Zero dimensional superconducting fluctuations and fluctuating diamagnetism in lead nanoparticles

High-resolution superconducting quantum interference device magnetization measurements in lead nanoparticles with particle size d less than the superconducting coherence length xi are used to study zero-dimensional fluctuating diamagnetism. The diamagnetic magnetization M-dia (H, T=const) as a function of the applied magnetic field H at constant temperature is reported in the critical region and compared with the observed behavior in the temperature range where the first-order fluctuation corrections are expected to hold. The magnetization curves are analyzed in the framework of exact fluctuation theories based on the Ginzburg-Landau functional for xi > d. The role of the upturn field H-up, where the slope of M-dia (H) changes sign, is discussed. The relevance of the magnetization curves over a wide range of magnetic fields and the role of H-up for the study of fluctuating diamagnetism, in particular, when the first-order fluctuation correction breaks down, is pointed out. The size and temperature dependences of H-up in the critical region are obtained from the experimental data and compared to the theoretical derivations for M-dia.