Effects of field-sweep rate on the magnetization of melt-textured ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$

The effects of field-sweep rate K=∂H/∂t on magnetization hysteresis loops M(H) and on flux-creep studies M(t) in high-temperature superconductors have been investigated both theoretically and experimentally. We find the basic relation between M and K is, to first order, the following: M=const-{[dM/d ln(t)] ln(K)}-[${\mathit{Kt}}_{\mathit{e}\mathit{f}\mathit{f}}$/10], where dM/d ln(t)=aC/30 is the flux-creep rate in a cylindrical sample of radius a, and ${\mathit{t}}_{\mathit{e}\mathit{f}\mathit{f}}$ is an effective attempt time for vortex hopping. The largest possible M, which corresponds to the critical current density ${\mathit{J}}_{\mathit{c}0}$ in the absence of thermal activation, develops when K≥${\mathit{K}}_{\max }$=aC/[(1+aα)${\mathit{t}}_{\mathit{e}\mathit{f}\mathit{f}}$] with α=∂J/∂H. The time origin of flux creep, which is essential in studying the initial stages of relaxation, is given by ${\mathit{t}}^{\mathrm{*}}$=aC/K(1+aα). The model agrees well with experiments on a melt-textured-growth sample of ${\mathrm{Y}}_1$ ${\mathrm{Ba}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$, yielding ${\mathit{t}}_{\mathit{e}\mathit{f}\mathit{f}}$∼0.24±0.03 s at 27 K. By incorporating the calculated time origin into flux-creep studies of M(t), we obtain a very good description in terms of the interpolation formula from vortex-glass–collective pinning theory.