Enhanced magnetodielectric response in Dy modified NiCr2O4

Article abstract of DOI:10.1016/j.jmmm.2017.01.090

The chemically synthesized high purity spinel NiCr_2?xDy_xO₄ (x?=?0, 0.1) samples have been characterized using magnetic and dielectric measurements in presence of high magnetic field. Crystal and magnetic structure of the samples have been determined by analyzing neutron diffraction data recorded between temperature of 6?K and 300?K. NiCr₂O₄ crystallizes in tetragonal phase with the space group of I41/amd whereas NiCr_1.9Dy_0.1O₄ crystallizes in the mixed phase of cubic (space group of Fd3ˉm) and tetragonal phases at room temperature. An additional phase of DyCrO₃ with orthorhombic structure has been found in the Dy doped compound. The lattice parameter a increases and the c decreases in tetragonal structure with the substitution of Dy in Cr site. Both the samples show superlattice reflection peak indicating the presence of long range AFM ordering (transverse component) below 40?K. But the saturation magnetization slightly increases after Dy doping. An anomaly observed near Curie temperature in ε′ (T) of NiCr₂O₄ and NiCr_1.9Dy_0.1O₄ demonstrates the contribution of coupling between ferroelectricity and ferrimagnetism in the compounds. A linear correlation between the difference in dielectric constant and the field dependent squared magnetization for both the samples has been observed. The spin–spin interactions are most likely responsible for the observed magnetodielectric (MD) effect due to the magnetodielectric hysteresis in both parent and doped samples. Interestingly the MD% is found to increase with Dy doping.

Full text of DOI:10.1016/j.jmmm.2017.01.090

Accepted Manuscript
Enhanced Magnetodielectric response in Dy modified NiCr O4
2
P. R. Mandal, Ripandeep Singh, A. Das, Tarapada Sarkar, T. K. Nath
PII:
S0304-8853(16)32856-6
DOI:
http://dx.doi.org/10.1016/j.jmmm.2017.01.090
MAGMA 62444
Reference:
To appear in:
Journal of Magnetism and Magnetic Materials
Received Date:
Revised Date:
Accepted Date:
2 November 2016
27 January 2017
28 January 2017
Please cite this article as: P. R. Mandal, R. Singh, A. Das, T. Sarkar, T. K. Nath, Enhanced Magnetodielectric
response in Dy modified NiCr O , Journal of Magnetism and Magnetic Materials (2017), doi: http://dx.doi.org/
2
4
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0.1016/j.jmmm.2017.01.090
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Enhanced Magnetodielectric response in Dy modified NiCr O
2
4
1, 3
2
2
3
1
P. R. Mandal , Ripandeep Singh , A. Das , Tarapada Sarkar , and T. K. Nath *
1
Department of Physics, Indian Institute of Technology Kharagpur, 721302, West Bengal, India
Solid State Physics Division, Bhabha Atomic Research Center, Trombay, Mumbai – 40008, India
Department of Physics, University of Maryland, College Park, Maryland 20742, USA
2
3
*
E-mail: tnath@phy.iitkgp.ernet.in
Abstract
x 4
The chemically synthesized high purity spinel NiCr2-xDy O (x=0, 0.1) samples have been
characterised using magnetic and dielectric measurements in presence of high magnetic
field. Crystal and magnetic structure of the samples have been determined by analysing
neutron diffraction data recorded between temperature of 6 K and 300 K. NiCr
crystallizes in tetragonal phase with the space group of I41/amd whereas NiCr1.9Dy0.1
crystallizes in the mixed phase of cubic (space group of Fd 3m) and tetragonal phases at
room temperature. An additional phase of DyCrO with orthorhombic structure has been
2 4
O
O
4
3
found in the Dy doped compound. The lattice parameter a increases and the c decreases in
tetragonal structure with the substitution of Dy in Cr site. Both the samples show superlattice
reflection peak indicating the presence of long range AFM ordering (transverse component)
below 40 K. But the saturation magnetization slightly increases after Dy doping. An anomaly
2 4 4
observed near Curie temperature in ε' (T) of NiCr O and NiCr1.9Dy0.1O demonstrates the
contribution of coupling between ferroelectricity and ferrimagnetism in the compounds. A
linear correlation between the difference in dielectric constant and the field dependent
squared magnetization for both the samples has been observed. The spin-spin interactions
are most likely responsible for the observed magnetodielectric (MD) effect due to the
magnetodielectric hysteresis in both parent and doped samples. Interestingly the MD% is
found to increase with Dy doping.

