Angular dependence of the magnetization of isotropic superconductors: which is the vortex direction?

We present studies of the dc magnetization of thin platelike samples of the isotropic type II superconductor PbTl(10%), as a function of the angle between the normal to the sample and the applied magnetic field ${\bf H}$. We determine the magnetization vector ${\bf M}$ by measuring the components both parallel and normal to ${\bf H}$ in a SQUID magnetometer, and we further decompose it in its reversible and irreversible contributions. The behavior of the reversible magnetization is well understood in terms of minimization of the free energy taking into account geometrical effects. In the mixed state at low fields, the dominant effect is the line energy gained by shortening the vortices, thus the flux lines are almost normal to the sample surface. Due to the geometrical constrain, the irreversible magnetization ${\bf M}_{irr}$ remains locked to the sample normal over a wide range of fields and orientations, as already known. We show that in order to undestand the angle and field dependence of the modulus of ${\bf M}_{irr}$, which is a measure of the vortex pinning, and to correctly extract the field dependent critical current density, the knowledge of the modulus and orientation of the induction field ${\bf B}$ is required.