# Evidence for magnetodielectric and magnetocaloric effect in double
perovskite La2-xSrxCoMnO6 ($x$=0.0, 0.5, 1.0) induced by antisite disorder

Anasua Khan1, P.R. Mandal2∗, Swastika Chatterjee1, T.K. Nath1 and A.
Taraphder1,3,4 1Department of Physics, Indian Institute of Technology,
Kharagpur 721302, India
2Center for Nanophysics $\&$ Advanced Materials and Department of Physics,
University of Maryland, College Park, Maryland 20742, USA
3Centre for Theoretical Studies, Indian Institute of Technology, Kharagpur
721302, India
4School of Basic Sciences, Indian Institute of Technology, Mandi 175005, India

###### Abstract

We report magnetic, dielectric, magnetodielectric and magnetocaloric responses
of La2CoMnO6 (LCMO) and Sr doped La2-xSrxCoMnO6 ($x$ = 0.5 and 1.0) induced by
antisite disorder. Using first principles DFT calculations we find that
antisite disorder is enhanced with Sr-doping at La-sites. Co ions, which
appeared in 2+ high spin state in LCMO, were found to take up a mixed valence
state on Sr-doping, with one of the Co (Co3+) being in an intermediate spin
state and the other in 2+ high spin state. The dielectric constant of Sr doped
LCMO was found to increase whereas the magnetodielectric coupling was found
suppressed due to increase of antisite disorder. The magnetic field-dependent
magnetodielectric effect clearly shows M2 behaviour for all the samples in the
field range 0 to $\pm$6 T in their respective ferroic phases. All the samples
show spin glass like ordering in the ground state. We also report the magnetic
entropy change in magnetoelectric materials La2-xSrxCoMnO6 ($x$ = 0, 1.0)
samples. The change in magnetic entropy $\Delta$Sm comes mainly from the
combined effect of FM/AFM interaction and magnetodielectric effect in
La2-xSrxCoMnO6 ($x$ = 0, 1.0). The observed high value of magnetocaloric
effect (1.2 J/kg-K) for $x$=1.0 is likely to originate from the antisite
disordered phases near Curie temperature.

###### pacs:

77.22.-d, 75.85.+t, 75.30.Sg, 75.50.Dd.

##  I Introduction

Multifunctional materials are in the forefront of research due to their
intriguing properties which make them useful for a variety of device
applications. For example, magnetoelectric multiferroic materials, such as
SeCoO3, TbMnO3, CdCr2S4, EuO and CuO1 ; 2 ; 3 , exhibiting strong coupling
between magnetism and ferroelectricity have spawned a great research interest
due to their potential applications in multifunctional devices including
sensors4 , memories5 ; 6 , magnetic recording readers7 , transformers and
energy harvesting devices8 . However, the applicability of these materials in
real life devices is restricted if the Curie temperature is well below room
temperature. In this context double perovskite oxides bring in a lot of
promise. Of special interest to us is La2CoMnO6 (LCMO), which is a
ferromagnetic insulator and has been extensively studied both in its bulk and
thin film forms. Although the nature of the precise valence, spin and magnetic
state of Co and Mn was a matter of confusion initially, this was resolved
using X-ray absorption spectroscopy (XAS)9  and X-ray absorption near edge
spectroscopy (XANES)10 , which confirmed that in the ordered state, Co and Mn
are in high spin with 2+ and 4+ state, respectively. On the other hand in the
disordered phase, both the transition metals are in 3+ state, with Co being in
its intermediate spin-state and Mn in its high spin state11 ; 12 ; 13 ; 14 .
For the ordered arrangement of Co/Mn, LCMO shows a ferromagnetic transition at
Tc = 240 K, whereas for disordered arrangement of Co/Mn, low temperature
ferromagnetic transition gets triggered at Tc =150 K15 ; 16 .
Magnetodielectric (MD) effect has also been reported in thin films of LCMO
near its Curie temperature12 . The MD effect in LCMO is attributed to the
spin-lattice coupling as shown by K. D. Truong et al. in LCMO bulk sample13 .
Lin et al. has reported MD% of 0.8% at 280 K in polycrystalline LCMO17 . LCMO
also exhibits reasonably high magnetocapacitance which opens up potential
applications for spintronic devicesM ; N ; O ; P ; Q ; R ; S ; T ; U ; V . The
electrical and magnetic properties of double perovskites are strongly
controlled by nature and oxidation state of transition metal ions. For
example, substitution of Mo ion with W in case of Sr2FeMoO6 changes the ground
state from a ferromagnetic metal to antiferromagnetic insulator18 . An
interesting problem to study in this respect is the effect of hole doping at
the La site: how do the electronic and magnetic properties of LCMO double
perovskite change and how do the magnetodielectric and magnetocaloric
properties are effected. We therefore study the effect of doping Sr at the La
sites of LCMO, i.e, La2-xSrxCoMnO6, where $x$=0.0,0.5,1.0. Since anti-site
disorder, defined as imperfections created by inter-changing the position of
the transition metal ions in the perfectly ordered double perovskite, is
inevitable, we have also investigated the probability of its occurrence with
Sr doping and studied its impact on the physical properties of the system.

##  II Experimental and computational details

Polycrystalline samples of La2-xSrxCoMnO6 ($x$=0.0, 0.5, and 1.0) have been
synthesized by conventional chemical sol-gel technique. La2O3, Sr2(NO3)2,
Co(NO3)2, 6H2O, Mn(CH3COO)2, 4H2O are taken as the precursor materials.
Stoichiometric amount of La2O3 is dissolved into minimum amount of nitric acid
to convert it into lanthanum nitrate. Then Sr(NO3)2, Co(NO3)2, 6H2O; Mn
(CH3COO)2, 4H2O are dissolved in distilled water to make a clear solution and
then it is mixed with lanthanum nitrate. The final solution is then mixed with
citric acid (C6H8O7.H2O) in 1:1 ratio. The solvent is heated at 180∘C and
stirred continuously until a solid resin is formed. The finally obtained black
fluffy powder is ground and sintered at 1050∘C in air for 4 hours to produce
polycrystalline double perovskite manganites. For dielectric measurements, the
powders has been pelletized with diameter of 10 mm and sintered at 1100∘C for
5 h. The bulk samples of La2CoMnO6, La1.5Sr0.5CoMnO6, and LaSrCoMnO6 have been
designated as L1 ($x$=0), LS1 ($x$=0.5), and LS2 ($x$=1.0), respectively.

The phase purity has been checked by high resolution X-ray powder diffraction
technique (XRD, Philips Panalytical XPERT PRO) using Cu-K$\alpha$ radiation
($\lambda$ = 0.1542 nm) at room temperature. The Raman spectroscopy studies
have been performed in backscattering geometry with 514.5 nm Ar+ laser
excitation using a micro-Raman equipment with a spectrometer (model T64000,
JY, France) and a Peltier cooled CCD detector. The static magnetic
measurements have been performed using a SQUID-VSM magnetometer (Quantum
design, USA). 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., 8TCFMVTI).

