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S:jine Properties of microwave ferritcs BMfcWWMBiTy-.ia'Jg'iWI—IKKHW

CHAPTER I

liNTRODUCTION

Ferrites, the ferromagnetic oxides, are a class of magnetic materials, in which the

magnetic ions are arranged in a particular fashion, in early days they were

considered as ferromagnetic materials. But later on it was realized that these

materials are having partially compensated antiparallel spins, resulting in to non zero

magnetic moment. Therefore these materials were named as ferrimagnetic materials

and an iron containing compounds as "ferrites" by Neel (1948) [1], During the last

few decades the ferrites have become firmly established as important magnetic

materials finding the wide range of applications in the field of liner digital and

microwave [2].The ferrites show high resistivity and negative temperature

coefficient of resistance like semiconductor. Hence they can be considered as

magnefic semiconductors. The ferrites are also good dielectrics. If the high electrical

resistivity of the ferrites is combined with useful magnetic properties, then the

resultant materials could be useful for the high frequency and microwave

applications.

Magnetite or ferrous ferrite is the naturally occurring ferrite having formula Fe204

and exhibits permanent magnetism named as loadstone by early navigators. Hilpert

was the first who prepared Fe204 in laboratory [3]. Then it was commercialized

therealter Snoek and his coworkers [4]. In 1947, Snoek gave the foundation of

physics and technology to the ferrites and then it got established in many branches

of telecommunications and electronic engineering [5J. The magnetite consists of

divalent and trivalent iron ions in the forni of oxides as FeO and Fe203. It is shown

that a significant improvement can be achieved by substitution of divalent iron ion

with other divalent ions such as Cd, Co, Ni, Zn, Cu, Mg, etc fi-om 3d series.

Therefore in general the spinel ferrite can be recognized with the formula MFe204,

\\ here M is divalent metal ions. Further the trivalent iron can also be substituted by

the ions like Al ^,Cr^\Ti^^,Sn'^^,etc,to achieve the required modificaUons in the

properties of spinel ferrites. Therefore the study of the spinel ferrites become of

interest to manv researchers.

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Some Properties of microwave Jerritcs

1.1 Short review: The short review of developments of ferrites could be taken

briefly as fallows. The mineral magnetite (Fe304) is the ferrous ferrites, naturally

occurring and known was lodestone. At the beginning the magnetization

phenomenon occurring in the material was scientifically studied and quantitative

idea about the saturation magnetization was laid down by Du Boise in 1960 [6].

Hilpert (1909) was first who synthetically prepared the ferrites in the laboratory and

laid down the foundation stone for ceramic magnate and suggested the formula

MFe204 for ferrites [7]. Handvall and Tammann attempted the preparation of ferrites

by solid state reaction [8, 9]. Thereafter the Japanese workers (1930) studied the

ferrites from the empirical and application point of view [10]. Snoek (1936)

developed the commercial ferrites [4]. Simultaneously it was developed by Takei

(1937) [5] and realized that this magnetic oxide is the best material to use as core for

inductors and transformers. By 1945 Snoek laid down the foundation of the physics

and technology of the ferrites and then some new industries came up [4]. Ferrites are

high resistive materials showing low mobility. The transport properties of the

ferrites were studied Verway et.al (1947) and suggested the hopping mechanism for

the electrical conduction [11]. Neel (1948) interpreted mathematically the magnetic

behavior of ferrites. He developed the mathematical model based on the molecular

field theory assuming that the existence of two sub lattice model in the spinel and

suggested a class of magnetism as ferrimagnetisms [IJ.Van Vleck (1951) Anderson

(1950), and Zener (1951), have proposed the exchange interaction mechanism for

ferrimagnetisms [12,13,14].The dielectric behavior of ferrites was explained by

Koops (1951) with the help of double layer capacitance model [15]. In order explain

the deviation from the Neel theory, Yafet and Kittle (1952) introduced the triangular

spin and three sub latfice model [16]. Gorter and Guilled (1954-55) found direct

experiment evidence for the modified Neel theory [17, 18], Waldron (1955)

supported the existence of two sub lattice by studying the internal models of the

vibrafions from [R spectroscopy [19]. Galileo (1957) developed the theoretical

model for calculation of cation distribution among two sub lattice based on Curie

temperature measurements [20]. Gruintjes et.al (1966) introduced a hot pressing

technique for the preparation of the high density of ferrites [21]. However,

Economas (1955) prepared the fine particle ferrites by co-precipitation method [22].

The mechanism of inifial penneability was explained by Globes et.al (1971) and

electrical properties of ferrites by microwave sintering method for MLCI application

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Some Properties of microwave fcrrites

was studied by M.Penchal Reddy et.al. (2010) [46], dielectric behavior of copper

substituted Ni-Zn-Mg ferrites by A.M Shaikh et.al (2011), [47], with the help of

microstructure. domains.

1.2 Classification of spinel ferrites:

In order to discuss the spinel structure in more detail, the unit cell can be subdivided

in to 8 octants of alternative kind with edge of l/2a, as shown in the figurel.2 (a).

The oxygen ions are arranged in identical manner in all the octants. Each octants

consists of four oxygen ions on the alternative body diagonal .Each oxygen is

located at a distance equal to VA of the length of the body diagonal as shown in the

figurel.2 (d). In one of the octants., an occupied tetrahedral sites is located at the

center and four more on the comer of the octants as shown in the figure 1.2 (b).

