Collective coordinate study of spin-wave emission from a dynamic domain wall

We study theoretically the spin-wave emission from a moving domain wall in a ferromagnet. Introducing a deformation mode describing a modulation of the wall thickness in the collective coordinate description, we show that thickness variation couples to the spin wave linearly and induces spin-wave emission. The dominant emitted spin wave turns out to be polarized in the out-of wall plane (ϕ ) direction. The emission contributes to the Gilbert damping parameter proportional to ℏ ω_ϕ/K , the ratio of the angular frequency ω_ϕ of ϕ , and the easy-axis anisotropy energy K .