Experimental studies and theoretical modeling of the levitation force between a permanent magnet and superconducting thin film are reported. Measurements of the force $F_z$ and magnetic stiffness ${\kappa }_z=|\delta F_z/\delta z|$ as functions of the magnet-superconductor separation z, show several features contrasting all previous levitation force data for bulk superconductors. In particular, the $F_z\mathrm{}\left(z\right)\mathrm{}$ curves measured for decreasing and increasing separation form hysteresis loops of nearly symmetrical shape, also displaying a peak in the repulsive force branch. Recent theories for flux penetration in thin type-II superconductors in transverse magnetic fields are invoked to explain the results, which were obtained using a cylindrical Nd-Fe-B magnet and a ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ circular disk made by laser ablation. We derive explicit formulas for both $F_z$ and ${\kappa }_z,$ reproducing quantitatively all the features seen experimentally.

• Received 14 September 1998

DOI:https://doi.org/10.1103/PhysRevB.60.9855