However in the adjacent octant, the central sites are not occupied. Due to the

translation symmetry, the half of the comer site is occupied, as shown in the

figure 1.2(c). The octant contains four octahedral metal ions situated at the sites,

analogs to those of the oxygen ions i.e. 1/4 of the body diagonal fi-om other end [23].

Every tetrahedral site is surrounded by the 12 octahedral ions and every octahedral

ion is surrounded by the six nearest neighbors' tetrahedral ions. Each oxygen ions is

sunounded by the one tetrahedral ion (A) and three octahedral ions (B ions) [24], as

shown in the figure 1.2(e), thus the spinel stmcture consists the number of inter

locked FCC lattices, hi order to accommodate the cations like Co, Cu, Mg, Mn, Ni

and Zn the lattice has to expanded. The difference in the expansion of octahedral and

tetrahedral site is characterized by oxygen ions (u) parameter and ideally it has the

value 3/8.Due to incorporation, bigger divalent metal ions in a A site the expansion

in the lattice takes place resulting in to increase in the value of u-parameter. The

stmctural detail of the spinel structure can be discussed with respect to the stmctural

parameter like .lattice constant ,ionic radii of the tetrahedral and octahedral sites(rA

and re) and cation oxygen bond lengths (A-O and B-0).The lattice constant which

can be obtained fi-om X-ray diffi-action studies, in sensifive to the ionic radii of the

substituted cation and cation distribution among A and B site. The linear variation of

this lattice constant is usually expressed by Vegards law .the site radii ra and rb and

bond distance A-O and B-O aie also found to depend upon cation distribufion.

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Some Fivperdes of microwave Jerri tes

According to crystal stnicturc, the ferrites are classified in to four groups, as spinel

ferritesMFe204Cubic), Garnet (3R203.5Fe2O:!; cubic) Hexaferrite (BaFeuOm) and

Pervoskite (ABO3), out of which the spinel fenite again classified according to the

cation distribution among A and B site and chemical composition.

Based on the cation distribution the spinel ferrites are classified in to three classes,

discussed as follows.

A) Normal spinel: In a "normal" spinel, the 8 A ions occupy the 8 tetrahedral sites,

the 16B ions the octahedral ones. That is divalent metal ions can occupy the

tetrahedral A sites and trivalent iron ions reside on octahedral B site, is called

normal spinel. The cation such as cadmium and others prominently occupy the A

site. Since they are paramagnetic at room temperature, the magnetic interaction J^B

is found to be zero. The cation distribution is (M^^T)^[Fe^"iFe^*T]^04.

B) Inverse spinel: In an "inverse" spinel, 8 of the B ions occupy the tetrahedral

sites, the other 8 and the 8A's occupying the octahedral sites. Therefore the

interaction JAB is strong giving net magnetic moment. The inverse spinel ferrites

they are magnetic in nature .The nickel feirite is inverse spinel ferrite and their

cation distribution is given by (Fe^+t)'^[M^'iFe^''iJ^04

C) Random spinel: It is found that the few cations show their place of occupancy

among the A and B site. The distribution depends on their characteristics

composition and sintering temperature. The copper ferrite is 84% inverse [25] and

magnesium ferrite is found to be about 90% inverse [26].The cation distribution can

be expressed as (M8Fei-s)' [Mi-5Fei+5]^04. Where 6 is normalcy of the metal ions.

1.2.1 Based on the chemical compositions: They are classified as three classes:

A) Simple ferrites: When Fe ' ions in Fe304 is replaced by single divalent metal ion,

such as Ni "Cu " .Cd ' ,Mg' ,Zn^ etc, maintain the stoichiometry, the resulting

compound is called the simple ferrite and expressed asMFe204.

B) Mixed ferrites: In this class Fe^^ ions are replaced by two metal ions in

stoichiometry proportion. The general formula is given by AxBi.xFe204

C) Substitution ferrites: In this replacement of the divalent as well as trivalent iron

ions Fe304 by another divalent or trivalent cation maintain the stoicheometry.

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Some Properties of microwave ferrites

resulted in substitution ferrites and the general chemical fomiula for this class is

given by AxBi.xFe2-yCy04 where C is trivalent ion.

Figure 1.2 (b)

Figurel.2 (c) Figure 1.2 (e)

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Some Properties of microwave ferrites A 'fiait-'KmtmmmmmM-s»twxmnmmuK»tii!amt^tPi:mmm MM—wsara

A. /

/

^^X>H. A>'

/

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^ok / • - y .

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Figure: (d)

Figurel.2 a: Flight octants of the unit cell each of edge length a/2.

Figure 1.2 b: Tetrahedral (A) site.

Figurel.2. c: Octahedral (B) site.

Figure 1.2 d: Spinel stracture of poly crystalline ferrites.

Figure 1.2e: Sarrounding of oxygen ion.

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Some Properties of microwave ferrifes

# iBtrahsdral 0 Octahedral ^Oxygwi

R

S

R*

•

Ifc Ba • Fe , Q

Figure: 1.2 f Schematic representation of spinel (a) and (b) Magnetoplumbite structures. The accompanying table provides information of cation site

occupation and symmetry.

