Parametric Traveling-Wave Acoustic Amplification in Ferromagnets

A theoretical evaluation is presented for the amplification of acoustic microwaves traveling in a ferromagnet by means of a parametric interaction with a spatially uniform pump magnetization and a spin-wave idler. In this interaction, the strong frequency dispersion of the idler wave suppresses the degenerative effect of the upper sideband frequency. Although the spin-wave boundary conditions would seem to require a standing-wave idler, the low group velocity, and resulting short decay length, permits traveling-wave operation. By means of a normal mode analysis including losses, expressions are found for the gain per unit length and the interaction bandwidth as a function of pump power. The ultimate interaction bandwidth is determined by the spin wave Q, but the usable bandwidth is reduced by the effect of acoustic mismatches. This amplifier, in common with the maser and laser, is bilateral and the usable gain is limited by regeneration. The range of usable gain is expressed in terms of the acoustic mismatches at the terminals. Nondegenerate operation is possible, permitting reduction of idler-wave thermal noise. Gain, bandwidth, and pump power, and their frequency dependence, are evaluated for a number of available materials. Performance limitations due to Suhl breakdown are also discussed.