Noncollinear Orientation of the Flux Lines Penetrating Into a Hard Isotropic Superconductor and the Applied Magnetic Field

The electrodynamics of hard superconductors turns out to be a very complex problem if the external magnetic field changes both in its modulus and direction. The major difficulties are connected to the specific properties of the flux-line system. It is well-known that, in spite of the vortex magnetic interaction, vortices in bulk hard superconductors cannot follow the direction of the external magnetic field. Indeed, the gain in the Gibbs free energy due to the vortex system orientation along the external magnetic field is proportional to the length L of the vortex, whereas the work against pinning forces is proportional to the second power of L. Therefore, the orientation of the vortex system in hard superconductors could be changed only due to the penetration of vortices with new direction into a sample. Penetration of Abrikosov flux lines into an isotropic hard superconductor induced by changes in the orientation of the external magnetic field is theoretically studied in this work. The analysis is based on the microscopic nonlocal critical state model where the forces of bulk and surface pinning, alongside magnetic forces of interaction of the row of penetrating vortices with the existing flux lines, Meissner current, and vortex images are taking into account. It is shown that the new vortices start to penetrate into a superconductor only when the angle through which the external magnetic field is rotated is larger than a certain critical value. This critical angle is shown to be strongly dependent on the magnetic prehistory of the sample and the pinning characteristics. It is found that the alignment of entering vortices is essentially different from that of the applied magnetic field. This difference can reach 90 degrees. The reason for this unexpected fact is related to the conditions of the force balance for the entering vortices, which are not defined by the direction of the external field only but by the direction of existing vortices also. Feasibility of detecting the predicted noncollinearity effects is discussed.