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The analytic expression for the nonlinear magnetic susceptibility of a thin disk derived from Bean’s model with a uniform JC for B ‖ n̂ predicts a peak-peak ratio of 7.1 (5.4) for the real (imaginary) components of the third harmonic χ3 susceptibility. Our measurements show a peak-peak ratio closer to 1.1 in the real component and a noise limited lower estimate of ≈ 7 in the imaginary component. The anomalous third harmonic can be explained by the presence of a geometrical surface barrier for flux entry and exit which we have included as a small region of enhanced current density, JC,G, close to the surface of the disk. The geometrical surface current density is predicted to be approximately equal to JC,G ≈ 2BC1/μ0d. In 2G HTS tapes with d ≈ 1μm and BC1 ≈ 5mT this is JC,G ≈ 8GAm−2. We have measured both JC,B and JC,G using the nonlinear susceptibility of a Superpower tape without artificial pinning in fields orthogonal to the tape up to 35T. We find a geometrical surface current of JC,G ≈ 10GAm−2 and an average critical current density JC which is in good agreement with transport measurements performed on material from the same reel of tape.

Geometrical surface pinning in the nonlinear AC susceptibility of HTS tapes