Rev. B, 80 (2009), 104418.
34. R. N. Bhowmik, R. Ranganathan, and R. Nagarajan, Phys. Rev. B, 73 (2006), 144413.
35. D. S. Williams, P. M. Shand, T. M. Pekarek, R. Skomski, V. Petkov, D. L. Leslie-Pelecky,
Phys. Rev. B, 68 (2003), 214404.
2
1

1
2
3
H. Singh, T. Ono, T. Chakraborty, K. Srikanth, A. Venimadhav, R. Chandra, C. Mitra and
U. Kumar, J. Nanoparticle Res., 16 (2014), 2354.
37. J. S. Smart, Phys. Rev., 94 (1954), 847.
3
6.
4
5
6
7
38. N. Mufti, A. A. Nugroho, G. R. Blake, T. T. M. Palstra, J. Phys. Condens. Matter, 22 (2010),
075902.
39. L. G. Wang, C. M. Zhu, Z. M. Tian, H. Luo, D. L. G. C. Bao, S. L. Yuan, Appl. Phys. Lett
107 (2015), 152406.
8
9
0.
N. S. E. Osman and T. Moyo, J Supercond Nov Magn, 29 (2016), 361–366.
4
1
0
Highlights:
1
1
1
1
1
2
3
4
 Polycrystalline Ni Mg Cr O (x = 0.0 – 0.50) samples were synthesized by sol gel
1
-x
x
2
4
route.
 Spin glass state was observed for the intermediate compositions x = 0.10, 0.20 and 0.30.
 Relaxation of magnetization, Exchange bias and Training effect were studied.
1
1
5
6
1
1
7
8
Conflict of Interest
1
2
9
0
There are no conflicts to declare.
2
2
1
2
2
2
2
3
4
5
2
6
Author statement
2
2

1
2
3
Ritupan Borah: Visualization, Investigation, Formal analysis, Original
draft preparation. S. Ravi: Conceptualization, Methodology, Resources,
Supervision, Reviewing and Editing.
4
5
6
2
3