Local Magnetic Relaxation in High-Temperature Superconductors

Abstract

A novel Hall probe array technique is used to measure the spatial distribution and time dependence of the magnetic induction in YBa 2 Cu 3 O 72d crystals. Analysis of the data based on the flux diffusion equation allows a direct, model-independent determination of the local activation energy U and the logarithmic time scale t 0 for flux creep. The results indicate that the spatial variations of U are small (6kT) and that U increases logarithmically with time. The time t 0 is inversely proportional to the field and it exhibits a nonmonotonic temperature dependence. These results confirm theoretical predictions based on the logarithmic solution of the flux diffusion equation.Thermally activated flux creep in high-temperature superconductors is a subject of intensive study. This phenomenon is commonly investigated by measuring the time dependence of the magnetic moment M averaged over the sample volume. Among the most significant parameters extracted from such data are the effective activation energy U and the logarithmic time scale t 0 for flux creep [1]. Recent models emphasize the nonlinear dependence of U on the current density j [2,3] and the macroscopic nature of the time scale t 0 [1-6]. While it is not possible to derive U͑j͒ directly from the experimental data, each of the above models gives a specific relaxation behavior that can be compared with experimental results. Such an approach for evaluating U͑j͒ is model dependent and involves fitting several parameters [7].Maley et al. [8] proposed a method to determine U͑j͒ avoiding the a priori assumption of a model for the dependence of U on the current density and field. Their method analyzes global magnetic relaxation data, utilizing an integrated form of the flux diffusion equation over the sample volume. It is important to realize that the activation energy determined by this method is actually the activation energy at the surface of the sample, while the current density j is averaged over the sample volume [9]. Although in the limit U͞kT ¿ 1 the activation energy should be almost constant over the sample volume [1,4], in the presence of surface barriers [10-12] the values of U at the surface and in the bulk may be different.In this work we propose a method to determine the local U and j in the bulk, utilizing the recent development of a miniature Hall probe array [12] to measure the local induction B at different locations simultaneously as a function of time. In contrast with the conventional techniques where only the time evolution of the total magnetization is recorded, we measure the time evolution of the spatial distribution of B, and thus are able to determine both the time and the spatial derivatives of B. This new information enables direct analysis of the local relaxation data using the basic diffusion equation governing the flux motion [4,13]:where D Bv is the flux current density and y y 0 exp͑2U͞kT ͒ is the effective vortex velocity. The preexponential factor y 0 Ajf 0 ͞ch, where f 0 is the unit flux, c is the light velocity, j is the current ...

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