Keywords: Spinel, Antiferromagnetism, Neutron diffraction, Magnetodielectric,
Ferrimagnetism.
PACS: 78.70.Nx, 71.70.Gm, 75.50.Ee, 75.50.Gg, 77.84.-s:
http://www.aip.org/publishing/pacs/pacs-2010-regular-edition
*
Corresponding author: tnath@phy.iitkgp.ernet.in
Tel: +91-3222-283862, 283848
Area code: 721302
INDIA
1
. Introduction
An important class of materials, namely, magnetodielectric materials that exhibit
neither spontaneous polarization nor gratify the symmetry constraints for magnetodielectric
effect; but nevertheless exhibit some kind of coupling between magnetization and dielectric
properties in magnetic insulators, depending upon the localized spin configuration and the
dielectric properties can be controlled by the magnetic field or conversely the magnetic
polarization can be controlled by the electric field. The dielectric constant in
magnetodielectric materials is modulated by an applied magnetic field depending on the spin-
charge coupling. The magnetodielectric coupling is often mediated by lattice dynamics [1].
The identification of the mechanism for strong spin-charge coupling for producing large
magnetically induced shift of dielectric constant is a big challenge in the study of
magnetodielectric materials. Many group of materials such as charge ordered LuFe
2 4
O [2],
EuTiO [3], orthoferrites, orthochromites, MnF [4], MnO [4], and Tb Fe 12 [5], and
3
2
3
5
O
different charge ordered manganites etc. are the examples of magnetodielectric materials.
Magnetodielectric measurement provides the information about the nature of the magnetic
exchange interaction in different frustrated magnets like Dy
magneto-dielectric coupling is suggested to originate from the electric and magnetic order
coupling for ferroelectric frustrated LuFe [8].
2
Ti
2
O
7
[6], Tb
2 2
Ti
O
7
[7]. The
2
O
4

The materials MCr
2
O
4
(M = Mn, Co and Ni) are ferrimagnetic spinels, in which the
2
+
3+
M cations occupy the tetrahedral (A) sites and the Cr cations occupy the octahedral (B)
2 4
sites. Above 310 K NiCr O shows fully ordered and stoichiometric cubic spinel structure
3
+
3
with Fd3m space group. The non-Jahn-Teller active Cr 3d ions preferentially occupy B-
sites because of its strong crystal field stabilization of the half occupied nondegenerate t2g
2
+
8
4
4
states and empty e
phase the fully occupied low-energy e levels and triply degenerate t
crystal field are responsible for potentially unstable structure of NiCr
NiCr is tetragonally deformed spinel structure by removing the orbital degeneracy [10],
where c/a>1. The Jahn-Teller active Ni ions are responsible for the deformation in this
system [9]. The coupling between spin and lattice degrees of freedom in NiCr suggests
this compound for a promising magnetodielectric material. Magnetodielectric properties in
normal spinel NiCr was first reported by Mufti et al. [11]. They have reported the change
in slope in dielectric constant at 75 K and 31 K and the change in dielectric constant under
g
states and Ni 3d (e
g
t
2g ) occupy the tetrahedral site [9]. But in cubic
levels of tetrahedral
. Below 310 K
2
2
O
4
2
O
4
2
+
2
O
4
2
O
4
-2
the applied magnetic field. The polarization of 13 µC m is observed by Maignan et al. [12].
Tomiyasu and Kagomiya performed the neutron diffraction study to describe the
magnetic structure of NiCr
2
O
4
[13]. They showed that the combined long range order
. The antiferromagnetic
ferrimagnetic and antiferromagnetic components exist in NiCr
2
O
4
ordering occurs at lower temperature (temperature with a superlattice structure) of 31 K and
the ferrimagnetic ordering occurs at relatively higher temperature (Curie temperature) below
7
2 4
4 K. Suchomel et al. investigates the magnetostructural coupling in NiCr O by employing
the high resolution temperature dependent powder X-ray diffraction, magnetic susceptibility,
and heat capacity measurements [14]. They also propose that a structural transition occurs
from tetragonal by symmetry lowering in orthorhombic NiCr
magnetic transition of 30 K.
2
4
O at lower temperature

