Zeeman Splitting and Spin-Orbit Torques in Single Ni Nanoparticles
We discuss measurements of discrete electron-in-a-box levels in Ni nanoparticles, using tunneling spectroscopy at 0.06K temperature. We use the amplitudes of the Zeeman-split levels to obtain the spin-transfer rate associated with sequential electron tunneling. In a strong magnetic field, the spin and the charge transfer rates are comparable, which demonstrates strong enhancement compared to the Slonczewski form of spin-transfer torque. In a low magnetic field, the discrete levels broaden into energy bands. The bandwidth is comparable to the spin-orbit energy $\epsilon_{so}\approx$ 0.6meV. The bands are interpreted in terms of the spectra of magnetic excitations close in energy and the van Hove singularity in their density of states, driven by mesoscopic spin-orbit torques. In those circumstances, the effective spin-transfer rate is far higher than the charge-transfer rate.