Harmonic Generation in the Alternating Magnetic Response of High-Temperature Superconductors
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HARMONIC GENERATION IN THE ALTERNATING MAGNETIC RESPONSE OF HIGH-TEMPERATURE SUPERCONDUCTORS A. SHAULOV*, R. BHARGAVA, AND D. DORMAN Philips Laboratories, North American Philips Corporation, Briarcliff-Manor, NY 10510
ABSTRACT We report a novel ac technique for characterizing the magnetic behavior of hightemperature superconductors. This technique is based on monitoring the spectrum of the magnetic response of these materials to small sinusoidal fields. A nonlinear magnetic behavior is indicated by the appearance of harmonic components in the spectrum. Measurements of these harmonics as a function of bias field, temperature and frequency provide valuable information about the processes of flux penetration, flux pinning and motion in these materials. INTRODUCTION Magnetic measurements using alternating fields have been widely employed in studying the magnetic behavior of high-temperature superconductors. The measuring circuit commonly consists of a primary coil coaxial with a pair of balanced coils, one containing the sample. A small sinusoidal magnetic field, generated by the primary coil, induces small oscillations in the magnetization of the material. The resulting off-balance voltage induced across the coil pair is measured using a two-phase lock-in amplifier. This measurement technique is well suited for characterizing materials with a linear magnetic behavior, i.e., materials in which a pure sinusoidal field induces pure sinusoidal oscillation in the magnetization. However, under certain temperature and bias field conditions, the high-temperature superconductors exhibit a nonlinear magnetic behavior. Thus, a nonsinusoidal voltage is induced across the sample coil and components of the voltage at harmonics of the driving frequency are generated [1,2]. A model predicting odd harmonics in the ac magnetic response of superconductors was first developed by Bean [3]. This model has been recently extended [4,5] to explain the appearance of even harmonics in the response of high-temperature superconductors. A different approach, based on a model of flux-quantized supercurrent loops with weak links, has been developed by Jeffries et al. [1,6,7]. The experiments described in this paper demonstrate the importance of the harmonic generation phenomenon as a tool for characterizing the magnetic behavior of high-temperature superconductors. Specifically, measurements of higher harmonics offer accurate determination of parameters of practical and fundamental importance such as the lower critical field and the irreversibility line [8,9]. EXPERIMENTS Superconducting transitions Figure 1 illustrates the phenomenon of harmonic generation near the superconducting transition of a sintered Y-Ba-Cu-O sample (Tc-89K). The traces in this figure show the power spectra of the magnetic response of this sample to a sinusoidal field of amplitude 0.04 Oe and frequency 20 kHz. The upper trace describes the spectrum of the response at 77K. It shows only the fundamental component at the driving frequency. The lower trace in Figure 1 describes
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