It has been shown in many cases that the rare-earth magnetic ordering plays an
important role to achieve magnetodielectric coupling [15 -17]. Some spinel structures by the
substitution with rare-earth ions like Dy, Er, Sm, Nd etc. lead to a structural distortion by
inducing lattice strain in the material and significantly modify the magnetic and electrical
properties in the materials. The doping of Dy (10.5 µ
magnetic coupling. The f electron orbital contribution to the magnetic coupling is supposed to
control the isotropic and anisotropic properties in the systems. NiCr is known to have
B
) in NiCr
2
O
4
assures to manipulate the
2
O
4
magnetostriction. Substitution of rare earth ions in the different spinel systems may lead to
the structural distortion via strain [18, 19]. Dy exhibits large anisotropy and large
-
6
magnetostriction values (linear strain 7500×10 at 20 K) [20]. So it is interesting to study the
effect of Dy doping in NiCr
properties.
2 4
O system on the dielectric and consequent magnetodielectric
In the present work we have carried out a detail investigation and analysis of the
temperature and magnetic field dependent dielectric properties of the polycrystalline parent
compound of NiCr
2
O
4
and Dy doped NiCr
2
4
O system. We have demonstrated the linear
correlation between the difference in dielectric constant and the field dependent squared
magnetization for both the samples and have also discussed about the relation between the
magnetodielectric properties and magnetostructural coupling in both NiCr
NiCr compounds.
2 4
O and Dy doped
2
O
4
2
. Experimental details
Polycrystalline samples of NiCr2-xDy
x
O
4
(x=0, 0.1) have been synthesized by
2
, Cr , Ni (NO .6H O,
chemical sol-gel reaction route. The starting materials are Dy
2
O
3
2
O
3
3
)
3
and citric acid. Stoichiometric amount of raw materials are dissolved into minimum amount
of nitric acid and distilled water to make a clear solution. The solution is then heated at

1
80°C following stirring the solution continuously. The finally obtained black fluffy powder
is ground and sintered at 1050°C in air for 4 hours to produce the polycrystalline manganites.
The pellet (10 mm in diameter) form of as calcined powder is prepared and finally sintered at
1
100°C for 4 hours.
The volume fractions of different phases and crystallographic details have been
determined from the neutron diffraction study. The temperature dependent magnetization
measurement and the magnetic hysteresis loop measurements up to ± 6 T magnetic field at
various temperatures have been performed with the help of a superconducting quantum
interference device (SQUID, Quantum Design) magnetometer. Neutron diffraction data has
been collected at different temperatures on the PD2 diffractometer (λ = 1.2443Å) at Bhabha
Atomic Research Centre, Mumbai, India. Rietveld refinements were carried out using
Fullprof program. The dielectric constant and magneto-dielectric response has been measured
with the help of a LCR meter (HIOKI Japan, model - 3532-50) employing a cryogen free
closed cycle helium refrigeration variable temperature cryostat fitted in a superconducting
magnet system with a maximum magnetic field of 8 Tesla (Cryogenics Ltd. U.K.,
8
TCFMVTI).
3
3
. Results and discussion
.1. Powder Neutron diffraction study
3
.1.1. Crystallographic structure
2 4
Figure 1 (a) and Fig. 1 (b) shows the neutron diffraction pattern of parent NiCr O and
4
NiCr1.9Dy0.1O samples, respectively at 300 K. For the parent compound the detail Rietveld
refinements of the neutron diffraction pattern confirms tetragonal centro-symmetric structure
with the space group of I4/amd whereas a coexistence of tetragonal (volume fraction 8%) and
cubic structure (volume fraction 86%) with space group of Fd-3m is observed in the case of
Dy doped NiCr
2
O
4
. Additionally, an orthorhombic phase of DyCrO having a small volume
3

