Magnetic force acting on a magnetic dipole over a superconducting thin film

Abstract

The magnetostatic interaction energy and corresponding magnetic force acting on a magnetic point dipole placed above a type-II thin superconducting film in the mixed state with a single vortex are calculated using electromagnetics coupled with the London theory of superconductivity. If a vortex is trapped by a circular defect of radius b much less than Lambda, the magnetic forces, caused by the vortex, differ from the results of free from defect pinning by the factor (1 - b/Lambda), where Lambda is the effective penetration depth. The possibility of formation of the vortex in the thin film only in the field of the magnetic point dipole is investigated. The critical position of the dipole for creating the first vortex under the electromagnetic pinning of a circular defect and that position in the absence of defect pinning are obtained for comparison. In particular, in the limit of a/Lambda much greater than 1, where a is the separation between the dipole and the thin film, the only difference between two results is in the cutoff length, i.e., in the case of a circular defect the only difference in the critical position calculation is the cutoff at radius b rather than at coherence length xi. The pinning force of a single vortex by a circular defect is also calculated. Further, we investigate the conditions of the vortex creation for various cases (including the first, second, and third vortices) for a free of pinning center in the examining region. It is found that the creation of a new single vortex in the thin film causes an abrupt change in vertical levitation force: the force changed discontinuously.