Mapping of a thin-film ferromagnet to electrodynamics: emission of spin waves by vortices

We consider a field-theoretic description of a thin-film ferromagnet with easy-plane anisotropy. An extension of the well-known duality with electrostatics in 2-dimensional space to (2+1)-dimensional spacetime maps this system to a theory of electrodynamics. The low-energy description is the familiar Maxwell electrodynamics. Spin waves become electromagnetic waves, whereas vortices turn into particles whose electric charge equals the vortex number. This analogy allows us to compute the emission of spin waves by a rotating vortex-antivortex pair. Energy dissipation from this process becomes noticeable when the pair separation decreases below a characteristic length scale of order $\alpha^{-1/2}R$, where $R$ is the radius of the vortex core and $\alpha$ is the Gilbert constant.