fraction of 6 % is observed in Dy doped sample. On lowering the temperature the volume
fraction of the tetragonal structure increases to 80% at 6 K. The presence of DyCrO depends
3
on the synthesis condition. Due to the higher ionic radius for Dy ions as compared to Cr the
secondary phases are formed at the grain boundary for higher concentration of Dy doped
samples. The substitution of Cr by Dy results in a small distortion in the system. Ni takes 16h
site and O occupies 4a site. Both Cr and Dy are distributed in 8d site. With the substitution of
Cr by rare-earth Dy the lattice parameter a is found to increase while the lattice parameter c
decreases within the tetragonal structure. For both parent and Dy doped sample a is found to
increase and c is found to decrease with increase in temperature. As a result tetragonal
distortion increases with lowering of temperature below 300 K. Table 1 shows the structural
parameters obtained from the refinement of the neutron diffraction pattern at 6 and 300 K
temperature for both the samples.
A structural change is observed in NiCr
When Dy is doped in NiCr , the deformation of NiO
mean bond angle O-Ni-O in NiO polyhedra for NiCr
in Table 1 at both 6 and 300 K. For ideal NiO tetrahedra all bond angles are near 109.5º. But
2
O
4
due to the deformation in NiO
may cause the structural change. The
has been listed
4
tetrahedra.
2
O
4
4
4
2
O
4
and Ni1.9Dy0.1Cr
2
O
4
4
in the tetragonal phase two O-Ni-O bond angles are observed in a distorted tetrahedron due to
orbital ordering for both samples.
3
.1.2. Magnetic structure
Figure 2(a) and (b) shows the neutron diffraction pattern of parent and Dy doped
sample at 6K. On lowering of temperature below 100K, enhancement in the intensity of the
low angle fundamental reflection (101) is observed below Curie temperature confirming the
ferrimagnetic like ordering below this temperature. On further lowering of temperature below
3
0K superlattice reflections (110) (01-1) (marked on the figure by *) are observed indicating
the antiferromagnetic ordering in these samples. The modelling of the magnetic structure was

done in a manner similar to that reported by Tomiyasu et al. [19]. The superlattice reflection
110) near 19.6º representing the transverse antiferromagnetic superlattice reflections is
indexed by the propagation vector (001). K. Tomiyasu et al. also reported earlier the Neutron
(
diffraction studies of NiCr
below 30 K [19].
2
4
O and showed the enhancement of superlattice (110) reflection
The space group of I41/amd of tetragonal crystal structure has been used to
demonstrate the magnetic structure of the samples. The moments of the transverse component
of A and B sublattices are oriented along z and x directions. The moments corresponding to
the longitudinal antiferromagnetic superlattice reflections of A sublattice orient along x
direction for both parent and Dy doped samples at 6 K. It is observed that the moments for
tetrahedral site of ferrimagnetic component increases with Dy doping, but the moments for
octahedral sites remain constant. The moment for tetrahedral site of antiferromagnetic
component enhanced from 1.4 to 1.8 µ
B
, but the moment for octahedral site decreases at 6 K.
The net moment for the antiferromagnetic component decreases from 1.2 to -0.6 µ
B
. Figure 3
shows the temperature dependent magnetic moment at tetrahedral and octahedral site for the
sample x=0.1.
3
.2. Magnetic properties study
Figure 4 (a) and 4 (b) show the temperature dependent magnetization under zero field
cooled (ZFC) and field cooled (FC) conditions at different applied magnetic field for x=0.0
and 0.1 samples, respectively. With increasing applied magnetic field from 100 Oe to 6 T,
T
ferri shifts towards higher temperature and become broad for both the samples. For x=0.0
sample as shown in the Fig. 4 (a) both FC and ZFC magnetization increases downward at
lower temperature even at higher applied magnetic field of 1 T and 6 T. The lower inset of
Fig. 4 (a) shows the enlarge view of FC magnetization at lower temperature in the applied
magnetic field of 1 T for x=0.0. On the other hand for x = 0.1 sample at higher magnetic field

