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We have experimentally and theoretically investigated the spin injection/detection polarization in a Si-based ferromagnetic tunnel junction with an amorphous MgO layer, and demonstrated that the experimental features of the spin polarization in a wide bias range can be well explained using our theoretical model based on the band diagram of the junction and the direct tunneling mechanism. It is shown that the spin polarization originates from the band diagrams of the ferromagnetic Fe layer and n+-Si channel in the junction, while the spin selectivity of the MgO tunnel barrier is not necessary. Besides, we clarified the mechanism of the reduction in spin polarization when the bias is high and nonlinear properties are prominent, where the widely-used spin injection/detection model proposed by Valet and Fert is not applicable. The dominant mechanism of such reduction is found to be spin accumulation saturation (SAS) at the n+-Si interface in contact with the MgO layer as the bias is increased in the spin extraction geometry, which is inevitable in semiconductor-based ferromagnetic tunnel junctions. We performed numerical calculations on a two-terminal spin transport device with a n+-Si channel using the junction properties extracted from the experiments, and revealed that the magnetoresistance (MR) ratio is suppressed mainly by SAS in a higher bias range. Furthermore, we proposed methods for improving the MR ratio in two-terminal spin transport devices. Our experiments and theoretical model provide a deep understanding of the spin injection/detection phenomena in semiconductor-based spin transport devices, toward the realization of high performance under reasonably high bias conditions for practical use., Comment: Main manuscript:32 pages, 18 figures Supplemental material: 18 pages, 10 figures

Semiconductor quantum dots are useful for controlling and observing quantum states and can also be used as sensors for reading out quantum bits and exploring local electronic states in nanostructures. However, challenges remain for the sensor applications, such as the trade-off between sensitivity and dynamic range and the issue of instability due to external disturbances. In this study, we demonstrate proportional-integral-differential feedback control of the radio-frequency reflectometry in GaN nanodevices using a field-programmable gate array. This technique can maintain the operating point of the charge sensor with high sensitivity. The system also realizes a wide dynamic range and high sensor sensitivity through the monitoring of the feedback signal. This method has potential applications in exploring dynamics and instability of electronic and quantum states in nanostructures., Comment: 13 pages, 5 figures

Here, we consider periodic homogenization for time-fractional Hamilton--Jacobi equations. By using the perturbed test function method, we establish the convergence, and give estimates on a rate of convergence. A main difficulty is the incompatibility between the function used in the doubling variable method, and the non-locality of the Caputo derivative. Our approach is to provide a lemma to prove the rate of convergence without the doubling variable method with respect to the time variable, which is a key ingredient., Comment: 23 pages

Department of Electrical Engineering and Information Systems, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan Center for Spintronics Research Network (CSRN), The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan, Comment: 26 pages, 5 figures, 1 table

We derive a fundamental solution $\mathscr{E}$ to a space-fractional diffusion problem on the half-line. The equation involves the Caputo derivative. We establish properties of $\mathscr{E}$ as well as formulas for solutions to the Dirichlet and Neumann problems in terms of convolution of $\mathscr{E}$ with data. We also study integrability of derivative of solutions given in this way. We present conditions sufficient for uniqueness. Finally, we show the infinite speed of signal propagation., Comment: 17 pages, no figures

We consider an initial-boundary value problem for the time-fractional diffusion equation. We prove the equivalence of two notions of weak solutions, viscosity solutions and distributional solutions., Comment: 17 pages

