This is Magnetic Properties Chapter of Solid State Physics

1. 4th Chapter: Magnetic Properties
Electrical Engineering Materials

2. According to the modern theories, magnetism in solids originates due to
the orbital and spin motions of electrons as well as spins of the nuclei. The motion
of electrons is equivalent to an electric current which produces the magnetic
effects. The major contribution comes from the spin of unpaired valence electrons
which produce permanent magnetic moments. The minor contributions arise due to
orbital motion of electrons and spins of nuclei.
Origin of Magnetism
Fig. 01: The orbit of a spinning electron about the nucleus of an atom.

3.  Magnetization
When a solid is placed in a magnetic field, it gets magnetized. The
magnetic dipole moment per unit volume is called magnetization and is denoted
by M. It is given as
V
m
M 

Volume
moment
dipole
Magnetic
 Magnetic Moment
The strength of a magnetic dipole, called the magnetic dipole moment,
may be thought of as a measure of a dipole's ability to turn itself into alignment
with a given external magnetic field. In a uniform magnetic field, the magnitude
of the dipole moment is proportional to the maximum amount of torque on the
dipole, which occurs when the dipole is at right angles to the magnetic field. The
magnetic moment ‗m‘ can be defined as vector relating the torque and external
magnetic field as
B
m






Unit of magnetic moment  A-m2.
Unit of magnetic moment  A-m-1.

4. Magnetic susceptibility is a measure of the quality of the magnetic
material and is defined as the magnetization produced per unit applied magnetic
field. It is a dimensionless constant that indicates the degree of magnetization of
a material in response to an applied magnetic field. It is given as
Magnetic permeability () is defined as the property of the material to
allow the magnetic lines of force to pass through it. The magnetic permeability of
the material is directly proportional to the number of lines of force passing through
it. It is the equal to the ratio of magnetic induction to magnetic field intensity. The
greater the magnetic permeability of the material, the greater the conductivity for
magnetic lines of force and vice versa. It is found experimentally that B is directly
proportional to H and is given by
Field
Magnetic
ion
Magnetizat


H
M

 Magnetic Susceptibility
 Magnetic Permeability
H
B

 Unit of magnetic moment  H-m-1.

5.  Curie Temperature
The Curie temperature Tc is the temperature above which the
spontaneous magnetization and then a ferromagnetic substance behaves as
paramagnetic substance. It separates the disordered paramagnetic phases at
T>Tc from the ordered ferromagnetic phase at T<Tc.
The Curie temperature of iron (Fe) is found to be 7400C.
 Relative Permeability
The relative permeability of the material is the comparison of the
permeability concerning the air or vacuum. It is the ratio of the permeability of
any medium to the permeability of air or vacuum. It is expressed as
0


 
r

6. Types Magnetic Materials
Magnetic materials are usually classified into different classes on the
basis of -values and its variation with magnetic field strength and
temperature. There are five types of magnetic materials such as
1. Diamagetism
2. Paramagnetism
3. Ferromagnetism
4. Antiferromagnetism
5. Ferrimagnetism

7. Diamagnetism
Diamagnetic substances are those which when placed in a magnetic
field becomes weakly magnetized. A diamagnetic substance contains no
permanent dipole moment in the absence of an external magnetic field. With
the application of an external field, a dipole moment opposing the magnetic
field is induced in the atoms or molecules. The diamagnetic property arises
due to this induced magnetic moment, hence the magnetic effects are very
small. Since the induced magnetic moments always oppose the applied field,
the susceptibility of diamagnetic substance is negative  < 0 and the relative
permeability, r of this substance is slightly less than one.  and r are
independent of temperature. A diamagnetic solid tends to repel the magnetic
lines of force.
Examples: Cu, Au, Ge, Si, Bi, NaCl, Al2O3 etc.

