Modeling electron-spin accumulation in a metallic nanoparticle

A model describing spin-polarized current via discrete energy levels of a metallic nanoparticle, which has strongly asymmetric tunnel contacts to two ferromagnetic leads, is presented. In absence of spin relaxation, the model leads to a spin accumulation in the nanoparticle, a difference between the chemical potentials of spin-up and spin-down electrons, proportional to the current and the Julliere tunnel magnetoresistance. Taking into account an energy dependent spin-relaxation rate , as a function of bias voltage V exhibits a crossover from linear to a much weaker dependence, when e equals the spin-polarized current through the nanoparticle. Assuming that the spin relaxation takes place via electron-phonon emission and Elliot-Yafet mechanism, the model leads to a crossover from linear to V1/5 dependence. The crossover explains recent measurements of the saturation of the spin-polarized current with V in aluminum nanoparticles, and leads to the spin-relaxation rate of 1.6 MHz in an aluminum nanoparticle of diameter 6 nm, for a transition with an energy difference of one level spacing.