Simple model for tunable vortex pinning by a magnetic dipole

The interaction between one vortex in a thin superconducting film and one magnetic dipole in the presence of a magnetic field applied parallel to the film surfaces is studied theoretically in the London limit. The dipole magnetic moment is assumed to be parallel to the film surfaces, to have constant magnitude, and freedom to rotate. The pinning potential for the vortex is calculated exactly. It is found that, due to the dipole freedom to rotate, the dependence of the pinning potential on the applied field is non-trivial, and allows both the spatial dependence and strength of the pinning potential to be changed by the field. As a consequence, the critical current can be tuned by the applied field. The critical current is obtained numerically as a function of the applied field. Order of magnitude changes in the critical current resulting from changes in the direction and magnitude of the applied field are reported, with discontinuous changes taking place in some cases. Possible application to vortices pinned by arrays of magnetic dots are briefly considered.