MAGNETIC PROPERTIES

MAGNETIC PROPERTIES

Introduction : The basic aim in the study of the subject of magnetic materials is to understand the effect of an external magnetic field  on a bulk material ,and also to account for its specific behavior. A dipole is an object that a magnetic pole is on one end and a equal and opposite second magnetic dipole is on the other end.

                               A bar magnet can be considered as a dipole with a north pole at one end and South Pole at the other. If a magnet is cut into two, two magnets or dipoles are created out of one. This sectioning and creation of dipoles can continue to the atomic level. Therefore, the source of magnetism lies in the basic building block of all the matter i.e. the atom.

                              Consider electric current flowing through a conductor. When the electrons are flowing through the conductor, a magnetic field is forms around the conductor. A magnetic field is produced whenever an electric charge is in motion. The strength of the field is called the magnetic moment.  

                             Magnetic materials are those which can be easily magnetized as they have permanent magnetic moment in the presence of applied magnetic field. Magnetism arises from the magnetic dipole moments. It is responsible for producing magnetic influence of attraction or repulsion.

Magnetic dipole : it is a system consisting of two equal and opposite magnetic poles separated by a small distance of ‘2l’metre.

Magnetic Moment ( μ_m )  :It is defined as the product of the pole strength (m) and the distance between the two poles (2l) of the magnet.

                                   i . e . .   μ_m   =  (2l ) m

Units: Ampere – metre²

Magnetic Flux Density or Magnetic Induction (B): It is defined as the number of magnetic lines of force passing perpendicularly through unit area.                            

                                      i . e . .   B  = magnetic flux / area  = Φ / A

Units: Weber  /  metre²  or Tesla.

Permeability:

Magnetic Field Intensity (H): The magnetic field intensity at any point in the magnetic field is the force experienced by a unit north pole placed at that point.

Units: Ampere / meter

The magnetic induction B due to magnetic field intensity H applied in vacuum is related by

                                 B = μ₀ H      where   μ₀  is permeability of free space = 4 Π x  10^-7 H / m

If the field is applied in a medium, the magnetic induction in the solid is given by                                

                                  B = μ H      where   μ  is permeability of  the material  in the medium

                                μ = B / H

Hence magnetic Permeability μ of any material is the ratio of the magnetic induction to the applied magnetic field intensity. The ratio of   μ /  μ₀  is called the relative permeability (μ_r ).                        

                                μ_r = μ /  μ₀ 

 Therefore            B =  μ₀ μ_r H

Magnetization: It is the process of converting a non – magnetic material into a magnetic material. The intensity of magnetization (M) of a material is the magnetic moment per unit volume. The intensity of magnetization is directly related to the applied field H through the susceptibility of the medium (χ) by

                                   χ = M / H   ------------(1)

The magnetic susceptibility of a material is the ratio of the intensity of magnetization produced to the magnetic field intensity which produces the magnetization. It has no units.

We know

                                B = μ H  

                                   =  μ₀ μ_r H

                   i.e      B = μ₀ μ_r H + μ₀ H - μ₀ H

                                 = μ₀ H + μ₀ H (  μ_r – 1 )

                                = μ₀ H + μ₀ M           where M is magnetization = H (  μ_r – 1 )

                              i.e      B =   μ₀   ( H + M ) ----------(2)

The first term on the right side of eqn (2) is due to external field. The second term is due to the magnetization.

                      Hence    μ₀   = B / H + M

Relative Permeability ,

                                     μ_r = μ /  μ_{0  =} ( B / H )  / ( B / H + M ) = H + M / H  = 1 + M / H

                                                               μ_r =  1 + χ ---------(3)

The magnetic properties of all substances are associated with the orbital and spin motions of the electrons in their atoms. Due to this motion, the electrons become elementary magnets of the substance. In few materials these elementary magnets are able to strengthen the applied magnetic field , while in few others , they orient themselves such that the applied magnetic field is weakened.

Origin of Magnetic Moment : In atoms , the permanent magnetic moments can arise due to the following :

1.      the orbital magnetic moment of the electrons

2.      the spin magnetic moment of the electrons

3.      the spin magnetic moment of the nucleus.

Orbital magnetic moment of the electrons: In an atom, electrons revolve round the nucleus in different circular orbits.

Let m be the mass of the electron and r be the radius of the orbit in which it moves with angular velocity ω.

