Considerations on the Propagation and Generation of Magnetostatic Waves and Spin Waves

A discussion is given of the dispersion relation, magnetization distribution, and group velocity of magnetostatic waves in an infinite circular cylinder with the static magnetic field parallel to the cylinder axis. The dispersion relation of the modes with $e^{i\varphi }$ angular dependence is, for $\mathrm{kR}\gg 1$, $\omega \cong \gamma H_0+\gamma 2\pi M_s{\left(\frac{x_i}{\mathrm{kR}}\right)}^2+\left(\frac{D}{\hslash }\right)k^2,$ where $x_i$ is a root of $J_0\mathrm{}\left(x\right)=0\mathrm{}$; $R$ is the cylinder radius; and $D$ is the exchange constant. The group velocity of magnetostatic pulses at low wave vectors is shown to be considerably higher than magnon velocities.