A

B

Figure 1.2 g. Two octants of the spinel unit cell showing A ions on tetrahedral sites and B ions on octahedral sites.

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Some Properties of microwave ferrites AoxtM m vtimmnMBiemmmummtmmmm'tiivjm:MerfKsn,rntamm

1.3 Theory of ferrimagnetism:

Neel (1948) proposed the mathematical model to explain the variation of

magnetization with temperature and the existence of spontaneous magnetization

below Curie temperature. Introducing the new class of magnetism as

ferrimagnetism, and his theory is based on the Weiss molecular field theory. He

developed the theory of ferrimagnetism, assuming the existence of two

crystallographic sites called tetrahedral site (A) and octahedral site (B) and

magnetism of the material is due to the interaction between the A and B ions. He

classified these interactions in to four types such as A-A.A-B, B-A, and B-B

interactions. The magnetic interaction A-B or B-A is found to be negative and hence

magnetic moments of A ion is more or less antiparallel to that of B ion.

According to Weiss molecular field theory the actual magnetic field acting upon the

atoms is given by H=Ho+Hn,. Where Ho is the externally applied field and Hm is the

molecular field (Hm== yM) arises due to interaction with other atoms, where y is

molecular field co-efficient and M is the magnetization. Applying the concept to the

ferrimagnetic materials, we have

HA=HAA+HAB and HB=HBA+HBB (1.3.i)

Where HA and HB are the magnetic fields acting on the A and B sites respectively.

The field HAA is the field on A ion due to tlie neighboring A ion and HAB is field on

A ion due to the neighboring B ion. The similar definition is for HsAand HAB- These

molecular field components may be written as

HAA=7AAMA and HAB^^ /ABMB and HBB=yBBMB and HBA ysAiMA (1.3.2)

Where MA and MB are the magnetic moments of A and B sub lattices. Neel showed

that yAB^BA and YAA is not equal to JBB- He also showed that yAA< 0 favoring the

antiparallel arrangement of MA and MB, which gives the ferrimagnetism. Thus the

total magnetic field on each lattice site, in the presence of applied field Ho can be

written as,

Ha=Ho+Ha=Ho+HAA+HBBand Hb=Ho+HB=H„+HBA+HBB (1 -3.3)

And Ha-Hy+yAAMA+YABMe and Hb=Ho+TBBMB-H'BAMA (1.3.4)

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Neel assumed that X and j.i be the fraction of the magnetic iOn on A and B sites

respectively so that k+\i=[ then the equation (1.3.4) becomes,

Ha=Ho+NgJuBYAB [XaoA-^ae] and Hb=Ho+NgJ}iByAB[ Pc7B- aA] (1.3.5)

Where a and P are the ratio given by,

a=(yAA/YBB and P=(7BB/YAB) (I -3.6)

Where the OA and OB is the reduced magnetization given by,

OA = MA/lNgJuB) and OB = MB/|.iNgJ^B) (1 -3.7)

After the mathematical treatment the volume susceptibility, is given by,

y=NgVB"J(J+l)/3KT==C/T (1.3.8)

this will describe the obser\'ed susceptibility against the temperature relationship

below the Curie temperature .Neel applied the similar treatment to each sub lattice

of ferromagnetic materials as,

Paramagnetic region: The magnetization of each sub lattice is given by

MA=XgVg'j(J+1 )/6KT Ha MB=[igWKi+1 )/6KT Hb (1.3.9)

In the ferromagnetic materials, (3d elements) the orbital magnetic moments is

quenched, because of weak L-S coupling. Therefore the above equation can be

reduced to

MA=X.g2^g2{S(S+l)/6KT }Ha MB= ^g2nB2{S(S+l)/6KT }Hh ( 1.3.10)

Now introducing the Curie constant C the equation (1.3.10) can be reduced to

MA=(A.C/T)Ha and MB=(nC/T)Hb (1.3.11)

Putting the values of Ha and Hbfrom equation (1.3.5) we get,

MA=( C/T)[H„+NgJ lBTAB(> aoA- OB) (1.3.12)

MB= ( C/T)[Ho+NgJ BYAB( pOB->.OA)- (1.3.13)

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Now the total susceptibility is given by x= (MA+MB)/HO. Substituting the values of

MA and MB from equation (1.3.12) and (1.3.13) and after the required mathematical

manipulation, Neel showed that,

1/X= T'-CYAB (>^a+^P) + cVYAB(ap-l)/C[T-XtiCYAB (2+a+p) (1.3.14)

l/X=T/0-l/xo-C/T-e (1.3.15)

The first two terms of the equation (1.3.15) denote the temperature dependence of

susceptibility as that of the ferromagnetic, above the Curie point .But the third term

is the counterpart in the ferromagnetic case. The equation (1.3.15) represents a

hyperbola which is asymptotic to the line,

l/X=T/C+l/Xo (1.3.16)

Which cuts the temperature axis at 0A=C/XO, which is asymptotic Curie point

according to Neel. The material becomes paramagnetic above Curie point (Tp) and

spontaneous magnetization in the region where 9o<T<Tp. The paramagnetic Curie

point Tp is given by,

TP=(YAB/2) C [>.a+nP+{(Xa-np)-+4XM}"']- (1.3.17)

If Tp is negative, the materials remain paramagnetic down to absolute zero. If Tp is

positive the susceptibility becomes theoretically infinite and below it spontaneous

magnetization will appear and remain finite as the applied field reduces to zero.