The electric current due to the moving electron  I = - ( number of electrons flowing per second x charge of an electron )

Therefore I = - e ω / 2 Π   --------------(1)

The current flowing through a circular coil produces a magnetic field in a direction perpendicular to the area of coil and it is identical to the magnetic dipole. the magnitude of the magnetic moment produced by such a dipole is                   

                                     μ_m = I .A

                                          = (  - e ω / 2 Π   ) ( Π r² )

                                      =  - e ω r² / 2 = ( - e / 2 m ) ( m ω  r² ) = - ( e / 2 m ) L -----------(2)

             where    L = m ω  r² is the orbital angular momentum of electron. The minus sign indicates that the magnetic moment is anti – parallel to the angular momentum L. A substance therefore possesses permanent magnetic dipoles if the electrons of its constituent atom have a net non-vanishing angular momentum. The ratio of the magnetic dipole moment of the electron due to its orbital motion and the angular momentum of the orbital motion is called orbital gyro magnetic ratio , represented by γ.

            Therefore   γ = magnetic moment / angular momentum = e / 2m

The angular momentum of an electron is determined by the orbital quantum number ‘l’ given by l = 0 , 1 , 2 , ……( n – 1 ) where n is principal quantum number  n = 1 , 2 , 3 , 4 , …… ……corresponding to K , L , M , N……shells .

The angular momentum of the electrons associated with a particular value of l is given by l( h / 2 Π )

The strength of the permanent magnetic dipole is given by

                                μ _el  = - ( e / 2 m ) ( l h / 2 Π  )

                   i.e      μ _el  = - ( e h l / 4 Π m )  = - μ_B l  ---------------(3)

The quantity   μ_B  =  e h / 4 Π m  is an atomic unit called Bohr Magneton and has a value 9.27 x 10 ^-24  ampere metre²

 In an atom having many electrons, the total orbital magnetic moment is determined by taking the algebraic sum of the magnetic moments of individual electrons. The moment of a completely filled shell is zero. An atom with partially filled shells will have non zero orbital magnetic moment.

Magnetic Moment Due to Electron Spin : The magnetic moment associated with spinning of the electron is called spin magnetic moment μ _es  .Magnetic moment due to the rotation of the electronic charge about one of the diameters of the electron is similar to the earth’s spinning motion around it’s north – south axis.

An electronic charge being spread over a spherical volume ,the electron spin would cause different charge elements of this sphere to form closed currents, resulting in a net spin magnetic moment. This net magnetic moment would depend upon the structure of the electron and its charge distribution.

    μ _es  =  γ ( e / 2 m ) S   -------------------(1)where   S= h / 4 Π is spin angular momentum

            therefore      μ _es  ≈  9.4 x 10 ^-24  ampere metre²          

Thus, the magnetic moments due to the spin and the orbital motions of an electron are of the same order of magnitude. The spin and electron spin magnetic moment are intrinsic properties of an electron and exist even for a stationary electron. Since the magnitude of spin magnetic moment is always same, the external field can only influence its direction. If the electron spin moments are free to orient themselves in the direction of the applied field B. In a varying field ,it experiences a force in the direction of the increasing magnetic field due to spin magnetic moments of its various electrons.

Magnetic Moment due to Nuclear Spin : Another contribution may arise from the nuclear magnetic moment. By analogy with Bohr Magneton, the nuclear magneton arises due to spin of the nucleus. It is given by                                  μ _ps  =  e h / 4 Π M_p

                                 μ _ps  =  5.05 x  10 ^-27  ampere metre²     where  M_p is mass of proton.

The nuclear magnetic moments are smaller than those associated with electrons.

Classification Of Magnetic Materials :All matter respond in one way or the other when subjected to the influence of a magnetic field. The response could be strong or weak, but there is none with zero response ie, there is no matter which is non magnetic in the absolute sense. Depending upon the magnitude and sign of response to the applied field , and also on the basis of effect of temperature on the magnetic properties, all materials are classified broadly under 3 categories.

1. Diamagnetic materials   2. Paramagnetic materials,  3. Ferromagnetic materials

                         two more classes of materials have structure very close to ferromagnetic  materials but possess quite different magnetic effects. They are     i. Anti ferromagnetic materials    and  ii . Ferri magnetic materials

1.      Diamagnetic materials: Diamagnetic materials are those which experience a repelling force when brought near the pole of a strong magnet. In a non uniform magnetic field they are repelled away from stronger parts of the field.

                            In the absence of an external magnetic field , the net magnetic dipole moment over each atom or molecule of a diamagnetic material is zero.

Ex: Cu, Bi , Pb .Zn and rare gases.