All the theoretical calculations presented here have been done using density
functional theory (DFT) within the framework of generalized gradient
approximation(GGA)19 . For our DFT calculations, we have considered a
combination of two different methods, namely a plane-wave based pseudo-
potential method as implemented in the Vienna ab-initio simulation package
(VASP)20 ; vasp  and full potential linear augmented plane wave (FPLAPW) as
implemented in WIEN2k code21 . The plane-wave-based VASP method was used for
structural minimization, while the electronic structures in the energy-
minimized crystal structures were calculated using both FPLAPW and
psedopotential method. The accuracy of the electronic structure calculations
within the scheme of the two methods have been checked with respect to each
other. In the plane wave based pseudopotential calculations, reciprocal space
integration was carried out with a $k$ mesh of 8$\times$8$\times$4\. We have
used projector augmented wave (PAW) potentials and the wave functions were
expanded in the plane-wave basis with a kinetic-energy cutoff of 450 eV. The
ionic positions have been relaxed using a conjugate-gradient algorithm, until
the Helmann-Feynman forces become less than 0.005 eV/Å. The spin-orbit
coupling was taken into account self-consistently. To include the strong
correlation effects in the 3$d$ electrons of Co and Mn, we used the spin-
polarized GGA plus Hubbard U (GGA + U)22  method, as in the Dudarev’s
implementation22 , with U-J = 3 eV. In the full potential linear augmented
plane wave, the muffin-tin radii are chosen to be 2.20, 2.00, 1.85, 1.96, and
1.45 a.u. for La, Sr, Co, Mn and O atoms, respectively. We have taken Lmax=12
for spherical harmonic expansion of the wave function inside the sphere and
Gmax=14 for the charge Fourier expansion. We have set the basis set parameter
RmtKmax=7.00 for the plane wave expansion where the Rmax is smallest muffin-
tin radius and largest K vector is Kmax. The energy convergence criteria for
self-consistence calculations are set to 10-5 eV. In the calculations spin-
orbit coupling was included in scalar relativistic form as a perturbation to
the original Hamiltonian. Hubbard on-site $d-d$ coulomb interaction U (nominal
value of U-J= 3 eV.) was also included at Co and Mn site.

##  III Results and discussion

###  III.1 Structural analysis

####  III.1.1 X-Ray diffraction study

Figure 1: Rietveld refined XRD pattern of (a) L1 (b) LS2 (c) LS2 sample with
red dot represent experimental data and black line represents the calculated
pattern. The green line represents the difference between the observed and
calculated fit pattern.

Figure 1 shows high resolution XRD patterns of samples at room temperature.
The Rietveld analysis of HRXRD patterns indicates that the parent compound L1
crystallizes in pure monoclinic structure with the space group of P21/n; LS1
and LS2 samples exhibit mixed rhombohedral (with the space group of
$R\overline{3}c$) and monoclinic (space group P21/n) crystal structures. In
$R\overline{3}c$ Co and Mn ions are randomly distributed in octahedral sites
having wyckoff position 6b whereas in monoclinic phase the ions are occupied
distinguished octahedral sites having wyckoff position of 2d and 2c. The
volume fraction ratio of rhombohedral to monoclinic phases are found to be
0.34:0.66 and 0.82:0.18 for LS1 and LS2 samples, respectively. It is observed
from Rietveld analysis that the volume of the cell enhances with substitution
of Sr at La site due to the larger ionic radius of Sr2+ (1.32 Å) than La3+
(1.17 Å). In case of hole doped samples having rhombohedral structure the
Mn/Co-O bond length lies around 1.96 Å and Mn-O-Co bond angle is greater than
165∘23 . The higher value of bond angle of L1 than LS2 leads to more
favourable ferromagnetic alignment24 . Distortion may arise in the perovskite
mainly for two reasons: (1) ionic radius mismatch at A site (rare earth site)
and (2) the Jahn-Teller distortion due to MnO6 and CoO6 octahedra. For larger
ionic size mismatch, local Jahn-Teller distortion is enhanced leading to the
tilting of transition metal ion octahedra25 ; 26 . Theoretically, the
tolerance factors is defined by geometrical index Goldschmidt tolerance
factor,

$t=\frac{\frac{(r_{A}+r_{A^{\prime}})}{2+r_{o}}}{\sqrt{2}{\frac{r_{B^{\prime}}+r_{B^{\prime\prime}}}{2+r_{o}}}}$
(1)

where $r_{A}$, $r_{A^{\prime}}$, and $r_{B^{\prime}}$, $r_{B^{\prime\prime}}$
are the average ionic radius of A site and B site ions, respectively and
$r_{o}$ is the ionic radius of O2-. The tolerance factor $t$ is unity for
cubic structure and less than unity for monoclinic structure. The tolerance
factor varies from 0.85 to 0.89 from undoped to Sr doped sample. Consequently,
the Mn-O and Co-O bond length are elongated with increasing Sr content. The
Co-O-Mn bond angle decreases with increasing doping concentration. It may be
inferred that the change in bond angle induces a distortion by the
substitution of Sr in the crystal lattice of La2CoMnO6.

####  III.1.2 Raman spectroscopy

Raman spectroscopy provides important information about the local structure of
different microphases and macrophases present in any system. We have performed
unpolarized Raman spectroscopy study with 514.5 nm Ar+ laser excitation at
room temperature. The peaks are analysed by fitting the Raman spectrum with
Lorentzian functions. The unpolarised Raman spectroscopy of undoped and Sr
doped samples at room temperature are shown in Fig. 2. The ideal double
perovskite A2BB′O6 consisting of B/B′ ordering is comprised of face-centered
cubic symmetry with space group of $Fm3m$. In Raman spectra the wave number
and relative intensity of the peaks for LCMO is intimately related to the
degree of distortion from the ideal cubic crystal structure. With substitution
of Sr2+ having larger ionic radius at La3+ results in rotations or tilting of
BO6 and B′O6 octahedra. As a result the A and B site cations shift or B site
ordering changes by disturbing the crystal symmetry, such that Raman active
modes appear at the Brillouin zone centre27 ; 28 . According to the
theoretical analysis Raman modes are forbidden in simple cubic perovskite
having space group of $Pm\overline{3}m$ because of the appearance of atoms at
the centre of symmetry. Two clear peaks in Raman spectra are observed at 485
and 642 cm-1 for La2CoMnO6 as shown in Fig. 2 (a). This experimental results
can be compared with the theoretical prediction of Raman shift with monoclinic
structure observed by Ilive et al.29 . In case of ordered monoclinic (P21/n)
structure 24 (12Ag+12Bg) Raman modes are allowed according to the lattice
dynamical calculations. The low frequency antistretching and bending modes
near 490 cm-1 corresponds to Bg symmetry and the high-frequency stretching
mode near 642 cm-1 corresponds to the Ag symmetry. According to group theory
analysis for an ideal rhombohedral structure with $R\overline{3}c$ space group
the $\Gamma$-point phonons (4A1g+9Eg) are Raman allowed where the eigenvectors
of A1g, doubly degenerate Eg modes involve oxygen motions.

