Instability of Magnetostatic Modes in a Microwave Magnetic Field Applied Parallel to the dc Field

Previous calculations of the instability threshold have been based on a plane-wave analysis which is strictly applicable only in an infinite medium. This paper describes a more rigorous theory in which the boundary conditions at the surface of the sample are taken into account. The refined theory admits instabilities at frequencies different from half the pump frequency, which are forbidden according to the less rigorous plane-wave analysis. The general theory is applied to the magnetostatic modes of a long, circular cylinder, which is magnetized along its axis. It is concluded that: 1. Pairs of surface modes (with frequencies higher than the highest plane-wave frequency) are not subject to instability. 2. Instability at half the pump frequency can occur only for those cases in which the magnetostatic potential is invariant under rotation around the cylinder axis $\text{(m\hspace{0.17em}=\hspace{0.17em}0)}$ . The instability threshold for these modes is identical to that deduced on the basis of the plane-wave analysis, except that the frequencies now have to satisfy the characteristic equation derived from the boundary conditions. 3. Instabilities at frequencies different from half the pump frequency can occur, but generally have a higher threshold.