Paramagnetic materials:  Paramagnetic materials are those which experience a feeble attractive force when brought near the pole of a magnet. They are attracted towards the stronger parts of magnetic field. Due to the spin and orbital motion of the electrons, the atoms of paramagnetic material posses a net intrinsic permanent moment.

Susceptibility χ is positive and small for these materials. The susceptibility is inversely proportional to the temperature T.

                    χ α  1/T

                   χ = C/T            where C is Curie’s temperature.

Below superconducting transition temperatures, these materials exhibit the Para magnetism.

Examples: Al, Mn, Pt, CuCl₂.

Ferromagnetic Materials:  Ferromagnetic materials are those which experience a very strong attractive force when brought near the pole of a magnet. These materials, apart from getting magnetized parallel to the direction of the applied field, will continue to retain the magnetic property even after the magnetizing field removed. The atoms of ferromagnetic materials also have a net intrinsic magnetic dipole moment which is due to the spin of the electrons.

Susceptibility is always positive and large and it depends upon temperature.

                    χ = C / (T- θ) ( only in paramagnetic region  i.e., T > θ)

                                                θ is Curie’s temperature.

When the temperature of the material is greater than its Curie temperature then it converts into paramagnetic material.

Examples: Fe, Ni, Co, MnO.

Antiferromagnetic matériels :   These  are the ferromagnetic materials in which equal no of opposite spins with same magnitude such that the orientation of neighbouring spins is in antiparallel manner are present.

Susceptibility is small and positive and it is inversely proportional to the temperature.

                 χ=C /(T+θ)

the temperature at which anti ferromagnetic material converts into paramagnetic material is known as Neel’s temperature.

Examples: FeO, Cr₂O₃.

Ferrimagnetic materials: These are the ferromagnetic materials in which equal no of opposite spins with different magnitudes such that the orientation of neighbouring  spins is in antiparallel manner are present.

Susceptibility positive and large, it is inversely proportional to temperature

                              χ=C /(T ± θ)           T> T_N ( Neel’s temperature)

Examples : ZnFe₂O₄, CuFe₂O₄

Domain theory of ferromagnetism:   According to Weiss, a virgin specimen of ferromagnetic material consists of a no of regions or domains (≈ 10-6 m or larger) which are spontaneously magnetized. In each domain spontaneous magnetization is due to parallel alignment of all magnetic dipoles. The direction of spontaneous magnetization varies from domain to domain. The resultant magnetization may hence be zero or nearly zero. When an external field is applied there are two possible ways of alignment fo a random domain.

i). By motion of domain walls: The volume of the domains that are favourably oriented with respect to the magnetizing field increases at the cost of those that are unfavourably oriented

ii) By rotation of domains:  When the applied magnetic field is strong, rotation of the direction of magnetization occurs in the direction of the field.

Hysteresis curve (study of B-H curve): The hysteresis of ferromagnetic materials refers to the lag of magnetization behind the magnetization field. when the temperature of the ferromagnetic substance is less than the ferromagnetic Curie temperature ,the substance exhibits hysteresis. The domain concept is well suited to explain the phenomenon of hysteresis. The increase in the value of the resultant magnetic moment of the specimen by the application of the applied field , it attributes to the  1. motion of the domain walls and    2. rotation of domains.

                                   When a weak magnetic field is applied, the domains that are aligned parallel to the field and in the easy direction of magnetization , grow in size at the expense of less favorably oriented ones. This results in Bloch wall movement and when the weak field is removed, the domains reverse back to their original state. This reverse wall displacement is indicated by OA of the magnetization curve. When the field becomes stronger ,the Bloch wall movement continues and it is mostly irreversible movement. This is indicated by the path AB of the graph. The phenomenon of hysteresis is due to this irreversibility.

                                      

 At the point B all domains have got magnetized along their easy directions. Application of still higher fields rotates the domains into the field direction which may be away from the easy direction. Once the domain rotation is complete the specimen is saturated denoted by C. on removal of the field the specimen tends to attain the original configuration by the movement of Bloch walls. But this movement is hampered by the impurities, lattice imperfections etc, and so more energy must be supplied to overcome the opposing forces. This means that a coercive field is required to reduce the magnetization of the specimen to zero. The amount of energy spent in this regard is a loss. Hysteresis loss is the loss of energy in taking a ferromagnetic body through a complete cycle of magnetization and this loss is represented by the area enclosed by the hysteresis loop.   

                                         A hysteresis curve shows the relationship between the magnetic flux density B and applied magnetic field H. It is also referred to as the B-H curve(loop).