of 1 and 6 T the FC and ZFC magnetization is observed to increase in upward direction
towards lower temperature. The increase of magnetization at lower temperature towards
upward direction indicates the existence of ferromagnetic component at low temperature. The
suppression of antiferromagnetic component at low temperature is also observed from
neutron diffraction study for x = 0.1 sample. The temperature derivative of ZFC
magnetization as a function of temperature has been plotted to understand the phase transition
for the samples as shown in the inset of Fig. 4 (a) and (b) for x=0.0 and 0.1, respectively. The
3
+
magnetic transition near 14 K may be attributed to the paramagnetic response of the Dy
ordering. For all the samples the low temperature magnetic transition is not affected for
higher applied magnetic field. Near 67 and 71 K temperatures an anomaly in ZFC and FC
curves as well as in inverse susceptibility curves is observed for x=0.0 and 0.1 samples,
respectively. Kagimiya and Tomiyasu describe the development of ferrimagnetic component
in the material near the temperature (Tferri) of 74 K using neutron diffraction experiments
[
13]. Ishibashi and Yasumi observed another low temperature anomaly in thermomagnetic
measurement at 31 K [21]. Tomitasu and Kagomiya reported this temperature to the onset of
the ordering of canted antiferromagnetic component of the magnetic structure of NiCr
13]. For the Dy doped samples same type of anomalies are observed near 33 K. Interestingly
this anomaly is not affected by Dy doping. At higher temperature above Tferri a magnetic
transition is observed in case of Dy doped NiCr samples. We have detected the secondary
phases of DyCrO as investigated from the neutron diffraction analysis. The high temperature
magnetic transition Tantiferro (139.4 K for x= 0.1) above Tferri is attributed to the canted
2
O
4
[
2
O
4
3
3
+
3
antiferromagnetic ordering due to the Cr spins in DyCrO [22]. It is interesting to notice that
the high temperature magnetic transition Tantiferro is absent in the thermomagnetic curve under
higher applied magnetic field.

The effective paramagnetic moment peff of the samples has been determined by the
Curie-Weiss law, χ = C (T −ΘCW ) (where C is Curie-Weiss constant and ΘCW is the Curie-
Weiss temperature) in the paramagnetic region of dc susceptibility for the samples. For
2
+
quenched orbital contribution the spin only effective moment ( µ = 2 S(S +1) ) for Ni is
S
3
+
2
.83 µ
B
. The spin only effective moment for Dy is 10.5 µ . The experimental values of peff
B
are observed to increase with increase in Dy content as listed in Table 2. The expected
effective paramagnetic moments for the samples are listed in the Table 2. The theoretical
values are slightly greater than the experimentally determined values of 5.74 and 6.41 µ
B
per
formula unit obtained from the fitting parameter in the paramagnetic regime using Curie-
Weiss law for x=0.0, 0.10 samples, respectively. The incomplete removal of frustration may
cause the comparatively low value of peff than the expected moment. The distortion leads to
the removal of frustration and therefore a long range order appears. The introduction of
3
+
3+
magnetic ions Dy having higher magnetic moment of 10.5 µ in place of Cr having
B
comparatively low magnetic moment leads to increase the magnetic moment with increasing
Dy contents. The decreasing magnitude of ΘCW with increasing Dy content reveals the
decreasing antiferromagnetic A-B interactions.
Néel-type ferrimagnetic temperature decreases with increase in Dy doping. The
frustration index is estimated by rearranging the Curie-Weiss equation as follows:
C
T
=
χΘCW ΘCW
−1
Figures 4 (c) and 4 (d) show the plot of C (χ ΘCW ) −1as a function of (T ΘCW ) for the
x=0.0 and 0.1 samples, respectively. The linear dependence of magnetization with the
magnetic field at higher temperature for the samples suggests that NiCr
2
O
4
is paramagnetic
above 70 K and NiCr1.9Dy0.1
O
4
is paramagnetic above 150 K. At the paramagnetic regime the

