Local magnetic measurements in a highly anisotropic Nd-Ce-Cu-O crystal reveal a sharp onset of an anomalous magnetization peak at a temperature-dependent field B on . The same field marks a change in the field profiles across the sample, from profiles dominated by geometrical barriers below B on to Bean-like profiles above it. The temperature dependence of B on and the flux distribution above and below B on imply a disorder-induced transition at B on from a relatively ordered vortex lattice to a highly disordered, entangled vortex solid. Local magnetic relaxation measurements above B on show evidence for plastic vortex creep associated with the motion of dislocations in the entangled vortex structure.[S0031-9007 (97)04113-6]
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 ...
Abulafia et al. Reply: Klein et al. [1] agree with the main point of our Letter [2], namely the observation of a crossover from elastic collective creep to plastic creep in YBaCuO (YBCO). However, they criticize the use of Eq. (1) in describing the plastic creep and rather propose to adhere to Eq. (2) which originates from the theory of elastic collective creep. To justify this approach they introduce a new term of "plastic collective creep" which so far has no published theoretical basis. Thus, it is not clear whether this approach can explain the details of our experimental results at high fields, especially the decrease of the exponent m and the activation energy U with the induction B. In the absence of a known theory for the dependence of U upon j for plastic creep in the limit j ! 0, we adopted Eq. (1) to describe the situation far from that limit. The question of diverging barriers in the plastic creep regime in the limit j ! 0 is of significant interest, however its resolution has to await more detailed theoretical and experimental investigations.Careful reading of our Letter clearly shows that we realize that Eq. (2) can mathematically be fitted to our data. In fact, the inset of Fig. 2 in our Letter shows the results of such fits, namely a strong decrease of m with field above the peak, tending towards approximately 0.2. This anomalous field dependence of m was one of the reasons which led us to abandon the elastic creep model at high fields. In their Comment, Klein et al. repeat this analysis and consent that the anomalous behavior of m is not consistent with the elastic model. Nevertheless, they choose to adopt Eq. (2) on the basis of the quality of the fit to data digitized from Ref. [2]. However, as demonstrated in Fig. 1(a), our original data for these and other fields, can be reasonably described by Eq. (1). Apparently, fits are rarely unique and, one can also obtain good fits for the same data using other expressions, e.g., the logarithmic barrier U U 0 ln͑j 0 ͞j͒, as shown in Fig. 1(b). For obvious reasons we prefer the fit which is based on a physical model.Klein et al.'s suggestion to include all the B dependence in the exponent m may sound interesting. However, the key question is what is the physical basis of such a formula and what is the physical significance of U 0 and j 0 being field independent. Clearly, this is against the spirit of the collective creep model which predicts strong field dependence of U 0 and j 0 in the relevant regimes of small and large bundles. Without describing the physical model which leads to such crucial modifications, their treatment becomes just a mathematical exercise.Finally, we note that the cited model of Ertas and Nelson [3] gives no predictions for the behavior of m. Furthermore, this model relates to the sharp "fishtail" peak in BiSrCaCuO [4], which may be of entirely
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