Levitation force and magnetic stiffness in bulk high-temperature superconductors

Levitation forces between a small permanent magnet and a disk of bulk high-temperature superconductor at 77 K were measured as a function of vertical separation for disks of composition Y-Ba-Cu-O, Ag/Y-Ba-Cu-O, (Pb,Bi)-Sr-Ca-Cu-O, and Tl-Ba-Ca-Cu-O. The forces were highly hysteretic; however, for all samples, on the initial descent of the magnet toward the disk, the force was unique, independent of magnet speed, and varied approximately as the negative exponential of the separation distance. Magnetic stiffness, associated with minor hysteresis loops, was found to be approximately proportional to the levitation force, and nearly independent of magnet configuration and superconductor composition.