8. Paramagnetism
Paramagnetism is related to the tendency of a permanent magnet to
align itself in the direction of magnetic field such that its dipole moment is
parallel to the field. A paramagnetic substance has a non-vanishing angular
momentum and hence it posse permanent dipole moments. In the absence of an
applied field the dipoles are randomly oriented and so the net magnetization in
any given direction is zero. When a field is applied, the atomic dipoles tend to
orient parallel to the field and make a positive -value. Susceptibility of a
paramagnetic substance is positive and less than unity and depends on the
temperature. The relative permeability, r is slightly greater than unity and is
independent of field strength. A paramagnet weakly attracts the lines of force.
They do not show hysteresis.
Examples: Platinum, Aluminium, Chromium, Manganese, etc.

9. Ferromagnetism
Ferromagnetic materials are very strong magnetic. When they are placed in a
magnetic field , become strongly magnetized in the direction of the applied field. A
ferromagnetic substance contains strong magnetic dipole moment. The ferromagnetic
substances have spontaneous magnetization. Even in the absence of applied field,
ferromagnetic substance have spontaneous magnetization due to the internal magnetic
filed of these materials below Curie temperature, i.e. when H = 0, M  0 in this case. The
-values are positive and very large. The relative permeability is much greater than
unity. The ferromagnetic solids strongly attract the lines of force. As temperature
increases, the value of  decreases and above a certain temperature Tc, known as Curie
temperature, ferromagnetics are changed into paramagnetics. One of the characteristics of
ferromagnetics is the phenomenon of hysteresis.
Examples: Familiar examples of ferromagnetics are Fe, Co, Ni and their alloys.

10.  Antiferromagnetism
In the magnetized state, a ferromagnetic has all its dipoles aligned exactly in the
same direction. But, an antiferromagnetic material has dipoles with equal moments but the
alternate dipoles point in the opposite directions. Consequently, the moments balance eavh
other leading to a zero net magnetization.
Examples: Familiar examples of antiferromagnetics are: Manganese oxide (MnO), iron
oxide (Fe2O3) etc.
 Ferrimagnetism
In ferrimagnetic materials, the neighbouring dipoles also point in opposite
directions but they are not equal. Hence they cannot completely nullify each other and has
a net finite magnetization. Like ferromagnetic materials, it also shows hysteresis
phenomenon and gives saturation magnetization.
Examples: Familiar examples of ferrimagnetics are: Cubic spinel ferrites such as
NiFe2O4, CoFe2O4, Fe3O4, CuFe2O4 etc.

11.  Spins of Different types of Magnetic Materials

12. Atomic theory of magnetism
Let an electron of mass m and charge –e move in a circular orbit of radius r with
a linear velocity v. Now, a moving charge constitutes an electric current as
dt
dq
I  , where dq is the charge
ev
dt
ds
dq
Ids 


 , where ds = distance covered by electron
For a circular orbit, ds = 2r and v = r,
where  is the angular velocity
r
e
r
I 
 

 2
.
)
..(
..........
2
2
, i
e
r
r
e
I
or



 



From electromagnetic theory, the magnetic field due to the current I flowing through
a stationary loop of cross sectional area A at right angles to the plane of the loop is
the same as the field developed by a magnetic dipole measured large distance.

13. Therefore, magnitude of the magnetic moment of such a dipole
2
.
2
2
2 r
e
r
e
IA
m










Where L = mr2 is the orbital angular momentum and is directed normal to the
orbital plane. The negative sign indicates that the magnetic moment m is
antiparallel to the angular momentum L.
Equation (ii) is valid only for the orbital motion of electron and not for spin of
the electron and of the nucleus.
)
.(
..........
)
2
(
2
2
ii
L
m
e
m
r
em
m 







14. Origin of permanent Magnetic Moment
dt
dq
I  , where dq is the charge
ev
dt
ds
dq
Ids 


 , where ds = distance covered by electron
l
l L
m
e
)
2
(



Three different sources that can provide permanent magnetic moment. These are
as follows:
a) Orbital magnetic moment of electrons
b) Spin magnetic moment of electrons
c) Spin magnetic moment of nucleus
a) Orbital magnetic moment of electrons:
From the atomic theory of magnetism, the orbital magnetic moment is given by
Quantum mechanically,
B
l
l
l m
m
m
eh
m
m
e
L
m
e
B
l
l 

 




  )
4
(
)
2
(
)
2
( , 
where, and is called Bohr magneton. It is the
quantum of orbital magnetic moment.
2
24
10
27
.
9
4 m
A
m
eh
B 


