Modelling Electron Spin Accumulation in a Metallic Nanoparticle

TL;DR

This paper presents a model for electron spin accumulation in metallic nanoparticles with asymmetric contacts, explaining experimental saturation effects and estimating spin-relaxation rates.

Contribution

It introduces a novel model incorporating energy-dependent spin-relaxation, explaining the crossover in spin accumulation behavior and matching recent experimental data.

Findings

Crossover from linear to V^{1/5} dependence of spin accumulation.

Estimated spin-relaxation rate of approximately 1.6 MHz in 6nm Aluminum nanoparticles.

Explains saturation of spin-polarized current with bias voltage.

Abstract

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 ($\Delta\mu$) between the chemical potentials of spin-up and spin-down electrons, proportional to the current and the Julliere's tunnel magnetoresistance. Taking into account an energy dependent spin-relaxation rate $\Omega (\omega)$, $\Delta\mu$ as a function of bias voltage ($V$) exhibits a crossover from linear to a much weaker dependence, when $|e|\Omega (\Delta\mu)$ 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 $V^{1/5}$ 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 $\approx 1.6 MHz$ in an Aluminum nanoparticle of diameter $6nm$, for a transition with an energy difference of one level spacing.