# Magnetic Materials

The introduction of material media into the study of magnetism has very different consequences as compared to the introduction of material media into the study of electrostatics. When we dealt with dielectric materials in electrostatics, their effect was always to reduce  below what it would otherwise be, for a given amount of free electric charge. In contrast, when we deal with magnetic materials, their effect can be one of the following:
1. To reduce  below what it would otherwise be, for the same amount of free electric current (diamagnetic materials)
2. To increase  a little above what it would otherwise be (paramagnetic materials)
3. To increase  a lot above what it would otherwise be (ferromagnetic materials)

# Magnetisation, or Magnetic Polarisation

Magnetisation is the property of some magnetic materials which describes a magnetic field created by those materials themselves and the effects of some external magnetic field on those materials.

Magnetisation  is defined as the amount of magnetic moment per unit volume. It is expressed in amperes per metre (A/m).

The origin of the magnetic moments that create the magnetisation can be microscopic electric currents (bound current, Ib) due to
• either the rotation of electrons around the positive nucleus, or
• the spin of the electrons
Both of these electronic motions produce internal magnetic fields  that are similar to the magnetic field produced by a current loop. The equivalent current loop has the magnetic moment,

where S is the area of the loop and Ib is the bound current.

# Magnetisation in Maxwellâ€™s Equations

Magnetic Susceptibility (χm)

The magnetic susceptibility χm of a magnetic material is a measure of the degree of magnetisation of a material in response to an applied magnetic field.

Permeability

Permeability (Î¼) is the degree of magnetisation of a material that responds linearly to an applied magnetic field.

# Classification of Magnetic Materials

Depending upon the values of the magnetic susceptibility (χm) or the relative permeability (Î¼r), magnetic materials are broadly classified into three groups as

1. Paramagnetism
2. Diamagnetism
3. Ferromagnetism
1. Paramagnetism
The atoms or molecules comprising paramagnetic materials have a permanent magnetic dipole moment. In the absence of any applied external magnetic field, the permanent magnetic dipoles in a paramagnetic material are randomly aligned and thus do not have any magnetisation  and thus, the average magnetic field  is also zero.

However, when we place a paramagnetic material in an external field , the dipoles experience a torque that tends to align  with , thereby producing a net magnetisation  parallel to . Since  is parallel to , it will tend to enhance the field. Hence, for paramagnetic materials, magnetic permeability, Î¼ > Î¼0.

In most paramagnetic substances, the magnetisation  is not only in the same direction as , but also linearly proportional to it. This is possible because without the external field there would be no alignment of dipoles and hence no magnetisation.

The linear relation between  and  is expressed as,

where χm is a dimensionless quantity called the magnetic susceptibility.

Thus, the net magnetic field can be written as,

where Î¼r = (1 + χm) is called the relative permeability of the material.

For paramagnetic materials, Î¼r > 1 or magnetic susceptibility, χm > 0 (positive), although χm is usually of the order of 10-6 to 10-3. Paramagnetism is temperature dependent.

Examples of Paramagnetic Materials are air, platinum, tungsten, potassium, aluminium, chromium, palladium, copper sulphate, manganese, etc.
1. Diamagnetism
In the case of diamagnetic materials, the magnetic fields due to electronic motions completely cancel each other and thus, the magnetic material does not have permanent magnetic dipoles. The presence of an external field  will induce magnetic dipole moments in the atoms or molecules. However, these induced magnetic dipoles are antiparallel to , leading to a magnetisation  and average field antiparallel to and therefore a reduction in the total magnetic field strength. Hence, for diamagnetic materials, magnetic permeability, Î¼ < Î¼0.

For diamagnetic materials, relative permeability, Î¼r<1, or magnetic susceptibility, χm < 0 (negative), although χm is usually of the order of -10-5 to -10-9.

Examples of Diamagnetic Materials are copper (χm = -0.95 Ã— 10-5), gold (χm = -3.2 Ã— 10-5), silver (χm = -2.6 Ã— 10-5), lead, silicon, diamond, bismuth (χm = -16.6 Ã— 10-5), antimony, mercury, tin, zinc, alcohol, hydrogen, nitrogen, water, etc.
1. Ferromagnetism
In ferromagnetic materials, there is a strong interaction between neighbouring atomic dipole moments. Ferromagnetic materials are made up of small patches called magnetic domains, as illustrated in Fig. An externally applied field  will tend to line up those magnetic dipoles parallel to the external field, as shown in Fig. The strong interaction between neighbouring atomic dipole moments causes a much stronger alignment of the magnetic dipoles than in paramagnetic materials.

Examples of Ferromagnetic Materials are iron, steel, nickel, cobalt.

# Hysteresis in Ferromagnetic Materials

The permeability Î¼ of a ferromagnetic material is not a constant, since neither the total field nor the magnetisation  increases linearly with . Although the relation  is applicable for all types of magnetic materials, the relation between  and  for ferromagnetic materials is not unique, but is dependent on the previous magnetic history of the material. The phenomenon is known as hysteresis. The variation of  as a function of the externally applied field  is shown in Fig. The curve is known as a hysteresis curve or magnetisation curve or Bâ€“H curve.

Hysteresis curve or magnetisation (B-H) curve

From the hysteresis loop, a number of primary magnetic properties of a material can be determined.
1. Retentivity

(The value of  at the point b on the hysteresis curve) It is a measure of the residual magnetic flux density corresponding to the saturation induction of a magnetic material. In other words, it is the ability of a material to retain a certain amount of residual magnetic field when the magnetising force is removed after achieving saturation.
2. Residual Magnetism or Residual Flux

It is the magnetic flux density that remains in a material when the magnetising force is zero. The residual magnetism and retentivity are the same when the material has been magnetised to the saturation point. However, the level of residual magnetism may be lower than the retentivity value when the magnetising force did not reach the saturation level.
3. Coercive Force

(The value of  at point c on the hysteresis curve.) This is the amount of reverse magnetic field which must be applied to a magnetic material to make the magnetic flux return to zero.
4. Hysteresis Loss

The area of a hysteresis loop gives the energy loss per unit volume during one complete cycle of periodic magnetisation of a ferromagnetic material. This is called hysteresis loss. This loss is in the form of heat.
5. Permeability

As has been previously mentioned, permeability is a material property that describes the ease with which a magnetic flux is established in a material. It is the ratio of the flux density to the magnetising force and is represented by the equation .
This equation describes the slope of the curve at any point on the hysteresis loop. The permeability value given in papers and reference materials is usually the maximum permeability or the maximum relative permeability. The maximum permeability is the point where the slope of the Bâ€“H curve for the unmagnetised material is the greatest. This point is often taken as the point where a straight line from the origin is tangent to the Bâ€“H curve as shown in Fig.

â€‹
Determination of permeability from hysteresis curve

The relative permeability is arrived at by taking the ratio of the materialâ€™s permeability to the permeability in free space (air).
1. Reluctance

It is the opposition that a ferromagnetic material shows to the establishment of a magnetic field. Reluctance is analogous to the resistance in an electrical circuit.

The shape of the hysteresis loop tells a great deal about the material being magnetised. The hysteresis curves of two different materials are shown in the graph.
â€‹Relative to other materials, a material with a wider hysteresis loop has
• Lower permeability
• Higher retentivity
• Higher coercivity
• Higher reluctance
• Higher residual magnetism
• Higher loss
Relative to other materials, a material with a narrower hysteresis loop has
• Higher permeability
• Lower retentivity
• Lower coercivity
• Lower reluctance
• Lower residual magnetism
• Lower loss
â€‹
Different shapes of hysteresis curves