AC Response of Thin Film Superconductors at Various Temperatures and Magnetic Fields

A common method for measuring the electromagnetic properties of superconductors is to measure their complex magnetic ac susceptibility χ as a function of frequency ω and amplitude H0, and of temperature T and applied dc magnetic field H dc a as parameters. The basic theory of the linear χ(ω) and nonlinear χ(H0, ω) is outlined for various geometries, e.g. disks, rings, and strips of thin films or thicker platelets in a perpendicular magnetic field. It is shown how χ(ω) explicitly depends on the linear resistivity ρac(ω) = E/J or penetration depth λac(ω), and χ(H0, ω) on the nonlinear current–voltage law E(J,B) where E(r), J(r), B(r) are the local electric field, current density, and induction. The dependence of E(J,B) on T and on various material properties like pinning forces or pinning energies, structural defects and granularity, leads to an implicit dependence of χ on these parameters.