 



15. B
s
s
s m
m
eh
m
m
e
S
m
e



2
1
)
4
(
)
2
(
)
2
( 





 
b) Spin magnetic moment of electrons:
The spin magnetic moment can be determined by substituting of spin angular
momentum , so that we have
Spin magnetic moment is half of a Bohr magneton.
]
2
1
[ 

s
m

The magnetic moment component sz along the field direction z is given by
s
s
s m
m
eh
m
m
e
)
4
(
)
2
(

 g
g 
 
where, g is called the Lande splitting factor or Lande g-factor and determines
the amount by which the original level splits up in a magnetic field.

s
m
S 
[Total magnetic moment of atomic system is: ]
B
J
 g


16. B
s
s
s m
m
eh
m
m
e
S
m
e



2
1
)
4
(
)
2
(
)
2
( 





 
c) Spin magnetic moment of Nucleus:
Like an electron, the nucleus has intrinsic spin called the nuclear spin and has a
magnetic moment. But the nuclear mass is more than 103 times greater than that
of an electron. So that the nuclear magnetic moment is three order smaller in
magnitude compared to that associated with the electron.
While the electronic magnetic moment is measured in the unit of Bohr magneton,
the nuclear magnetic moment is measured in the unit of nuclear magneton.
2
27
10
05
.
5
4
m
A
m
eh
p
N 


 


The nuclear magneton is defined as
where, mp is the mass of proton.

17. Classical Langevin’s Theory of Diamagnetism
)
....(
..........
2
0
2
i
r
m
r
mv
Fcp 


Diamagnetic substances are those which placed in an external magnetic
field become weakly magnetized in a direction opposite to the field direction.
So, diamagnetic material possesses a small value of negative susceptibility
which is independent of temperature.
Let us consider the motion of an electron round the nucleus in a circular orbit
of radius r . In the absence of an external field, the centripetal force acting on
the electron due to the nucleus is
where, m is the mass of the electron, v and
0 are the linear and angular velocity of
electron‘s motion.

18. When an external magnetic field B is applied perpendicular to the
plane (xy plane) of the orbit, an additional force FL called Lorentz force acts on
the electron. The Lorentz force is given by
)
....(
..........
90
sin
)
( 0 ii
eBr
evB
B
v
e
FL 









The resultant force will be
L
cp F
F
F 
 

 eBr
r
m
r
m
or 
 2
0
2
,
0
, 2
0
2


 


m
eB
or
Solving the quadratic equation in ,
2
4
)
( 2
0
2





 m
eB
m
eB

19. m
eB
m
eB
or
2
)
2
(
, 2
2
0 


 

For eB/2m << 0, we obtain
)
....(
..........
2
0
0 iii
m
eB
L



 





This shows that the frequency of revolution of an electron changes by a factor of
eB/2m in the presence of magnetic field B. The frequency is called
the Larmour frequency.
m
eB
L 2


Due to the change in frequency, the current for each electron is given by
m
B
e
e
I
L




4
2
-e
time)
unit
per
n
(Revolutio
(Charge)
2
L 








20. If each atom contains Z electrons, then the current becomes
)
..(
..........
4
2
2
iv
m
B
Ze
A
I
m 


 



The magnetic moment of the elementary current is
m
B
Ze
I

4
2



where, is the mean square radius of the projection of the orbit on a plane
perpendicular to the field axis.
2

As the field is acting parallel to the z-axis, therefore
2
2
2
y
x 


The mean square distance of the electron from the nucleus is
2
2
2
2
z
y
x
r 


For spherically symmetric charge distribution, we have
2
2
2
z
y
x 


21. Hence, we have
2
2
3
2
r


Thus from equation (iv), we have
)
..(
..........
6
3
2
4
2
2
2
2
v
r
m
B
Ze
r
m
B
Ze
m 




If there are N atoms per unit volume, then the magnetization M is given by
)
..(
..........
6
6
2
0
2
2
2
vi
m
H
r
N
Ze
r
m
BN
Ze
N
M m

 




