The phenomenon whereby individual atomic magnetic moments will attempt
to align all other atomic magnetic moments within a material with
itself is known as the *exchange*
interaction (*Aharoni*, 2000). If the magnetic moments align in
a parallel fashion, the material is *ferromagnetic*; if the
magnetic moments align antiparallel, the material is
*antiferromagnetic*.

The exchange energy between two neighbouring magnetic moments
** and
**** is usually described by:
**

The exchange energy between two neighbouring magnetic moments

where
is the unit vector of the direction of the magnetic moment:

and
is the *exchange integral* which
originates from the wave function overlap of two electrons.

Consequently, the exchange energy for a system of particles, under the assumption that the exchange energy is short-ranging and subsequently only acts on direct neighbours, is:

Used to represent nearest neighbours in summations

where represents the nearest neighbours . The value of is derived experimentally and expressed as a function of (see equation 2.25).

The sign of is important -- if is positive, it indicates the material exhibits ferromagnetic behaviour and the exchange energy is at a minimum when two neighbouring moments are in parallel alignment.

Antiferromagnetic materials have a negative , and as such have a minimum exchange energy when aligned antiparallel.

If a ferromagnet is heated above a critical point known as the
*Curie* temperature (*Curie*, 1895), when the applied field is
zero, the average magnetisation also becomes zero.

Typical values of exchange energy between two parallel ferromagnetic magnetic moments for iron, cobalt and nickel are given in table 2.2.