Pinning and creation of vortices in superconducting films by a magnetic dipole

TL;DR

This paper develops an exact theoretical framework for understanding how a magnetic dipole outside a superconducting film influences vortex creation and configuration, revealing energy minimization principles and vortex structures.

Contribution

It generalizes London theory solutions to include external dipoles, providing a detailed energy functional and numerical methods for vortex configuration analysis.

Findings

Vortex-dipole interaction energy expressed as -m·b^{vac}.

Vortex configurations include curved lines and loops.

Energy minimization determines vortex arrangements.

Abstract

Interactions between vortices in planar superconducting films and a point magnetic dipole placed outside the film, and the creation of vortices by the dipole, are studied in the London limit. The exact solution of London equations for films of arbritrary thickness with a generic distribution of vortex lines, curved or straight, is obtained by generalizing the results reported by the author and E.H. Brandt (Phys. Rev. B {\bf 61}, 6370 (2000)) for films without the dipole. From this solution the total energy of the vortex-dipole system is obtained as a functional of the vortex distribution. The vortex configurations created by the dipole minimize the energy functional. It is shown that the vortex-dipole interaction energy is given by $- {\bf m}\cdot {\bf b^{vac}}$, where ${\bf m}$ is the dipole strength and $ {\bf b^{vac}}$ is the magnetic field of the vortices at the dipole position, and that it can also be written in terms of a magnetic pinning potential acting on the vortices. The properties of this potential are studied in detail. Vortex configurations created by the dipole on films of thickness comparable to the penetration depth are obtained by discretizing the exact London theory results on a cubic lattice and minimizing the energy functional using a numerical algorithm based on simulated annealing. These configurations are found to consist, in general, of curved vortex lines and vortex loops.