Critical current density and third-harmonic voltage in superconducting films

When a sinusoidal drive current I-0 cos omegat flows in a small coil close to the surface of a superconducting film, third-harmonic voltage V-3 cos(3omegat+theta(3)) is induced in the coil if the film causes a nonlinear response. We have developed an approximate theoretical method yielding the relationships among I-0, V-3, and theta(3), thus providing the scientific basis for a widely used inductive method for measuring the critical current density J(c) in large-area superconducting films. Our results show that V-3 is near zero when I-0 is smaller than a threshold value I(c0)proportional toJ(c)d, where d is the film thickness. When I-0>I-c0, on the other hand, the third-harmonic voltage is expressed as V-3 exp (-itheta(3))=omegaI(c0)G(I-0/I-c0), where G(x) is a scaling function determined by the configuration of the coil. We demonstrate the scaling law of V-3/I-c0 vs I-0/I-c0 in a YBa2Cu3O7-delta film. (C) 2002 American Institute of Physics.