Figure 2:  Raman spectroscopy data of (a) L1 (b) LS1 (c) LS2 samples at room
temperature. Inset shows the Raman modes near 240 cm-1 corresponding to
rhombohedral structure with A1g symmetry.

As shown in the inset of Fig. 2 (b) Raman modes near 240 cm-1 corresponds to
rhombohedral structure with A1g symmetry for LS1 sample. The Raman spectra is
dominated by two broad peaks at around 490 and 640 cm-1 which can be compared
with the Raman shifts corresponding to the monoclinic structure in LS2 sample
as shown in the Fig. 2 (c). The peak position at 240 cm-1 as shown in the
inset of Fig. 2 (c) corresponds to the vibrations of rhombohedral structure of
LS2 sample.

###  III.2 Structural optimization using first principles DFT

In order to theoretically study the effect of Sr doping at La site of
La2CoMnO6(LCMO), we have performed a comparative study of LCMO and LSCMO.
La2CoMnO6(LCMO) is known to crystallize in the P21/n space group. The unit
cell contains two formula units, such that there are 4 La, 2 Co, 2 Mn and 12 O
atoms per unit cell. Starting from the experimentally obtained crystal
structure we have optimized the lattice parameters and atomic positions of the
LCMO to obtain the ground state crystal structure. Figure 3 shows ordered
arrangement of pure LCMO. Here every CoO6 octahedra shares its corners with
six MnO6 octahedra. Any other type of arrangement of Co and Mn will result in
antisite disorder. For example, in a unit cell of LCMO, anti-site disorder can
arise in two different ways, namely, when the center of all the octahedra in a
given ab-plane is occupied by the same species, i.e, Co or Mn and when the
centres of all the octahedra belonging to a given ac-plane is occupied by the
same species. We will therefore have alternating layers of CoO6 and MnO6 in
the [001] and [010] direction, respectively. We find that the difference
between the ordered structure and the energetically most favoured disordered
structure is 0.22 eV/$f.u$. We next try to see the effect of Sr doping on the
crystal, electronic and magnetic structure of LCMO. With increased doping of
Sr at La sites of La2CoMnO6, a rhombohedral phase having a space group or
$R\overline{3}c$ becomes more and more dominant. With La:Sr = 1:1, we
experimentally find that the volume ratio of P21/n and $R\overline{3}c$
structures is 0.66 : 0.34. Therefore, we have investigated both the phases of
LaSrCoMnO6. Since Sr2+ having a ionic radius of 1.32 Å is doped in place of
La3+ which has a ionic radius of 1.17 Å, it is expected that the crystal,
electronic and magnetic structure will be altered. In the monoclinic phase,
which is the dominant phase for 50% Sr doping at La sites, Sr can be doped in
three different ways, namely alternating layers of A-site in the ab-plane
consisting of Sr and La respectively, alternating layers of A-site in the ac-
plane consisting of Sr and La respectively and each Sr ion has La ions as
first nearest neighbour and vice-versa.

Figure 3: Room temperature ordered structure of (a) LCMO and (b) Sr doped
LCMO. Here the centre of the blue and yellow octahedra are occupied by Co and
Mn respectively. The La and Sr atoms presented as green and light blue big
ball sit in the hollow formed by Mn and Co Octahedra.

For each of these three atomic arrangement of Sr, the Co and Mn ions can take
up either the ordered configuration, where each CoO6 octahedra shares its
corners with six MnO6 octahedra and vice-versa and two disordered
configurations where there are alternating layers of Co and Mn along the [001]
and [010] direction, respectively as already explained earlier. In the
monoclinic phase, which is dominant, the MnO6 and CoO6 octahedra are no longer
regular. The octahedra around Mn and Co ions are both distorted and tilted. We
have calculated the total energy for all these configurations. We find that
the ordered structure always posesses lowest energy, i.e, it is the most
stable configuration even in the presence of Sr doping. However, the
difference between the lowest energy ordered structure and the lowest energy
disordered structure is found to decrease significantly with Sr-doping, the
difference being 0.11 eV/$f.u$.

We have also seen the effect of Sr-doping on the rhombohedral phase. Each unit
cell of rhombohedral LCMO contains 3 formula units and 6 La atoms, 3 Co atoms,
3 Mn atoms and 18 O atoms. The energy difference between LCMO in monoclinic
phase and LCMO in rhombohedral phase is seen to decrease by about 40% with Sr
doping. Hence, total energy calculations suggest that with Sr doping, the
appearance of rhombohedral phase becomes favorable, thus corroborating our
experiments. In the rhombohedral structure, Co and Mn both occupy a single
crystallographically in-equivalent site, with wykoff position 6b. Therefore
out of the 6 crytallographycally equivalent site, 3 are Co and 3 are Mn. These
Co and Mn atoms can therefore be arranged in 20 different ways. By analysis of
these 20 structures, we find that symmetrically there are just three in-
equivalent configurations. We perform total energy calculations of these three
configurations and find that the energy difference between the lowest energy
structure and the energy of the structure that is closest to this equilibrium
structure is 0.29 eV/$f.u.$. We next dope 50% Sr at the La sites and see its
effect on the said difference. Similar to the monoclinic case, we see that
this difference (0.18 eV/$f.u.$) decreases. Therefore, we can conclude from
total energy calculations that with Sr doping at La sites, disorder becomes
favourable as compared to when there was no Sr doping.

###  III.3 Electronic Structure

Using first principles DFT we find that pristine LCMO is a ferromagnetic
insulator. The Co and Mn ions are in their high spin 2+ and 4+ valence state
and total moment of the unit cell comes out to be 6 $\mu_{B}$/$f.u.$.
Experimentally the magnetic moment of LCMO is 5.78 $\mu_{B}$/$f.u$. at 5 K and
50 kOe11  which is close to our calculated moment. Spin-polarized partial
density of states (PDOS) of ordered LSCMO is shown in the Fig. 4. There is a
very strong hybridization between O-$p$ and Co/Mn-$d$ states and the $d-p$
hybridized bands extend from an energy range about -8 eV below the Fermi level
(EF) to about 4 eV above EF. For ordered LSCMO there are two in-equivalent Co
and Mn ions. For both the Mn ions, the up-spin channel of the $t_{2g}$ band is
completely occupied whereas the down-spin channel of the $t_{2g}$ is
completely empty with the $e_{g}$ level lying above EF. This suggests that the
Mn ions are in high spin 4+ charge state.

