Superconductors with anisotropic critical-current density j(c) exhibit characteristic anisotropic flux-density patterns during penetration of magnetic flux. We investigate this anisotropic flux penetration in detail by observations using the magneto-optical Faraday effect and by first-principles calculations which describe the superconductor as a nonlinear anisotropic conductor. Our samples are thin plates of DYBa2Cu3O7-delta into which anisotropic pinning is introduced by oblique irradiation with 340-MeV Xe ions creating linear defects. Excellent agreement between experiment and theory is obtained. In particular, we find that in rectangular plates with j, anisotropy equal to the side ratio, the intrinsic and shape anisotropies may compensate such that the flux pattern looks like that in an isotropic square stretched to the rectangular shape. This means the current streamlines are concentric rectangles which shrink to a point rather than to a line, and the discontinuity lines where the current bends sharply, coincide with the diagonals of the rectangle rather than forming the usual double-Y structure.

The penetration of magnetic flux into flat type-II superconductors of various shapes in a perpendicular magnetic field is investigated in detail. The magnetic field distribution at the sample surface is observed by the magneto-optical Faraday effect and calculated from first principles. The investigations are performed on ${\mathrm{DyBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ and ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ samples which were shaped into a cross or an indented rectangle by a laser-cutting technique. Magnetic and electric field and current distributions are calculated from Maxwell's equations treating the superconductor as a conductor with a highly nonlinear current-voltage law and zero reversible magnetization. A large concentration of magnetic flux and electric field and a high flux-line velocity occur at concave sample corners. This results from the fact that the flux lines can penetrate into regions of the sample which are bounded by the extensions of the sample edges only at these points. This large electric field and related energy dissipation are particularly relevant for superconducting tapes, in which ``sausaging'' effects (variations of the filament cross section) reduce their performance as an ideal conductor. Huge jumps of the electric field occur where the current flow changes from a straight to a circular path. This jump diverges as one over the distance to the corner at sharp indents or concave corners. \textcopyright{} 1996 The American Physical Society.

Magnetic-relaxation measurements M(t, T) have been carried out on DyBa2Cu3O7-delta single crystals before and after irradiation with 340 MeV Xe ions. The data are analyzed within the framework of first-order kinetics assuming a distribution of activation energies. The results are in good agreement with the assumption, that the most important pinning mechanism is given by the core interaction of pancake vortices or short sections of a flux line with defects. The irradiation-induced enhancement of the average activation energies of just about 70% can be explained by the broadening of the flux-line core if the flux line is located in the amorphous channels with radius R > xi caused by irradiation damage.

Using capacitance torque magnetometry, hysteresis loops were measured on a Pb-ion irradiated DyBa2Cu3O7−δ single crystal as a function of magnetic field, temperature and angle Θ between the field direction and the c axis of the sample. The superconducting current densities, jc (T, B, Θ), determined using the extended Bean model, show a clear fishtail effect at temperatures above 30 K despite the large enhancement of jc due to the columnar tracks. The enhancement of jc due to irradiation was magneto-optically determined to jc(φt)/jc(0) = 10 at T = 30 K. The pinning energy U0 is, however, only slightly increased by the irradiation. Our measurements indicate clearly that the fishtail effect is a general feature of the high-Tc superconductors and not related to a special arrangement of pinning centres.

Using the high-resolution Faraday effect (HRF) technique, flux distributions of sintered, granular YBa2Cu3O7−δ samples are obtained. The flux penetration is found to occur stepwise and only the last step of the penetration of Abrikosov vortices into individual grains can be observed directly. The high spatial resolution of the HRF technique enables one to determine the flux-density profiles inside individual grains. From these profiles, the intragranular critical current densities and acting local pinning forces are obtained. The intragranular critical current densities and the corresponding volume pinning forces are found to be reciprocally dependent on the grain size. This behavior could be explained by pinning at the grain boundaries between superconducting YBa2Cu3O7−δ grains and non-superconducting phases like BaCuO2 assuming a disturbed layer Δx with a thickness of approximately 0.1 μm. Furthermore, the influence of melt processing on the weak-link behavior can be directly observed in the flux distributions. Melt-processed samples are found to show an intermediate behavior of flux penetration between sintered, polycrystalline samples and single-crystalline materials like single crystals and epitaxial thin films. It is shown that the parameter γ=Hgcl/HJcl, linking the lower critical field of the grains, Hgcl, to the lower critical field of the matrix, HJcl, has a significant influence on the flux-penetration behavior in type-II superconductors.

The anisotropy of the critical current density introduced in the (a, b) plane of DyBa2Cu3O7-delta single crystals by oblique irradiation with heavy ions is observed by magneto-optics. The pinning forces on vortices oriented perpendicular to the (a, b) plane are largest when directed perpendicular to the columnar defects. Two modes of vortex motion are considered. Effects of flux creep and thermal depinning on the critical current density are discussed.

Using the high-resolution Faraday effect (HRF) technique, flux distributions of sintered, granular YBa2Cu3O7-delta samples are obtained. The flux penetration is found to occur stepwise and only the last step of the penetration of Abrikosov vortices into individual grains can be observed directly. The high spatial resolution of the HRF technique enables one to determine the flux-density profiles inside in&vidual grains. From these profiles, the intragranular critical current densities and acting local pinning forces are obtained. The intragranular critical current densities and the corresponding volume pinning forces are found to be reciprocally dependent on the grain size. This behavior could be explained by pinning at the grain boundaries between superconducting YBa2Cu3O7-delta grains and non-superconducting phases like BaCuO2 assuming a disturbed layer DELTAx with a thickness of approximately 0.1 mum. Furthermore, the influence of melt processing on the weak-link behavior can be directly observed in the flux distributions. Melt-processed samples are found to show an intermediate behavior of flux penetration between sintered, polycrystalline samples and single-crystalline materials like single crystals and epitaxial thin films. It is shown that the parameter gamma=H(c1)g/H(c1)J, linking the lower critical field of the grains, H(c1)g, to the lower critical field of the matrix, H(c1)J, has a significant influence on the flux-penetration behavior in type-II superconductors.

The current progress of magneto-optical techniques for direct investigations of magnetic flux structures in type-II superconductors with high spatial resolution is presented. Wide possibilities are offered by the high-resolution Faraday effect technique requiring a thin layer of EuSe as an indicator and the method using ferrimagnetic garnet films with in-plane anisotropy. The advantages of both methods are combined to investigate flux structures of an YBa2Cu3O7 (YBCO) thin film partly irradiated with 25 MeV oxygen ions and for inhomogeneously twinned YBCO single crystals.

The high resolution Faraday effect requires a magneto-optical active thin film coating for observations of penetrated flux in superconductors. The use of EuSe for this coating offers many advantages, such as better handling during the evaporation process and a higher achievable contrast compared to the 'classical' mixture of EuS and EuF2. In this paper the apparatus is described and the conditions discussed for achieving optimal thickness of the magneto-optical layer. This technique was used for observations of penetrating flux in niobium and in the high T(c) superconductors YBa2Cu3O7-delta-(single crystals, sintered specimens and epitaxial thin films) and Bi2Sr2CaCu2O8-delta-single crystals.