Lecture 6 Magnetic materials

In this lecture;

• The Magnetic Dipole Moment is defined,

• Ferromagnetism is described,

• Magnetisation and Hysteresis are introduced,

• Applications in computing and medicine are given,

• Paramagnetism and Diamagnetism are distinguished, and

• Curie's law and Temperature are given.

Magnetic Dipole Moment

Inside atoms, the electrons and protons are in rapid and unceasing motion.

They are effectively orbiting and rotating, and so, as current loops, they induce microscopic (really yoctoscopic) magnetic dipole fields.

The strength of the magnetic dipole field of a current loop is measured by its magnetic dipole moment.

The dipole moment puts numbers to the turning effect ("torque" or "moment") that an applied magnetic field will exert on the loop. To get the torque you multiply the dipole moment by the applied magnetic induction.

An applied magnetic field will tend to rotate the plane of the loop into an orientation that is at right angles to the applied magnetic field.

The magnetic dipole moment is defined for a circular current, as the product of the current and the area of the circle.

It has a direction which follows the right hand screw rule, i.e. anticlockwise currents give a dipole moment towards you and clockwise current have a dipole moment away from you.

Note: This symbol and concept should not be confused with the magnetic permeability μ₀.

The rotating Earth has a magnetic moment of 8.0x10⁺²² A.m², whereas for an electron "rotating" it is 9.3x10^-24 A.m².

Protons and neutrons have very small magnetic moments so atomic dipole moments are really due to the electrons.

Ferromagnetism

In regular materials the dipole moments of its atoms are randomly oriented and so there is no net magnetic effect.

However some materials have naturally aligned dipole moments which produce macroscopic magnetic effects.

Such elements are called Ferromagnetic because the phenomenon was first observed with Ferrous (Iron) materials.

Examples:

• the elements Iron (26), Cobalt (27), Nickel (28), Gadolinium (64) and Dysprosium (66), also

• Compounds such as CrO₂.

Usually, the net magnetic field is small because the atomic dipole moments align in small volume elements about 1000 atom diameters across (called magnetic "domains") and there is no consistent orientation between neighbouring domains.

However when an external magnetic field is applied to ferromagnetic materials, the boundaries of the domains change.

The domains in the direction of the external field grow and merge with each other and those domains in other directions shrink so the net magnetic effect is multiplied thousands of times.

If the external field is then removed the old domains start to re-emerge, but some residual order (remanence) remains to produce a permanent magnet.

This dependence of a material on its history is called "hysteresis".

A Ferromagnetic material in a Solenoid

The magnetic field induced by the current in the solenoid is given by:

As the current varies in size and direction, the applied magnetic field follows it exactly.

However the domain re-organisation in the ferromagnetic material lags behind the changes in the applied field.

Magnetisation

The magnetisation of the material is defined as the net magnetic moment per volume.

A plot of Magnetisation vs Current for a ferromagnetic material in a solenoid gives a hysteresis curve.

When all the atomic dipole moments that can be aligned are aligned, then the material is saturated.

The magnetisation when the current is zero is the remanence.

The area between the curves (or the width between d and g on the diagram) measures how hard it is to magnetise and demagnetise the material.

If the area or width is large, the material is magnetically hard (e.g. steel).

If the area is small, the material is magnetically soft (e.g. iron).

In practical applications:

• Speaker coils, motors and computer disk material, use magnetically hard materials because a persistent field is needed.

• Transformers and computer disk read/write heads use magnetically soft materials so that the magnetisation can change quickly.

Magnetic Disk Storage

In computers, data is often stored on magnetic disks.

During manufacture, disks are coated with a liquid that has small iron oxide particles suspended in it.

The particles are about 1mm by 0.1mm and are magnetically hard permanent magnets.

As the liquid dries the particles are aligned by an external magnetic field so that they end up lying in the plane of the disk and at right angles to the radius of the disk.

The particles form a kind of circular magnet.

Data are read or written along narrow circular tracks by a read/write head, which is a (magnetically soft) electromagnet.

To write a binary "1", a current flows in the read/write head to produce a reversal in magnetisation across the boundary between two sections.

A binary "0" is represented by no reversal in magnetisation at the boundary.

Ferromagnetism in diagnosis and therapy

Diagnosis

Ferromagnetic particles can get into the human body by eating and breathing.

Food can have ferromagnetic particles it accidently includes from harvesting or from processing, and eating will deposit those particles in the stomach.

Breathing air with iron oxide particles from arc welding, or laden with asbestos dust, will deposit particles in the lungs.

Placing a person's body in a strong magnetic field will align the ferromagnetic particles, and a scan afterwards will show any dangerous concentrations.

Therapy

Some tumours can be destroyed by heat (hyperthermia).

Implanting ferroelectric particles (NiCu and PdCo) in the tumour and inductively heating them with a radiofrequency magnetic field can breakdown the tumour.

Relative magnetic permeability

When a magnetic field is applied to a material and the material is magnetised, the net magnetic field is a multiple (k_m) of the applied field.

B_net = k_m B_applied

The multiplier (k_m) is called the relative magnetic permeability or simply the permeability constant.

This constant enables us to distinguish three types of magnetic material, ferromagnetic, paramagnetic and diamagnetic.

For ferromagnetic materials the permeability "constant" varies by up to 10⁴x but the other two have k_m ~ 1.

 

Paramagnetism

Paramagnetic materials are materials whose atoms have permanent magnetic dipole moments.

They are attracted by a magnet and so are slightly magnetic.

Material	km
Gd2O3	1.012
CuCl2	1.00035
Cr	1.00033
W	1.000068
Al	1.000022
Mg	1.000012

 

Diamagnetism

Michael Faraday noticed (in 1847) that a sample of Bismuth was repelled from a strong magnet placed near it. Materials that repel instead of being attracted are called diamagnetic.

Diamagnetic materials are materials whose atoms have no permanent magnetic dipole moments, but have dipoles induced by an applied magnetic field.

The effect is much smaller than paramagnetism as can be seen from the following table.

Material	km
Bi	0.99983
Hg	0.999968
Ag	0.999974
Cu	0.9999903

 

Curie's Law

Pierre Curie found that magnetisation decreases with temperature.

Above the Curie Temperature, magnetisation disappears completely. For Iron this is 1043⁰C.

 

 

Summarising:

The Magnetic Dipole Moment gives the turning effect of an external magnetic field on a current loop.

The Magnetisation of a material is the net magnetic moment per volume.

Ferromagnetism comes from the large increase in magnetisation when domains are aligned.

Hysteresis occurs because the domain re-organisation lags behind the changes in the applied field.

Paramagnetic materials are weakly attracted to a magnet.

Diamagnetism materials are weakly repelled from a magnet.

Temperature decreases magnetisation.

 

 

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