Download Soft and Hard Magnetic Materials:- Ferromagnetic

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Magnetic Properties of Materials & Super conducting Materials
Magnetic properties of a material arise due to three mechanisms. They are 1. Magnetic moment
arising due to orbital motion of electron, 2. Magnetic moments arising out of electron spin and 3.
Magnetic moments associated with the nucleus. Of the above three the magnetic moments
associated with the nucleus are very small and are neglected whenever any of the other two are
present. Similarly the magnetic moments associated with orbital motion of the electron are small
compared to magnetic moments associated with electron spin and can be neglected when spin
magnetic moment is present. Depending how a material reacts to an applied magnetic field, the
materials are classified into 1 Diamagnetic, 2. Paramagnetic, 3. Ferromagnetic, 4. Anti
ferromagnetic and 5. Ferry magnetic materials.
Important Definitions
The magnetic or magnetic flux density (B) is defined as the number of magnetic flux lines passing
through unit area perpendicular to the applied field. The units for B are Tesla or Weber/𝑚2 .
The magnetic field intensity (H) at any point in the magnetic field is the magnetic force
experienced by a unit north pole. Its unit is A/m
If a magnetic field of strength H is applied in free space or vacuum then the magnetic flux density
B= µ𝑜 H where µ𝑜 is permeability of free space (4π 10−7 )H/m
If the field is applied near a material then B = µH where µ is permeability of the medium, µ=B/H.
The ratio µ/µ0 =µ𝑟 is called relative permeability of the medium.
Magnetization (M):- In presence of a material the magnetic flux density B for given material is
different from flux density of free space. This is due to certain magnetization changes occurring in
the material, and this change is called Magnetization (M) of the material.
The Magnetic Susceptibility (х) of a material is defined as the ratio of magnetization to applied field
strength. Х = M/H (it has no units)
If a field of intensity B is applied near a material, then B = µH =( µ/ µ0 ) µ0 H = µ𝑟 µ0H - - -> 1
If M is the Magnetization then B = µ0 (H+ M) - - - -> 2
From equations 1 and 2
B = µ𝑟 µ0H = µ0 H + µ0 M = µ0 H (µ𝑟 - 1) = µ0 M
M = H (µ𝑟 -1) and µ0 = B/ (H+M). The relative permeability µ𝑟 = 1 + M/H.
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Origin of Magnetic Moments:- Magnetic properties of a material arise due to three
mechanisms. They are 1. Magnetic moments arising out of orbital motion of electrons, 2. Magnetic
moments arising out of electron spin and 3. Magnetic moments associated with the nucleus. Of the
above three the magnetic moments associated with the nucleus are very small and are neglected
whenever any of the other two are present. Similarly the magnetic moments associated with
orbital motion of the electron are small compared to magnetic moments associated with electron
spin and can be neglected when spin magnetic moment is present. Depending how a material
reacts to an applied magnetic field, the materials are classified into 1 Diamagnetic, 2.
Paramagnetic, 3. Ferromagnetic, and a mechanism similar to the mechanism responsible for
ferromagnetism gives rise to 4. Anti- ferromagnetic and 5. Ferri-magnetic materials.
Orbital Magnetic moment and Bohr Magnetron:- The orbital motion of the electron round
the nucleus can considered to be equal to passage of electrical charge i.e. electrical current in
closed circular loop. The current I due to a revolving electron
I = charge of the electron x No. revolutions per second = e.ν= -e.ω/2π
Where ν is electron revolving frequency around nucleus and w= 2πν is angular frequency of the
electron.
The current passing through a circular loop produces a magnetic
field in a direction perpendicular to the area of the coil and this
magnetic field is identical to that of a magnetic dipole. The
magnetic moment due to current I in circular coil of area A is given
by
µ𝒎 =I.A =
µ𝒎 = −
𝑒
2𝑚
- (e.ω/2π) 𝜋𝑟 2 = - (e.ω𝑟2)/2 = - 2𝑚𝑒 mω𝑟 2
L - - -- > 1
Where L= mω𝑟 2 is the orbital angular momentum of the electron.
The possible orientation values of angular momentum vector in an external field are
L = 𝑚𝑙 . h/2π
-- - - - 2 where 𝑚𝑙 is angular momentum quantum number, and can have
2L+1 values from -L to +L including zero. i.e. 2L+1 integer values.
From equations 1 and 2
µ𝒎 = −
𝑒
2𝑚
𝑒ℎ
µ𝐵 = 4𝜋𝑚 = 9.2710−24 A−𝑚2
µ𝐵 is called Bohr Magnetron.
𝑚𝑙 . h/2π =
-
𝑒ℎ
4𝜋𝑚
-
𝑚𝑙 = µ 𝐵 𝑚𝑙
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For atoms having many electrons the total magnetic moment due to all electrons is the algebraic
sum of individual magnetic moments of all the electrons and magnetic moment due to two paired
electrons is zero.
Magnetic moment due to electron Spin:Magnetic moment due electron spin is given by µ𝑠 =
1
2
(eh/4πm) spin magnetic moment is half a
Bohr Magneton, from spectroscopic theory the magnetic moment component due to electron spin
along the applied field direction is
µ𝑆𝑧 = 𝑔
µ𝑠𝑧 =g(
𝑒 𝑚 ℎ
2𝑚 𝑠2𝜋
𝑒ℎ
4𝜋𝑚
)𝑚𝑠 where g is called Landes’ factor.
Classification of materials:- Materials on the basis of how they interact with an external
magnetic field are classified in to diamagnetic, paramagnetic and ferromagnetic materials, antiferromagnetic and Ferrimagnetic materials.