Figure 4: Spin polarised partial density of states of Co-$d$, Mn-$d$ and O-$p$
in ordered LSCMO.

The calculated magnetic moment of 2.9 $\mu_{B}$ also suggests the same. In
case of Co ions, the majority spin channel of both $t_{2g}$ and $e_{g}$ is
completely filled, whereas the minority spin channel of the $t_{2g}$ band is
partially filled. The magnetic moment at Co is calculated to be 2.8 $\mu_{B}$.
This suggests that Co is in high spin 2+ charge state. The hole (which appears
because of Sr2+ doping at La3+ site) is seen to be accommodated by the Co and
O atoms. The moment of the Co ion increases by 0.3 $\mu_{B}$ and the average
moment on the O-ions increases by 0.1 $\mu_{B}$ with hole doping. The
saturation magnetic moment is found to be 7.0 $\mu_{B}$/$f.u$. in confirmation
with previous results11 .

Figure 5: Spin-polarised partial density of states of Co-$d$, Mn-$d$ and O-$p$
in lowest energy disordered LSCMO structure.

The partial DOS for disordered LSCMO is shown in Fig. 5. Similar analysis of
the Mn ions shows that Mn is in high spin 4+ charge state with a magnetic
moment of 2.96 $\mu_{B}$. Co ions are found to be in mixed valence state with
the calculated magnetic moment of Co1 ion being 1.97 $\mu_{B}$ and Co2 ion
being 2.87 $\mu_{B}$. A study of the PDOS of Co2 suggests that it is in a
high-spin 2+ charge state. In order to analyze the spin and charge state of
Co1 ion we plot the partial DOS (Fig. 6) of the Co1 ion projected onto its
individual d-orbitals. The PDOS character and the moment of the Co1 ion
suggests that it is in an intermediate spin state ($t_{2g}^{5}$ $e_{g}^{1}$
with spin (S=1)). Total magnetic moment of the cell 6 $\mu_{B}$/$f.u$. It is
to be noted, that because of very strong co-valency between O-$p$ and
Co/Mn-$d$, the calculated magnetic moments at the transition metals sites do
not comply very well with what calculated using a ionic model. For example, in
ordered LSCMO we found that because of very strong co-valency, the hole is
shared by Co and O ions.

Figure 6: Spin polarised partial density of states of Co1-eg levels (upper
panel) and Co1-t2g levels (lower panel).

Similarly, in the case of disordered LSCMO, as we replace 50% of La3+ by Sr2+,
it is expected that two of the Co2+ ions will convert to Co3+ to maintain
charge balance. However, we find one of the Co converts to 3+ and the other
stays back in 2+ charge state. Analysis of the crystal structure shows that
one of the Co2-O bonds along the z axis is much smaller than the other (Fig.
7(b)).

Figure 7: (a) Charge density plot of disordered LSCMO projected onto the bc
plane. (b) Schematic diagram showing the Co1-O and Co2-O bond lengths along
the Z direction in disordered LSCMO. (c) Schematic showing the energy level
splitting of Co1-$d$ and their respective occupancies.

As a result the co-valency is very strong along this shortened bond making the
hole being shared to a great extent by the O ion of this bond as can be seen
from the charge density plot given in Fig. 7(a). We find that the magnetic
moment on this O-atom is higher than the rest by 0.3 $\mu_{B}$. In order to
unravel the microscopic origin of the spin state of Co1, we perform further
analysis of the crystal structure of disordered LSCMO. We find that the
average bond length along the x-y plane is shorter by 0.05 Å in the case of
Co1 as compared to Co2. This makes the $d_{{x^{2}}_{-}{y^{2}}}$ level rise
higher up in energy as compared to the $d_{z^{2}}$ level, thus giving rise to
an intermediate spin state. The schematic energy level diagram is shown in
Fig. 7(c).

###  III.4 Dc magnetisation study

In order to understand the magnetic properties of the samples temperature
dependent dc magnetization measurements have been performed. The magnetization
as a function of temperature under the applied magnetic field of 100 Oe is
shown in the Fig.8 (a), (b), and (c) for L1, LS1, and LS2 samples,
respectively. The transition temperature TC (paramagnetic $\rightarrow$
ferromagnetic phase transition) of each sample is determined from the point of
inflection in the differential curve of magnetization (dM/dT) as shown in the
inset. It is clear from the Fig. 8 that all the magnetization curves show two
phase

Figure 8: Temperature dependent dc magnetisation under the magnetic field of
100 Oe. Insets show dM/dT vs T curves indicating the magneting transition
temperature.

transitions except L1 sample. The high and low temperature magnetic transition
are denoted as TC1 and TC2, respectively. The atomically ordered superexchange
interaction of high spin Co2+ (${\bf d^{7}}$:
$t_{2g}^{5}e_{g}^{2}$)-O-Mn4+(${\bf d^{3}}$: $t_{2g}^{3}e_{g}^{0}$) is
responsible for the high temperature magnetic transition at TC1. The vibronic
superexchange interaction of intermediate spin Co3+(${\bf d^{6}}$:
$t_{2g}^{5}e_{g}^{1}$)-O-high spin Mn4+(${\bf d^{3}}$: $t_{2g}^{3}e_{g}^{0}$)
causes the low temperature transition at TC2. It can be observed from Fig. 8
that with increasing doping concentration the features of two phase transition
are more salient. The long range ferromagnetic ordering originating from the
superexchange interaction of Co2+-O-Mn4+ is supressed due to the Sr doping at
A site30 . Furthermore antiferromagnetic Co3+-O-Co3+ or Co2+-O-Co2+
interactions appear by the antisite disorder with Sr doping31 .

###  III.5 Dependence of linear ac susceptibility on average A-site radius

In order to understand the magnetic behaviour and relaxation process of the
parent and doped compounds we have performed the first harmonic in-phase ac
susceptibility measurement under an applied magnetic field of 3 Oe. The
temperature dependent in-phase component of ac susceptibility ($\chi_{1}^{R}$)
at several frequencies is shown in the Fig. 9 (a), (b), and (c) for L1, LS1,
and LS2 samples, respectively. The parent compound shows frequency dispersion
below Curie temperature (200 K) whereas the doped LS1 sample shows frequency
dispersion near Curie temperature. For all samples, the susceptibility peaks
shift towards higher temperature and are reduced in magnitude with increase in
frequency suggesting the glassy nature of the systems. In case of LS2 sample
the glassy transition is observed near 174 K. As shown in the inset of Fig. 9
(a), (b), (c) for L1, LS1, LS2 samples, respectively the critical slowing down
model is used to determine the critical relaxation time ($\tau$0) expressed as

Figure 9:  Temperature dependent real part of ac susseptibility of (a) L1, (b)
LS1, and (c) LS2 samples. The inset of figures show the plot of $ln\tau$ as
afunction of temperature T for the corresponding samples.