Hard and Soft Magnetic Materials:

   Hysteresis loop of the ferromagnetic materials vary in size and shape. This variation in hysteresis loops leads to a broad classification of all the magnetic materials into hard type and soft type.

Hard Magnetic Materials:

                                Hard magnetic materials are those which are characterized by large hysteresis loop because of which they retain a considerable amount of their magnetic energy after the external magnetic field is switched off. These materials are subjected to a magnetic field of increasing intensity, the domain walls movements are impeded due to certain factors. The cause for such a nature is attributed to the presence of impurities or non-magnetic materials, or the lattice imperfections. Such defects attract the domain walls thereby reducing the wall energy. It results in a stable state for the domain walls and gives mechanical hardness to the material which increases the electrical resistivity. The increase in electrical resisitivity brings down the eddy current loss if used in a.c conditions. The hard magnetic materials can neither be easily magnetized nor easily demagnetized.

Properties:

1.      High remanent magnetization

2.      High coercivity

3.      High saturation flux density

4.      Low initial permeability

5.      High hysteresis energy loss

6.      High permeability

7.      The eddy current loss is low for ceramic type and large for metallic type.

Examples of hard magnetic materials are, i) Iron- nickel- aluminum alloys with certain amount of cobalt called Alnico alloy. ii) Copper nickel iron alloys. iii) Platinum cobalt alloy.

Applications of hard magnetic materials: For production of permanent magnets, used in magnetic detectors, microphones, flux meters, voltage regulators, damping devices and magnetic separators.

Soft Magnetic Materials:

    Soft magnetic materials are those for which the hysteresis loops enclose very small area. They are the magnetic materials which cannot be permanently magnetized. In these materials ,the domain walls motion occurs easily. Consequently, the coercive force assumes a small value and makes the hysteresis loop a narrow one because of which, the hysteresis loss becomes very small. For the sane reasons, the materials can be easily magnetized and demagnetized.

Properties:

1.      Low remanent magnetization

2.      Low coercivity

3.      Low hysteresis energy loss

4.      Low eddy current loss

5.      High permeability

6.      High susceptibility

Examples of soft magnetic materials are

i)                   Permalloys ( alloys of Fe and Ni)

ii)                Si – Fe alloy

iii)              Amorphous ferrous alloys ( alloys of Fe, Si, and B)

iv)              Pure Iron (BCC structure)

Applications of soft magnetic materials: Mainly used in electro- magnetic machinery and transformer cores. They are also used in switching circuits, microwave isolators and matrix storage of computers.

Meissner effect: When a weak magnetic field applied to super conducting specimen at a temperature below transition temperature Tc , the magnetic flux lines are expelled. This specimen acts as on ideal diamagnet. This effect is called meissner effect. This effect is reversible, i.e. when the temperature is raised from below Tc , at T = Tc  the flux lines suddenly start penetrating and the specimen returns back to the normal state. Under this condition, the magnetic induction inside the specimen is given by

                                  B = m₀(H + M)      -------------------------------------(2)

Where H is the external applied magnetic field and M is the magnetization produced inside the specimen.

When the specimen is super conducting, according to meissner effect inside the bulk semiconductor  B= 0.

Hence                        m₀(H + M) = 0

                    Or               M = - H   ---------------------------------------------(3)

Thus the material is perfectly diamagnetic.

Magnetic susceptibility can be expressed as

 χ=M/H = -1-----------------------------------------------------(4)

Consider a superconducting material under normal state. Let J be the current passing through the material of resistivity ρ. From ohm’s law we know that the electric field

                                      E = Jρ

On cooling the material to its transition temperature, ρ tends to zero. If J is held finite.

E must be zero. Form Maxwell’s eqn, we know

▼X E = - dB/ dt              ----------------------------(5)

Under superconducting condition since E = 0, dB/dt = 0, or B= constant.

This means that the magnetic flux passing through the specimen should not change on cooling to the transition temperature. The Meissner effect contradicts this result.

According to Meissner effect perfect diamagnetism is an essential property of defining the superconducting state. Thus

From zero resistivity E = 0,

From Meissner effect B= 0.

TYPE I & TYPE II SUPER CONDUCTORS:

Depending upon their behavior in an external magnetic field, superconductors are divided into two types:

a) Type I superconductors and b) Type II superconductors

Let us discuss them one by one:

1) Type I superconductors:

a). Type I superconductors are those superconductors which loose their superconductivity very easily or abruptly when placed in the external magnetic field. As you can see from the graph of intensity of magnetization (M) versus applied magnetic field (H), when the Type I superconductor is placed in the magnetic field, it suddenly or easily looses its superconductivity at critical magnetic field (Hc) (point A).

