Interpretation of the harmonic response of superconducting films to inhomogeneous ac magnetic fields

Abstract

We present a quantitative analysis of the response of a thin superconducting film to an applied nonuniform ac magnetic field. The analysis is directly applicable to the single-coil inductive measurement technique where a small coil driven by an ac current produces a nonuniform field, with Jz determined by the appearance of a third-harmonic component of the voltage generated across the coil. We derive a simple model to explain the response of the film to the applied magnetic field in the absence of weak links. This model is used to predict the third-harmonic voltage generated across the coil. The derivation of the model explains why superconducting films having thicknesses even less than the penetration depth screen out the nonuniform ac magnetic fields generated by the coil. A simplified version of the model yields analytic expressions that describe the magnitude and phase of the third-harmonic component at high drive currents while the full model yields excellent agreement with experimental measurements for our highest quality epitaxial films. In other films, the presence of weak links leads to a characteristic signature in the harmonic response at low drive currents. We have also found that ion irradiation can reduce the critical current densities by significant amounts without introducing weak links into the film.

Nondestructive determination of current–voltage characteristics of superconducting films by inductive critical current density measurements as a function of frequency

“…Figure 1 shows a schematic of the electrical circuit. This circuit is similar to those used in previous studies, 3,4 and our method also involves the single-coil approach in which the coil is used to generate an ac magnetic field and to detect the inductive voltage. In our method, however, an additional cancel coil is used to compensate for harmonic noise voltages generated in the signal generator and the power amplifier.…”

“…Then, the breakdown of complete shielding leads to a third-harmonic voltage generated in the coil. 3,4,7 When I 0 ϭI th , full penetration of the magnetic field in the film is reached, and the amplitude of the ac magnetic field at the upper surface of the film ͑nearly parallel to the surface͒ is H 1 ϭ2H 0 ϭJ c d. 3,7,8 Then, I th can be expressed using a coil factor k as J c d/k, and J c can be determined by measuring V 3 with increasing I 0 .…”

“…This method is an extension of well-known inductive methods that measure the J c distribution of large-area superconducting films. [3][4][5] In those methods, J c is measured at a frequency f and the E induced in the superconductor is proportional to f, and thus the CVCs can be obtained by measuring J c at various frequencies.…”

Flux domes in weak-pinning superconducting films without edges

“…When the current amplitude exceeds the value at which the maximum induced sheet-current density reaches K c = j c d, a third-harmonic voltage appears in the coil. 26,27,28,29 A similar technique was introduced by Hochmuth and Lorenz. 30 The effects discussed in this paper and applied to type-II superconducting films are quite general and also should be observed in type-I superconductors.…”

Higher harmonics of ac voltage response in narrow strips of YBa2Cu3O7 thin films: evidence for strong thermal fluctuations

“…For example, the estimate of the order parameter relaxation time [1], probe of a chiral glass phase [2] and π-junction Josephson behavior [3] in granular superconductors, as well as detection of superconducting phases with different critical temperatures T c in inhomogeneous samples. Recently, special attention has been paid to the role of non-ohmic harmonics in thermodynamic and transport properties of high-temperature superconductors (HTS) [4][5][6][7][8] and in a contactless inductive method to measure critical currents in superconducting films [9][10][11], which complements the nonlinear ac susceptibility first harmonic method to measure critical currents [12]. Moreover, some interesting theoretical predictions have been made regarding third harmonics generation based on the anisotropic scattering rate of normal charge carriers [13,14] as well as produced by electric field modified fluctuation effects in the electrical conductivity [15] or in the thermal response of the film to an harmonic current [16].…”