Spontaneous magnetization: The spontaneous magnetization appears below Curie

temperature. Now taking positive square root, equation (1.3.17) can be written as,

Tp= (YAB/2) C['ka+\i^+{(Ka-\i^f +4X^} "^] (1.3. i 8a)

Tp=(YA3/2) C[Xa+\i^-{{-ka-\i^f +4X^}"^] (1.3.18b)

Full analysis shows that the Tp is Curie temperature of the assembly where the sub

lattice are spontaneously magnetized with MA and MB anti parallel and Tp is the

Curie temperature when MA and Ms are parallel. Since Tp>Tp the antiparallel

arrangement is present and stable below Tp. This is good support for the assumption

of negative interaction between A and B sub lattices. Therefore the resultant

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Some Properties ojmicrowave ferrites

magnetization M could be M=MA+MB. Since they are antiparallei MB>MA the net

magnetization will be

| M | = | M B | - | M J (1.3.19)

Therefore the .spontaneous magnetization in the ferrimagnetic materials is given by,

Msp = Mesp - MASP (1.3.20)

The ferrites have particular shape of temperature dependent magnetization curves.

The different curves reported by Neel are presented in the figure 1.4. There are three

different shapes. In case of normal, shape of the temperature dependence of A and B

site magnetization is identical. Secondly the magnetization of B sites reduces rapidly

than that of A sites, this results in to N-type cur\'e. However if the reduction in the

magnetization of A sites is faster, then it results in to P-type curve.

Yafet-Kittle (1952) extended the Neel s theory by suggesting the possibilities of

triangular spin arrangement with sub lattices. According to them, strong interaction

exists with the B sub lattice then it get divided in to Biand B? with their net

magnetization neither be exactly antiparallei to each other nor to A sub lattice. But

the angle between A and B is other than 180". The resultant should be antiparallei

with A, as shown in the figl.5, and this triangular arrangement of the spin vector

reduces the resultant magnetization. According to them, the angle between Biand B2

is proportional to the exchange interaction JAB as COS avK a (JABSA/JBBSB), where J

is the exchange integral and S is the spin vector.

i t

I

^ L T p

Figure 1.3: Susceptibility curve of a ferromagnetic material above Curie point.

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M Hg

- >

M

>

MA

M- t3p<i-

} . — .rtfc

. 4 — . ^

^ ^ MA

P-"t^pt

Figure 1.4: Magnetization versus temperature curves of the spinel ferrites

8, 6 .

N'on--Ce>P,.»\eaf ?p~in- Q»v>ua5vai»«rt.t>«-*i

-?i

Figure 1.5 A Figure 1.5 B: Triangular spin arrangement

M t f M . '

T i , r o T , .

M,- M & • . a

• c * » » ••;•

M, M h i

M ^ -

M,

W„-

M b '

T,^ T» CTK

Figure: 1.5 C

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Some Properties of inicrouave ferrites mv • iwwifiiwi[iiii>s'«««^>aaM»M*w«iaB»<yjrfc'!i3!fT;i^ EMMMMiUHH

AB

4-^!2^S ^=l54'i4' I ^-9f?i

1 v5^%

f i t j^fi ' ; ,|;;.^<fy

Figure: 1.6 Magnetic interactions in the spinel ferrites

1.4 Properties of the spinal ferrites:

The polycrystalline ferrites have interesting intrinsic properties. Tliese properties are

found to be sensitive to the method of preparation, sintering temperature, chemical

composition and also the substitution of tiie foreign ions. Due to this they find wide

application in various fields. The magnetic and electrical properties are discussed

below in brief

1.4.1 Magnetic properties:

Magnetic properties of the spinel ferrites can be discussed based on the magnetic

parameter such as saturation magnetization, magnetic moments, and retentivity,

coercivity, magnetic loss, susceptibility, permeability etc. These magnetic

parameters depend upon chemical compositions, preparation condition, cation

distribution and microstaicture of the spinel ferrite. Magnetization in ferrites is due

to the super exchange interactions between magnetic ions. However it depends upon

the substitution of divalent or trivalent ions. Variations in susceptibility and

permeability with temperature as well as with fi-equency can be explained with the

help of the grains, grain boundaries and porosity. The initial susceptibility, the ratio

of magnetic induction to the magnetic tleld at H—>0 is due to two mechanisms;

domain wall motion and spin rotation. The m.agnetic parameters are also sensitive to

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Some Properties of microwave ferrites Bq-MwxiiMeanMunr 'mirsiuj».vi

anisotropy energy. Thus the magnetic properties of spinel ferrites are the function of

magnetic interaction, anisotropy, domains, and domain wall and the micro structure.

Therefore these factors are discussed in brief as fallows.

