Study of higher-order harmonics of complex ac susceptibility in YBa2Cu3O7−δ thin films by the mutual inductive method

Abstract

We have applied the mutual inductive method to study higher-order harmonics of complex ac susceptibility χ n = χ n −iχ n for YB 2 C 3 O 7−δ thin films as function of the temperature and the applied field. The experimental results were compared with analytical and numerical results obtained from the Ishida-Mazaki model and the solution of the integral equation for the current density, respectively. Both models allow us to reproduced the main experimental features, however, as n increases the numerical model shows notable discrepancies. This failure can be attributed to the current-voltage characteristics. Also this investigation yields the activation energy U c and the critical current density J c for two samples both at T = 0.

Determination of the Critical Current Density in <inline-formula> <tex-math notation="TeX">$\hbox{YBa}_{2}\hbox{Cu}_{3}\hbox{O}_{7-\delta}$</tex-math></inline-formula> Thin Films Measured by the Screening Technique Under Two Criteria

“…We can see that, as the amplitude increases, the peak shifts toward lower temperatures, and at the same time, the width of the curve increases. It is well known that these effects are due to the field and temperature dependence of J c [4], [5], [11]. From these curves, we obtained the value of the temperature at the maximum (T p ) of each curve, and using (3), J c (T p ) was estimated for a temperature range between 85 and 88 K.…”

“…The I th (T ) curve was determined considering a third-harmonic resistance criterion of 0.2 mΩ [9]. However, for the V 3 criterion, the k coil factor is required [see (4)] to obtain the J c (T ) curve. In order to obtain the k coil factor, we performed the transport measurements of microbridge #1 simultaneously.…”

“…If a power-law current-voltage characteristic E = αJ n (with α as a constant) is assumed, the difference caused by the 100-times different E is calculated to be 26% for n = 20, 17% for n = 30, and 12% for n = 40. According to flux creep theories [4], n = U c (J)/k B T , where U c is the activation energy, and k B is the Boltzmann constant. Thus, at lower temperatures, the I − V curves for the films should exhibit a sharp increase, indicating a high n value.…”

“…Due to the nonlinear magnetization of the sample, the harmonics of the voltage will emerge. It has been suggested that the harmonics of the magnetic susceptibility are proportional to the harmonics of the voltage [3], [4]. With the help of this technique and based on the analysis of the imaginary part of the fundamental harmonic of the complex magnetic susceptibility as a function of the temperature χ 1 (T ), Xing et al [5] proposed a method to determine J c in superconducting thin films.…”

“…With the help of this technique and based on the analysis of the imaginary part of the fundamental harmonic of the complex magnetic susceptibility as a function of the temperature χ 1 (T ), Xing et al [5] proposed a method to determine J c in superconducting thin films. The second alternative, i.e., the inductive technique or the screening technique [6], [7], offers a practical approach not only to determine J c [7]- [10] but also to measure the harmonics of the magnetic susceptibility [3], [4]. In this experimental setup, one or two coils can be used.…”