We have experimentally and theoretically investigated the electron spin transport and spin distribution at room temperature in a Si two-dimensional (2D) inversion channel of back-gate-type spin metal-oxide-semiconductor field-effect transistors (spin MOSFETs). The magnetoresistance ratio of the spin MOSFET with a channel length of 0.4$\mu$m was increased by a factor of 6 from that in our previous paper [Phys. Rev. B 99, 165301 (2019)] by lowering the parasitic resistances at the source/drain junctions with highly-phosphorus-doped n+-Si regions and by increasing the lateral electric field in the channel along the electron transport, called "spin drift". Clear Hanle signals with some oscillation peaks were observed for the spin MOSFET with a channel length of 10 $\mu$ m under the lateral electric field, indicating that the effective spin diffusion length is dramatically enhanced by the spin drift. By taking into account the n+-Si regions and the spin drift in the channel, one-dimensional analytic functions were derived for analyzing the effect of the spin drift on the spin transport through the channel and these functions were found to explain almost all the experimental results. From the calculated spin current and spin distribution, it was revealed that almost all the spins are unflipped during the spin-drift-assisted transport through the 0.4-$\mu$m-long inversion channel, but the most part of the injected spins from the source electrode are relaxed in the n+-Si regions of both the source and drain junctions. This means that the spin drift is useful and precise design of the device structure is essential to obtain a higher magnetoresistance ratio. Furthermore, we showed that the effective spin resistances that are introduced in this study are very helpful to understand how to improve the magnetoresistance ratio of spin MOSFETs for practical use.

We demonstrated that the spin injection/extraction efficiency is enhanced by an ultrathin Mg insertion layer (<= 2 nm) in Fe/Mg/MgO/n+-Si tunnel junctions. In diode-type vertical three-terminal devices fabricated on a Si substrate, we observed the narrower three-terminal Hanle (N-3TH) signals indicating true spin injection into Si, and estimated the spin polarization in Si to be 16% when the thickness of the Mg insertion layer is 1 nm, whereas no N-3TH signal was observed without Mg insertion. This means that the spin injection/extraction efficiency is enhanced by suppressing the formation of a magnetically-dead layer at the Fe/MgO interface. We have also observed clear spin transport signals, such as non-local Hanle signals and spin-valve signals, in a lateral four-terminal device with the same Fe/Mg/MgO/n+-Si tunnel junctions fabricated on a Si-on-insulator substrate. It was found that both the intensity and linewidth of the spin signals are affected by the geometrical effects (device geometry and size). We have derived analytical functions taking into account the device structures, including channel thickness and electrode size, and estimated important parameters; spin lifetime and spin polarizations. Our analytical functions well explain the experimental results. Our study shows the importance of suppressing a magnetically-dead layer, and provides a unified understanding of spin injection/detection signals in different device geometries., Comment: 32 pages, 7 figures, 2 tables

Group-IV-based ferromagnetic semiconductor Ge1-xFex (GeFe) is one of the most promising materials for efficient spin injectors and detectors for Si and Ge. Recent first principles calculations (Sakamoto et al., Ref. 9) suggested that the Fermi level is located in two overlapping largely spin-polarized bands formed in the bandgap of GeFe; spin-down d(e) band and spin-up p-d(t2) band. Thus, it is important to clarify how these bands contribute to spin injection and detection. In this study, we show the first successful observation of the tunneling magnetoresistance (TMR) in magnetic tunnel junctions (MTJs) containing a group-IV ferromagnetic semiconductor, that is, in MTJs composed of epitaxially grown Fe/MgO/Ge0.935Fe0.065. We find that the p-d(t2) band in GeFe is mainly responsible for the tunneling transport. Although the obtained TMR ratio is small (0.3%), the TMR ratio is expected to be enhanced by suppressing leak current through amorphous-like crystal domains observed in MgO.

We have investigated the influence of anisotropic magnetoresistance (AMR) on nonlocal signals in Si-based multi-terminal devices with ferromagnetic Fe electrodes. The AMR of the Fe electrodes was found to have a significant influence on nonlocal signals when the in-plane device structure is not optimized. Moreover, realization of a pure spin current by spin diffusion was found to be virtually impossible because of the electric potential distribution in the depth direction in the Si channel. Although apparent signals indicating the spin-valve effect were not detected, we mainly present structural influence on the electric potential distribution which is indispensable for the analyses of spin-dependent transport., Comment: 14pages, 3figures