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In solid state physics, a magnon is the term for an elementary excitation in which the direction of magnetization in a ferromagnetic material, or that of a sublattice moment in an antiferromagnetic material, is spatially nonuniform and propagates as a wave (spin wave).

Reference: http://www.harcourt.com/dictionary/def/6/1/5/0/6150600.html

Just as a photon is a quantum of energy in the form of an electromagnetic wave so also a magnon is a quantum of energy in the form of a spin wave. It is still an electromagnetic interaction but in this case the spin waves are propagating through the rotating electromagnetic fields of precessing spins.

In a sample of pure iron, it is the unpaired valence electrons shared between atoms that are responsible for the material's magnetic properties. These electrons have spin and an associated magnetic moment creating individual magnetic dipoles through each electron's spin axis. Each electron's spin axis can also precess like a gyroscope and spin waves propagate through these precessing magnetic dipoles of the electrons as their individual magnetic fields interact with each other. In other magnetic materials a combination of both axial and orbital electron spin can create magnetism if the combination is not compensated for by equal and opposite combined spins of other electrons. Spin waves can propagate through the precession of these resulting uncompensated spins. Spin waves can also propagate through uncompensated nuclear spins but the magnetic moments and coupling between spins is weaker than with electron spins.

Compensated spins can also precess under the influence of electromagnetic interaction with other particles but due to the compensation, electromagnetic radiation to/from these compensated spins at the frequency of precession is not detectable as a typical form of electromagnetic radiation.