We report on electrical magnetoconductivity experiments near the superconducting transition of a granular sample of ${\mathrm{GdBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }.$ The measurements were performed in magnetic fields ranging from 0 to 500 Oe applied parallel to the current orientation. The results show that the transition proceeds in two steps. When the temperature is decreased we first observe the pairing transition, which stabilizes superconductivity within the grains at a temperature practically coincident with the bulk critical temperature $T_c.$ Analysis of the fluctuation contributions to the conductivity shows that the universality class for this transition is that of the three dimensional $\left(3\mathrm{}\mathrm{D}\right)-XY$ model in the ordered case, with dynamic critical exponent $z=3/2.\mathrm{}$ Close to the zero-resistance state, the measurements reveal the occurrence of a coherence transition, where the phases of the order parameter in individual grains become long-range ordered. The critical temperature $T_{\mathrm{co}}$ for this transition is close to the point where the resistivity vanishes. A strong enlargement of the fluctuation interval preceding the coherence transition is caused by the applied magnetic field. In this region, a 3D-Gaussian regime and an asymptotic critical regime were clearly identified. The critical conductivity behavior for the coherence transition is interpreted within a $3\mathrm{D}-XY$ model where disorder and frustration are relevant. The irreversibility line is determined from magnetoconductivity measurements performed according to the zero-field-cooled (ZFC) and field-cooled data collected on cooling (FCC) recipes. The locus of this line coincides with the upper temperature limit for the fluctuation region above the coherence transition. The irreversibility line is interpreted as an effect of the formation of small clusters with closed loops of Josephson-coupled grains.

• Received 14 September 1999

DOI:https://doi.org/10.1103/PhysRevB.61.12457