The guidance of vortex–antivortex pairs by in-plane magnetic dipoles in a superconducting finite-size film

The possibility of manipulating vortex matter by using various artificial pinning arrays is of significant importance for possible applications in nano and micro fluxonics devices. By numerically solving the time-dependent Ginzburg–Landau equations, we study the vortex–antivortex (v–av) dynamics in a hybrid structure consisting of a finite-size superconductor with magnetic dipoles on top which generate v–av pairs in the presence of an external current. The v–av dynamics is analyzed for different arrangements and magnetic moments of the dipoles, as a function of angle α between the direction of the magnetic dipole and that of the Lorentz force produced by the applied current. The interplay of the attractive interaction between a v–av pair and the Lorentz force leads either to the separation of (anti)vortices and their motion in opposite directions or to their annihilation. We found a critical angle αc, below which vortices and antivortices are repelled, while for larger angles they annihilate. In case of a single (few) magnetic dipole(s), this magnetic dipole induced v–av guidance is influenced by the self-interaction of the v–av pairs with their images in a finite-size sample, while for a periodic array of dipoles the guidance is determined by the interaction of a v–av pair with other dipoles and v–av pairs created by them. This effect is tunable through the external current and the magnetization and size of the magnetic dipoles.