1.4.1.1 Magnetic interaction :

Magnetism in ferrites is due to the interaction between magnetic ions [1]. As

discussed previously spinel ferrites consists of magnetic ions distributed among the

two sites; A sites and B site. Hence the magnetization is due to the interaction

between A and B ions. Three kinds of interaction are possible, between the metallic

ions through oxygen ions (i.e super exchange interaction) namely AA, BB and AB

interactions. It has been established experimentally that the interaction energies are

negative; as a result of the antiparallel orientation of the spins. The magnitude of the

interaction decrease with increase in the A-O-B, angle could be highest for 180" and

very small for 90" for a given distance. Gorter suggested the favorable distance and

the angle for effective magnetic interaction [27], which is illustrated in the figure!.6.

Based on these values of distance and angle it can be shown that the interaction A-B

is larger in magnitude due to small distance and fairly large angle. The interaction

A-A is the weakest and magnitude of interaction B-B is intermediate between these

two extremes. The spins of A and B are oppositely oriented and hence the resultant

magnetization is M=MB-MA

1.4.1.2 Anisotropy: The magnetic parameters, susceptibility and permeability

depend upon the anisotropy. In these materials the magnetization has preferred

orientation with respect to the crystallographic direction, called as easy direction of

magnetization. To change this direction of magnetization, energy has to be spend

because of the crystal is anisotropic in its magnetic properties. This energy is called

as anisotropy energy. The anisotropy arises due to the spin orbit interaction.

Therefore the anisotropy are of three types namely (i) Magneto crystalline

anisotropy, (ii) Magnetostrictive anisotropy and the (iii) Shape anisotropy.

The magneto crystalline anisotropy arises due to the spin orbit interaction and the

resultant energy depends upon the orientation of magnetization with respect to

crystallographic axis .This anisotropy energy is given by

Fk=K| (a iW+a |a i+a | a^)+K2(afaia|)+ (1.4.1.3)

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Where K-, and K2 are the first and second order anisotropy constants and are the

direction cosines relating the magnetization direction with respect to the cube edges.

The constant Ki is dominant than K? in case of the ferrites. The magneto crystalHne

anisotropy constant K| is found to be negative and strongly sensitive to the

temperature. However the cobalt feirites have positive anisotropy constant.

Therefore the small amount of cobalt can substituted in ferrites to compensate the

anisotropy. The anisotropy constant decrease with temperature and reaches to zero at

a particular temperature. This variation of anisotropy constant Ki decides the nature

of variation of permeability with temperature. Grater the anisotropy, more stiffiiess

of the spins and hence more difficult to change the magnetization direction by

external magnetic field, as a result the permeability decrease. The low anisotropy

leads to large induced magnetization for a given magnetic field, resulting in a large

value permeability and susceptibility.

The fractional change in the length of material when it is magnetized fi-om the ideal

demagnetized state resulted in magneto-strictive anisotropy. It is expressed in terms

of the coefficient X and it is either positive or negative. The anisotropy can be

reduced by proper combination of the materials having positive and negative X

values.

Depending on the physical shape of the magnetic materials, irrespective of the

magnetic moment, what is called the shape anisotropy arises. The inherent part of

ceramic material like pores and inclusion are the cause for the shape anisotropy. The

anisotropy energy is given by

E shape=I/2 [NxM|NyM^NzM|] (1.4.1.4)

Where N^ and Ny Nz are demagnetization factors.

1.4.2 Domains and domain wall: Domains are the small regions of the magnetic

materials, formed according to the principal of minimization of energy, in which all

the spins are lined up. In the absence of the magnetic field the domains are randomly

oriented, so that the resullatant magnetizafion is zero. However in the presence of

the magnetic field, the domains are aligned parallel to the direction of the applied

field. The domain structure decides magnetic properties such as susceptibility and

permeability. The domain wall is nothing but the boundary between the two

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oppositely oriented domains [28, 29]. It also called the domain boundary or Bloch

wall. At the domain wall the sudden change in the direction of the spins does not

occur, but there is the gradual transition of spin orientation from one domain to the

other domain as shown in the figure 1.7. The domain wall has finite width and its

energy correlated with the exchange energy constant (A) and anisotropy constant

(K)as

Ew=4/ (AK) 1/2 (1.4.1.5)

b II

^ 8" Figure 1.7: Symmetrically distinct crystallographic relationship between cubic and monoclinic phases of magnetite. The cubic unit cell is shown as a shaded box. 12 of the 24 possible unique orientation as shown .The other 12 orientation can be obtained by 180" rotation about monoclinic axis.

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The domain structure is found to be affected by the grain size and therefore the

grains are classified in two groups; single domain, multidomain. The presence of the

single domain or multidomain grains decides the variation of the susceptibility and

permeability. The motion of the domain walls which decides the magnetic parameter

also depends on the presence on the pores, inclusions and irregular pores. The

domain wall does not follow the alternating field at the high fi-equency and produces

the magnetic loss.

1.4.3 Electrical conductivity: Electrical properties such as high resistivity, low

mobility make the ferrites suitable for the various applications. Electrical properties

are dc resistivity, thermoelectric power and ac conductivity. These properties are

sensitive to the temperature and applied frequency. Also they show their dependence

on chemical composition. The study of electrical properties provides information

regarding the transport phenomenon.