The diamagnetic susceptibility is given by
)
..(
..........
6
2
2
0
vii
m
r
N
Ze
H
M
dia

 


This is the classical Langevin equation for diamagnetism

22.  Sources of Paramagnetism
Paramagnetic materials are non-magnetic when a magnetic field is
absent and magnetic when a magnetic field is applied.
Sources of paramagnetism are:
1. Atoms and molecules having an odd number of electrons; that is, all atoms
that have unpaired electrons. Free sodium atoms, gaseous nitric oxide etc
are some examples.
2. Atoms with incomplete inner shells: Transition elements (Z = 57-72) and (Z
= 91-102), rare earth and actinite elements have atoms with incomplete
inner shells.
3. Free radicals : Triphenylmethyl C(C6H5)3, F-centres in alkali halides satisfy
this criterion.
4. Metals: The electrons in a metal are considered to be free like molecules in
a gas. They tend to pair up but there are always a few unpaired electrons to
produce a weak temperature dependent paramagnetism known as Pauli
paramagnetism.

23. Classical Langevin’s Theory of Paramagnetism
)
..(
..........
cos
. i
B
B
U 

 





Paramagnetism occurs in substances where the individual atoms, ions or
molecules possess a permanent magnetic dipole moment which is randomly
oriented in the absence of an external field. When a field B is applied, each
dipole experiences a torque ×B, where  is the dipole moment. These torque
tend to orient the dipoles along the direction of field in order to minimize their
energy. The potential energy of each dipole in the magnetic field is given by
Suppose that B is applied along the z axis, so that  is the angle made by the
dipole with the z-axis.
According to the Maxwell-Boltzmann statistics, the probability of
finding the dipole within the solid angle d is proportional to the Boltzmann
factor
)
...(
..........
)
(
cos
ii
e
e
f
T
k
B
T
k
U




 



24. 










0
0
)
(
)
(
d
f
d
f
z
z
The average value of z then is given by:
The integration is carried out over the solid angle with element d. It thus takes
into account all possible orientations of the dipoles.
To do the integral, substitute z =  cos and d = 2 sin d which gives






 

 

 

 




















0
cos
0
cos
0
cos
0
cos
sin
sin
cos
sin
2
sin
2
.
cos
d
e
d
e
d
e
d
e
T
k
B
T
k
B
T
k
B
T
k
B
z
…………..(iii)

25. So the mean value of z has the form














0
cos
0
cos
sin
sin
cos
d
e
d
e
a
a
z
a
T
k
B



Let





















a
e
e
e
e
dx
e
dx
e
x
a
a
a
a
ax
ax
z
1
1
1
1
1 


Then








a
a
z
1
)
coth(

 a
a
a
a
e
e
e
e
a





)
coth(
where,
Let cos = x, then sin d = -dx and limits -1 to + 1.
…………..(iv)

26. The function is known as Langevin function. Fig. 04
illustrates the variation of L(a) with a.
Fig. 04
)
.(
..........
)
( v
a
L
z 
 

a
a
a
L
1
)
coth(
)
( 


27. If N is the number of dipole per unit volume, then the magnetization is given by
)
.........(
)
( vi
a
L
N
N
M z 
 

3
1
....
45
3
1
)
coth(
3 a
a
a
a
a
a 





For small values of a, i.e., a<<1 (low B and high T), we have
So that
3
1
3
1
)
(
a
a
a
a
a
L 



In this limit, the magnetization is
)
(
..........
3
3
3
. 0
2
2
vii
T
k
H
N
T
k
B
N
a
N
M





 


The paramagnetic susceptibility is then given by
T
k
N
H
M
para




3
2
0



28. The expression (viii) is called the Curie law. This shows that the
paramagnetic susceptibility is inversely proportional to the absolute temperature.
where, is known as Curie constant.
)
.(
..........
3
2
0
viii
T
C
T
k
N
H
M
para 









k
N
C
3
2
0

Fig. 05

29. This is the saturation magnetization which corresponds to the complete
alignment of the magnetic dipoles in the field direction. This shows that
saturation occurs when the temperature T is low and applied magnetic field B is
high and the dipole moment  is large.
For large values of a, i.e., a>>1 (high B and low T), L(a) approaches to unity.
Then equ. (vi) gives
s
M
N
M 
  Ms= saturation magnetization