Diamagnetic materials:- These materials weakly repel the magnetic lines of force ,the
magnetization produced in these materials is always opposite to the direction of the applied field
and small. Hence magnetic susceptibility is negative and small. Relative magnetic permeability of
diamagnetic materials is always less than unity that is μr < 1.Materials whose atoms / molecules have
completely paired electrons exhibit this property of diamagnetism. Since electrons are completely
paired up spin magnetic moment is zero and magnetic moments due to orbital motion of the
electrons always aligns opposite to the direction of the applied field and hence magnetic field
intensity near a diamagnetic material decreases. All diatomic gas molecules like hydrogen oxygen,
nitrogen etc and Alkaline earth materials, many organic molecules have this property.
Superconducting materials exhibit perfect diamagnetic property with magnetic susceptibility -1.
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Properties:-1. Small negative values of susceptibility 2. No temperature dependence 3. No
magnetic properties in the absence of external field.
Para magnetism:- These materials in the absence of an external field do not have any magnetic
properties and when placed in an external field weakly attract the magnetic lines of force, thereby
increasing field intensity by small margin. The magnetic susceptibility of these materials is positive
and small. The molecules / atoms of these materials have unpaired electrons and hence have
permanent spin magnetic moments. However in the absence of an external field due to random
orientation these materials do not have magnetic properties. When placed in an external fields the
spin magnetic moments present on atoms and molecules try to orient themselves in the direction
of the applied force and hence flux density increases slightly as complete alignment can take place
only at very high fields.
The magnetic susceptibility is small and positive. Temperature
dependency is not high. Atoms and molecules have permanent
magnetic moments.
Examples of paramagnetic materials are alkaline materials,
transition metals, rare earths etc.
Ferromagnetic Materials:-These materials very strongly attract magnetic lines of force and hence
magnetic flux density increases to large values near these materials. The magnetic materials have
large positive values of magnetic susceptibility. Like paramagnetic materials atoms and molecules
of these materials have unpaired electrons and hence have permanent magnetic moments due to
electron spin. The permanent magnetic moments present individual atoms/ molecules in
ferromagnetic materials due to exchange interaction couplings are aligned permanently in one
direction even in the absence of an external field. Hence these materials exhibit spontaneous
magnetization. The magnetic susceptibility of ferromagnetic materials is large and positive. The
susceptibility follows Curi-Weiss law and temperature dependency is given by
𝐶
Х = 𝑇−𝜃
For T> 𝜃𝑓 the material behaves like paramagnetic material i.e. ferromagnetism is not present and
T< 𝜃𝑓 ferromagnetism is present. 𝜃𝑓 is called ferromagnetic Curi temperature.
Iron, nickel, cobalt, Gadolinium etc are examples for ferromagnetic materials.
Anti-ferromagnetic materials:- Like para and ferromagnetic materials atoms/ Molecules
of these materials also have unpaired electrons and hence have permanent magnetic moments. In
these materials these spin magnetic moments are all coupled permanently in anti-parallel manner
so that the material as a whole will not exhibit any magnetic moment due to the spins of unpaired
electrons and hence these materials behave like diamagnetic materials due to orbital magnetic
moments like diamagnetic materials. Below a certain temperature called Neel temperature only
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above behavior will be present and above coupling break due to increasing thermal energies and
material reverts to paramagnetisim.
Ferrimagnetic Materials:- In these materials as in
anti-ferromagnetic materials permanent anti parallel
coupling takes place between the spins of unpaired
electrons present on the molecules. However these anti
parallel couplings are unequal as no. of electrons one
direction are different from the number of electrons in
opposite direction and hence each anti parallel coupling will
result in net spin magnetic moment in one particular
direction. Therefore these materials like ferromagnetic
materials exhibit spontaneous magnetization and have large
positive values of magnetic susceptibility.
These materials also fallow Curi- Weiss law below a certain temperature called Ferrimagnetic Curi
temperature only exhibit spontaneous magnetization above behave like paramagnetic materials.
Weiss theory of Domain Structure of ferromagnetic materials.
Ferromagnetic Materials very strongly attract magnetic lines of force and hence magnetic flux
density increases to large values near these materials. The atoms and molecules of these materials
have unpaired electrons and hence have permanent magnetic moments due to electron spin. The
permanent magnetic moments present on individual atoms/ molecules in ferromagnetic materials
due to exchange interaction couplings are aligned permanently in one direction even in the absence
of an external field. Hence these materials exhibit spontaneous magnetization Iron, nickel, cobalt,
Gadolinium etc are examples for ferromagnetic materials.
In spite of the fact that magnetic moments due to spins of unpaired electrons are aligned parallel in
one direction, a ferromagnetic material if not previously exposed to an external magnetic field will
not exhibit spontaneous magnetization. This was explained by Weiss theory of Domain structure.
According to this theory A ferromagnetic material is made up of large number of small regions called
‘Domains’ and all the electrons in a domain are aligned permanently parallel to one another. Each
domain has spontaneous magnetization due to parallel alignment of all magnetic dipoles present in
that domain. However the material as a whole cannot exhibit spontaneous magnetization as domains
have random orientations.
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(a)Domain arrangement in virgin ferromagnetic specimen when no magnetic field, (b) Growth of favorable domains
in presence of external field, (c ) Rotation of unfavorable domains into applied field direction.
When an external field is applied the ferromagnetic materials acquire magnetic properties due to 1.
Domain growth and 2. Rotation of domains.
Domain Growth:- The volume of the domains in which orientation of spin alignment if in the
direction of applied magnetic field, called favorably oriented domains increase in size at the
expense of unfavorably oriented domains.
