2.1.Sample h. Appropriate amount of high purity (99.9%) raw

2.1.Sample
preparation

Multiferroic composite with the formula x Li0.1Ni0.2Mn0.6Fe2.1O4
+ (1–x) BiFeO3 (x=0.0, 0.1, 0.2, 0.3, 0.4 and 0.5) were prepared by mixing stoichiometric
proportions of pure phase BiFeO3 and Li0.1Ni0.2Mn0.6Fe2.1O4
powder which were prepared by the standard solid state reaction technique. For the preparation of BFO
powders, high purity (99.9%) raw materials of Bi2O3, and
Fe2O3 were mixed thoroughly according to stoichiometric formula
in a mortar with pestle for 5–6 h using acetone as mixing medium. The mixed
powder of BFO was calcined at 1073 K for 4 h and pre-sintered at 1123 K for 4 h.
Appropriate amount of high purity (99.9%) raw materials of Li2CO3,
NiO, MnCO3 and Fe2O3 were mixed to synthesize LNMFO
by the same procedure as BFO. The mixed powder was then dried and pre-sintered
at 1473 K for 4h. The pre-sintered powders were again ground thoroughly in an
agate mortar. For preparing the composites, we have mixed LNMFO and BDFO powders
together according to the stoichiometric ratio and ground in acetone media for
3 – 4 h to allow good mechanical mixing. The composite powders were mixed with
polyvinyl alcohol (PVA) as a binder for granulation. From these powders disk-
and toroid-shaped samples were prepared by applying a uniaxial pressure of 55
MPa. Finally the samples were sintered at 1148K(x=0.0), 1173K(x=0.1 and 0.2)
and 1198K(x=0.3, 0.4 and 0.5) for 4 h.

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2.2. Characterizations

The structural analysis of the sintered samples were carried out
with the help of X-ray diffractometer with CuK? radiation (?= 1.5418×10-10
m) at room temperature. The lattice parameters were calculated from X-ray
diffraction (XRD) data. In order to analyze the distribution of grain on the
surface of sintered samples, Field Emission Scanning Electron Microscopy
(FESEM) images were taken with the help of JEOL JSM 7600F electron microscope.
The average grain size was calculated using linear intercept technique. The
bulk density (?B) of each composite was calculated using the formula:

 where r is the radius, m is the mass and t is the thickness of the
sample. The X-ray density of the composites was measured by the formula,

, where

 is (1-x) times molecular weight of BFO and

 is x times molecular weight of LNMFO,

 (ferroelectric)
and

 (ferrite), x is the
weight fraction of LNMFO in the samples 26. The ?x (ferroelectric
and ferrite) are calculated by the general formula,

, where n is the number of atoms in a unit cell, M is the molar mass of the sample, NA is Avogadro’s number and V is the volume of the unit cell. The
porosity of the compositions was determined using the relation

. The dielectric and magnetic properties were studied at room
temperature as a function of frequency by using a WAYNE KERR 6500B Impedance
Analyzer. To determine dielectric properties, the samples were painted with
conducting silver paste on both sides of the samples to ensure good electrical
contacts. The dielectric constant (??) was measured from the capacitance using
the formula:

, where

 is the capacitance of the pellet,

 is the cross-sectional area of the electrode
and

 (= 8.85×10-12 F/m) is the permittivity
in free space. The ac
conductivity (?ac) of the compositions was calculated using room
temperature dielectric data from the relation:

, where ? is the angular
frequency and tan? is the dielectric
loss.
The real part

 of the
complex initial permeability and loss
tangent (

) were calculated using the formula:

 and 

, where Ls is the self-inductance of the sample core,

 is the
inductance of the winding of the coil without the sample, and

 is the imaginary part of complex initial
permeability.

 is derived from the geometrical relation,
where,

 is the
permeability in vacuum, N is the number of turns of the coil (N = 4), S is the
area of cross section ,

 is the mean diameter of the toroidal sample, where
d1 and d2 are the inner and outer diameter of the
toroidal sample, respectively 28. The magnetic hysteresis (M-H) loops were determined using a
vibration sample magnetometer (VSM, model Micro Sense, EV9). The number of Bohr
magneton, n(?B), was measured using the relation:

, where

 is the molecular weight of the composition,

 is the saturation magnetization and NA is Avogadro’s number and ?B
is 9.27×10-21 emu. The ME effect was obtained by applying an ac
magnetic field superimposed on a dc magnetic field on the sample, and then
measuring the output signal with applied dc magnetic field. An electromagnet
was used to supply a dc magnetic field of up to 0.77 T. A signal generator was
used to drive the Helmholtz coil to generate an ac magnetic field of 0.0008T. The
output voltage generated from the composite was determined using a Keithley
multimeter (Model 2000) with of dc magnetic field. ME voltage coefficient (?ME) was measured using relation
29

, where

is the ME voltage across the
sample surface and h0 is
the amplitude of the ac magnetic field.