Elastic and plastic behavior of a fluxoid lattice in the saturation region of the global pinning force in superconducting Nb-Ta

We investigate the elastic and plastic behavior of the fluxoid lattice in the saturation region of the global pinning-force density using the ac technique. The specimens were Nb-50-at. % Ta deformed by various amounts. The elastic modulus α obtained from the force-distance profile increased with the pinning strength and decreased gradually with increasing magnetic field. No remarkable change in α was observed between the saturation region near the upper critical field and the nonsaturation one at lower fields. This reveals that fluxoids were prevented from flowing by the pinning forces but not by the shear force of the fluxoid lattice even in the saturation region as assumed in Kramer’s model. On the other hand, the interaction distance $d_i$, the displacement necessary for fluxoids to be depinned, changed drastically between the two regions: It decreased abruptly with the magnetic field in the saturation region. Values of $d_i$ in this region decreased with the pinning strength. The abrupt decrease of $d_i$ indicates that the fluxoid lattice becomes more fragile with increasing magnetic field and that a transition to the resistive state is initiated by a catastrophic flow of the whole fluxoid lattice. In this paper the authors propose that the catastrophic global flux flow in the saturation region is caused by the occurrence of a local plastic deformation of the fluxoid lattice. Local plastic deformations are expected to be induced around defects of the fluxoid lattice which already exist before an application of the driving force. In this model, the probability of occurrence of a plastic deformation is assumed to be proportional to the concentration of fluxoid-lattice defects. This model explains qualitatively the present experimental results as well as the magnetic field dependence of the global pinning-force density known as Kramer’s formula.