Rotation of Unfavorable domains:- When the domains reach a certain optimum size further
growth is not energetically possible and the second mechanism involving the rotation of
unfavorably oriented domains in to the direction of applied field begins. Saturation magnetization
occurs when all the domains are completely in the direction of the applied field.
Hysteresis Curve:- A graph between applied magnetic field strength H and resulting magnetic
flux density B, in a ferromagnetic material is called ‘hysteresis curve or hysteresis loop. This plot
also indicates lag of magnetization behind the applied magnetic field in Ferromagnetic materials.
Hysteresis curve or Hysteresis loop
The hysteresis behavior ferromagnetic materials can be explained by Weiss theory of domain
structure. In the initial stages the magnetization is fast as it is due to domain growth due to reversible
and irreversible domain growth which are fast process with less energy requirement. Once the
domains reach their optimum size further increase in magnetization can be only due to domain
rotation which is a slow process with large energy requirement and hence magnetization increases
slowly.
Saturation magnetization occurs when all the domains completely get rotated in to the direction of
applied field.
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When magnetic field is decreased B also decreases however the specimen retains certain
magnetization even at zero field due to irreversible domains. This left over magnetization at zero
fields is called ‘Receptivity’.
The negative field required to reduce residual magnetization is called ‘Coercive field’
Hysteresis loss is the energy lost in one complete cycle of magnetizing and demagnetizing a
ferromagnetic specimen and is given by the area covered under the hysteresis loop.
Soft and Hard Magnetic Materials:- Ferromagnetic materials on the basis of the hysteresis loss i.e.
depending on the amount of energy lost in one complete cycle of magnetization demagnetization are
classified in to Soft and Hard Magnetic materials.
Soft magnetic materials:- In these materials hysteresis are very low and are used in applications
requiring frequent reversals of magnetic fields.
Hard Magnetic Materials:- In these materials Hysteresis lasses are large and are used as permanent
magnets.
S.No.
Hard Magnetic Materials
Soft Magnetic Materials
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Materials which retain their
magnetism and are difficult to
demagnetize are called hard
magnetic materials.
Soft magnetic materials are easy to
magnetize and demagnetize.
These materials retain their
magnetism even after the removal
of the applied magnetic field.
Hence are used for making
permanent
magnets.
In
permanent magnets the movement
of the domain wall is prevented.
They are prepared by heating the
magnetic materials to the required
temperature and then quenching
them. Impurities increase the
strength
of
hard
magnetic
materials.
These materials are used for making
temporary magnets. The domain wall
movement is easy. Hence they are easy to
magnetize. By annealing the cold worked
material, the dislocation density is
reduced and the domain wall movement
is made easier. Soft magnetic materials
should not possess any void and its
structure should be homogeneous so that
the materials are not affected by
impurities.
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They have large hysteresis loss
due to large hysteresis loop area.
They have low hysteresis loss due to
small hysteresis area.
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Susceptibility
are low.
Susceptibility and permeability are high.
and
permeability
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Coercivity and retentivity values
are large.
Coercivity and retentivity values are less.
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Magnetic energy stored is high.
Since they have low retentivity and
coercivity, they are not used for making
permanent magnets.
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They possess high value of BH
product.
Magnetic energy stored is less.
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The eddy current loss is high.
The eddy current loss is less because of
high resistivity.
Examples of Hard magnetic materials and applications: - Iron-Silicon alloys, Ferrous-Nickel alloys,
Ferrites, Garnets
Hard magnetic materials are used as permanent magnets and find extensive application where
permanent magnetic are used, such as, microphones, flux meters, voltage regulators magnetic
separators.
Examples of soft magnetic materials: Soft iron, iron- aluminum alloys, cupper iron nickel alloys.
Soft magnetic materials are used in applications requiring frequent reversals of magnetic fields,
such as electromagnetic, Transformer core materials, communication equipment, isolators,
switching circuits etc.
Anti Ferromagnetic and Ferrimagnetic materials:Ant ferromagnetic materials:- Like para and ferromagnetic materials atoms/ Molecules of these
materials also have unpaired electrons and hence have permanent magnetic moments. In these
materials these spin magnetic moments are all coupled permanently in anti - parallel manner so
that the material as a whole will not exhibit any magnetic moment due to the spins of unpaired
electrons and hence these materials behave like diamagnetic materials due to orbital magnetic
moments just like diamagnetic materials. Below a certain temperature called Ant ferromagnetic
Curi- Neel temperature only above behavior will be present and above coupling break due to
increasing thermal energies and material reverts to paramagnetisim. Magnetic susceptibility X
𝐶
above Neel temperature is given by =𝑇+𝜃 . C is curi constant and θ is paramagnetic Curi
temperature.
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Ferrites (Ferrimagnetic Materials):- In these materials as in anti ferromagnetic materials
permanent anti parallel coupling takes place between the spins of unpaired electrons present on
the molecules. However these anti parallel couplings are unequal as no. of electrons one direction
are different from the number of electrons in opposite direction and hence each anti parallel
coupling will result in net spin magnetic moment in one particular direction and hence these
materials like ferromagnetic materials exhibit spontaneous magnetization and have large positive
values of magnetic susceptibility. These materials also fallow Curi- Weiss law below a certain
temperature called Ferrimagnetic Curi temperature only exhibit spontaneous magnetization above
behave like paramagnetic materials.
Ferrimagnetic materials are called Ferrites and have the general chemical formula
Me2+ 𝐹𝑒2+3 𝑂42−
where Me2+ is a metal ion. (Example Fe, Co, Me is doubly ionized ions.)
