Off-resonance excitation of spin waves by a four-magnon process

Recent experiments have shown that driving ferromagnetic resonance in thin films generates noisy stray fields over a broad frequency spectrum [1-3]. The noise has been attributed to spin waves excited through a four-magnon mechanism, although the specifics of the mechanism have not been identified. In this paper we present modeling of one such mechanism that relies on nonuniform fluctuations in M_s owing to thermal excitation. With M_z fluctuating, a uniform driving field at frequency f₀ will excite spin waves at frequencies f_k. The uniform processional mode adds a resonant amplification of the driving field. The predicted spin wave noise power is proportional to input microwave power, T², and 1/f_k⁴ (temperature T, spin wave frequency f_k). We find the most relevant spin waves for this process are near the bottom of the spin wave band. Numerical evaluation yields spin wave noise power that is roughly a factor of 10² weaker than the noise power due to pure thermal excitation. However, this result can be regarded as a lower bound. The effect may be much larger if the M_z fluctuations are due to spin waves that are excited above equilibrium [3].
[1] C. S. Wolfe et al., Phys. Rev. B 89 180406 (2014).
[2] M. R. Page et al., arXiv:1607.07485 (2016).
[3] C. Du et al., Science 357, 195 (2017).