Magnetization scaling on thick ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathit{x}}$ single crystals

Magnetic-hysteresis curves of ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathit{x}}$ single crystals are found to exhibit scaling features. The scaling parameters, the full penetration field ${\mathit{H}}_{\mathit{p}}$, and the associated magnetization ${\mathit{M}}_{\mathit{p}}$, are determined experimentally as the merging point between the virgin magnetic curve and the M-H loop envelope. Scaling is performed by dividing M and H by ${\mathit{M}}_{\mathit{p}}$ and ${\mathit{H}}_{\mathit{p}}$, respectively. For magnetic fields higher than ${\mathit{H}}_{\mathit{p}}$, the M-H loops, once scaled, lie on a unique envelope, independent of temperature up to the irreversibility line. This result suggests that there is no evidence of any phase transition for H>${\mathit{H}}_{\mathit{p}}$. This scaling has been performed on the data obtained for two ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathit{x}}$ single crystals, one oxygenated under atmospheric pressure and the other one under high oxygen pressure. The results have shown that pinning in the latter crystal is more effective at intermediate magnetic fields, H∼${\mathit{H}}_{\mathit{p}}$, but less effective at fields H significantly higher than ${\mathit{H}}_{\mathit{p}}$.