Theory of pinning in a Superconducting Thin Film Pierced by a Ferromagnetic Columnar Defect

摘要

This is an analytical study of pinning and spontaneous vortex phase is asystem consisting of a superconducting thin film pierced by a longferromagnetic columnar defect of finite radius $R$. The magnetic fields,screening currents, energy and pinning forces for this system are calculated.The interaction between the magnetic field of vortices and the magnetizationoutside the plane of the film and its close proximity enhances vortex pinningsignificantly. Spontaneous vortex phase appears when the magnetization of thecolumnar defect is increased above a critical value. Transitions between phasescharacterized by different number of flux quanta are also studied. Theseresults are generalized to the case when the superconductor is pierced by anarray of columnar defects.