Editing Magnons (section)

=== Spin Wave Dispersion Relation ===
The energy of magnons is typically described by the spin wave dispersion relation, which relates the energy of a magnon to its wave vector. For a simple ferromagnet, the dispersion relation can be expressed as:

<math>
\omega(\mathbf{k}) = \gamma H + D_s k^2
</math>

where:
* <math>\omega(\mathbf{k})</math> is the angular frequency of the magnon as a function of the wave vector <math>\mathbf{k}</math>,
* <math>\gamma</math> is the gyromagnetic ratio,
* <math>H</math> is the external magnetic field,
* <math>D_s</math> is the spin wave stiffness constant,
* <math>k</math> is the magnitude of the wave vector <math>\mathbf{k}</math>.

This equation shows that the magnon energy increases with both the applied magnetic field and the wave vector.