30. Hysteresis Loop
 A hysteresis loop shows the relationship between the induced magnetic flux density
(B) and the magnetizing force (H). It is often referred to as the B-H loop. An example
hysteresis loop is shown below. The phenomenon of flux density B lagging behind
the magnetic field H in a magnetic material is known as Magnetic Hysteresis.
If the field is now reduced, the new curve
does not retrace the original curve oa. Even
when the field reduced to zero, the value of
B will not be zero. This value ob of B is the
residual magnetization Mr. To destroy the
magnetization completely, a negative field
(–Hc) is required, which is known as
Coercive force.
For a complete cycle of B from a positive
to a negative field and from a negative to
positive filed, the curve encloses a certain
area forming a closed loop. This loop is
called the hysteresis loop.
Fig.07 illustrates the progress of magnetization process as the external field increases.
Starting at the origin, B increases slowly at first, but more rapidly as the field is
increased to reach the saturation point.

31. Domain Theory
The domain theory was proposed by Weiss in 1907. He proposed that
1. A ferromagnetic specimen is divided into a large number of small regions called
domains. Each domain is like a tiny magnet.
2. Each domain is spontaneously magnetized.
3. The direction of magnetization varies from domain to domain and the net magnetization is
zero in the absence of magnetic field.
4. The spontaneous magnetization of the specimen is the vector sum of the magnetic
moments of the individual domains.
5. Within each domain the spontaneous magnetization is due to the existence of a
‗molecular field’ (Weiss field) which tends to produce a parallel alignment of the atomic
dipoles.
6. Domains typically contain from 1012 to
1015 atoms and are separated by domain
walls called ‗Bloch walls‘.

32. When the magnetic field is applied to the ferromagnetic materials, the
magnetization produced by two ways.
1. By the motion of domain walls
If the weak magnetic field is applied, the volume of domains favourably
oriented with respect to the field increases at the expense of unfavourably
oriented domains. The intensity of the magnetization increases rapidly and the
growth of domains stops as the saturation region is approached .
2. By the rotation of domain wall
If the strong magnetic field is applied, rotation of unfavorably aligned
domain occurs towards the direction of the field. The magnetization changes
by means of rotation of domains. Domain rotation requires more energy than
domain growth.
The direct experimental evidence for the physical existence of the domains was provided in 1931 by F. Bitter.

33. Bloch Wall
The domains are separated from one another by boundaries. These are the regions
within which the moments (spins) change their spatial directions. The transition layer that
separates adjacent domains is called a ―domain wall‖ or ―Bloch wall‖. Its thickness is not
infinitely small, but it has a finite value, i.e., the spin orientation changes gradually in the
transition region. In this manner the spin reversal is accompanied over a number of steps.
This leads to a reduction in the exchange energy associated with the wall.
For iron, the wall is about 1000 Å thick and its energy about 10-3 J/m2.
Fig.10 Schematic representation of a 180º domain wall

34. Hysteresis on the basis of Domain Theory
 The hysteresis of ferromagnetic materials refers to the lag of magnetization (M) behind
the magnetizing field H. Formation of hysteresis curve may be describe as follows:
a) When a weak magnetic field is applied, domains where the magnetization is parallel to field grow
at the expanse of unfavourably oriented domains. This results in a small magnetization as indicated
by the path OA. Such displacements of domain boundaries are mostly reversible.
b) When the magnetic field becomes stronger, the Bloch wall movement is sharp and is irreversible.
The steeper part AB of the magnetization curve is due to larger, irreversible domain wall motion.
c) If the field is gradually increased, the domains rotate from their easy directions to the direction of
the applied field. At C, all the domains are in the field direction and the specimen is said to be
saturated. A further increase in the field produces no change in the magnetization.
d) When the applied field is gradually decreased,
the decrease in magnetization follows a
different path because the aligned domains do
not regain their random state orientation easiliy.
Even when the applied field is zero, there is a
residual magnetization. A reverse field (-Hc)
called coercive force is required to destroy the
residual magnetization.
A similar variation in the reverse magnetization is
observed as the reverse field is first increased
and then decreased. The closed loop CEFKC is
called the hysteresis loop.
Thus, the reversible and irreversible domain
wall movements and domain rotation give rise
to hysteresis in the ferromagnetic materials.
Fig. 11

