Dynamics of a vortex near the edge of a thin-film ferromagnet*

The low-frequency dynamics of magnetization in a thin-film ferromagnet with an easy-plane anisotropy can be efficiently described by a mapping to electrodynamics in 2+1 dimensions. Magnons turn into photons, whereas vortices become massless particles with an electric charge equal to the vortex number. In a previous work [1], we showed that a vortex-antivortex pair with equal skyrmion numbers revolve around the geometrical center and gradually spiral down towards annihilation. Their motion was accurately modeled by considering the balance of forces acting on these topological defects: the Coulomb attraction, the gyroscopic forces, and the viscous force from Gilbert damping. A vortex-antivortex pair with opposite skyrmion numbers will move mostly in the same direction, gradually approaching each other. A similar motion is expected of a vortex near a straight edge, which creates the image of an antivortex attracting the vortex toward the edge. We study this motion numerically and model it analytically.

[1] D. Reitz, A. Ghosh, and O. Tchernyshyov, "Viscous dynamics of vortices in a ferromagnetic film," Phys. Rev. B 97, 373 (2018).