# Angle-dependent reversible and irreversible magnetic torque in single-crystall

## Abstract

A systematic study of the angle-dependent reversible and irreversible magnetic torque in single-crystalline (Formula presented)(Formula presented)(Formula presented)(Formula presented) is presented. The high purity of the crystals allows us to show some intrinsic pinning properties of vortices due to the layered crystal structure. The irreversible component of the torque, which is unusually small, exhibits a peculiar angular dependence: It is minimal as the magnetic field B is applied along the ab plane and displays a pronounced maximum at finite angles, reminiscent of the “fishtail” effect. The unusual shape of the irreversible torque is attributed to the pinning of the vortex core, which becomes discontinuous below the two- to three-dimensional (2D-3D) crossover temperature. Another property shown by the angle-dependent torque is the lock-in of the vortex lines between the (Formula presented) layers for B parallel to the ab plane. Applying the anisotropic 3D London model to fit the reversible torque data, we derive the in-plane London penetration depth (Formula presented)=143 nm, the coherence length (Formula presented)=1.9 nm, and the effective mass anisotropy ratio γ=12.3 for (Formula presented)(Formula presented)(Formula presented)(Formula presented). © 1996 The American Physical Society.