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/sub c/ in superconducting films. In the inductive measurement, an ac drive current I/sub 0/ cos (Omega)t flows in a small coil close to the surface of a superconducting film, and third-harmonic voltage V/sub 3/ cos(3(Omega)t +(theta)/sub 3/) induced in the coil is detected. The relationships among the ac drive current I/sub 0/, the amplitude V/sub 3/, and the phase (theta)/sub 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 I/sub c0/, the third-harmonic voltage is near zero, V/sub 3/ ~~0 for I/sub 0/ < I/sub c0/. For I/sub 0/ > I/sub c0/, on the other hand, the third-harmonic voltage is expressed as V/sub 3/ exp(-i(theta)/sub 3/) = (omega)I/sub c0/ G/sub 3/(I/sub 0//I/sub c0/), where G/sub 3/((gamma)) is a scaling function determined by the configuration of the coil. The predicted scaling law of V/sub 3//I/sub c0/ and (theta)/sub 3/ as functions of I/sub 0//I/sub c0/ is clearly observed in an YBa/sub 2/Cu/sub 3/O/sub 7-(delta)/ film.