In this model the magnetization
where  is the volume. The propagation of spin waves is described by the Landau-Lifshitz equation of motion:
where  is the gyromagnetic ratio and  is the damping constant. The cross-products in this forbidding-looking equation show that the propagation of spin waves is governed by the torques generated by internal and external fields. (An equivalent form is the Landau-Lifshitz-Gilbert equation, which replaces the final term by a more "simple looking" equivalent one.)
The first term on the right hand side of the equation describes the precession of the magnetization under the influence of the applied field, while the above-mentioned final term describes how the magnetization vector "spirals in" towards the field direction as time progresses. In metals the damping forces described by the constant  are in many cases dominated by the eddy currents.
One important difference between phonons and magnons lies in their dispersion relations. The dispersion relation for phonons is to first order linear in wavevector , namely , where  is frequency, and  is the velocity of sound. Magnons have a parabolic dispersion relation:  where the parameter  represents a "spin stiffness." The  form is the third term of a Taylor expansion of a cosine term in the energy expression originating from the  dot product. The underlying reason for the difference in dispersion relation is that the order parameter (magnetization) for the ground-state in ferromagnets violates time-reversal symmetry. Two adjacent spins in a solid with lattice constant  that participate in a mode with wavevector  have an angle between them equal to .