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

TL;DR

This study investigates how the magnetization vector in isotropic type II superconductors depends on the angle of the applied magnetic field, revealing the importance of vortex orientation and geometrical effects in understanding magnetization behavior.

Contribution

It provides a detailed analysis of the angular dependence of magnetization and vortex orientation in isotropic superconductors, emphasizing the role of geometrical constraints and vortex pinning.

Findings

Vortices tend to align normal to the surface at low fields.

Irreversible magnetization remains locked to the sample normal over various conditions.

Understanding the induction field's orientation is crucial for analyzing vortex pinning.

Abstract

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.