First-order melting and dynamics of flux lines in a model for YBa2Cu3O7- delta.

Abstract

We have studied the statics and dynamics of flux lines in a model for ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$, using both Monte Carlo simulations and Langevin dynamics. The lines are assumed to be flexible but unbroken in both the solid and liquid states. For a clean system, both approaches yield the same melting curve, which is found to be weakly first order with a heat of fusion of about 0.02${\mathit{k}}_{\mathit{BT}\mathit{m}}$ per vortex pancake at a field of 50 kG. The time-averaged magnetic field distribution experienced by a fixed spin is found to undergo a qualitative change at freezing, in agreement with NMR and muon spin resonance experiments. The calculations yield, not only the field distribution in both phases, but also an estimate of the measurement time needed to distinguish these distributions: We estimate this time as \ensuremath{\ge}0.5 \ensuremath{\mu}sec. The magnetization relaxation time in a clean sample slows dramatically as the temperature approaches the mean-field upper critical field line ${\mathit{H}}_{\mathit{c}2}$(T) from below. Melting in the clean system is accompanied by a proliferation of free disclinations and a simultaneous disappearance of hexatic order. Just below melting, the defects show a clear magnetic-field-dependent two- to three-dimensional crossover from long disclination lines parallel to the c axis at low fields, to two-dimensional ``pancake'' disclinations at higher fields. Strong point pins produce an energy varying logarithmically with time. This lnt dependence results from slow annealing out of disclinations in disordered samples. Even without pins, the model gives subdiffusive motion of individual pancakes in the dense liquid phase, with mean-square displacement proportional to ${\mathit{t}}^{1/2}$ rather than to t as in ordinary diffusion. The calculated melting curve and many dynamical features agree well with experiment. \textcopyright{} 1996 The American Physical Society.