35. Why and How Domains form?
The formation of the domain and its shape depend on the competition among a
number of energy terms (exchange energy, magnetic field energy, anisotropy energy, domain
wall energy etc) present in the magnetic crystal. A large region of ferromagnetic material with
a constant magnetization throughout will create a large magnetic field extending into the
space outside itself. This requires a lot of magnetostatic energy stored in the field.
In order to reduce the magnetostatic energy of the system, the sample divides into
domains. This is the magnetic potential energy generated when a magnetic body is placed in a
magnetic field. The division into two opposite domains causes the sample‘s magnetostatic
energy to be reduced by about one-half. This is because the demagnetizing field inside the
sample is reduced significantly. Similarly dividing the crystal into N domains, reduces the
magnetostatic energy by 1/N or more.
Thus, it can be
concluded that the presence of
large domains is energetically
unfavourable; a ferromagnetic
material must possess a domain
structure consisting of a number
of smaller domains which
corresponds to a state of
minimum energy. Fig. 12

36. Curie-Weiss Law for Ferromagnetism
Langevin‘s theory of paramagnetism was extended by Weiss to give a
theoretical explanation of the behavior of ferromagnetism. He made the
following two hypothesis in 1907:
1. Weiss assumed that a ferromagnetic specimen contains, in general, a large
number of small regions called domains which are spontaneously
magnetized. The total spontaneous magnetization of the specimen is
determined by the vector sum of the magnetic moments of the individual
domains.
2. Within each domain the spontaneous magnetization is due to the existence
of an internal ‗molecular field’ (Weiss field) which tends to produce a
parallel alignment of the atomic dipoles.
Weiss also assumed that the internal molecular field Bi is proportional to the
spontaneous magnetization M. Thus we have,
M
Bi 
 The proportional constant  is known as Weiss constant.

37. Now, if the field Ba is applied, the effective field will be
)
.(
.......... i
B
B
B a
i
eff 

Since above the Curie temperature the ferromagnetic materials behave as
paramagnetic, we can apply Curie law
)
.......(
..........
3
2
0
ii
T
C
TK
Nm




where, constant
Curie
2
0


K
Nm
C

Then above the Curie temperature magnetization M is given as
)
(
)
(
0
0
M
B
T
C
B
B
T
C
H
M a
i
a
eff 


 




TM
MC
CB
or a 0
, 
 

)
(
, 0
0 C
T
M
H
C
or 

 

]
[ 0H
B 


38. Now, the susceptibility is defined as the ratio of the magnetization M to the
applied field H. So we can write
We know that Curie temperature is given by
)
(
, 0
0 C
T
M
H
C
or 

 

)
(
..........
0
0
iii
C
T
C
H
M






0
0
0






C
T
C
C
T
C
H
M





0

 C
Tc 
)
....(
.......... iv
T
T
C
c


 
which is known as Curie-Weiss law.

39. Variation of Ms and  with T
The figures shows that while Ms start dropping at TC and then dies off
slowly as there is a divergence in 1/χ at Tc in the paramagnetic region. This is
the signature of a phase transition to a spontaneously ordered phase. A positive
value of TC indicates that molecular field is acting in the same direction as of
applied field and acts to align the magnetic moments parallel to each other, as
should be the case with a ferromagnetic material.

40.  Low coercivity
 Small hysteresis loss due to small hysteresis area
 Low magnetization
 Low retentivity
 High initial permeability and susceptibility
 Eddy current loss is less because of high resistivity
 Soft Magnetic Materials
Soft magnetic materials are those materials that are easily magnetized and
demagnetized. This magnetic material has a narrow magnetic hysteresis loop and
results in a small amount of dissipated energy. These materials have
These are generally used for cores of transformer, alternators, electromagnets,
motors, generators, magnetic amplifier, solenoid, relays which require minimum
energy dissipation. Examples of soft magnetic materials are soft iron, silicon
steel, nickel-iron alloy and soft ferrites.