Ferrites of spinel structure have the general formula MeFe2O4, where Me can represent Ni2+, Co2+, Fe2+,
Mn2+, Mg2+, Li1+, and Cu2+. The unit cell of these ferrites is a cube formed by eight molecules of
MeOFe2O3 and consisting of 32 O2– anions, among which there are 64 tetrahedral (A) sites and 32 octahedral
(B) sites partially occupied by Fe3+ and Me2+ cations (Fig. 1). Depending on the ions that occupy
sites A and B and the order in which the sites are occupied, a distinction is made between straight spinel
ferrites (nonmagnetic spinel ferrites) and reversed spinel ferrites (ferrimagnetic spinel ferrites). In the latter
type, one-half of the Fe3+ ions are in the tetrahedral sites, with the remaining one-half, along with the
Me2+ ions, in the octahedral sites. The magnetization MA, of the octahedral sub-lattice is greater than the
magnetization MB of the tetrahedral sub-lattice, a difference giving rise to ferrimagnetism.
Ferrites are usually non-conductive Ferrimagnetic ceramic compounds derived from iron oxides such
as hematite (Fe2O3) or magnetite (Fe3O4) as well as oxides of other metals.
Chemical formulas
Many ferrites are spinels with the formula AB2O4, A𝐵2 𝑂3 where A and B represent various metal cations,
usually including iron Fe. Spinel ferrites like 𝐹𝑒2 𝑂3 oxygen ions form close packed fcc cubic structure. In this
structure for every four Oxygen ions there are 2 octahedral voids and 1 tetrahedral voids. Fe3+ and Fe23 these
sites in such a way Fe23 ions cancel their magnetic moments through antiparallel coupling and Fe
2+ ions
align
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parallel to one another resulting in spontaneous magnetization. Some ferrites have hexagonal crystal structure, e.g.
barium ferrite BaO:6Fe2O3 or BaFe12O19.
Ferrites are, like most other ceramics, hard and brittle. In terms of their magnetic properties, the different
ferrites are often classified as "soft" or "hard", which refers to their low or high magnetic coercivity.
Soft ferrites
Ferrites that are used in transformer or electromagnetic cores contain nickel, zinc,
and/or manganese compounds. They have a low coercivity and are called soft ferrites. The low coercivity
means the material's magnetization can easily reverse direction without dissipating much energy (hysteresis
losses), while the material's high resistivity prevents eddy currents in the core, another source of energy loss.
Because of their comparatively low losses at high frequencies, they are extensively used in the cores
of RF transformers and inductors in applications such as switched-mode power supplies.
The most common soft ferrites are:

Manganese-zinc ferrite (MnZn, with the formula MnaZn(1-a)Fe2O4). MnZn have
higher permeability and saturation induction than NiZn.

Nickel-zinc ferrite (NiZn, with the formula NiaZn(1-a)Fe2O4). NiZn ferrites exhibit higher resistivity than
MnZn, and are therefore more suitable for frequencies above 1 MHz
Hard ferrites
In contrast, permanent ferrite magnets are made of hard ferrites, which have a high coercivity and
high remanence after magnetization. These are composed of iron and barium orstrontium oxides. The high
coercivity means the materials are very resistant to becoming demagnetized, an essential characteristic for a
permanent magnet. They also conduct magnetic flux well and have a high magnetic permeability. This
enables these so-called ceramic magnets to store stronger magnetic fields than iron itself. They are cheap,
and are widely used in household products such as refrigerator magnets. .
The most common hard ferrites are:

Strontium ferrite, SrFe12O19 (SrO·6Fe2O3), a common material for permanent magnet applications.

Barium ferrite, BaFe12O19 (BaO·6Fe2O3), a common material for permanent magnet applications.
Barium ferrites are robust ceramics that are generally stable to moisture and corrosion-resistant.

They are used in e.g. subwoofer magnets and as a medium for magnetic recording, e.g. on magnetic
stripe cards.
Applications:- Soft ferrites are used in Magnetic recording devices for audio. Video And Computers., Ferrite
core memories in computers., Transformer materials Hard ferrites find applications in devices requiring
permanent magnets.
Super conductors:- The electrical resistances of all metals decreases with temperature and
all metals are expected to have zero electrical resistances at 0o K. However due to impurities
resistance the electrical resistance will be non zero even at 0o K.
Super Conductivity refers to the property of certain materials in which electrical resistance suddenly
falls to zero when the material is cooled to very low temperatures, below a certain well defined
temperature called critical temperature or superconducting transition temperature ( Tc). This was
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observed first in 1911 by K.H Onnes in mercury which lost all of its electrical resistance when cooled below a
temperature of 4.2oK.
Properties of superconducting materials:- The important properties of superconductors are
1.) A well defined critical temperature which is the characteristic property of the material.
2.) Presence of ferromagnetic impurities reduces the critical temperature and may even completely
destroy the superconducting properties.
3.) Most good conductors at normal temperature do not exhibit super conductivity and many
materials with superconducting properties at low temperatures are not good conductors at
ordinary temperatures. 4.) Presence of magnetic field lowers critical temperature and at certain
field called critical field critical temperature will become 0ok. and hence above this critical field HC
the material can exist only in normal state. At T=Tc ,Hc=0. At temperature below Tc, Hc increases.
The dependence of the critical field upon the temperature is given by
Hc(T) = Hc(0)[1- (T/Tc)2 ] where Hc(0) is the critical field at 0 degrees and
Tc is critical temperature for zero fields are constants of the material.
Meissner Effect:- one of the most important properties of superconducting materials is called
Meissner effect.
When a magnetic field less than the critical field is applied to a superconducting specimen at a
temperature less then transition temperature Tc for that field, then the magnetic flux lines are
completely expelled out of the specimen. This effect is reversible, i.e. when temperature is raised
above Tc , as the material undergoes transformation into normal state flux lines suddenly penetrate
the specimen. Thus superconductors behave like perfect diamagnetic materials repelling magnetic
lines of force completely from their bodies.