fitted straight line passed through the origin indicates the ideal Curie-Weiss behavior. The
negative deviation from the ideal line normally results in uncompensated antiferromagnetism
whereas the positive deviation from the straight line reveals the pure compensated
antiferromagnetic interactions. As shown in the Figs. 4 (c) and 4 (d), the samples exhibit
negative deviation from ideal line indicating uncompensated antiferromagnetism or
ferrimagnetism. The negative value of ΘCW as well as the low saturation magnetization for
the samples indicates the existence of non-collinear ferrimagnetic ordering in the samples. To
indicate which compound is more frustrated we have calculated the frustrated index of both
the parent and Dy doped samples. The frustrated index is defined as f= ΘCW /TN. The value of
frustration index f is listed in the Table 2. It is observed that all the samples are frustrated and
f decreases with increasing Dy content. The reduction of f with increasing x indicates the
most stabilization in Dy doped sample. The higher value of f indicates that pure NiCr
2
4
O is
magnetically more frustrated.
Figure 5 (a) shows the M-H hysteresis loops for x=0.0 at different temperatures. The
linear dependence of magnetization on the applied magnetic field above 70 K for x=0.0
sample reveals the paramagnetic ordering. The coercive field grows below the ferromagnetic
ordering temperature for x=0.0 sample. The suppression of magnetization hysteresis loop and
the linear increase of magnetization with applied magnetic field above 2.7 T are observed for
x=0.0 sample. It is interesting to notice that the linear increase of magnetization starts at
relatively higher applied magnetic field for x=0.1 sample. The linear increase of
magnetization is observed above 5.5 T magnetic field for x=0.1 sample near 5 K. At 5 K the
saturation magnetization is observed to be 0.3 µ
magnetization value by taking the collinear ferromagnetic configuration in NiCr
According to Kagimiya and Tomiyasu, the magnetic structure possibly consists of
B
per formula unit. But the expected
2
O
4
is 2.4 µ .
B

longitudinal ferromagnetic and transverse antiferromagnetic sublattices [13]. The linear
magnetization at higher field occurs due to the contribution of the slightly canting spins.
Figure 5 (b) shows the M-H hysteresis loops for x=0.0 and 0.1, respectively at 5 K.
The saturation magnetization is observed to increase with increase in Dy content. With
increasing Dy doping the initial field of saturation magnetization shifts to higher field due to
the presence of antiferromagnetic ordering requiring higher magnetic field to saturate. The
saturation magnetization increases with increase in Dy content below T may be due to the
N
3
+
3+
continuous rotation of Dy ions with canted Cr ions.
3
.3. Dielectric and magnetodielectric properties
NiCr
2
4
O is known to have magnetostriction. Substitution of rare earth ions in the
different spinel systems may lead to the structural distortion via strain [18,19]. Dy exhibits
large anisotropy and large magnetostriction values [20]. So it is interesting to study the effect
of Dy doping in NiCr
2
4
O system on the dielectric and magnetodielectric properties.
To investigate the effect of changes of spin and lattice structure between 71 and 30 K
on the magnetodielectric effect we have performed a careful study of applied magnetic field
and temperature dependent dielectric and magnetodielectric properties of NiCr
systems. Temperature dependent dielectric constant ε' of NiCr
anomalies near 30 K and near the ferrimagnetic Curie temperature of 72 K as shown in Fig. 6
a). Figure 6 (b) shows the derivative of the dielectric permittivity with respect to temperature
2
O
4
and
NiCr1.9Dy0.1
O
4
2
O
4
shows the
(
of Dy doped sample. Three shallow minima are observed near 30, 71, and 139 K as shown in
the Fig. 6 (b). The existence of dielectric anomaly near the magnetic and structural transition
temperature is a clear indication of the correlation between structural, magnetic, and
dielectric properties in the system. The slight change in dielectric permittivity near 71 K may
be attributed to the magnetostriction properties of NiCr
2
4
O . The anomaly in ε' near 140 K for

