Hot magnon gas as an amplifier of a localized low-frequency mode

Rapid cooling of a hot magnon gas leads to significant accumulation of magnons at the minimum of the magnon spectrum [1], which causes an increase of a chemical potential of the magnon gas and may lead to Bose-Einstein condensation of magnons [1, 2]. Although magnons tend to accumulate at the bottom of the spin-wave spectrum, some magnetic systems also have isolated modes (IM) having frequencies below the continuous spectrum of propagating spin waves [3]. We developed a simple model of interaction of an IM with a hot magnon gas in the process of rapid cooling. We demonstrated that in such a system four-magnon scattering leads to an additional contribution to IM damping ΔΓ ∝ (hf₀ - μ), where f₀ is the frequency of IM and μ is the chemical potential of the magnon gas. Thus, if the chemical potential of the magnon gas exceeds the IM frequency, ΔΓ becomes negative, which leads to IM amplification. Numerical simulations based on kinetic equations for magnon population numbers [1] confirm our analytical predictions. We discuss several possible setups in which this phenomenon can be observed experimentally.

[1] M. Schneider et al., Nat. Nanotechnol., 15, 457 (2020).

[2] M. Schneider et al., Phys. Rev. Lett., 127, 237203 (2021).

[3] R. V. Verba et al., Phys. Rev. B, 93, 214437 (2016)