Permanent Magnetism

Soham Khapre, 210150012

Introduction to Magnetism

Magnetism, phenomenon associated with

magnetic fields, which arise from the motion of
electric charges.
It can be an electric current in a conductor or
charged particles moving through space, or it can
be the motion of an electron in an atomic orbital.
Magnetism is also associated with elementary
particles, such as the electron, that have a
property called spin.
Permanent Magnetism

A magnet is said to be a permanent magnet, when it possesses permanent

magnetic properties, even when it is not located within a magnetic material.

Hard ferromagnetic material with great retentivity and coercivity is what makes up
a permanent magnet.

Permanent magnets are made of iron, cobalt, nickel, steel, and some alloys of rare
earth metals.

The strength and size of the magnet have an impact on how large the magnetic
field is. In a permanent magnet at room temperature, domains are partially aligned
due to thermal agitation.
Cause of Magnetism
The orbital motion of electron gives it an orbital angular
moment which also gives rise to the orbital magnetic
moment.

The total magnetic moment of the electron gives the atom its
magnetic character. In atoms with full or nearly full shells
these electrons pair up and cancel the net magnetic
moment.

However, for elements where atoms have half-full shells the

spins don't cancel out and the atoms retain the spin
magnetic moment of the electrons.
In a crystal, atoms form magnetic domains

where their magnetic moments align, either

cancelling out or amplifying. When domains

are similar in size, the solid remains weakly

magnetic. But in a strong magnetic field,

domains align parallel to it, creating a

permanent magnet.
Manufacturing of Permanent Magnet
Sintering (Rare-earths, Ferrites and
Alnicos)
Rare-earth, ferrite and Alnico magnets can be manufactured

with this method.

The sintering process involves compacting fine powders at high

pressure in an aligning magnetic field and then sintering to fuse

into a solid shape.

After sintering, the magnet shape is rough, and will need to be

machined to achieve close tolerances.

Pressing (Rare-earths)
Other than sintering, some Rare-earth magnets are manufactured by die

pressing (with pressure applied in one direction) or isostatic pressing (with

equal pressure applied in all directions).

The aligning magnetic field for die pressed magnets can be either parallel

or perpendicular to the pressing direction.

Isostatically pressed magnets achieve higher magnetic properties than die

pressed ones.
Pressure Bonding or Injection Molding (Rare
Earths and Ferrites)
Both Rare-earth and Ferrite magnets can be manufactured by pressure

bonding or injection molding the magnet powders in a carrier matrix.

The density of magnet materials manufactured in this way is lower than that

of the pure sintered ones, yielding lower magnetic properties.

However, bonded or injection molded magnets may be machined into

relatively intricate shapes with close tolerances.

Casting (Alnicos)

Alnico magnets can be manufactured with casting and sintering methods. Cast

ones may be in large or complex shapes such as the common horseshoe while

sintered ones are in relatively small sizes, normally one ounce or less, and in

simple shapes.

Calendaring and Extruding (Flexible)

Flexible or Ferrite magnets are made by calendering or extruding magnet

powders in a flexible carrier matrix such as vinyl. Magnetic properties of this type

of magnet are even lower than the bonded or injection molded form. However,

flexible magnets are easily cut or punched into different shapes.

Magnetic Anisotropy
In condensed matter physics, magnetic anisotropy describes how an object's magnetic properties
can be different depending on direction.

In the simplest case, there is no preferential direction for an object's magnetic moment. This is
known as magnetic isotropy.

The opposite of this is magnetic anisotropy, where the materials are easier or harder to magnetize
depending on the way the object is rotated.

For most magnetically anisotropic materials, there are two easiest directions to magnetize the
material, which are a 180° rotation apart. The line parallel to these directions is called the easy
axis.
Sources of Magnetic Anisotropy
Magnetocrystalline anisotropy:
The atomic structure of a crystal introduces preferential directions for the magnetization.
Shape anisotropy:
When a particle is not perfectly spherical, the demagnetizing field will not be equal for all
directions, creating one or more easy axes.
Magnetoelastic anisotropy:
Tension may alter magnetic behaviour, leading to magnetic anisotropy.
Exchange anisotropy:
Occurs when antiferromagnetic and ferromagnetic materials interact.
Types of Magnetic Anisotropy
This is discussed for the case of single domain
magnets. ∝, β, γ are the direction cosines, which
imply components of a unit vector. ∝2 + β2 + γ2 = 1.

