Glassy properties of vortex creep in superconductors

We study a model for the dynamics of vortices in type II superconductors. In particular, we discuss glassy properties and “aging” in magnetic creep. At low temperatures a crossover point is found, Tg, where relaxation times seem to diverge á la Vogel-Tamman-Fulcher. Magnetic creep changes by crossing Tg: above Tg power law creep is found asymptotically followed by stretched exponential saturation; below Tg the creep is logarithmic and vortex motion strongly subdiffusive. Despite apparent structural differences, the dynamics of vortices in superconductors [1–3] has many common features with glass formers such as supercooled liquids, spin glasses or polymers [4,5]. In superconductors even simple quantities such as the sample magnetisation, M , exhibit strong “glassy” behaviours and a variety of “history dependent” effects has been discussed [6]. Common examples are hysteretic magnetisation loops which at low temperature exhibit “memory” effects: the value of M for a given applied field, H , depends on the sweep rate of H , i.e., on the history of the sample. Interestingly, very similar phenomena are found in other glassy systems such as supercooled liquids. For instance, after a quench, “cooling rate” dependences and “aging” effects are usually recorded in particle density measurements [4]. As another signature of dynamical anomalies, in these systems, as much as in vortex matter [3], at low temperatures apparent crossover effects are typically observed in relaxation data [4]. Those similarities are striking when one considers the profound differences which exist at a microscopic level between these systems. One is apparent: the interaction ranges