$\tau=\tau_{0}(\frac{T_{f}}{T_{g}}-1)^{-z\nu}$ (2)

where Tf is frequency dependent peak of ($\chi_{1}^{R}$), z$\nu$ is the
critical exponent of correlation length and Tg is spin glass transition
temperature. The parameters for L1, LS1 and LS2 samples which are obtained
from best fitting are shown in Table I. The values for different parameters
indicate that a spin glass like signature is present in L1 sample.

Table 1: The obtained fit parameters for different samples from ac susceptibility measurements. Samples |  $\tau$0 (sec) | z$\nu$ | Tg (K)
---|---|---|---
L1 | 2$\times$10-11 | 3.3 | 200
LS1 | 1.38$\times$10-11 | 4.06 | 216
LS2 | 3$\times$10-11 | 4.65 | 174

For LS1 sample the spin glass like ordering around FM-PM transition
temperature is confirmed by the values of parameters shown in the Table I.
Also the presence of spin clusters with FM ordering near transition
temperature is confirmed by frequency dependent ($\chi_{2}^{R}$) measurement
(not shown here). So for LS1 sample the FM state is assigned to the formation
of glassy ferromagnetic state. The signature of spin glass like ordering is
also present in LS2 sample. The presence of various ferromagnetic exchange
interactions Co2+-O-Mn4+, Co3+-O-Mn4+ and antiferromagnetic exchange
interactions Co2+-O-Co2+, Co3+-O-Co3+ due to antisite disorder may cause the
glassy state in the doped and undoped LCMO system.

###  III.6 Dielectric and Magnetodielectric properties

Figure 10 (a), (b), and (c) show the temperature dependent real part of
dielectric constant $\epsilon^{\prime}$ at different frequencies for partially
disorder L1, Sr doped LS1 and LS2 samples. At low temperature the dielectric
constant becomes frequency and temperature independent revealing the intrinsic
dielectric properties. Two types of dielectric relaxations (as marked) are
evident as shown in the Fig. 10 for the samples.

Figure 10: Temperature dependent real part of dielectric constant at different
frequency of (a) L1, (b) LS1, and (c) LS2 samples. In the inset of (c) the
black symbols denote $tan$ $\delta$ and red symbol denotes
$\epsilon^{\prime\prime}$.

The dielectric relaxation may arise from the dipolar relaxation which
originates from the asymmetric hopping of charge carriers under the applied
electric field32 . The presence of different number of accumulated charge
carriers in different regions in the sample (may be near grain boundaries) may
also cause the dielectric relaxation which is known as Maxwell-Wagner
relaxation. The strong frequency dependent large variation of
$\epsilon^{\prime}$ indicates the extrinsic polarization due to Maxwell-Wagner
effect for the samples at low frequencies. With lowering temperature the step
like drop in dielectric anomaly shifts to low temperature with decreasing
frequency. Same type of dielectric anomaly is reminiscent of different systems
such as CaCuTi4O12, La2-xSrxNiO4 etc. having colossal dielectric
permittivity33 ; 34 ; 35 . With increasing temperature the dielectric constant
possesses a colossal value which is attributed to the extrinsic effect on
polarization due to Maxwell-Wagner interfacial polarization effect.
Interestingly, with increasing Sr content the temperature corresponding to the
step like drop shifts to lower temperature and $\epsilon^{\prime}$ is found to
increase.

The electrons hop between Co2+ and Mn4+ ions in B-sites resulting in charge
transfer which introduces dipole moment yielding the relaxation in dielectric
property. This hopping of electrons will produce a charge transferred state
with Co2+δ and Mn4-δ, and it introduces a large dipole moment resulting in
dielectric relaxation. The hopping of electrons between Co2+ and Mn4+ ions,
cannot follow the applied external electric field at higher frequencies
leading to relaxor-like behaviour36 . The relaxor-like behaviour instead of
relaxor dielectrics can also be evidenced from the peak mismatch of
temperature dependant $tan$ $\delta$ and $\epsilon^{\prime\prime}$ as shown in
the inset of Fig. 10 (c) for LS2 sample. In Sr doped LS1 sample the
introduction of hole carriers enhance the hopping of electrons by the antisite
disorder. With more antisite disorder introduced in the LS2 system, the
probability of hopping is enhanced and it leads to the large dielectric
constant. The activation of electrons in Mn3+/Mn4+ and Co2+/Co3+ is another
possible reason for dielectric relaxation in the parent compound whereas for
hole doped LS1 sample the dielectric relaxation happens due to activation of
electrons in Mn4+ and Co2+/Co3+. Each Co2+ surrounded by Co3+ may cause local
polarization by forming dipole. The electron hopping between Co2+, Co3+ and
Mn4+, under an applied electric field contributes to the large dielectric
constant. Similarly, the giant dielectric constant is attributed to the
ordering of Fe2+ and Fe3+ in the arrangement of polar symmetry in LuFe2O437 ;
38 .

Figure 11:  (a) Temperature dependent MD% at 500 kHz for L1. Upper inset shows
the field dependent square of magnetisation plotted against the field-
dependent dielectric permittivity recorded at 200 K for L1 sample. Lower inset
shows temperature variation of real part of dielectric
constant($\epsilon^{\prime}$) at frequency of 500 kHz and the magnetic field
of 0 and 5 T for L1 sample. (b) and (c) show temperature dependent
$\epsilon^{\prime}$ at the frequency of 500 kHz for LS1 and LS2 samples,
respectively at 0 and 5 T field. Upper and lower inset of (b) and (c) show MD%
and the field-dependent square of magnetisation plotted against the field-
dependent dielectric permittivity recorded for LS1 and LS2 samples,
respectively.

The magnetodielectric effect is defined as MD% = [$\epsilon^{\prime}$(H) -
$\epsilon^{\prime}$(0)/$\epsilon^{\prime}$(0)]%, where $\epsilon^{\prime}$(H)
and $\epsilon^{\prime}$(0) are dielectric constant under applied and zero
magnetic field, respectively. In order to investigate the Sr doping effect on
magnetodielectric (MD) coupling we have performed MD measurements under the
magnetic field of 5 T. Figure 11 (a), (b), (c) show the dielectric constant at
the magnetic field of 0 and 5 T for L1, LS1, and LS2 samples, respectively at
500 kHz. The high frequency measurement at 500 kHz has been recorded to avoid
the polarization due to external effect. The MD value at low and high
temperature is nearly 2% for L1, whereas it increases with increase in
temperature from 175 K and attain maximum value of 11% near the dielectric
step and magnetic transition temperature. The [Fig. 11(a)] appearance of MD
peak near magnetic transition temperature probably is an evidence of
correlation between dielectric and magnetic ordering. Large magnetodielectric
shifts are observed in the more disorder LS1 and LS2 samples away from the FM
$\rightarrow$ PM transition temperature region. The observed maximum value of
MD% [Fig. 11(b and c)] near the peak in temperature dependent MD curve reduces
from 11% to 6% at 500 kHz for L1 to LS2 samples. The increasing magnetic field
supresses the antiferromagnetic antisite disorder phases, which results in a
reduction of MD effect for higher concentration of Sr doped samples.