After Hc, the Type I superconductor will become conductor.

b). Type I superconductors are also known as soft superconductors because of this reason that is they loose their superconductivity easily.

c) Type I superconductors perfectly obey Meissner effect.

d) Example of Type I superconductors: Aluminum (Hc = 0.0105 Tesla), Zinc (Hc = 0.0054)

2) Type II superconductors:

a). Type II superconductors are those superconductors which loose their superconductivity gradually but not easily or abruptly when placed in the external magnetic field. As you can see from the graph of intensity of magnetization (M) versus applied magnetic field (H), when the Type II superconductor is placed in the magnetic field, it gradually looses its superconductivity. Type II superconductors start to loose their superconductivity at lower critical magnetic field (Hc1) and completely loose their superconductivity at upper critical magnetic field (Hc2).

b) The state between the lower critical magnetic field (Hc1) and upper critical magnetic field (Hc2) is known as vortex state or intermediate state.

After Hc2, the Type II superconductor will become conductor.

c). Type I superconductors are also known as hard superconductors because of this reason that is they loose their superconductivity gradually but not easily.

c) Type I superconductors obey Meissner effect but not completely.

d) Example of Type I superconductors: NbN (Hc = 8 x 106 Tesla), Babi3 (Hc = 59 x 103 Tesla)

e) Application of Type II superconductors: Type II superconductors are used for strong field superconducting magnets.

MAGNETIC LEVITATION: Magnetic levitation, maglev, or magnetic suspension is a method by which an object is suspended with no support other than magnetic fields. Magnetic pressure is used to counteract the effects of the gravitational and any other accelerations.

Essentially it is the use of magnetic fields (or magnetic forces) to levitate a (usually) metallic object.

By manipulating magnetic fields and controlling their forces an object can be levitated. The word 'levitation' comes from

 the latin word 'levis' meaning 'light'.

Why is magnetic levitation important?

Magnetic levitation is useful in a variety of applications. Simply levitating an object immediately suggests a number of things:

Transport systems eg magnetically levitated trains.

Moving of metallic objects in the steel industry using so-called magnetic floaters.

Possible military applications eg the so-called Rail-gun. Which uses a magnetic field to push projectiles.

Understanding the principles of magnetic levitation may lead to some innovative solutions to problems.

Applications Of Superconductors :  Electric generators : superconducting generators are very smaller in size and weight when compared with conventional generators. The low loss superconducting coil is rotated in an extremely strong magnetic field. Motors with very high powers could be constructed at very low voltage as low as 450V. this is the basis of new generation of energy saving power systems.

1.      Low loss transmission lines and transformers : Since the resistance is almost zero at superconducting phase, the power loss during transmission is negligible. Hence electric cables are designed with superconducting wires. If superconductors are used for winding of a transformer, the power losses will be very small.

2.      Magnetic Levitation : Diamagnetic property of a superconductor ie , rejection of magnetic flux lines is the basis of magnetic levitation. A superconducting material can be suspended in air against the repulsive force from a permanent magnet. This magnetic levitation effect can be used for high speed transportation.

3.      Generation of high Magnetic fields : superconducting materials are used for producing very high magnetic fields of the order of 50Tesla. To generate such a high field, power consumed is only 10kW whereas in conventional method for such a high field power generator consumption is about 3MW. Moreover in conventional method ,cooling of copper solenoid by water circulation is required to avoid burning of coil due to Joule heating.

4.      Fast electrical switching :A superconductor possesses two states , the superconducting and normal. The application of a magnetic field greater than H_c  can initiate a change from superconducting to normal and removal of field reverses the process. This principle is applied in development of switching element cryotron. Using such superconducting elements, one can develop extremely fast large scale computers.

5.      Logic and storage function in computers : they are used to perform logic and storage functions in computers. The current – voltage characteristics associated  with Josephson junction are suitable for memory elements.

6.      SQUIDS ( superconducting Quantum Interference Devices ) : It is a double junction quantum interferometer. Two Josephson junctions mounted on a superconducting ring forms this interferometer. The SQUIDS are based on the flux quantization in a superconducting ring. Very minute magnetic signals are detected by these SQUID sensors. These are used to study tiny magnetic signals from the brain and heart. SQUID magnetometers are used to detect the paramagnetic response in the liver. This gives the information of iron held in the liver of the body accurately.