Spin injection, accumulation, and precession in a mesoscopic nonmagnetic metal island

We experimentally study spin accumulation in an aluminum island with all dimensions smaller than the spin-relaxation length, so that the spin imbalance throughout the island is uniform. Electrical injection and detection of the spin accumulation are carried out in a four-terminal geometry by means of four cobalt electrodes connected to the island through tunnel barriers. We model the system theoretically and we investigate the role of the ferromagnetic electrodes on the spin accumulation at the limit at which the electron diffusion time can be neglected. We present measurements of spin accumulation at room temperature and at $4.2\mathrm{K}$: in both cases the spin accumulation signal is larger than the Ohmic resistance of the aluminum island. From magnetization precession measurements at room temperature, we extract a spin-relaxation time ${\tau }_{sf}=60\mathrm{ps}$ and a polarization $P=8\%$ for tunnel barriers with resistances as low as $20\Omega \mu {\mathrm{m}}^2$. We show that the precession measurements are invariant under the interchange of voltage and current electrodes, and under the reversal of magnetic fields and magnetizations, according to the reciprocity theorem. We show that spin accumulation and spin precession in a system with uniform magnetization can be described in terms of the (relative) orientation of the ferromagnetic contacts’ magnetizations and we determine from precession measurements the angles between the magnetization direction of the contacts.