Magnetization Process

The main objectives of the present research work are

2.2 Magnetization Process

4

f=quBsinO (2.8)

The force on a positive charge is at right angles to the plane containing u and B and points in the direction of a right-hand screw turned from u to B.

The same force also acts in the axial direction on the conduction electrons in a wire moving in a magnetic field, and this force generates an emf in the wire. The emf in an element of wire of length dl is greatest when the wire is at right angles to the B vector, and the motion is at right angles to both. The emf is then given by Eq'. (2.9)

emf

⁼

u B dl (2.9)

More generally, u is the component of velocity normal to B, and the emf depends on the sine of the angle between dl and the plane containing the velocity and the B vectors. The sign is given by the right-hand screw rule, as applied to Eq. (2.8)

2.2.2 Origin of Magnetic Moments

The magnetic moment or magnetic dipole moment is a measure of the strength of a magnetic source. In the simplest case of a current loop, the magnetic moment is defined as:

m

⁼

I fda (2.10)

where 'a' is the vector area of the current ioop, and the current, I is a constant. By convention, the direction of the vector area is given by the right hand rule.

In the more complicated case of a spinning charged solid, the magnetic moment can be found by the following equation:

m=frxfdv,

where dv

⁼

r 2 sin8drd0dØ and J is the current density.

The magnetic moment in a magnetic field is a measure of the magnetic flux set up by the gyration of an electric charge in a magnetic field. The moment is negative, indicating it is diamagnetic, and equal to the energy of rotation divided by the magnetic field. In atomic and nuclear physics, the symbol m represents moment, measured in Bohr magnetons, associated with the intrinsic spin of the particle and with the orbital motion of the particle in a system, also called

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magnetic dipole moment. For a system of charges, the magnetic moment is determined by summing the individual contributions of each charge-mass-radius component.

2.2.3 Magnetic Properties of Solid

Materials may be classified by their response to externally applied magnetic fields as diamagnetic, paramagnetic and ferromagnetic. These magnetic responses differ greatly in strength. Diamagnetism is property of all materials and opposes applied magnetic fields, but is very weak paramagnitism, when present, is stronger than diamagnetism and produces magnetization in the direction of the applied field and proportional to the applied field.

Ferromagnetic effects are very large, producing magnetizations sometimes orders of magnitude greater than the applied field and as such arte much larger than either diamagnetic or paramagnetic effects. The magnetization of a material is expressed in terms of density of net magnetic dipole moments

t

in the material. We define a vector quantity called the magnetization M by

M

^{= Piojai}

(2.12)

V

when the total magnetic field B in the material is given by

B=B0 +,u0 M, (2.13)

where

^jio

is the magnetic permeability of space and B0 is the externally applied magnetic field.

When magnetic fields inside of materials are calculated using Ampere's law or the Biot- Savart law, then the

po

in those equations is typically replaced by just

t

with the definition

PPrPO ^'

(2.14)

where 1r is called the relative permeability. If the material does not respond to the external magnetic field by producing any magnetization then

tr =

1. Another commonly used magnetic quantity is the magnetic susceptibility

Z =

Pr

1 (2.15)

For paramagnetic and diamagnetic materials the relative permeability is very close to I and the magnetic susceptibility very close to zero. For ferromagnetic materials, these quantities may be very large. Another way to deal with the magnetic fields which arise from magnetization of

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materials is to introduce a quantity called magnetic field strength H. It can be defined by the relationship

H

=

B

0 = -

M

/10

H0 (2.16)

and has the value of unambiguously designating the driving magnetic influence from external currents in a material independent of the materials magnetic response. The relationship for B above can be written in the equivalent form

B=u0 (H+M), (2.17)

H and M will have the same units, amperes/meter

The magnetic susceptibility

()

is defined as the ratio of magnetization to magnetic field M

Zij (2.18)

The permeability and susceptibility of a material is correlated with respect to each other by (2.19)

2.2.4 Magnetic Domain and Domain Wail Motion

In addition to susceptibility differences, the different types of magnetism can be distinguished by the structure of the magnetic dipoles in regions called domains.

Each domain consists of magnetic moments that are aligned, giving rise to a permanent net magnetic moment per domain.

• Each of these domains is separated from the rest by domain boundaries/domain walls.

Boundaries, also called Bolch walls, are narrow zones in which the direction of the magnetic moment gradually and continuously changes from that of one domain to that of the next.

The domains are typically very small about 50 gm or less, while the Bloch walls are about 100 nm thick. For a polycrystalline specimen, each grain may have more than one microscopic sized domain.

• Domains exist even in absence of external field.

& •

In a material that has never been exposed to a magnetic field, the individual domains have a random orientation. This type of arrangement represents the lowest free energy.

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When the bulk material is un-magnetized, the net magnetization of these domains is zero, because adjacent domains may be orientated randomly in any number of directions, effectively canceling each other out.

The average magnetic induction of a ferro-magnetic material is intimately related to the domain structure.

• When a magnetic field is imposed on the material, domains that are nearly lined up with the field grow at the expense of unaligned domains. This process continues until only the most favorably oriented domains remain.

In order for the domains to grow, the Bloch walls must move, the external field provides the force required for this moment.

When the domain growth is completed, a further increase in the magnetic field causes the domains to rotate and align parallel to the applied field. At this instant material reaches saturation magnetization and no further increase will take place on increasing the strength of the external field.

Under these conditions the permeability of these materials becomes quite small.

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