Implications of magnetic-hysteresis-loop scaling in high-temperature superconductors

We show how to incorporate the commonly observed scaling behavior of magnetic hysteresis loops M(H) in (R)${\mathrm{Ba}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ (R=rare earth) crystals into a systematic and straightforward analytical procedure that yields the key parameters associated with the vortex dynamics. If the effective barrier height for vortex motion is written in terms of a scale energy ${\mathit{U}}_0$(B,T) and a scale current density ${\mathit{J}}_0$(B,T), both the field and temperature dependences of these quantities can be found directly from the experimental data, without any deconvolution. The procedure is illustrated with the data on one specific sample of ${\mathrm{TmBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$. Over a substantial region of the B-T plane, ${\mathit{J}}_0$(B,T) is found to be ∝B and essentially temperature independent; ${\mathit{U}}_0$(B,T) is approximately ∝1/B and decreases steadily as ${\mathit{T}}_{\mathit{c}}$ is approached. The competition between the field dependences of ${\mathit{J}}_0$(B,T) and ${\mathit{U}}_0$(B,T) gives rise to the ubiquitous ‘‘fishtail’’ in the magnetization loops.