Magnetization decay in high-Tcsuperconductors analyzed as a simple two-dimensional trapping problem

A simple statistical treatment which assumes that vortices may be trapped and eliminated by a network of nonsuperconducting walls separating cells of superconductor material in ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ is able to provide an explanation for (i) the essentially time-logarithmic decay of the magnetization at low temperatures; (ii) clear deviations from a strict time-logarithmic law at high temperatures; and (iii) the presence—or absence—of a minimum in the plot of the relative magnetization relaxation rate against temperature, depending on the wall thickness and cell size of the network. Possible extension of the model to other ceramic superconductors is also discussed.