Levitation force from high-Tc superconducting thin-film disks

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 K-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(z) 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 YBa2Cu3O7-delta circular disk made by laser ablation. We derive explicit formulas for both F-z and K-z, reproducing quantitatively all the features seen experimentally.