Angle-Dependent Reversible and Irreversible Magnetic Torque in Single-Crystalline Y$_2$Ba$_4$Cu$_8$O$_{16}$

A systematic study of the angle-dependent reversible and irreversible magnetization in single-crystalline Y$_2$Ba$_4$Cu$_8$O$_{16}$ is presented. For temperatures far below $T_{\rm c}$, the irreversible component of the torque is largely suppressed, but exhibits an anomalous angular dependence having minimal irreversibility for the field $B$ applied along the $ab$-plane. This unusual behavior is interpreted in terms of a model that considers the strong pinning anisotropy of vortex segments parallel and perpendicular to the intrinsic layered crystal structure. The weak pinning present in the clean sample gives rise to an anomalous reversible torque for the applied field close to the $ab$-plane, which is associated with lock-in of flux lines between the CuO$_2$ layers. Furthermore, the in-plane penetration depth $\lambda_{ab}=143$~nm, the coherence length $\xi_{ab} = 1.92$~nm and the effective mass anisotropy ratio $\gamma = 12.3$, have been derived from the angle-dependent reversible torque data.