1.4.4 D.C Conductivity: Spinel ferrite is also named as the magnetic

semiconductor, due to the fact that, like semiconductor it shows negative

temperature coefficient of resistance. The temperature dependence of resistivity can

be expressed as p=po exp (-AE/KT), where AE is the activation energy and K. is the

Boltzmann constant. This behavior was explained by Verway et.al[30], introducing

the mechanism for the conduction based on the hopping of the charge carriers from

Fe ^ to Fe ^ ions located at octahedral (B) site. Further the concept of polron

hopping was also introduced [31]. Eatah et al have introduced the concept of

localized charge carriers [32]. The details of the conduction mechanism is discussed

in the chapter electrical conductivity.

1.4.5 A.C Conductivity: the conductivity of the ferrites studied as function of

frequency of the ac applied field, gives the information regarding the dielectric

properties of the ferrites. These dielectric properties are most applicable at

microwave frequency. The dielectric constant, the loss shows the dispersion with the

frequency. However the electrical conductivity increases exponentially with

frequency. This behavior was explained by Koops [16], developing the

phenomenological theory based on Maxwell-Wagner double layer capacitance

model [33, 34]. The dielectric constant gives the probability of electron hopping.

The dispersion in the dielectric constant gives the probability of electron hopping.

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Some Properties of micro\yave ferritcs

The dispersion in the dielectric constant is a grain and grain boundary phenomenon.

Therefore the ac conductivity gives better insight in to conduction process.

1.4.6 Application of ferrites:

A combination of good magnetic properties and high electrical resistivity make the

ferrites suitable for the wide range of applications. The application of metallic

magnets are limited due to their low resistivity and high eddy current losses, which

could slightly improved by the limitation in the core. But the poly crystalline

magnetic materials, ferrites, due to the high resistivity and low loss are the best for

the core. The technical important magnetic properties on which its applications

depends on Ms Hc,|a and loss. Depending on these parameters, ferrites find their

application in different fields, which reviewed briefly below.

Ferrites are used in the field of telephone transmission, where in high performance

inductor and transformers are essential, due to the fact that the carrier contains

analog signal and is operated on fi-equency division multiplexing technique (FDM).

Ferrites find application in the field of television receivers as core materials for line

time base /FHT transformers and field shaping Yoke due to high resistivity to

facilitate winding on the ferrites [35]. The most important use of the ferrites for

recording and erasing heads [36] for audio and video recorder along with the

inductive element required audio interference suppression. The low magnetic loss

and high resistivity permit the ferrites to be used as transformer elements in the high

fi-equency power supplies, commonly known as switch mode power supply(SMPS)

[37,38]. Ferrites having the rectangular hysteresis loop [39], with riny toroidal cores

can be used as the recording media, in which rapid storage and retrieval of digital

details done by switching. The magnetization between two stable states

[40].However the thin wafers of the garnet , due to presence of microscopic

domains, can be use as high density data storage media.

The Faraday rotation and ferromagnetic resonance shown by the ferrites lead to their

suitability for microwave applications. A variety of microwave devices have been

developed by using ferrites, such as wave guides and stipline isolators, switches,

circulators, m.odulators and limiters etc.

Department of Physics Kiivempii University Sharikarghatta


Changing the appHed field can vary the permeabiHty of the ferrites. Hence they can

be used as controlled inductance applications and the controlling can be done

manually or remotely. Hence the ferrites have applications in the fields of telemetry,

high frequency remote tuning, automatic antenna matching, television raster

correction etc. Ferrites are the best core for the magnetic amplifiers.

The ferrites having the Curie temperature at or below room temperature can in

principal be used in variety of temperature sensitive application. As a miscellaneous,

it also used for cladding the buildings or vehicles to suppress the reflecfion of the

radio waves. Ferrites also found many applications in the field of sensor like

temperature sensor, humidity sensor etc.

There exists an increasing demand for signal processing devices in radar detection,

communication, and instrumentation. Wider use of microwave devices in consumer,

automotive and industrial radar systems will drive the production quantity up and

cost down [41], it shows a typical application of circulators in wireless

communication (mobile phones).Microwave technology is moving up to higher

frequencies and higher bandwidths, into the mm wave range, up to 100 GHz. Non

conducting materials are essential to ensure total penetration of electromagnetic

fields. Ferrimagnetic oxides of iron combine the properties of a magnetic material

with that of an electrical insulator. Ferrite elements are widely used in microwave

devices, isolators, circulators, phase shifters. For applications, requiring

nonreciprocal operation, as in circulators and isolators, there is no alternative to

magnetic devices. Due to the very high specific resistance, remarkable flexibility in

tailoring the magnetic properties, ease of preparation, price and performance

considerations make ferrites the first choice materials for microwave applications.

However, the frequency range of operation, the power handling capacity and the

temperature sensitivity of ferrite devices should be improved. Detailed information

about magnetic properties of microwave ferrites can be found in monographs and

handbooks [42, 43]. After a short overview of the species of high-frequency

magnetic phenomena and magnetic losses, representative applications of ferrites in

nonreciprocal, magneto static wave (MSW) and nonlinear devices, and absorbers of

electromagnetic energy are illustrated.

