Precise determination of the threshold current for third-harmonic voltage generation in the ac inductive measurement of critical current densities of superconducting thin films

In an ac inductive method to measure critical current densities J_c of superconducting films by detecting third-harmonic voltages V₃ cos 3ωt, ac magnetic fields are generated with ac currents I₀ cos ωt in a small coil mounted just above the film. J_c is calculated from the threshold coil current I_th, at which full penetration of magnetic field is achieved and V₃ starts to emerge. For convenience, I_th has been usually determined by a constant-voltage criterion, e.g., V₃/√2 = 50 μV. However, V₃ is proportional to I_th, and the determination of I_th by the constant-voltage criterion inherently causes a systematic error. We confirmed this by comparing the obtained J_c with those obtained from dc magnetization and by a transport method. We propose to use a constant-resistance criterion, such as V₃/I₀ = 2 mΩ, as an alternative method to determine I_th accurately.