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 ξ are used to study zero-dimensional fluctuating diamagnetism. The diamagnetic magnetization Mdia (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 ξ⪢d. The role of the upturn field Hup, where the slope of Mdia (H) changes sign, is discussed. The relevance of the magnetization curves over a wide range of magnetic fields and the role of Hup 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 Hup in the critical region are obtained from the experimental data and compared to the theoretical derivations for Mdia.