The magnetic flux density in a material is given by B = µo (H+M) for superconductors B=0 and hence M = H, the magnetic susceptibility of a superconductor material X = -1. This perfect diamagnetic property of
superconductors is an independent property not related with zero electrical resistance.
From Maxwell equations Del X E = -dB/dt
E is the electric field intensity and if j is current density and ρ is resistivity, then E=ρj=0 as ρ=0 for
superconductors. Hence for superconductors - dB/dt = 0 and therefore B should remain constant in
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superconductors instead of becoming zero .Hence Meissner effect is considered to be an independent property
of superconductors.
Based on how Meissner effect occurs in superconductors, they are classified into type1 and Type 2 super
conductors. In type 1 superconductor the complete Meissner effect is shown right up to critical field, where as in
type 2 superconductors complete Meissner effect is exhibited only up to a certain lower field called first critical
field, H and if magnetic field is increased above H
c1
c1, the flux lines begin to penetrate the specimen with
increasing magnitude and finally at a substantially higher field called second critical field Hc2 the
penetration is complete and the material reverts into normal state.
Though only partial Meissner effect is shown by type 2 superconductors between Hc1 and Hc2, the
electrical resistance continues to be zero right up to Hc2.
Magnetic Levitation:Magnetic levitation is the use of magnetic fields to levitate a (usually) metallic object. Manipulating
magnetic fields and controlling their forces can levitate an object. Superconductors are perfect
diamantes and when placed in an external magnetic field expel the field lines from their interiors.
The magnet is held at a fixed distance from the superconductor or vice versa. This is the principle is
behind the magnetic levitation of maglev trains. This system relies on superconducting magnets.
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A maglev is a train, which is suspended in air above the track, and propelled forward using
magnetism. Because of the lack of physical contact between the track and vehicle, the only friction
is that between the carriages and air. So maglev trains can travel at very high speeds (650 km/h)
with reasonable energy consumption and noise level.
The same magnetic levitation principle can be used to design magnetic bearings that can work
without friction as no contact takes place in these bearings.
SQUID:- Super conducting quantum interference devices are one of the most sensitive censers
available for measuring extremely weak magnetic and electric fields. SQUID uses Josephson Effect
for this purpose. If two super conductors are placed with a small gap between them than super
current is found pass from one two other as if there is no gap between them. Same result is
obtained even when a non-super conductor material is present in the gap. The current passing
through the gap is found to be very sensitive to presence of Electric or magnetic fields and this
property is used to measure very weak magnetic & electric fields.
Super conducting Storage rings:- If an electric current is set up in a superconductor in the
form of a ring and if the external power source used to setup this current is switched off than the
super currents are found to travel round and round the superconductor ring almost indefinitely.
This property called Persisting Currents has the potential of using superconductors as current
storage systems
Other applications of Superconductors:1.
For transmission lines to reduce power losses
2.
For generation of very high magnetic fields required for MRI scanning used as medical
diagnostic tool.
3.
Fast electrical switches, logic and storage functions.
4.
Confining High temperature and pressure plasma,
5.
For magnetic field screening and enhancing
6.
Squids: These are superconducting quantum interference devices that can act as
extremely sensitive probes to measure and detect weak magnetic and electric fields. They work
on the principle of Josephson Effect. Even if a small gap is present between two super
conductors, the super currents are found to pass through the gap as if the super conductor is
continues. The current passing through the gap is changes in presence of even very weak
magnetic field and in squids this property is utilized to detect weak magnetic fields.
7.
Transmission lines over short distances at present for carrying very heavy currents.
8.
Supercomputers for minimizing power loses due to Ohmic losses.
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Questions & Answers
Q.1. What is Bohr Magnetron and obtain an expression for it.
Ans: Bohr Magnetron is unit used to express the magnetic moment associated with a single unpaired
electron. The orbital motion of the electron round the nucleus can considered to be equal to passage of
electrical charge i.e. electrical current in closed circular loop. The current I due to a revolving electron
I = charge of the electron x No. revolutions per second = e.ν= -e.ω/2π
Where ν is electron revolving frequency around nucleus and w= 2πν is
angular frequency of the electron.
The current passing through a circular loop produces a magnetic field in
a direction perpendicular to the area of the coil and this magnetic field
is identical to that of a magnetic dipole. The magnetic moment due to
current I in circular coil of area A is given by
µ𝒎 =I.A = - (e.ω/2π) 𝜋𝑟 2 = - (e.ω𝑟 2 )/2 = -
𝑒
mω𝑟 2
2𝑚
𝑒
µ𝒎 = − 2𝑚 L - - -- > 1
Where L= mω𝑟 2 is the orbital angular momentum of the electron.
The possible orientation values of angular momentum vector in an external field are
L = 𝑚𝑙 . h/2π
-- - - - 2 where 𝑚𝑙 is angular momentum quantum number, and can have 2L+1
values from -L to +L including zero. i.e. 2L+1 integer values.
From equations 1 and 2
µ𝒎 = −
𝑒
𝑚 . h/2π
2𝑚 𝑙
= -
𝑒ℎ
𝑚
4𝜋𝑚 𝑙
= - µ𝐵 𝑚𝑙
𝑒ℎ
µ𝐵 = 4𝜋𝑚 = 9.2710−24 A−𝑚2
µ𝐵 is called Bohr Magnetron.
For atoms having many electrons the total magnetic moment due to all electrons is the algebraic sum of
individual magnetic moments of all the electrons and magnetic moment due to two paired electrons is zero.
