Effect of microstructure on the magnetic-field dependence of the local critical current density in ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ superconductors

A contactless method for determining the local critical current density ${\mathit{J}}_{\mathit{c}}$(B) and the effective magnetic permeability of μ of ceramic superconductors is presented. Using this method we have carried out systematic investigations of the magnetic field and temperature dependence of the local critical current density in ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ samples with different microstructures. The results show that the character of Josephson junctions in sintered ceramics changes as a function of heat treatment temperature. In spite of the differences in the values of ${\mathit{J}}_{\mathit{c}}$(B) and in the types of Josephson junctions, the dependence of ${\mathit{J}}_{\mathit{c}}$(B) for various kinds of ceramics has a common universal behavior. Using a scaling procedure it is possible to plot all experimental values of ${\mathit{J}}_{\mathit{c}}$(B), obtained for samples prepared by solid-state sintering, on a single curve. At low magnetic fields this universal function is nearly constant with field and at higher fields it varies as ${\mathit{B}}^{\mathrm{-}3/2}$. The universal behavior of ${\mathit{J}}_{\mathit{c}}$(B) breaks down as the field exceeds the first critical magnetic field of the grains, when the function ${\mathit{J}}_{\mathit{c}}$(B) approaches a constant value. The universal behavior is completely defined by the critical current properties of individual Josephson junctions, a set of which forms the network of weak links in ceramics. Flux pinning therefore does not need to be considered when describing the current carrying capabilities of isotropic sintered ceramics which are weak linked. Analogous universal properties of ${\mathit{J}}_{\mathit{c}}$(B) are observed in nontextured samples prepared by melt-processing technology.