In order to understand the possible intrinsic or extrinsic MD effect the
isothermal field variation of dielectric constant measurements have been
performed near the MD peak temperature. In a multiferroic the thermodynamic
potential in the framework of Ginzburg-Landau theory for second order phase
transition is defined as39 .

Figure 12: Isothermal magnetisation curves recorded at different temperatures
between 110 K and 290 K in the temperature interval of (a) 3 K for L1 and (b)
5 K for LS2 sample. (c) and (d) show Arrott plots (H/M vs M2) of different
magnetic isotherms for L1 and LS2 samples, respectively.

$\Phi=\Phi_{0}+\alpha P^{2}-PE+\alpha^{\prime}M^{2}-MH+\gamma P^{2}M^{2}$ (3)

where $\Phi$ is the thermodynamic potential; $\alpha$, $\alpha^{\prime}$, and
$\gamma$ are temperature dependent magnetodielectric coupling coefficients; M
and P denote magnetic and electric polarization, respectively; E and H are
electric and magnetic field, respectively. The difference of relative
dielectric constant at zero and 5 T magnetic field is proportional to the
square of the magnetic-order parameter (magnetisation) below ferromagnetic
transition temperature $\delta$$\epsilon^{\prime}$$\approx$ $\gamma$M2. The
sign of $\delta$$\epsilon^{\prime}$ depends on the sign of constant
magnetodielectric interaction $\gamma$. We have measured the magnetodielectric
effect at a frequency of 500 kHz as the Maxwell-Wagner contribution to the
dielectric constant is suppressed at higher frequencies. In case of L1 sample
(as shown in the inset of Fig. 11 (a)) the change of magnetization square with
respect to the applied magnetic field depicts almost identical variation of
field dependent MD% indicating the spin mediated magnetodielectric coupling.
The relative change in MD% with changing magnetic field trace the squared
magnetization vs H curves below 2 T near 125 K for LS1 sample. The field
dependent magnetodielectric effect at low fields (up to 4 T) follow the trends
of the change of isothermal field dependent squared magnetization for LS2
sample at 110 K as shown in the lower inset of Fig. 11 (c). The agreement
between M2 and MD% for all the three samples illustrates that the spin
mediated magnetodielectric coupling term $\gamma P^{2}M^{2}$ of Ginzburg-
Landau theory is significant in all the three samples.

###  III.7 Magnetocaloric effect

To observe the magnetocaloric effect (MCE) in the undoped and Sr doped samples
we have chosen the samples L1 and LS2. Fig. 12 (a) and (b) show the isothermal
initial M (H) plots in the vicinity of TC with temperature interval of 3 K and
5 K for L1 and LS2 samples, respectively. For L1 sample the isothermal curves
of M (H) have been recorded in the temperature range of 110 to 290 K with the
applied magnetic field up to 6 T. As shown in the Fig. 12 (a) and (b) it is
clear that M (H) curves show rapid increase at low field as expected from
sample with ferromagnetic ordering. The magnetization is observed to decrease
with increase in temperature for both the samples. To determine the nature of
the magnetic phase transition from ferromagnetic to paramagnetic state in L1
and LS2, the Arrott plots, i.e., H/M versus M2 isotherms around TC deduced
from M (H) isotherms have been analysed. According to Banerjee criterion the
positive and negative slopes in the Arrott plots indicate second and first
order magnetic phase transition, respectively. In the present investigation
the observed positive slopes in the Arrott plots around TC is a clear
indication of second order like magnetic phase transition for both L1 and LS2
samples as shown in the Fig. 12 (c) and (d), respectively. Magnetocaloric
effect can be determined either by isothermal entropy change $\Delta$$S_{m}$
by the measurement of M (H) isotherms at different temperatures (or specific
heat measurements) or the adiabatic temperature change $\Delta$T by the
application of magnetic field. Since calorimetric measurement is a long
process, the measurement of magnetocaloric effect generally is carried out by
the Maxwell relation and M (H) isotherms. The temperature dependent change in
magnetic entropy can be evaluated from the isothermal magnetization curves at
different temperatures using the integral of Maxwell relation

$\Delta S_{m}=\int_{0}^{H}|{\frac{\partial M}{\partial T}}|dH$ (4)

For the undoped and hole doped LCMO sample the change in entropy is estimated
from the isothermal magnetization curves at different temperatures for the
applied magnetic field of 1 to 6 T. The change in entropy can be approximated
as

$\Delta S_{m}=\sum\frac{M_{i+1}-M_{i}}{T_{i+1}-T_{i}}\Delta H$ (5)

where Mi+1 and Mi are experimental values of magnetization measured with a
corresponding magnetic field of H at the temperatures of Ti+1 and Ti,
respectively. $\Delta$$S_{m}$ is equivalent to the area difference between two
isotherms divided by the temperature difference between the corresponding
isotherms. Figure 13 shows the temperature dependent magnetic entropy change
for the compounds under different applied magnetic fields using Eq. 5. The
value of magnetic entropy change ($\Delta$$S_{m}$) is expected to be maximum
at the magnetic phase transition temperature where the M (T) changes rapidly.

In paramagnetic region magnetization changes linearly whereas below Curie
temperature the magnetization rapidly increases with application of smaller
magnetic field and it is a basic characteristics of a ferromagnetic material.
The value of $\Delta S_{m}$ shows maximum near transition temperature TC and
it decreases above and below TC. The broad peak near TC reveals the presence
of short range ferromagnetic ordering above TC. It is observed that for L1
sample $\Delta S_{m}$ exhibits a maximum with a broadening near 210 K and
reaches a maximum value of 1.17 J/kg-K for $\Delta$H= 6T where the magnetic
phase transition as well as dielectric anomaly are observed. LS2 sample
exhibits two ferromagnetic phase transitions at 266 K and 187 K corresponding
to order and disorder phases. Figure 13 (b) shows $\Delta S_{m}$ as a function
of temperature at different applied magnetic fields corresponding to the
disorder phases whereas the inset of Fig. 13 (b) shows $\Delta S_{m}$ of order
phase at the same applied magnetic fields. The maximum entropy change is
observed to be 1.2 J/kg-K near 185 K for disorder LS2 sample when the magnetic
field is changed from 0 to 6 T whereas for order LS2 sample the value of
$\Delta S_{m}$ is found to be quite low (0.32 J/kg-K at 6 T).

