Reversible magnetization and torques in anisotropic high-κ type-II superconductors

Abstract

The reversible magnetization of anisotropic high-\ensuremath{\kappa} type-II superconductors in an applied field H of arbitrary orientation with respect to the principal axes of the sample is considered in the framework of the Ginzburg-Landau theory with an anisotropic effective mass. We examine the procedure of obtaining the free-energy density F from its corresponding expression in the isotropic case by simply replacing the Ginzburg-Landau parameter \ensuremath{\kappa} by a \ensuremath{\kappa}\ifmmode \tilde{}\else \~{}\fi{} that depends on the orientation of H relative to the principal axes. This procedure is valid when H is along one of the principal axes for arbitrary values of H between ${\mathit{H}}_{\mathit{c}1}$ and ${\mathit{H}}_{\mathit{c}2}$ and is also valid to a good approximation when H is not along one of the principal axes, but only when H\ensuremath{\gg}${\mathit{H}}_{\mathit{c}1}$. Because of the dependence of F on the orientation of H, when H is not parallel to one of the principal axes, the average magnetic-flux density B is not parallel to H, and a torque associated with the transverse magnetization exists, tending to orient the sample so that the value of \ensuremath{\kappa}\ifmmode \tilde{}\else \~{}\fi{} is the largest. Expressions for the magnetization and the torque are obtained from a variational model that permits the analytic calculation of F in the Ginzburg-Landau regime including, 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. It is also pointed out that a comparison of the present theory with torque measurements can provide a way to estimate the upper critical field ${\mathit{H}}_{\mathit{c}2}$(\ensuremath{\theta},\ensuremath{\varphi}), the thermodynamic field ${\mathit{H}}_{\mathit{c}}$, and the ratio ${\mathit{m}}_{1}$:${\mathit{m}}_{2}$:${\mathit{m}}_{3}$ (${\mathit{m}}_{\mathit{i}}$, i=1,2,3, are the principal values of the effective-mass tensor ${\mathit{m}}_{\mathit{i}\mathit{j}}$) in the temperature region where the Ginzburg-Landau theory is appropriate.