# Magnetism

(A detailed introduction to magnetism can be found at: Magnetism (11-14 age group).)

## Magnetic properties of materials

The science of magnetism has come a long way since 600 B.C. when the Greeks discovered that the iron ore lodestone (first found in Magnesia in Asia Minor and now known as magnetite) had some interesting properties. A piece of lodestone suspended by a thread, would always point in the same direction. The word lodestone comes from the Saxon loedan (to lead).

Permanent magnetic materials are now used in many applications from magnetic ink on cheques to magnetic door catches.

Magnetic materials possess a property known as susceptibility (c) defined as follows:

B = mo(H + M) = moH(1 + M/H) = moH(1 + c) where the quantity M/H (= c) is the susceptibility.

Magnetic materials are of three types: (a) diamagnetic, (b) paramagnetic and (c) ferromagnetic.

(a) Diamagnetics
If a sample of diamagnetic material is placed in a magnetising coil and a current passed through the coil, then a field is produced in the specimen that opposes the direction of the original magnetising field. The susceptibility is therefore negative (-1.7 x 10-8 for bismuth, for example).
The electron magnetic moments will cancel out in a diamagnetic material, because of their orbital motion and spin. The value of the relative permeability for diamag- netics is slightly less than 1, usually about 0.9999.

(b) Paramagnetics
An application of an external field produces a field within the specimen in the same direction as the initial magnetising field. The susceptibility is therefore positive (+0.82x10-8 for aluminium).

In the paramagnetic material the electron magnetic moments tend to add up; thermal motion disturbs them but if an external field is applied they realign. Paramagnetism is temperature-dependent, since at low temperatures there is little thermal motion and so the susceptibility is higher.

The value of the relative permeability of paramagnetic materials is slightly greater than 1, usually about 1.001.

(c) Ferromagnetics
In ferromagnetic materials there is a strong linkage between neighbouring atoms to form what are known as magnetic domains. The relative permeability of ferromagnetics is large, of the order of 104, but does depend on the past history of the specimen. The only ferromagnetic elements are iron, nickel, cobalt, gadolinium and dysprosium, but there are many ferromagnetic alloys. Modern quantum physics actually predicts that ferromagnetism will only occur for the elements listed above.

A simplified diagram of magnetic domains is shown in Figure 1. It is not meant to show any particular domain shape or size.
However the length of a magnetic domain in a ferromagnetic material is of the order of 20 m (2x10-2 mm).

In diagram (a) an unmagnetised specimen is shown and diagram (b) shows the effect of magnetizing the specimen. The direction of the magnetic axis in each domain is changed to become more aligned with the external field and some of the boundaries of the domains have changed.

When all the domains have been aligned the material is said to be saturated and any further increase in he external field will not produce an increase in the magnetisation of the specimen. Generally big samples give big magnetic fields.

## The Barkhausen effect

The existence of domains in a ferromagnetic material may be shown by the Barkhausen . effect, using the apparatus shown in Figure 2. If the north pole of the magnet is moved slowly across the top of the bundle of iron wires a rushing sound is heard from the loudspeaker. This is due to currents induced in the coil as the molecular domains align themselves during magnetisation. No subsequent noise is produced if the north pole is moved across again, the effect returning only if a south pole is used.

## The Curie temperature

When a ferromagnetic material is heated the domain boundaries are destroyed, and above a certain temperature known as the Curie point (about 1043 K for iron, 1384 K for cobalt, and 631 K for nickel) ferromagnetics become paramagnetics.

## Hysteresis

Hysteresis (the name comes from the Greek word meaning 'delay') describes the relation between the magnetising field and the magnetisation produced within a specimen.

Figure 2 shows the relation between the magnetising force and the resultant magnetisation of the specimen. You will see that there is a maximum flux that can be produced within a given specimen, shown as Bm on the graph. This is known as saturation. In other words you need a physically large permanent magnet to produce a large magnetic field.

If a specimen is fully magnetised and then demagnetised, it will not return to a condition where both the magnetising field and the magnetisation produced in the specimen are both zero.

When the magnetising field is reduced to zero there will still be a small amount of magnetisation left in the specimen. This is known as the remanent flux and the effect as remanence (Br). This is shown by the length OA in Figure 2.

The area enclosed by the hysteresis loop represents the work done in taking the material through the hysteresis cycle. This is typically about 2x10-2 J for a soft magnetic material such as iron.

The reverse field needed to reduce the magnetisation in the specimen to zero is known as the coercivity (H) of the specimen and is shown as OD in Figure 2.

The loop produced when the magnetising field is taken through a full cycle is called a hysteresis loop. One very important factor is the area within the loop, since this represents the loss of energy within the specimen when it is magnetised and demagnetised. This energy is lost as heat within the specimen, and the larger the area within the loop the more energy is lost in magnetising and demagnetising the specimen.

A soft magnetic material (soft iron) will have a small energy loss and therefore a narrow hysteresis loop while that for a hard magnetic material (steel) will be wider. Figure 3 shows the effect of hysteresis in two different types of specimen. This also shows that it is hard to magnetise and demagnetise steel while it is relatively easy to do this for iron.

(Compare the hysteresis loop formed by magnetizing and demagnetizing a specimen with that formed by taking a rubber cord through a cycle of stretching and relaxing).

We can demagnetize a magnetised piece of iron by putting it in a coil of wire through which an alternating current is passing. This will magnetise it in alternate directions but if we now slowly reduce the current (as therefore the magnetising field) to zero the amount of magnetisation will become less and less and finally the bar will be effectively demeagnetised.
This is shown in Figure 4.

The table below gives the remanence and coercivity for a number of magnetic materials.

 Material Composition (%) B (T) A (Am-1) Alnico 55 Fe, 10 Al, 17 Ni, 12 Co, 6 Cu 0.76 42x103 Carbon steel 98 Fe, 0.86 C, 0.9 Mn 0.95 3.6x103 Cobalt steel 52 Fe, 6 Co, 7 W, 3.5 Cr, 0.5 Mn, 0.7 C 0.95 18x103 Magnadur Ba, Fe 0.36 110x103 Mumetal 76 Ni, 17 Fe, 5 Cu,2 Cr 0.5 0.002x103

Permanent magnets are made with hard magnetic materials with a high remanence, so that the magnet will retain its magnetism after magnetisation, and a high coercivity so that stray fields will not affect it.

Soft magnetic materials are used in transformer cores so that the energy losses are small. For example, at a frequency of 50 Hz the power loss per kilogram of mumetal is 0.2 W for a saturation field of 0.1 T. This rises to 175 W for a frequency of 2.4 kHz

© Keith Gibbs 2011