41.  Hard Magnetic Materials
Hard magnetic materials are difficult to magnetize and demagnetize. The hard
magnetic material has a wider magnetic hysteresis loop and results in a large
amount of energy dissipation and the demagnetization process is more difficult to
achieve. These materials have
 High coercivity
 High saturation magnetization
 High retentivity
 Large hysteresis loss due to large hysteresis loop area
 Low initial permeability and susceptibility
 Eddy current loss is high
Such materials are used for making permanent magnets and magnetic tap, hard
disc, credit card, audio recording, loudspeakers as its memory is not easily
erased. These are soft carbon steel, cobalt steel, tungsten steel, hard ferrites etc.

42.  Anisotropy Energy
Experiments on ferromagnetic materials show that it is easier to
magnetize a substance in one direction than in another direction. The more
favourable direction is referred to as the easy direction, while the least
favourable is known as the hard direction. Since it requires a larger field to
magnetize the substance in the hard direction, the magnetization requires a
larger energy. The difference in energy between the easy and the hard directions
is called the magnetic anisotropy energy.

43.  Curie Temperature
The Curie temperature Tc is the temperature above which a
ferromagnetic substance behaves as paramagnetic substance. It separates the
disordered paramagnetic phases at T>Tc from the ordered ferromagnetic phase
at T<Tc. Below the Curie temperature, the atoms are aligned and parallel,
causing spontaneous magnetism; the material is ferromagnetic. Above the
Curie temperature the material is paramagnetic, as the atoms lose their
ordered magnetic moments when the material undergoes a phase transition.
The Curie temperature of iron (Fe) is found to be 7400C.
 Neel Temperature
The Néel temperature or magnetic ordering temperature, TN, is the
temperature above which an antiferromagnetic material becomes
paramagnetic—that is, the thermal energy becomes large enough to destroy the
microscopic magnetic ordering within the material.

44. Ferrites
 Ferrites constitute the special branch of ferrimagnetics. Ferrites are double oxides of iron
and another metal (MO.Fe2O3, M is the transition metals such as Ni, Co, Mn, Mg, Zn, Cu
etc.). They have two unequal sublattices and are antiparallel to each other. Because of
unequal magnetization in the two sublattices, the materials have resultant magnetization.
Like ferromagnetics, ferrites have spontaneous magnetization and show the phenomena of
magnetic saturation and hysteresis. They have a critical temperature called Curie
temperature above which they become paramagnetic.
• Significant saturation magnetization
• High electrical resistivity (102 to 1010 Ohm-cm ). This outstanding property of
ferrites makes them highly demandable for high frequency applications.
• Low electrical loss
• Very good chemical stability
Properties of ferrites include:

45. Applications of Ferrites
The applications of different types of ferrites:
 Typically ferrites have high electrical resistance which results in very low eddy current losses.
Ferrites are used for inductors, transformers and electromagnets.
 Data storage (e.g. magnetic recording tapes and hard disks)
 Ferrites are used for microwave applications in the frequency ranges of 1-300 GHz such as phase
shifters, circulators and isolators.
 Loudspeakers, motors, deflection yokes, electromagnetic interference suppressors, radar absorbers,
antenna rods, proximity sensors, humidity sensors, memory devices, recording heads, broadband
transformers, filters, inductors, etc are frequently based on ferrites.
 Multilayer chip inductors (MLCI) are made from soft ferrites became more and more miniaturized
and integrated. The MLCIs are important components for the latest electronic products such as
cellular phones, video cameras, notebook computers, hard and floppy drives, etc which require
small dimensions, light weight, and better functions.
 Spinel type ferrites are commonly used in many electronic and magnetic devices due to their high
magnetic permeability and low magnetic losses.
 It is also used in electrode materials for high temperature applications because of their high
thermodynamic stability, electrical resistivity, electrolytic activity and resistance to corrosion.
 Ferrite nanoparticles have a wide range of biomedical applications such as contrast agents in
Magnetic Resonance Imaging (MRI), in targeted drug delivery and in magnetic hyperthermia etc.

46. Comparison of Magnetic Materials