a. How can one achieve a Bose Einstein Condensation of Magnons?
In the previous section we have seen that a magnon is an elementary collective excitation in a lattice of spins. It carries the spin 1 has a definite energy and propagates with a certain velocity in a certain direction with respect to an external magnetic field.
As magnons have spin one and can be treated like particles, it seems to be natural to use Bose-Einstein statistics to describe the energy distribution of a thermal magnon gas in a ferromagnet. This assumption is also supported through measurements of the energy distribution on a thermal magnon gas.
It comes out that magnons form a Bose gas with chemical potential zero. Now remember that the universal condition for Bose Einstein condensation is that the energy of the magnon with lowest energy in the gas has to become equal to the chemical potential.
Now we have a problem, there are no magnons with zero energy!
The energy of magnons is always greater than zero!
So the only possibility to achieve the condition for Bose-Einstein condensation is to raise the chemical potential. Thus the next section will try to give an answer to the question: