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

Abstract

The reversible magnetization of anisotropic high-κ 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 κ by a κ̃ 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 Hc1 and Hc2 and is also valid to a good approximation when H is not along one of the principal axes, but only when H≫Hc1. 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 κ̃ 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 Hc2(θ,φ), the thermodynamic field Hc, and the ratio m1:m2:m3 (mi, i=1,2,3, are the principal values of the effective-mass tensor mij) in the temperature region where the Ginzburg-Landau theory is appropriate.