Magnetic relaxation in hard type-II superconductors

Magnetic relaxation in a type-II superconductor is simulated for a range of temperatures T in a simple model of the 2D Josephson junction array (JJA) with finite screening. The high-T phase, that is characterised by a single time scale $\tau_{\alpha}$, crosses over to an intermediate phase at a lower temperature Tcr wherein a second time scale $\tau_{\beta}\ll\!\tau_{\alpha}$ emerges. The relaxation in the time window set by $\tau_{\beta}$ follows a power law which is attributed to self-organization of the magnetic flux during relaxation. Consequently, for $T<T_{\rm cr}$, a transition from super-critical (current density $J>J_{\rm c}$) to sub-critical ($J<J_{\rm c}$) state separated by an intermediate state with frozen dynamics is observed. Both $\tau_{\alpha}$ and $\tau_{\beta}$ diverge at $T_{\rm sc}