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

Abstract

Two methods of calculating the instability threshold are described. The first is a plane‐wave analysis which is strictly applicable only in an infinite medium. The second is 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: (a) 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 (m=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. (b) Instabilities at frequencies different from half the pump frequency can occur, but generally have a higher threshold. (c) Pairs of surface modes (with frequencies higher than the highest plane‐wave frequency) are not subject to instability. (d) Instabilities involving a surface mode and a volume mode are not strictly forbidden. It is very likely, however, that such instabilities will be masked by the instability of spin waves of shorter wavelength.