Uniaxial:

A magnetic particle with uniaxial anisotropy has one

easy axis. If the easy axis is in the z direction, the
anisotropy energy can be expressed as one of the
forms: E = KV(1-γ2) = KVsin2θ. V is the volume, K is
the anisotropic constant and θ is the angle between
the easy axis and the particle’s magnetization.
Triaxial:

A magnetic particle with triaxial anisotropy still has a single

easy axis, but it also has a hard axis (direction of maximum
energy) and an intermediate axis (direction associated with a
saddle point in the energy). The coordinates can be chosen so
the energy has the form E = KaV∝ 2 + KbVβ2

If Ka > Kb the easy axis is in z direction, intermediate axis is in y

direction and hard axis is in the x direction.
Cubic:

A magnetic particle with cubic anisotropy has three or

four easy axes, depending on the anisotropy parameters.
The energy has the form E = KV(∝ 2β2 + β2γ2 + γ2∝ 2) .

If K>0, the easy axes are the x, y and z axis. If K<0, there
are four easy axes characterized by
Curie Temperature
Curie point, also called Curie Temperature, temperature
at which certain magnetic materials undergo a sharp
change in their magnetic properties.

This temperature is named for the French physicist

Pierre Curie, who in 1895 discovered the laws that relate
some magnetic properties to change in temperature.

At low temperatures, magnetic dipoles are aligned.

Above the curie point, random thermal motions nudge
dipoles out of alignment.
Curie’s Law
Curie's Law describes the magnetic susceptibility
of a paramagnetic material in relation to
temperature.
It was formulated by Pierre Curie, a French
physicist, in 1895.
The law states that the magnetic susceptibility (χ)
of a paramagnetic material is inversely
proportional to the absolute temperature (T) of the
material, and it can be expressed mathematically
as:
χ = C/T, where C is the material-specific Curie
Constant.
Curie-Weiss Law
The Curie-Weiss law states that the magnetic susceptibility (χ) of a ferromagnetic material
above its Curie temperature (Tc) is inversely proportional to the difference between the
temperature (T) and the Curie temperature:
χ = C/(T-Tc)
Above the Curie temperature, they lose their permanent magnetic properties and behave more
like paramagnetic materials.
In many materials, the Curie–Weiss law fails to describe the susceptibility in the immediate
vicinity of the Curie point, since it is based on a mean-field approximation. Instead, there is a
critical behavior of the form

with the critical exponent γ.

Magnetic Saturation and Saturation Field
Magnetic saturation refers to a condition in which a magnetic material has reached its maximum
level of magnetization under the influence of an applied magnetic field.

The term "saturation field" typically refers to the strength of the magnetic field required to fully
saturate a magnetic material.

The Saturation Field Hs is related to the saturation flux density Bs and permeability of the material
as Bs=μ⋅Hs where Permeability (μ) is a measure of the material's ability to support the formation
of a magnetic field within itself in response to an applied magnetic field.

This saturation point occurs because all or nearly all of the magnetic domains within the material
have aligned with the external magnetic field. At this point, the material cannot become any more
magnetized.
Hysteresis Loop
The hysteresis loop shows the relationship between the magnetic
flux density and the magnetizing field strength. The loop is
generated by measuring the magnetic flux coming out from the
ferromagnetic substance while changing the external magnetizing
field.

Advantages of the Hysteresis Loop

1. A smaller region of the hysteresis loop is indicative of less loss of

hysteresis.

2. Hysteresis loop provides a substance with the importance of

retentivity and coercivity. Therefore, the way to select the right
material to make a permanent magnet is made simpler by the heart
of machines.

3. Residual magnetism can be calculated from the B-H graph, and it

is, therefore, simple to choose material for electromagnets.
Retentivity

The amount of magnetization present when the

external magnetizing field is removed is known as
retentivity.The value of B at point b in the hysteresis
loop.

Coercivity

The amount of reverse (-ve H) external magnetizing

field required to completely demagnetize the
substance is known as the coercivity of the
substance.The value of H at point c in the hysteresis
loop.
Thank you