Q.2. Explain the classification of Magnetic materials.
Ans: Classification of materials:- Materials on the basis of how they interact with an external magnetic field
are classified in to diamagnetic, paramagnetic and ferromagnetic materials, anti-ferromagnetic and
Ferrimagnetic materials.
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S.n
o
1.
2.
3.
4.
5
6.
7.
8.
Type of
Material
___________
Property
Reaction to
Applied
external
Magnetic
Field
Diamagn
etic
Material
Paramagnet
ic material
Ferromagnetic
Material
Antiferro
Magnetic
Material
Ferri Magnetic
Material
Weakly
repel
Magnetic
Field
Lines.
Weakly
attract
Magnetic
Field Lines
Strongly
attract
Magnetic Field
Lines.
Weakly
Repel
Magnetic
Field Lines
Strongly attract
Magnetic
Field Lines.
Mag. Flux
density B
near the
material
Decrease
s Slightly
Increases
Slightly
Greatly
Increases
Decreases
Slightly
Greatly
Magnetization
M & Magnetic
Susceptability
Small
and
Negative
Small and
Positive
Large and
Positive
Small and
Negative
Large and
Positive
No
unpaired
electrons
Random
spin
alignment
Parallel
Alignment
Equal
antiparallel
Unequal
antiparallel
Orbital
magnetic
moment
Not
much
effect
Spin
magnetic
moment
Paramagnet
ic Curi
Temperatur
e
Spin magnetic
moment
Orbital
magnetic
moment
Above Neel
temperatur
e spin
alignment is
destroyed
Spin magnetic
moment
χ
Unpaired
electrons Spin
alignment
Contribution
to Magnetic
moment
Effect of
temperature
Relative
dielectric
constant
Examples of
Materials
Increases
<1
O2, N2,
C, H2O
etc
>1
Al, Na, Mg
Above
ferromagnetic
Curi
temperature
spin alignment
is destroyed
Very large
Fe, Ni, Co
<1
Fe3O4.
Mixed
metal
oxides with
iron/
Manganese
etc
Above
ferrimagnetic Curi
temperature spin
alignment is
destroyed
Very large
Fe2O3, mixed
metal oxides
with general
formula
Fe2+++Me++O4- where Me is a
Transition
metal ion
16
9.
Applications
Magnetic
Levitatio
n, MRI
(diamagn
etism of
water &
H2)
Paramagnet
ic dyes used
to improve
MRI
images,
censers
Permanent
magnets,
Transformer
core materials,
electromagnet
ics
Giant
magneto
striction,
censers
Permanent
magnets,
Transformer core
materials,
electromagnetics
Q.3. Explain Weiss theory of Domain Structure and Hysteresis Curve
Ans: Weiss theory of Domain Structure of ferromagnetic materials.
Ferromagnetic Materials very strongly attract magnetic lines of force and hence magnetic flux density
increases to large values near these materials. The atoms and molecules of these materials have unpaired
electrons and hence have permanent magnetic moments due to electron spin. The permanent magnetic
moments present on individual atoms/ molecules in ferromagnetic materials due to exchange interaction
couplings are aligned permanently in one direction even in the absence of an external field. Hence these
materials exhibit spontaneous magnetization Iron, nickel, cobalt, Gadolinium etc are examples for
ferromagnetic materials.
In spite of the fact that magnetic moments due to spins of unpaired electrons are aligned parallel in one
direction, a ferromagnetic material if not previously exposed to an external magnetic field will not exhibit
spontaneous magnetization. This was explained by Weiss theory of Domain structure. According to this
theory A ferromagnetic material is made up of large number of small regions called ‘Domains’ and all the
electrons in a domain are aligned permanently parallel to one another. Each domain has spontaneous
magnetization due to parallel alignment of all magnetic dipoles present in that domain. However the
material as a whole cannot exhibit spontaneous magnetization as domains have random orientations.
(a)Domain arrangement in virgin ferromagnetic specimen when no magnetic field, (b) Growth of favorable domains
in presence of external field, (c ) Rotation of unfavorable domains into applied field direction.
When an external field is applied the ferromagnetic materials acquire magnetic properties due to 1. Domain
growth and, 2. Rotation of domains.
Domain Growth:- The volume of the domains in which orientation of spin alignment if in the direction of
applied magnetic field, called favorably oriented domains increase in size at the expense of unfavorably
oriented domains.
Rotation of Unfavorable domains:- When the domains reach a certain optimum size further growth is not
energetically possible and the second mechanism involving the rotation of unfavorably oriented domains in
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to the direction of applied field begins. Saturation magnetization occurs when all the domains are
completely in the direction of the applied field.
Hysteresis Curve:- A graph between applied magnetic field strength H and resulting magnetic flux density B,
in a ferromagnetic material is called ‘hysteresis curve or hysteresis loop. This plot also indicates lag of
magnetization behind the applied magnetic field in Ferromagnetic materials.
Hysteresis curve or Hysteresis loop
The hysteresis behavior ferromagnetic materials can be explained by Weiss theory of domain structure. In
the initial stages the magnetization is fast as it is due to domain growth due to reversible and irreversible
domain growth which are fast process with less energy requirement. Once the domains reach their optimum
size further increase in magnetization can be only due to domain rotation which is a slow process with large
energy requirement and hence magnetization increases slowly.
Saturation magnetization occurs when all the domains completely get rotated in to the direction of applied
field.
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When magnetic field is decreased B also decreases however the specimen retains certain magnetization
even at zero field due to irreversible domains. This left over magnetization at zero fields is called
‘Receptivity’.
The negative field required to reduce residual magnetization is called ‘Coercive field’
Hysteresis loss is the energy lost in one complete cycle of magnetizing and demagnetizing a ferromagnetic
specimen and is given by the area covered under the hysteresis loop.
