MAGNETIZATION OF TYPE-Ⅱ SUPERCONDUCTORS. VARIATIONAL WIGNER-SEITZ APPROXIMATION

摘要

We proposed an approximate method to solve the Ginzburg-Landau equations for the regular flux-line lattice at any values of the magnetic induction and the Ginzburg-Landau parameter. The Wigner-Seitz approximation is used, and the local order parameter within the unit cell is approximated by the trial function. The use of this function allows us to find the magnetic flux density self-consistently from the second Ginzburg-Landau equation. The comparison between the variational results and the results of exact numerical solution of the Ginzburg-Landau equations reveals good accuracy of our approach. An analytical expression for the reversible magnetization is proposed. At low fields, the obtained dependence agrees with the predictions of London theory at κ 1. At high fields, it is in good agreement; with the Abrikosov result. It is shown that the values of the magnetization calculated within the framework of our variational model and of the numerical method of solution to the Ginzburg-Landau equations are close. The presented analytical formulas for the magnetization may be used to analyze experimental data. As an illustration we compared the experimental and calculated magnetization curves for different high-T_c superconductors (YBa_2Cu4O_8 and Nd_(1.85)Ce_(0.15)CuO_(4-δ)) and found good agreement between theory and experiment.