When researching magnets it seemed that the main difference between ferromagnetic and paramgnetic elements was that ferromagnets stay magnetised after a magnetic field is removed. This then lead me to the 'exchange interaction'. Can someone explain in simple English how the exchange interaction leads to ferromagnetism (permanent magnetism)?
In both paramagnets and ferromagnets, the little magnetic spin arrows want to point in the same direction as the applied magnetic field. The difference is that in ferromagnets, each spin also wants to point in the same direction as its neighbors. Once the magnetic field is removed, this second effect takes over from the first one and keeps the spins pointing in the same direction as the magnetic field pointed - the spin's direction gets locked in by its neighbors.
The exchange interaction is a kind of chemical bond, in that the electrons of nearby atoms come into a mutual state that has better likelihood than random for spins to align. This (weak) bonding causes a permanent magnetic moment for the ferromagnet (or at least, for domains within a bulk ferromagnet).
Just as solids becomes liquids, the ferromagnetic state vanishes at high temperature (but there is very little mechanical strength lost as a result- it is a very weak bond).
At its core, the nature of the exchange interaction is quantum mechanical minimization of Gibbs free energy by spin and orbit pattern.