Q.4. Describe Soft and Hard Magnetic Material and Ferrites.
Ans: Soft and Hard Magnetic Materials:- Ferromagnetic materials on the basis of the hysteresis loss i.e.
depending on the amount of energy lost in one complete cycle of magnetization demagnetization are
classified in to Soft and Hard Magnetic materials.
Soft magnetic materials:- In these materials hysteresis are very low and are used in applications requiring
frequent reversals of magnetic fields.
Hard Magnetic Materials:- In these materials Hysteresis lasses are large and are used as permanent
magnets.
S.No.
Hard Magnetic Materials
Soft Magnetic Materials
1
Materials which retain their magnetism
and are difficult to demagnetize are called
hard magnetic materials.
Soft magnetic materials are easy to magnetize
and demagnetize.
These materials retain their magnetism
even after the removal of the applied
magnetic field. Hence are used for making
permanent magnets. In permanent
magnets the movement of the domain
wall is prevented. They are prepared by
heating the magnetic materials to the
required
temperature
and
then
quenching them. Impurities increase the
strength of hard magnetic materials.
These materials are used for making temporary
magnets. The domain wall movement is easy.
Hence they are easy to magnetize. By annealing
the cold worked material, the dislocation density
is reduced and the domain wall movement is
made easier. Soft magnetic materials should not
possess any void and its structure should be
homogeneous so that the materials are not
affected by impurities.
2
They have large hysteresis loss due to
large hysteresis loop area.
They have low hysteresis loss due to small
hysteresis area.
3
Susceptibility and permeability are low.
Susceptibility and permeability are high.
4
Coercivity and retentivity values are
large.
Coercivity and retentivity values are less.
19
5
Magnetic energy stored is high.
Since they have low retentivity and coercivity,
they are not used for making permanent
magnets.
6
They possess high value of BH product.
Magnetic energy stored is less.
7
The eddy current loss is high.
The eddy current loss is less because of high
resistivity.
Examples of Hard magnetic materials and applications: - Iron-Silicon alloys, Ferrous-Nickel alloys, Ferrites,
Garnets
Hard magnetic materials are used as permanent magnets and find extensive application where permanent
magnetic are used, such as, microphones, flux meters, voltage regulators magnetic separators.
Examples of soft magnetic materials: Soft iron, iron- aluminum alloys, cupper iron nickel alloys.
Soft magnetic materials are used in applications requiring frequent reversals of magnetic fields, such as
electromagnetic, Transformer core materials, communication equipment, isolators, switching circuits etc.
Ferrites: In ferrimagnetic materials as in anti ferromagnetic materials permanent anti parallel coupling
takes place between the spins of unpaired electrons present on the molecules. However these anti
parallel couplings are unequal as no. of electrons one direction are different from the number of electrons
in opposite direction and hence each anti parallel coupling will result in net spin magnetic moment in one
particular direction. Therefore these materials like ferromagnetic materials exhibit spontaneous
magnetization and have large positive values of magnetic susceptibility. These materials also fallow CuriWeiss law below a certain temperature called Ferrimagnetic Curi temperature only exhibit spontaneous
magnetization above behave like paramagnetic materials.
Ferrites and have the general chemical formula
Me2+ 𝐹𝑒2+3 𝑂42−
where Me2+ is a metal ion. (Example Fe, Co, Me is doubly ionized ions.)
Ferrites of spinel structure have the general formula MeFe2O4, where Me can represent Ni2+, Co2+, Fe2+, Mn2+, Mg2+,
Li1+, and Cu2+ etc. The unit cell of these ferrites is a cube formed by eight molecules of MeOFe 2O3 and consisting of 32
O2– anions, among which there are 64 tetrahedral (A) sites and 32 octahedral (B) sites partially occupied by Fe3+ and
Me2 . All ferric ions have complete anti-parallel coupling and Me++ ions are coupled in parallel manner so that
there are 5 electrons in one direction and only 3 in the opposite direction. These results in a net magnetic
moment and the ferrite materials like ferromagnetic material have large spontaneous magnetization.
Ferrites are usually non-conductive Ferrimagnetic ceramic compounds derived from iron oxides such
as hematite (Fe2O3) or magnetite (Fe3O4) as well as oxides of other metals.
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Ferrites are, like most other ceramics, hard and brittle. In terms of their magnetic properties, the different ferrites are
often classified as "soft" or "hard", which refers to their low or high magnetic coercivity.
Soft ferrites
Ferrites that are used in transformer or electromagnetic cores contain nickel, zinc, and/or manganese compounds.
They have a low coercivity and are called soft ferrites. The low coercivity means the material's magnetization can easily
reverse direction without dissipating much energy (hysteresis losses), while the material's high resistivity prevents eddy
currents in the core, another source of energy loss. Because of their comparatively low losses at high frequencies, they
are extensively used in the cores of RF transformers and inductors in applications such as switched-mode power
supplies.
The most common soft ferrites are:

Manganese-zinc ferrite and .Nickel-zinc ferrite. NiZn ferrites exhibit higher resistivity than MnZn,
and are therefore more suitable for frequencies above 1 MHz
Hard ferrites
In contrast, permanent ferrite magnets are made of hard ferrites, which have a high coercivity and
high residual magnetization. These are composed of iron and barium or strontium oxides. The high
coercivity means the materials are very resistant to becoming demagnetized, an essential characteristic for a
permanent magnet. They also conduct magnetic flux well and have a high magnetic permeability. This
enables these so-called ceramic magnets to store stronger magnetic fields than iron itself. They are cheap,
and are widely used in household products such as refrigerator magnets. .
