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 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 T_{cr} wherein a second time scale \tau_{\beta}<<\tau_{\alpha} emerges. The relaxation in the time window set by \tau_{\beta} follows power law which is attributed to self-organization of the magnetic flux during relaxation. Consequently, for T<T_{cr}, a transition from super-critical (current density J>J_{c}) to sub-critical (J<J_{c}) state separated by an intermediate state with frozen dynamics is observed. Both \tau_{\alpha} and \tau_{\beta} diverges at T_{sc}<T_{cr}, marking the transition into a state with true persistent current.