Exponential critical state model applied to ac susceptibility data for the superconductor YBa2Cu3O7−δ

Abstract

We derive new expressions for the average magnetization loops, M (H), based on the exponential critical state model. The components Ј and Љ of the complex susceptibility are calculated and an algorithm to fit ac susceptibility data is discussed. This algorithm is employed to study the intergranular response Ј(H m) and Љ(H m) measured for two samples of YBa 2 Cu 3 O 7Ϫ␦ as a function of the ac field amplitude H m. One sample is a porous sintered cylinder and the other is a very dense melt-textured bar. In both cases good fits of the calculated components Ј and Љ are obtained using an algorithm that involves two free parameters, the full penetration field, H p , and the sample quality factor, p. An interesting result for the melt-textured sample is the observation of a step in Ј(H m) curves at very low H m , possibly associated with grain clustering.

Dynamical reentrance and geometry imposed quantization effects in Nb–AlOx–Nb Josephson junction arrays

“…On the micrometric scale, granularity results from the existence of extended defects, such as grain and twin boundaries. From this picture, granularity could have many contributions, each one with a different volume fraction (Araujo-Moreira et al 1994, Araujo-Moreira et al 1996, Passos et al 2000. The small coherence length of HTS implies that any imperfection may contribute to both the weak-link properties and the flux pinning.…”

“…In this case, the intragranular screening currents prevent the magnetic field from entering the grains, whereas intergranular currents flow across the sample to ensure a null magnetic flux throughout the whole specimen. This temperature dependence of the magnetic response gives rise to the well-known double-plateau behavior of the DC susceptibility and the corresponding double-drop/double-peak of the complex AC magnetic susceptibility (Araujo-Moreira et al 1994, Araujo-Moreira et al 1996, Passos et al 2000, Goldfarb et al 1992. On the other hand, by cooling the sample in the presence of a magnetic field, by following a field-cooling (FC) process, the screening currents are restricted to the intragranular contribution (a situation that remains until the temperature reaches a specific value below which the critical current associated to the intragrain component is no longer equal to zero).…”

Evaluating the critical current magnitude and distribution width of tridimensional Josephson junction arrays

“…Not surprisingly, the numbers obtained for the average critical current density of the 3D-DJJA are comparable to those reported previously for the intergranular critical current of a melt-textured YBa 2 Cu 3 O 7−δ sample 7 , an ordered 2D-JJA of Nb-AlO x -Nb 1 and a 3D-DJJA of YBCO 13 , among others. As could be anticipated, the critical current distribution of the array broadens as T approaches T c , as can be inferred by the continuous decrease of its typical dispersion, p(T ) 7 . A corresponding decrease on the granular fraction, measured by the volume fraction of superconducting grains to the normal matrix, f g , occurs as the superconducting properties degrade with increasing T , weakening at the grain boundaries and, from there, towards the center of the grains.…”

“…For a sample of cylindrical shape of radius a, h p = a < J c >. The exponential critical state model (ECSM) 7 was used to simultaneously fit χ' and χ", from which the temperature dependence of < J c >, its typical distribution width, p(T ), and the granular fraction of the sample, f g (T ), are determined. It is worth mentioning that, as expected, the ECSM fits well the experimental data above hp, but fails to fit the whole curve, as below hp the JJA behavior substitutes that of a critical state.…”

Influence of nonuniform critical current density profile on magnetic field behavior of AC susceptibility in 2D Josephson junction arrays

“…It is worthwhile to mention that in view of Eq. ( 2), in the mixed-state region the above distribution leads to approximately exponential field dependence of the maximum supercurrent I s (T, h AC ) ≃ I s (T, 0)e −hAC/h0 which is often used to describe critical-state behavior in type-II superconductors [12]. Given the temperature dependencies of the London penetration depth λ L (T ) and the Josephson critical current density j c0 (T ), we find h 0 (T ) = Φ 0 /2πµ 0 λ J (T )L ≃ h 0 (0)(1 − T /T C ) 1/4 for the temperature dependence of the characteristic field near T C .…”