Noncontacting measurement of the inductive nonlinearity of a superconducting thin film

Superconducting films are expected to contribute nonlinear effects in microwave circuits due to a current dependence of penetration depth λ. Data from a two-coil mutual inductance measurement can be used to extract the coefficient J0 representing a dependence of the form λ2(J)=λ2(0)[1+(J/J0)2]. A method of extracting J0, using a measurement of third-harmonic generation, is compared to one previously reported. The method is significantly easier to use and probably more accurate. Measurements on a number of YBa2Cu3O7−x films at 78 K have shown no sign of a nonquadratic nonlinearity, and give values of J0 as high as ∼100 MA/cm2.