Figure 13: Temperature dependent magnetic entropy $\Delta S_{m}$ at different
magnetic field for (a) L1 and (b) LS2 samples.

The large broadening of $\Delta S_{m}$ profile over a wide temperature range
causes an increase in refrigerant capacity (RC). To understand the efficiency
of the magnetic refrigerant we have calculated the relative cooing power (RCP)
which can be calculated by the relation, RCP=$\int_{T_{1}}^{T_{2}}{\Delta
S(T)}dT$, where T1 and T2 are the temperature corresponding to the full width
at half-maximum40 . The RCP value as a function of applied magnetic field of
L1 and LS2 is shown in Fig. 14 (a) and (b), respectively. The maximum value is
obtained to be 42 J/kg and 112 J/kg at the magnetic field of 6 T for L1 and
LS2, respectively. The estimated values of $\Delta S_{m}$ and RCP for LS2 is
in good agreement with those observed in various manganites41 . RCP increases
almost linearly with increasing field. There are different experimental
evidence where the coexistence of two magnetic phases in the magnetocaloric
materials having first order phase transition affect the dynamic properties
like the magnetic resonance spectra42 . But recent theoretical and
experimental studies have been shown that the magnetocaloric materials which
exhibit different magnetic phases with second order phase transition shows
larger refrigerant capacity43 ; 44 ; 45 . In magnetic cooling system the
active magnetic refrigeration process (AMR) over a wide temperature span
between hot and cold sources is required in thermodynamic cycle. For this
purpose a magnetocaloric materials having sufficient MCE values over a wide
temperature range will bring lot of promises46 . So people are interested to
combine different magnetocaloric materials with different TC in a single
specimen to cover the wide temperature range to fulfil the need of efficient
AMR47 ; 48 . In this context Sr doped disorder LCMO with wide temperature
range and having Curie temperature below 300 K as discussed earlier is an
important element.

Figure 14: The value of RCP and $\Delta$Sm as a function of magnetic field are
shown for (a) L1 and (b) LS2 samples, respectively.

Vopsonet al. proposed that in magnetoelectric (ME) materials the MCE is
enhanced by the ME coupling term49 . In LCMO near transition temperature the
magnetodielectric effect is observed as discussed above. We have also
discussed about the antiferromagnetic Mn4+-O-Mn4+, Co2+-O-Co2+ and
ferromagnetic Mn4+-O-Co2+ exchange interactions in LCMO. This results show
that the observed MCE in LCMO is likely originate from the combined effect of
FM/AFM interaction and magnetodielectric effect. For LS2 the MD effect is
observed at relatively lower temperature as compared to the magnetic
transition temperature. The high value of MCE in LS2 can be attributed to the
disorder phases near TC2.

##  IV Conclusion

In conclusion, antisite disordered LCMO and Sr doped LCMO have been studied by
using experimental techniques followed by DFT based theoretical analysis.
Structural refinement shows that LCMO appears in a monoclinic phase whereas
Sr-doped LCMO appears in a mixed phase having both monoclinic and rhombohedral
components. This is supported by Raman spectroscopy studies. The pristine
sample shows a single magnetic transition whereas with Sr-doping we obtain two
transition temperatures, the second being triggered due to change in valence
of Co due to Sr-doping and antisite disorder. The dielectric constant is found
to get enhanced due to Sr-doping which can be attributed to assymetric charge
hopping and antisite disorder induced dielectric relaxation. First principles
calculations show that hole doping at La site enhances the antisite disorder.
Also it is found that one of the Co2+ ion converts to Co3+ (intermediate spin
state) and the other stays back as Co2+(high spin state). The extra hole
introduced due to Sr doping in LCMO is found to be accommodated by the Co and
O ions. The charge and spin state of Mn ions remain invariant under Sr doping.
The MD value was found to decrease from 11% to 6% at 500 kHz with 50% Sr-
doping in LCMO as antisite disorder weakens the MD coupling. The observed MCE
effect in LCMO is likely originating from the combined effect of FM/AFM
interaction and magnetodielectric effect.

##  V Acknowledgment

The authors acknowledge UGC and MHRD for their financial support and
appreciate the access to computing facilities of DST-FIST (phase-II) installed
in department of physics at IIT Kharagpur.