Department of Physics Kuvempii University Shankarghatta

Some Properties of microwave ferriies m\ wm:*namM »>!• j.jMi>'«a(«CTTrw>Mriitt>Kv<j^ifcrt»g>aswa«Pw^^

1.5 Microwave ferrites: Static magnetic properties

A low-coercivity, high-rcmanence, soft magnetic material, having a square

hysteresis loop, is required for microwave operation. For a magnetic material to be

applied in microwave devices, the most important static magnetic properties, to be

controlled, are: the saturation magnetization (4pMs , G), anisotropy constants (/vl,

ATu.erg/'cm ), Neel temperature (TN, K), magnetostriction

(constants {X), remanent magnetization {M„ , G), permeability {\i), coercivity (//c,

G) and the temperature derivative of these quantities. In general, high TN, low

coercivity, high Mx , high |x, and low A. are required. Low anisotropy is one of the

conditions for low coercivity and low losses. The magnetization specifications

depend on the operating conditions and on the actual device design. The dependence

of these parameters on frequency and temperature is limiting the stability of ferrite

devices. The problem is eiihanced at high-power levels, due to the dissipation into

lattice heating. By proper substitution in both magnetic sublattices, the temperature

dependence of the magnetization can be controlled to have a plateau, i.e. dA//dT=0

near room temperature. Another possible way to reduce temperature sensitivity is to

use permanent magnets, having temperature coefficients opposite to the ferrites.

Stable hysteresis characteristics are cmcial to microwave devices, not only with

respect to temperature and the operating frequency range, but to stress sensiti^'ity

too. The magnetic effect of stress is caused by finite magnetostriction. Stresses can

be caused by environmental tolerances, device assembly, or lattice mismatch in the

case of films. For the overall reduction of microwave losses, the microwave

magnetic materials should be a good insulator in order for full penetration of the RF

field. The dielectric permittivity should be moderate to prevent dielectric losses in

the device. At the operating point of circulators, the prototype microwave ferrite

devices, the magnetic losses are usually smaller than the metallic and dielectric

losses, thus the elimination of the nonmagnetic sources of loss is of primary

importance [44]. One possibility to eliminate conductor losses is to use ferrites

combined with superconducting circuits. This design has another advantage, that at

low temperatures the fenite magnetization is increased. Phase shifters, circulators

and switches have been fabricated on ferrite-superconducting structures [45-47].

Ferrites are the choice materials for microwave applications.

Department of Physics Kiiventpn University Shankargliatta


1.6 Orientation of the present work: During the last few decades, feirites have

been finally established, as an important class of magnetic materials, fmding wide

range of applications due to their interesting intrinsic properties. The properties like,

electrical, and magnetic properties are found to be sensitive to the method of

preparation, chemical composition,, sintering temperature and substitution of foreign

ions. Therefore it becomes a field of interest of many researchers. The Cadmium

zinc ferrite shows no saturation magnetization at and above the room temperature,

while inverse ferrites show magnetization. However the ions like copper, cobalt and

magnesium show about the 90% inversion giving small amount of magnetic

moment. The substitution of zinc or cadmium in the magnesium ferrites plays an

important role for the increasing in the magnetism and resistivity. The magnesium

ferrite has small coercivity and moderate value of the initial permeability. The initial

permeability could be increased by decreasing the anisotropy. The zinc ion could be

substituted on A site for reduction of anisotropy. Therefore it is found to be more

interesting to study the effect of zinc substitution on intrinsic properties of

magnetism ferrites.

The substitution of multivalent cations like Zr*' Sn'*\Ti'**Al^^Al^^Cu^^Mn^\Li" etc

have also been studied by many workers . But the study of Cu-Zn and Co-Zn ferrites

at higher frequency are rot concentrated by the much of the researchers we have

chosen the above combination of ferrites different concentration and studied the

properties like dielectric loss and permittivity of all samples in the frequency range

from LMHz to 1.8GHz range and the temperature dependence of permittivity and

loss of the sample are measured from IKHz to 120MHz.

Considering these facts, it is propose to carry out the investigation on ferrites CoxZi.

xFe203 and CuxZn|.xFe203 at microwave frequency range.

1. The preparation of poly crystalline ferrites by standard ceramic technique

2. The characterization of prepared samples by standard and easily available tools

like X-ray diffraction, FTIR,SEM technique. The SEM is used to identify the

porosity grain size and grain growth. The thermal properties like TGA, DTA, DSC

for the material are performed to know the thermal degradation and the stable state

of the composition.

Department ofPbysies Kuvempu University Shcmkarghatta

Some Properties ojmicrowave ferrites

3. Most of the intrinsic properties are found to sensitive to the distribution of cation

among tetrahedral (A) and Octahedral (B) sites of the spinels. We also proposed to

carry out the X-ray line profile analysis to know the % of the strain occuned in the

crystal after the substitution of the divalent metal ion and shape of the crystallite

shape ellipsoid.

4. To understand the transport phenomenon the dc electrical conductivity

measurement proposed to carried out as fiinction of temperature.

5.The study of the ac conductivity in terms of the dielectric constant and dielectric

loss as a function of frequency of the applied field and also as a function of the

temperature.

6.The magnetic hystereses are also be proposed study to know the saturation

magnetization and coercivety, and remanance magnetization.

Department of Physics Kuxempu University Shankarghatta


References:

[1]. L.Neel, proceed.Phys.Soc, London,A65 (1948) 869.