NiCr1.9Dy0.1
O
4
occurs due to the contribution of the orthorhombic DyCrO . The structural and
3
magnetic changes near 30 and 72 K have been investigated from neutron diffraction analysis
and magnetic study.
The magnetodielectric measurements have been carried out by measuring the change
in dielectric constant under applied magnetic field. The magnetodielectric effect is denoted as
MD% =
( )
ε′(H) − ε′(0) ×100/ ε′(0)where ε' is the dielectric constant. We have measured the
isothermal field dependent dielectric permittivity which shows a parabolic dependence on the
applied magnetic fields near magnetic transition temperature. The dielectric profile depends
on the applied magnetic field as shown in the Fig. 7. For NiCr
.045% is obtained with the existence of a hysteresis in MD% profile whereas the MD% is
observed to increase in NiCr1.9Dy0.1 . For Dy doped NiCr maximum MD% of 0.22% is
observed at 30 K. Figure 7 (c) and (d) show the magnetodielectric effect and square of
magnetization for NiCr1.9Dy0.1 at different temperatures of 50 and 90 K, respectively. In
2
4
O at 30 K maximum MD% of
0
O
4
2
O
4
O
4
order to understand magnetodielectric effect the parabolic dependence of isothermal field
dependent dielectric constant measurements have been performed. The thermodynamic
potential in a ferroelectromagnetic system in the framework of Ginzburg-Landau theory is
defined as [23]
2
2
2
2
Φ = Φ + αP − PE + α ′M − MH + γP M
0
where Φ is the thermodynamic potential; α, α′, and γ are temperature dependent
magnetodielectric coupling coefficients; M and P represent magnetic and electric
polarization, respectively; E and H denote electric and magnetic field, respectively. The
relative change in MD% with the change in magnetic field trace the curve similar to square of
magnetization vs. magnetic field behaviour for the samples at 30 K. The agreement between
MD% and the square of magnetization behaviour suggest that the magnetodielectric coupling

2
2
is originated from the term γP M of Ginzburg-Landau in the samples, as was earlier
proposed by Mufti et al. [11]. So the spin mediated magnetodielectric response is significant
in the samples. In order to demonstrate the magnetodielectric coupling effect one should
consider the spin-orbit coupling (λ. S. L, where L is orbital angular momentum and S is the
2
+
2+
total spin) of Ni . In case of NiCr
2
O
4
, Ni cation exhibit larger spin orbit coupling constant
of - 315 cm resulting in high magnetodielectric coupling [24]. DyCrO shows the
ferroelectricity and the magnetocapacitance effect. So the MD% can be affected by the
DyCrO phase in Dy doped NiCr . To understand the details of magnetodielectric response
further investigation is required in single crystals of NiCr
-1
3
3
2
O
4
2
4
O .
4
. Summary
In summary, both magnetic, dielectric and magnetodielectric properties have been seen to
increase with the substitution of Dy for Cr in NiCr . The antiparallel alignment of Cr and
2
O
4
Dy spin is confirmed from neutron diffraction studies. The AFM moments in A site and B
site are perpendicular to each other and therefore non collinear. The grown of tetragonal
structure possibly takes place by expansion of the lattice parameter a (plotted as 2 ) but
contraction of c for the distortion due to the substitution of Cr by rare-earth Dy. The Dy
modified sample shows higher magnetic moment and reveals the decreasing
antiferromagnetic A-B interactions after Dy doping in NiCr
2
O . The frustration index f
4
indicates the Dy doped sample as the most stabilized one and it may be due to the removal of
frustration after distortion by doping effect. The existence of dielectric anomaly near
magnetic and structural transition temperature is a clear indication of the correlation between
structural, magnetic, and dielectric properties in the samples. The MD% has been enhanced
may be due to the large magnetostriction value of Dy. Further investigation is required to
understand the details of the improved magnetodielectric response in the Dy modified
NiCr
2
4
O .

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Table 1
Structural parameters obtained from the neutron diffraction pattern at 6 and 300 K
temperatures for x=0.0 and 0.1 of spinel NiCr2-xDy
O
x 4
samples.
x=0
x=0.1
6
K
300K
6K
300K
I4/amd
5.7712
5.7712
8.5491
284.74
I4/amd
5.8315
5.8315
8.4096
285.98
I4/amd
5.7908
5.7908
8.5275
285.95
Fd-3m
8.3180
8.3180
8.3180
575.52
I4/amd
5.865
5.865
8.347
287.12
Fd-3m
8.3176
8.3176
8.3176
575.4321
a (Å)
b (Å)
c (Å)
3
V (Å )
Vol. fraction
80
14
8
86
(
%)
Ni-O (Å)
1.954
116.8
1.955
1.965
1.864
1.919
1.968
O-Ni-O (°)
115.9
110.9
116.2
112.1
116.4
109.5
116.7
113.3
117.49
112.53
112.9