## References

  * (1) M. A. Subramanian, A. P. Ramirez, and W. J. Marshall,Phys. Rev.Lett.82, 1558 (1999).
  * (2) B. T. Matthias, R. M. Bozorth, and J. H. Van Vleck, Phys. Rev. Lett.7, 160 (1961).
  * (3) P. K. Baltzer, H. W. Lehmann, and M. Robbins, Phys.Rev.Lett.15, 493 (1965).
  * (4) J. Gao, L. Shen, Y. Wang, D. Gray, J. Li, D. Viehland, J. Appl. Phys 109, 074507 (2011).
  * (5) M. Gajek, M. Bibes, S. Fusil, K. Bouzehouane, J. Fontcuberta, A. Barthelemy, Nature Materials 6, 296 (2007).
  * (6) J.F. Scott, Nature Materials 6, 256 (2007).
  * (7) L. Y. Zhang, D. Zheng, M.Chaoyong, L. J. Yuanhua, C. W. Nan, Appl. Phys. Lett. 92, 152510 (2008).
  * (8) V. Srivastava, Y. Song, K. Bhatti, R.D. James, Adv. Energy Mater. 1, 97 (2011).
  * (9) V. L. Joseph Joly, Y. B. Khollam, P. A. Joy, C. S. Gopinath, andS. K. Date,J. Phys. Condens. Matter 13, 11001 (2001).
  * (10) T. Kyomen, R. Yamazaki, and M. Itoh, Chem. Mater. 15, 4798 (2003).
  * (11) R. I. Dass and J. B. Goodenough, Phys. Rev. B 67, 014401 (2003).
  * (12) M. P. Singh, K. D. Truong, and P. Fournier, Appl. Phys. Lett. 91, 042504 (2007).
  * (13) K. D. Truong, J. Laverdiere, M. P. Singh, S. Jandl, and P. Fournier, Phys. Rev. B 76, 132413 (2007)
  * (14) H. Z. Guo, A. Gupta, J. Zhang, M. Varela, and S. J. Pennycook, Appl. Phys. Lett. 91, 202509 (2007)
  * (15) P.A. Joy, Y.B. Khollam, S.K. Date, Phys. Rev. B 62, 8608 (2000)
  * (16) V.L.J. Joly, P.A. Joy, S.K. Date, C.S. Gopinath, J. Phys. Condens. Matter 13, 649 (2001)
  * (17) Y. Q. Lin and X. M. Chen, J. Am. Ceram. Soc. 94, 782 (2011).
  * (18) N. S. Rogado, J. Li, A. W. Sleight, and M. A. Subramanian, Advanced Materials 17, 2225 (2005).
  * (19) M. Azuma, K. Takata, T. Saito, S. Ishiwata, Y. Shimakawa, and M. Takano, J. Am. Chem. Soc. 127, 8889 (2005).
  * (20) S. Kumar, G. Giovannetti, J. van den Brink, and S. Picozzi, Phys. Rev. B 82, 134429 (2010).
  * (21) S. Yanez-Vilar, A. Castro-Couceiro, B. Rivas-Murias, A. Fondado, J. Mira, J. Rivas, and M. A. Senarıs-Rodrıguez, Z. Anorg. Allg. Chemie 631, 2265 (2005).
  * (22) M. P. Singh, S. Charpentier, K. D. Truong, and P. Fournier, Appl. Phys. Lett. 90, 211915 (2007).
  * (23) H. Guo, J. Burgess, S. Street, A. Gupta, T. G. Calvarese, and M. A. Subramanian, Appl. Phys. Lett. 89, 022509 (2006).
  * (24) H. Guo, A. Gupta, M. Varela, S. Pennycook, and J. Zhang, Phys. Rev. B 79, 172402 (2009).
  * (25) M. N. Iliev, H. Guo, and A. Gupta, Appl. Phys. Lett. 90, 151914 (2007).
  * (26) M. P. Singh, C. Grygiel, W. C. Sheets, P. Boullay, M. Hervieu, W. Prellier, B. Mercey, C. Simon, and B. Raveau, Appl. Phys. Lett. 91, 012503 (2007).
  * (27) M. P. Singh, K. D. Truong, S. Jandl, and P. Fournier, Phys. Rev. B 79, 224421 (2009).
  * (28) J. Linden,T. Yamamoto, J. Nakamura, H. Yamauchi, and M. Karppinen, Phys. Rev. B 66, 184408 (2002).
  * (29) J. P. Perdew, K. Burke, and M.Ernzerhof, Phys. Rev.Lett. 77, 3865 (1996).
  * (30) G. Kresse and J. Hafner, Phys. Rev. B 47, R558 (1993).
  * (31) G. Kresse and J. Furthmuller, Phys. Rev. B 54, 11169 (1996).
  * (32) P. Blaha, K.Schwarz, P.Sorantin, and S. B. Trickey, Comput.Phys, Commun. 59, 399 (1990).
  * (33) S. L. Dudarev, G. A. Botton, S. Y. Savrasov, C. J. Humphreys,and A. P. Sutton, Phys. Rev. B 57, 1505 (1998).
  * (34) R. Mahendiran, S. K. Tiwary, A. K. Rachaudhuri, T. V. Ramakrishnan, Mahesh R, Rangavittal N and Rao C N R Phys. Rev. B 53, 3348 (1996).
  * (35) J. B. Goodenough, Magnetism and the chemical bond, Inter science Publishers, 1963
  * (36) Y. Tokura, et al., Phys. Rev. Lett. 76, 3184 (1996).
  * (37) F. Damay, et al., J. Appl. Phys. 81, 1372 (1997).
  * (38) C. L. Bull and P.F. McMillan, J. Sol. Stat. Chem. 177, 2323 (2004).
  * (39) Y. Bai, Y. Xia, H. Li, L. Han, Z. Wang, X. Wu, S. Lv, X. Liu, and J. Meng, J. Phys. Chem. C 116, 16841 (2012).
  * (40) M. N. Iliev, Phys. Rev. B 75, 10411 (2007).
  * (41) J.S. Zhou, H. Q. Yin, and J. B. Goodenough, Phys. Rev. B 63, 184423 (2001).
  * (42) T. Kyômen, R. Yamazaki, and M. Itoh, Chemistry of Materials 16, 179 (2004).
  * (43) A. R. von Hippel, Dielectrics and Waves (MIT Press, Cambridge, MA, 1966)
  * (44) P. Lunkenheimer, R. Fichtl, S. G. Ebbinghaus and A. Loidl, Phys. Rev. B 70, 172102 (2004).
  * (45) N. Biškup, A. de Andrés, J. L. Martinez and C. Perca, Phys. Rev. B 72, 024115 (2005).
  * (46) P. Lunkenheimer, S. Krohns, S. Riegg, S. G. Ebbinghaus, A. Reller and A. Loidl, Eur. Phys. J.—Spec. Top. 180, 61 (2009).
  * (47) Y. Q. Lin, X. M. Chen, and X. Q. Liu, Solid State Commun. 149,784 (2009).
  * (48) N. Ikeda, H. Ohsumi, K. Ohwada, K. Ishii, T. Inami, K. Kakurai, Y. Murakami, Y. Yoshii, S. Mori, Y. Horibe, and H. Kito, Nature 436, 1136 (2005).
  * (49) P. Lunkenheimer, V. Bobnar, A. V. Pronin, A. I. Ritus, A. A. Volkow, and A. Loidl, Phys. Rev. B 66, 052105 (2002).
  * (50) T. Kimura, S. Kawamoto, I. Yamada, M. Azuma, M. Takano, and Y. Tokura, Phys. Rev. B 67, 180401(R) (2003).
  * (51) A. Chaturvedi, S. Stefanoski, M. H. Phan, G. S. Nolas, and H. Srikanth, Appl. Phys. Lett. 99, 162513 (2011).
  * (52) A. Rebello and R. Mahendiran, Appl. Phys. Lett. 93, 232501 (2008).
  * (53) V. Franco and A. Conde, Int. J. Refrig. 33, 465 (2010).
  * (54) R. Caballero-Flores, V. Franco, A. Conde, K. E. Knipling, and M. A. Willard, Appl. Phys. Lett. 98, 102505 (2011).
  * (55) A. Chaturvedi, S. Stefanoski, M. H. Phan, G. S. Nolas, and H. Srikanth, Appl. Phys. Lett. 99, 162513 (2011).
  * (56) S. C. Paticopoulos, R. Caballero-Flores, V. Franco, J. S. Blazquez, A. Conde, K. E. Knipling, and M. A. Willard, Solid State Commun. 152, 1590 (2012).
  * (57) A. M. Tishin and Yu. I. Spichkin, The Magnetocaloric Effect and its Applications (IOP Publishing, Bristol, UK, 2003).
  * (58) M. Balli, D. Fruchart, and D. Gignoux, J. Phys.: Condens. Matter 19, 236230 (2007).
  * (59) M. Balli, D. Fruchart, D. Gignoux, E. K. Hlil, S. Miraglia, and P. Wolfers, J. Alloys. Compd. 442, 129 (2007).
  * (60) M. M. Vopson, Theory of giant-caloric effects in multiferroic materials, J. Phys. D: Appl. Phys. 46, 345304 (2013).