Analysis of 3-terminal Hanle signals in Si-based spintronic devices

We have investigated 3-terminal Hanle (3TH) signals and inverted 3-terminal Hanle (Inv3TH) signals [1] obtained in a temperature range of 5 -- 300 K in devices with a Si channel and Fe/SiO$_{2}$/Si tunnel junctions. The Hanle signals were measured with a magnetic field applied in various directions from parallel (Inv3TH) to normal (3TH) to the plane. The shape of the 3TH signals was a positive Lorentzian, whereas that of the Inv3TH signals was composed of two negative Lorentzians whose centers are at around $\pm$ 1000 Oe. We analyzed the signals using the Eq.(2) in [1], in which the effective magnetic field acting on electron spins is assume to be composed of the following fields; an applied field, a constant stray field, and a stray field proportional to the magnetization of the Fe electrode. Note that the last two fields are introduced in the present analysis. All the experimental signals in any applied field directions were well fitted by the formula. From the fitting parameters at various measurement temperatures, we found that the FWHM of the 3TH signals is determined by the stray field of the Fe electrode, and that the spin-polarized electrons accumulate in electronic states between the Fe electrode and the Si channel.\\[4pt] [1] S. P. Dash et al., Phys. Rev. B84, 054410 (2011).