Labusch parameter of flux line lattice with planar pinning centers

Abstract

Field dependence of the Labusch parameter α L v ( B ) is calculated for vortex arrays assuming planar pinning defects parallel to the vortices, taking into account the discreteness of the vortex lattice, i.e. beyond the framework of the elasticity theory. Considering both compressional and shear vortex oscillations the distribution of the vortex displacements are obtained. For the compressional case a region of instability is found near the vortex pinning layers. This region is important for determination of α L v ( B ) . In contrast, the distribution of the vortex displacements for the shear oscillations is smooth and independent of the field. This results in saturation of α L v ( B ) at high fields. Considering also nonlinear effects the dependence of α L v on the vortex displacement is obtained up to displacements where depinning of the vortices occurs.