Cooperative flux pinning in single crystals of YBa2Cu3O7- delta.

Abstract

We have investigated thermally activated magnetic flux creep in single crystals of superconducting ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ in the low-field, low-temperature regime of the H,T phase diagram where flux motion is expected to occur via individual fluxoid jumps. Between 5 and 15 K the creep data are accurately described by a current-dependent activation barrier of the form U(j)\ensuremath{\propto}${\mathit{j}}^{\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\mu}}}$, with \ensuremath{\mu}=1.20\ifmmode\pm\else\textpm\fi{}0.12. The functional form for U(j) can be understood within the framework of cooperative pinning models that ascribe fluxoid pinning to the collective effects of a large number of weak-pinning defects. We argue that the appropriate extension of scaling arguments to the ``individual fluxoid'' regime implies \ensuremath{\mu}\ensuremath{\approxeq}1.0, as measured. Some successful features of the model include (1) a natural interpretation for the measured ``four-volume'' VX, the volume of the moving flux bundle times the mean distance to the pinning barrier (this interpretation leads to a value for the length of a fluxoid segment that can move in a single activated jump; the shortest length observed in our experiments is approximately 75 nm); (2) an explicit correction for the temperature dependence of U(j) that agrees with experiment; (3) a physically plausible value for the ``flux velocity'' ${\mathit{v}}_{\mathit{f}}$\ensuremath{\approxeq}1000 m/sec; and (4) a satisfactory description of the temperature dependence of the ``critical current'' ${\mathit{j}}_{\mathit{c}}$ between 5 and 15 K. For self-consistency the concentration of pinning defects must be greater than 3\ifmmode\times\else\texttimes\fi{}${10}^{19}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$, and oxygen vacancies are the likely candidates. The results strongly confirm that a simple collective pinning model of individual fluxoids accurately describes the basic physics of the creep process in ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ in the region of phase space investigated here. \textcopyright{} 1996 The American Physical Society.