A spin wave or its quasi-particle equivalent, the magnon, is "an elementary excitation of a magnetic system which is usually long-range-ordered, such as a ferromagnet."
(Reference: http://www.accessscience.com) search words="magnon".
For example, in a sample of pure iron, it is the unpaired electrons within the atomic lattice 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.
Select the following hyperlinked text to see a good symbolic diagram of spin waves moving through the precessing of uncompensated electron spins in a 2 dimensional crystal lattice layer of a magnetic material. In real life, spin waves can propagate in all directions in a magnetic material and not just across a 2 dimensional surface as the diagram shows. But materials can be engineered to promote the development of coherent spin waves in preferred directions.
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.
Read more about spin waves from wikipedia https://en.wikipedia.org/wiki/Spin_wave or stay here and click "Read more ..." below to learn about spin wave lasers, power generation and much more.
UPDATE Oct. 5th, 2020: Here is an excellent Youtube animation of a spinwave: https://www.youtube.com/watch?v=cBo91aGls0E
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