Bulk critical state and fundamental length scales of superconducting nanocrystallineNb3Alin Nb-Al matrix

Abstract

We present the results of magnetization measurements on an as-cast nanocrystalline ${\text{Nb}}_{3}\text{Al}$ superconductor embedded in Nb-Al matrix. The typical grain size of ${\text{Nb}}_{3}\text{Al}$ ranges from about 2--8 nm with the maximum number of grains at around 3.5 nm, as visualized using transmission electron microscopy. The isothermal magnetization hysteresis loops in the superconducting state can be reasonably fitted within the well-known Kim-Anderson critical-state model. By using the same fitting parameters, we calculate the variation in field with respect to distance inside the sample and show the existence of a critical state over length scales much larger than the typical size of the superconducting grains. Our results indicate that a bulk critical current is possible in a system comprising of nanoparticles. The nonsuperconducting Nb-Al matrix thus appears to play a major role in the bulk current flow through the sample. The superconducting coherence length $\ensuremath{\xi}$ is estimated to be around 3 nm, which is comparable to the typical grain size. The penetration depth $\ensuremath{\lambda}$ is estimated to be about 94 nm, which is much larger than the largest of the superconducting grains. Our results could be useful for tuning the current carrying capability of conductors made out of composite materials which involve superconducting nanoparticles.