Examples of ferromagnetic materials include iron, cobalt, nickel, and an alloy called Alnico. The atoms in these materials have permanent magnetic moments, and a phenomenon called exchange coupling takes place in which the magnetic moments of nearby atoms line up with one another. This forms domains, small neighborhoods where the magnetic moments are aligned. Typical dimensions of domains are 0.1 to 1 mm.

When a ferromagnetic material is not magnetized it still has domains, but the domains have random magnetization directions. If an external field is turned on two things happen. Domains aligned with the field grow at the expense of domains aligned against the field, and the magnetization direction within each domain tends to shift towards the direction of the applied field.

If the external field is removed the ferromagnetic material does not return to its original state, but retains some of its net magnetization. The degree to which the magnetization is retained depends on the material.

In "hard" ferromagnetic material it is hard to shift the domains, so a significant fraction of the magnetization is retained when the external field is removed. This is how permanent magnets are made.

In "soft" ferromagnetic material the domains more closely follow the external field, and not much net magnetization remains when the external field is removed. A good application of this is an electromagnet, which has a strong magnetic field when a current is turned on and very little field when the current is removed.

A ferromagnetic material has a hysteresis curve that shows the net field as a function of H. In the case of a cylindrical piece of ferromagnet with a coil of wire wrapped around it, for instance, this can be interpreted as a plot of the net field as a function of the current through the coil, as the current is cycled from some maximum in one direction to the same maximum in the other.

The curve is double-valued - the value of B, the net field, depends not just on the magnetic field from the current in the coil but also on whether the current is increasing or decreasing. B generally lags behind H because the domains don't like to change.

The area enclosed by the B-H curve is proportional to the work required to take the material around the cycle once.

Another feature of the graph is that it levels off at large values. This is known as saturation, the point where all the domains are aligned and the maximum M is reached. You can turn the current in the coil up all you want after this point but it doesn't do much good because the domains are already aligned.

When you have a permanent magnet there are two things you don't want to do to it. You don't want to have it experience an impact and you don't want to heat it. Either of these tends to shake up the domains, making them more random and destroying the alignment necessary for the magnet to remain magnetic.

Changing temperature is interesting. Above a certain temperature called the Curie temperature a ferromagnetic material actually becomes paramagnetic. The Curie temperature (named for Pierre Curie, not Marie) depends on the material, as shown in the table below.

When a paramagnetic substance is exposed to a magnetic field the magnetic moments of the atoms tend to align with the field. The paramagnetic substance is therefore weakly attracted by a magnet.

Pierre Curie found that the magnetization in a paramagnet is proportional to the applied magnetic field and inversely proportional to the absolute temperature:

Curie's Law:

M

=

C Bo T

As T goes to zero Curie's Law predicts that the magnetization goes to infinity, which is not possible. What actually happens as T approaches zero is that the magnetization reaches the saturation value where all the magnetic moments are aligned.

When a diamagnetic substance is exposed to a magnetic field a weak magnetic moment is induced opposite to the applied field. A diamagnetic substance is weakly repelled by a magnet.

On an atomic level, the interaction between the electrons and the magnetic field, in combination with electrostatic effects, is such that the orbital speed is increased for electrons with orbital magnetic moments opposite the field, increasing the magnetic moment, and decreased for electrons with orbital magnetic moments aligned with the field, decreasing their magnetic moments. These magnetic moments cancel in the absence of the field, but do not completely cancel when the field is applied.

All materials exhibit diamagnetism, but paramagnetic and ferromagnetic effects dominate in paramagnetic and ferromagnetic substances.

Superconductors have a very interesting magnetic property. Remember that in a superconductor currents flow with zero resistance, and that superconducting materials are only superconducting below a certain temperature.

When a superconductor is exposed to a magnetic field currents set up in the superconductor swirl in such a way as to create a magnetic field inside the superconductor that exactly cancels the applied field. In other words, the net magnetic field inside a superconductor is zero. This exclusion of magnetic field is known as the Meissner effect.

A neat application of this is a levitating magnet - a magnet placed over a superconductor can actually be levitated by the repelling magnetic fields.

Another way to look at this is that a superconductor acts like a perfect diamagnetic material. All diamagnetic materials try to cancel external fields, but most do so very weakly.