Exponential $H$ and $T$ decay of the critical current density in $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ single crystals

We report magnetic measurements on single crystals of $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$. The magnetic critical current density in the Cu-O basal planes (1.5×${10}^6$ A/${\mathrm{cm}}^2$ at 4.2 K) decreases exponentially with temperature as well as with field for $T\gtrsim 50$ K. This is ascribed to current tunneling through micro-Josephson-junctions. The behavior is radically different from that associated with macro-junctions typical of "granular" samples. It is argued that the anisotropy and the $T-H$ anomalous behavior of $J_c$ are connected with the $T$ dependence and the anisotropy of both the coherence length and the electron mean free path.