First-Order Melting and Dynamics of Flux Lines in a Model for YBa$_2$Cu$_3$O$_{7-\delta}$

TL;DR

This study investigates the melting and dynamics of flux lines in YBa$_2$Cu$_3$O$_{7-}$ using simulations, revealing a weakly first-order melting transition and the effects of disorder on flux line relaxation.

Contribution

It provides a comparative analysis of Monte Carlo and Langevin dynamics for flux line melting, and explores the impact of disorder on flux line relaxation in YBCO.

Findings

Melting is weakly first order with a small heat of fusion.

Qualitative change in magnetic field distribution at freezing matches experiments.

Disorder induces a logarithmic relaxation due to disclination dynamics.

Abstract

We have studied the statics and dynamics of flux lines in a model for YBCO, using both Monte Carlo simulations and Langevin dynamics. 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 $0.02 k_BT_m$ per vortex pancake at a field of $50 {\rm kG}.$ 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 $\mu {\rm SR}$ experiments. Melting in the clean system is accompanied by a proliferation of free disclinations which show a clear B-dependent 3D-2D crossover from long disclination lines parallel to the c-axis at low fields, to 2D ``pancake'' disclinations at higher fields. Strong point pins produce a logarithmical $\ln t$ relaxation which results from slow annealing out of disclinations in disordered samples.