Current densities $j_s$ and volume pinning forces $F_p$ are obtained in a wide temperature $(5\mathrm{}<~T<~92\mathrm{K})$ and field range $(0\mathrm{}<~{\mu }_0{H}_a<~9\mathrm{T})$ on different ${\mathrm{NdBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ samples. Above 60 K a good scaling of the volume pinning force $F_p$ versus the reduced field ${h=H}_a{/H}_{\mathrm{irr}}$ can be established. The scaled pinning curves are compared to several theoretical predictions. Experimental evidence for strong pinning at extended superconducting defects (interaction volume $V_{\mathrm{pin}}\sim {\xi }^{2}d$) is given. These defects are ascribed to spatial composition fluctuations found in light rare-earth superconductors, providing a scatter of the transition temperature $T_c.$ Such a pinning mechanism is especially important for applications of high-$T_c$ superconductors operating at $T=77\mathrm{}\mathrm{K}.$

In this paper, magneto-optical observations and analyses of skeleton structures of flux distributions in type-II superconductors are presented. It will be shown that these structures are formed by lines where the critical current is bending. Such lines are a characteristic feature of a vortical vector field if the absolute value of the vector is constant as for the current distribution in a type-II superconductor in the full critical state. Thin samples offer enhanced sensitivity to observe these current discontinuity lines magneto-optically due to two facts: The Meissner phase contracts to these lines and remains there up to fields, which are higher than the full penetration field ${\mathit{H}}^{\mathrm{*}}$. At much higher magnetic fields, when the Meissner phase has vanished, the logarithmic infinity of the magnetic flux density at these lines leads to sufficiently high contrast. The positions of the discontinuity lines are not affected directly by particular defects, but are determined by the shape of the sample. Because the vortices are not able to cross these lines, the current discontinuity lines determine the flux distribution in the superconductor like a magnetic skeleton. An analysis of the observed structures yields characteristic parameters of the sample as anisotropy, inhomogeneity, or irradiation-induced enhancement of the critical current density. Additionally, the presence of defects allows the observation of the direction of flux motion and, thus, to visualize directly the current distribution. A strong concentration of flux motion near defects without any pecularities of the current and magnetic flux distribution can be predicted using the consideration presented in this paper.

The scaling and relaxation behavior around the fishtail minimum is studied in detail in a wide temperature range (3–70 K) on ${\mathrm{DyBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ single crystals exhibiting a pronounced fishtail effect. Magnetic hysteresis loops (MHL's) normalized with respect to the height and position of the fishtail maximum fall on a universal curve which form can be derived from the phenomenological model of a thermally activated flux creep proposed by Perkins et al. [Phys. Rev. B 51, 8513 (1995)]. This universal curve tends at low fields towards zero. At low temperatures, the drop of ${\mathrm{j}}_{\mathrm{s}}$ at low fields is usually masked by a wide central peak. By subtracting the universal curve from the experimental ${\mathrm{j}}_{\mathrm{s}}$(B) data we separate the contribution of the central peak. It has a simple, exponentially decaying field dependence. This implies that the fishtail minimum at low fields might be understood as a result of an overlapping of two contributions originating from separate pinning mechanisms: one active mainly at high fields and dying away with B going to zero and another one (responsible for the central peak of the MHL) vanishing rapidly with increasing field. This concept is also supported by relaxation experiments. These experiments confirm that the shape of MHL's is given by a dynamic equilibrium between the induction, pinning, and relaxation processes.