Theoretical investigation on 3rd harmonic voltage in inductive measurements of critical current density in superconducting films

We have theoretically investigated third-harmonic voltage detected in a widely-used inductive, measurement of critical current density J(c) in superconducting films. In the inductive measurement, an ac drive current I-0 cos omegat flows in a small coil close to the surface of a superconducting film, and third-harmonic, voltage V-3 cos(3omegat + theta(3)) induced in the coil is detected. The relationships among the ac drive current I-0, the amplitude V-3, and the phase theta(3) of the third-harmonic voltage are derived on. the bases of the critical state model. When the drive current is smaller than a threshold value 10, the third-harmonic voltage is near zero, V-3 approximate to 0 for I-0 < I-c0. For I-0 > I-c0, on the other hand, the third-harmonic voltage is expressed as V-3 exp(-itheta(3)) = omegaI(c0)G(3)(I-0/I-c0), where G(3)(gamma) is a scaling function determined by the configuration, of the coil. The predicted scaling law of V-3/I-c0 and theta(3) as functions of I-0/Ic(0) is clearly observed in an YBa2Cu3O7-delta film.