Flux Creep in Type-II Superconductors

Abstract

We have made measurements of the evanescent decay of the irreversible magnetization induced by magnetic cycling of solid superconducting cylinders in order to elucidate the mechanisms of Anderson's thermally activated flux-creep process. A superconducting quantum interferometer device coupled to the creep specimen by a superconducting flux transformer made possible observations of flux changes with a resolution of one part in ${10}^9$. The general applicability of Anderson's theory of flux creep was confirmed and the results were analyzed to show that: (1) The total flux in the specimen changed logarithmically in time, i.e., $\Delta \phi \propto \frac{\ln t}{t_0}$. (2) The logarithmic creep rate $\frac{d\phi }{d\ln t}$ is proportional to the critical current density $J_c$ and to the cube of the specimen radius. (3) The logarithmic creep rate appears to be only weakly temperature-dependent because a proportionality to $T$ is nearly compensated by the proportionality to $J_c$, which decreases as $T$ increases. (4) The creep process is a bulk process that is not surface-limited (in this case). (5) Flux enters and leaves the surface in discrete events containing from about one flux quantum up to at least ${10}^3$ flux quanta. (6) On departing from the critical state to a subcritical condition, the creep process tends to remain logarithmic in time, but the rate is decreased exponentially by decreasing $T$ and is decreased extremely rapidly by backing off of the applied field from the critical state. (7) At magnetic fields $H<\mathrm{}{H}_{c1\mathrm{}}$ on the initial magnetization curve, no flux creep was observed, but the logarithmic creep rate showed a modest increase above $H_{c1\mathrm{}}$ and a broad rise as $H$ approached $H_{c2\mathrm{}}$. The creep process is characterized by a dimension parameter $\mathrm{VX}$ consisting of a flux bundle volume $V$ and pinning length $X$, and by an energy $U_0$, both of which are supposed to be material-sensitive parameters characteristic of the irreversible processes. These parameters were determined from the experiments. Bundle volumes $V\approx {10}^{-12\mathrm{}}$ ${\mathrm{cm}}^3$ and energies $U_0\approx 1$ eV were found, indicating that groups of fluxoids must be pinned and must move cooperatively. The results are found compatible with a recent model for flux pinning that includes these cooperative effects.