[2]. Gerald F. Dionne, Proceed, of IEEE, 65 5(1975) 777

[3]. S.Hilpert, Ber. Disch. Chem. Ges. 42 (1909) 2248.

[4]. J.L Snoek, physica Amsterdam 39 (1936) 463

[5]. J.L Snoek New development in the magnetic materials Elsevier publications Co.

New York

Amsterdam (1947).

[6]. H.E.Du Boise, Phil. Mag., 29 (1980) 193

[7] S. Hilpert and Wille, Z.Phys. Chem., B18 (1932) 291

[8] G.Tammann, Z.Aner. Allen. Chem.,111 (1921) 87.

[9] J.A. Handvall, Ber. Deut.Chemie.Ges., 45 (1912) 411

[10] Y.Kato and T. Takei, Trans Amer. Electro ceramic .Soc.57 (1930) 297.

[11] E.J.W .Verway, F.C Romeija and pw Heilman, J. Chem. phys.l5 (1947) 181

[12] D.W. Anderson, Phys, Rev., 79 (1950) 350

[13] J.N. Van-Vleck, Phys.Rev.,78 (1951) 266

[14] C.Zener, ibibd 81 (1951) 440 and ibid 82 (1951 403..

[15] C.G Koops ,Phys.Rev.83 (1951) 123

[16] Y.Yafet and C.Kittle,Phys.Rev 87 (1952) 290

[17] E.W.Gorter, Nature, 173.(1954) 123.

[18] C.Guillaud, J.Phys.Rev.99(1955) 1727.

[19] R.D. Waldron, Phys. Rev. 99 1955 1727.

[20] M.A.Galleo and S Geller,Acta.Cryst. 10 (1957) 239.

[21] G.S.Gruintjes,G.J.Oudemans, J.Ceram.Bull.(1966) 411.

[22] G Economos, J. Amer.Ceram.Soc.38. (1955) 241.

[23] B.Viswanathan and VRK Murthy 'Territe Materials " (Science and

Technology), Springer-

Verlag, Narosa Publish House., (1990) p-3

[24] L.K.Leung, B,J.Evans and A.H Morrish ibid B8 (1973) 29.

[25] N.S Satyamurthy, M.G.Matera, R.G Begum and S.I Youssef, Ferrites

proceed.ICF Japan

(1970)60.

[26] A.Globus, P.Duplex and M. Guyot, IEEE trans. Magn vol.Mag-7 (1971) 617

Department of Physics Kuvempii University Shankarghatta

http://Amer.Ceram.Soc.38

Some Properties of inicrowave fcrrites •vjMSWBiriWKAjMnun

[27] T.Yamashiro, Jpn. J.Appl. Phys., 12 (1973)146.

[28] Kyoshio-Seki, Jun-[chi,Shida Koichi and Murakani, IEEE Tran.on Instum.And

Measurem.39(1988)3

[29] EJ.W .Verway, F.C Romeija and pw Heilman, J. Chem. phys. 15 (1947) 181

[30] M.I Klinger, J.Phys.C. (GB) 821 (1975) 3595.

[31] 46 H,P Peloschek," Progress in Dielectrics '' Ed.by J.B.Birks and

J.Hart.Heywood and

Co.London5(1963).

[32] A.I Eatah, A, A Ghani,M.E Sahanor and E.E Faramaway, Phys Stat.Sol.(a) 104

(1987)793.

[33] J.C.Maxweir'Electricity and Magnetism" Vol I Oxford University Press

.London(1973)828

[34] K.W.Wagner, Ann .physs.40 (1913) 817

[35] S,G Snellings " Soft Ferrites "' Properties and applications'\2"'' Ed

Butterw'orths, London

(1980)2

[36] E.Hirota, K. Hirota and K.Kugimiya,Proceed.ICF 3 91980) 667.

[37] E.Roess .IEEE Trans .On .Magn., MAG-18 (1982) 1529

[38] L.P.M Bracke ,Electronic Component and applications,5 (1983) 171.

[39] E.Albers-Schonberg, J.Appl.Phys.25 (1964) 152

[40] D.Bahadur,Bull.Mater.Sci., 155 (1992)431.

[41] S.E. Harrison, H.S. Belson, C.J. Kriessman, J. Appl. Phys. 29 (1958) 337.

[42] M. Pardavi-Horvath, P.E. Wigen, G. Vertesy, P. DeGasperis, IEEE Trans.

Magn. 23 (1987) 3730

[43] F. Chen, P. DeGasperis, R. Marcelli, M. Pardavi-Horvath,J. Appl. Phys. 67

(1990)5530.

[44] E.F. SchloK mann, IEEE Trans. Magn. 34 (1988) 3830.

[45] P.J. van der Zaag, J. Magn.Magn.Mater.196917 (1999)315.

[46] M.Penchal reddy ,G.Balakrishianiah,W.Madhuri, M,Venktaramana ,N

Ramamonhor ready K.V.Shivakiimar, V.R.K. Murthy. R.Ramakrishana

Readdy.Joumal of physics and chemistry of solids. 71 (2010) 1373-1380.

[47]. M.R.Bhandre, H.V.Jamadar, A.T.Pathan, B.K.Chougle,AM.Shaikhjounal of

alloys and compounds 509 (2011) LlB-LllS.

Department of Physics Kiivenipit University Shankarghatta

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