Model for the reversible magnetization of high-κ type-II superconductors: Application to high-Tcsuperconductors

Abstract

A simple theoretical model is proposed for the reversible magnetization of type-II superconductors as a function of the applied field H for the entire field region between ${\mathit{H}}_{\mathit{c}1}$ and ${\mathit{H}}_{\mathit{c}2}$. For H\ensuremath{\simeq}${\mathit{H}}_{\mathit{c}1}$, the theory reduces to a variational model, from which ${\mathit{H}}_{\mathit{c}1}$ can be accurately computed in the Ginzburg-Landau regime. In calculating the free energy, we include, in addition to the supercurrent kinetic energy and the magnetic-field energy, the kinetic-energy and the condensation-energy terms arising from suppression of the order parameter in the vortex core. The model is further extended to include anisotropy by introducing an effective-mass tensor for the case when H is parallel to one of the principal axes. The theory is compared to reversible-magnetization data on a ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$ single crystal. The method permits an accurate determination of ${\mathit{H}}_{\mathit{c}2}$ versus temperature from measurements of the magnetization versus temperature at fixed magnetic field and explains why the measurements have different slopes in different fields, contrary to what might have been expected from the linear Abrikosov formula near ${\mathit{H}}_{\mathit{c}2}$. The deduced ${\mathit{dH}}_{\mathit{c}2}$/dT is (-1.65\ifmmode\pm\else\textpm\fi{}0.23) T/K for H parallel to the c axis near ${\mathit{T}}_{\mathit{c}}$, implying ${\ensuremath{\xi}}_{\mathit{a}\mathit{b}}$(0)=(17\ifmmode\pm\else\textpm\fi{}1) \AA{}.