Magnon amplification of a localized low-frequency mode

By rapidly cooling a hot magnon gas one can achieve significant accumulation of magnons at the minimum of the magnon spectrum [1]. Such accumulation of magnons causes an increase of a chemical potential of the magnon gas and may lead to Bose-Einstein condensation of magnons [1, 2]. Usually magnons accumulate at the bottom of the spin-wave spectrum. However, some magnetic systems have more complex spectrum which includes isolated low-frequency modes (ILFM) lying below the continuous spectrum of propagating spin waves. We developed a simple model of interaction of ILFM with a rapidly cooling hot magnon gas. We showed that in this case four-magnon scattering leads to appearance of a new term in kinetic equation acting as an additional ILFM damping ΔΓ ∝ (hf₀ - μ), where f₀ is the frequency of ILFM and μ is the chemical potential of the magnon gas. Thus, if the chemical potential of the magnon gas exceeds the ILFM frequency, ΔΓ becomes negative, which should lead to amplification of ILFM. We developed a simple model of interaction of ILFM with a hot magnon gas in the process of rapid cooling. We demonstrated that the increase of the chemical potential of the magnon gas leads to amplification of ILFM. The model predicts nonlinear increase of amplification with the increase of the achieved chemical potential of the magnon gas.