Table 2.
Comparison between the Curie Weiss temperature, Curie Weiss constant, effective
paramagnetic moment, frustration index, theoretical value of moment, saturation
magnetization for x=0.0 and x=0.1 samples.
Θ
CW
C
peff
f
Theoretical Saturation
Sample
value (µ
B
)
magnetization at 5
K (µ
0.30
0.44
B
)
x=0.0
x=0.1
-286.7
-187.2
4.216 5.74 3.98
5.255 6.41 1.34
6.16
6.89
Figure Captions
Figure 1. Rietveld refined neutron diffraction pattern for (a) x=0.0 (b) x = 0.1 measured at
00 K. The tick marks (from top to bottom) indicate the position of reflections for tetragonal,
cubic and DyCrO phases.
3
3
Figure 2. Rietveld refined neutron diffraction pattern for (a) x=0.0 (b) x = 0.1 measured at 6
K. The tick marks (from top to bottom) for x= 0 sample indicate reflections corresponding to
tetragonal phase, propagation vector k=(001) and k=(000). The tick marks (from top to
bottom) for x= 0.1 sample indicate reflections corresponding to tetragonal phase, propagation
vector k=(000), k=(001), cubic phase and DyCrO .\\
3

Figure 3. Temperature dependent magnetic moments at tetrahedral (A) and octahedral (B)
sites for x=0.1 sample.
Figure 4. (a) ZFC and FC magnetization under the applied magnetic field of 100 Oe, 1 and 6
T for x=0.0. Upper inset shows dMFC/dT curves under the applied magnetic field of 100 Oe.
Lower inset shows the enlarge view of FC magnetization at lower temperature in the applied
magnetic field of 1 T for x=0.0. (b) Temperature dependent ZFC and FC magnetization at
different applied magnetic field for x=0.1 sample. Inset shows dMFC/dT curves under the
applied magnetic field of 100 Oe. (c) Normalized inverse susceptibility showing ideal Curie-
Weiss paramagnetism for x=0.0 sample. Inset shows temperature dependent inverse
susceptibility for x=0.0 (d) Normalized inverse susceptibility showing ideal Curie-Weiss
paramagnetism for x=0.1 sample. Inset shows temperature dependent inverse susceptibility
for x=0.1.
Figure 5. (a) M-H hysteresis loops at different temperatures for x=0.0. (b) Comparison
between M-H hysteresis loops measured at 5 K for x=0.0 and x=0.1 samples.
Figure 6. (a) Temperature dependent dielectric permittivity of x=0.0 at 10 kHz. (b)
Temperature dependent dielectric permittivity of x=0.1 collected at 10 kHz shows three
dielectric anomalies near 30, 71, and 140 K. The derivative of dielectric permittivity as a
function of temperature shows maxima near 30, 71, and 140 K.
Figure 7. The squared field-dependent magnetization plotted against the field-dependent
dielectric permittivity data collected at (a) 30 K for x=0.0 and (b) for x=0.1. Field-dependent
changes in the dielectric constant correlate with trends in the field-dependent squared
magnetization for x=0.1 at (c) 50 K and (d) 90 K.

Figures
Figure 1. P. R. Mandal et al.

Figure 2. P. R. Mandal et al.

Figure 3. P. R. Mandal et al.

Figure 4. P. R. Mandal et al.

Figure 5. P. R. Mandal et al.

Figure 6. P. R. Mandal et al.

Figure 7. P. R. Mandal et al.

•
•
2 4
NiCr O crystallizes in tetragonal phase with the space group of I41/amd whereas
3
4
NiCr1.9Dy0.1O crystallizes in the mixed phase of cubic (space group of Fd m) and
tetragonal phases at room temperature.
Both the samples show superlattice reflection peak indicating the presence of long
range AFM ordering (transverse component) below 40 K.
The saturation magnetization slightly increases after Dy doping.
•
•
2 4 4
An anomaly observed near Curie temperature in ε' (T) of NiCr O and NiCr1.9Dy0.1O
demonstrates the contribution of coupling between ferroelectricity and
ferrimagnetism in the compounds.
•
The spin-spin interactions are most likely responsible for the observed
magnetodielectric (MD) effect due to the magnetodielectric hysteresis in both parent
and doped samples. Interestingly the MD% is found to increase with Dy doping.