Amplification of Magnetization Waves in Ferromagnetic Conductors

A general linear theory of spin wave amplification similar to the theory of amplification of acoustic waves in crystals is presented which takes into account the space charge arising in the course of spin wave propagation in the crystal. The treatment is given for the case of an arbitrary orientation of the wave propagation vector and an external electric field with respect to the vector of crystal magnetic moment. It is found that in an approximation linear in the deviation from the unperturbed spin value the spin—spin interaction does not contribute to spin wave amplification. It is the spin—orbit interaction that contributes to the amplification in a linear approximation. The spin wave amplification factor proves to be proportional to the value of the direct current through the sample and attains appreciable values (about 25 cm−1) at rather weak currents (about 3.5 A/cm2) and wave vectors about 103 cm−1. With increasing wave vector the amplification factor diminishes inversely proportional to the first power of the wave vector in the case of time amplification, and inversely proportional to the second power of the wave vector in the case of space amplification.