The most common hard ferrites are: Strontium ferrite, a common material for permanent magnet applications
and Barium ferrite, a common material for permanent magnet applications. Barium ferrites are robust
ceramics that are generally stable to moisture and corrosion-resistant.

Ferrites are also used in subwoofer/ loud speaker magnets and as a medium for magnetic
recording. Soft ferrites are used in Magnetic recording devices for audio. Video And Computers., Ferrite
core memories in computers., Transformer materials Hard ferrites find applications in devices requiring
permanent magnets.
Q.5. What is superconductivity and describe some important properties of super conductors. Describe
how Meissner Effect classifies superconductors into Type - I and Type – II
Ans: Super conductors:- Super Conductivity refers to the property of certain materials in which electrical
resistance suddenly falls to zero when the material is cooled to very low temperatures, below a certain
well defined temperature called critical temperature or superconducting transition temperature ( T c). This
was observed first in 1911 by K.H. Onnes in mercury which lost all of its electrical resistance when cooled
below a temperature of 4.2oK.
Properties of superconducting materials:- The important properties of superconductors are
1.) A well-defined critical temperature which is the characteristic property of the material.
2.) Presence of ferromagnetic impurities reduces the critical temperature and may even completely destroy
the superconducting properties.
3.) Most good conductors at normal temperature do not exhibit super conductivity and many materials with
superconducting properties at low temperatures are not good conductors at ordinary temperatures.
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4.) Superconductors above certain current called critical or saturation current Tc undergo transformation to
normal state.
5.) Presence of magnetic field lowers critical temperature and at certain field called critical field critical
temperature will become 0ok. and hence above this critical field HC the material can exist only in normal
state. At T=Tc ,Hc=0. At temperature below Tc, Hc increases. The dependence of the critical field upon the
temperature is given by
Hc(T) = Hc(0)[1- (T/Tc)2 ] where Hc(0) is the critical field at 0 degrees and
Tc is critical temperature for zero fields are constants of the material.
Meissner Effect:- one of the most important properties of
superconducting materials is called Meissner effect. When a
magnetic field less than the critical field is applied to a
superconducting specimen at a temperature less then transition
temperature Tc for that field, then the magnetic flux lines are
completely expelled out of the specimen. This effect is reversible,
i.e. when temperature is raised above Tc , as the material
undergoes transformation into normal state flux lines suddenly
penetrate the specimen. Thus superconductors behave like
perfect diamagnetic materials repelling magnetic lines of force
completely from their bodies.
The magnetic flux density in a material is given by B = µo (H+M) for superconductors B=0 and hence M = - H,
the magnetic susceptibility of a superconductor material X = -1. This perfect diamagnetic property of
superconductors is an independent property not related with zero electrical resistance.
From Maxwell equations Del X E = -dB/dt
E is the electric field intensity and if j is current density and ρ is resistivity, then E=ρj=0 as ρ=0 for
superconductors. Hence for superconductors - dB/dt = 0 and therefore B should remain constant in
superconductors instead of becoming zero .Hence Meissner effect is considered to be an independent
property of superconductors.
Based on how Meissner effect occurs in
superconductors, they are classified into type1 and Type
2 super conductors. In type 1 superconductor the
complete Meissner effect is shown right up to critical
field, where as in type 2 superconductors complete
Meissner effect is exhibited only up to a certain lower
field called first critical field, Hc1 and if magnetic field is
increased HC1, the flux lines begin to penetrate the
specimen with increasing magnitude and finally at a
substantially higher field called second critical field HC2
the penetration is complete and the material reverts into
normal state.
22
Though only partial Meissner effect is shown by type 2 superconductors between HC1 and HC2, the electrical
resistance continues to be zero right up to HC2.
Applications :
Magnetic Levitation:- Magnetic levitation is the use of magnetic fields to levitate a (usually) metallic object.
Manipulating magnetic fields and controlling their forces can levitate an object. Superconductors are perfect
diamantes and when placed in an external magnetic field expel the field lines from their interiors. The
magnet is held at a fixed distance from the superconductor or vice versa. This is the principle is behind the
magnetic levitation of maglev trains. This system relies on superconducting magnets. A maglev is a train,
which is suspended in air above the track, and propelled forward using magnetism. Because of the lack of
physical contact between the track and vehicle, the only friction is that between the carriages and air. So
maglev trains can travel at very high speeds (650 km/h) with reasonable energy consumption and noise
level.
The same magnetic levitation principle can be used to design magnetic bearings that can work without
friction as no contact takes place in these bearings.
SQUID:- Super conducting quantum interference devices are one of the most sensitive censers available for
measuring extremely weak magnetic and electric fields. SQUID uses Josephson Effect for this purpose. If
two super conductors are placed with a small gap between them than super current is found pass from one
two other as if there is no gap between them. Same result is obtained even when a non-super conductor
material is present in the gap. The current passing through the gap is found to be very sensitive to presence
of Electric or magnetic fields and this property is used to measure very weak magnetic & electric fields.
Super conducting Storage rings:- If an electric current is set up in a superconductor in the form of a ring and
if the external power source used to setup this current is switched off than the super currents are found to
travel round and round the superconductor ring almost indefinitely. This property called Persisting Currents
has the potential of using superconductors as current storage systems
Other applications of Superconductors:1. For transmission lines to reduce power losses
2. For production of very high magnetic fields needed for MRI scanning and Industry.
3. Fast electrical switches, logic and storage functions.
4. Confining High temperature and pressure plasma.
5. For magnetic field screening and enhancing.
6. Transmission lines over short distances at present for carrying very heavy currents.
7. Supercomputers for minimizing power losses due to resistance.