The spin-orbit interaction (SOI) of a two-dimensional hole gas in the inversion symmetric semiconductor Ge is studied in a strained-Ge=SiGe quantum well structure. We observe weak antilocalization (WAL) in the magnetoconductivity measurement, revealing that the WAL feature can be fully described by the k-cubic Rashba SOI theory. Furthermore, we demonstrate electric field control of the Rashba SOI. Our findings reveal that the heavy hole (HH) in strained Ge is a purely cubic Rashba system, which is consistent with the spin angular momentum m j ¼ AE3=2 nature of the HH wave function. DOI: 10.1103/PhysRevLett.113.086601 PACS numbers: 72.25.Dc, 73.20.Fz, 73.21.-b The spin-orbit interaction (SOI) in a two-dimensional system is a subject of considerable interest because the SOI induces spin splitting at a zero magnetic field, which is important in both fundamental research and electronic device applications [1]. Recent developments of SOI-induced phenomena in the solid state demonstrate many possibilities utilizing spin current and the emergence of new physics such as the spin interferometer [2,3], persistent spin helix [4,5], spin Hall effect [6][7][8], and quantum spin Hall effect [9,10]. Up to now, there have been two well-known SOIs existing in solids: the Dresselhaus SOI [11] due to bulk inversion asymmetry (BIA) in the crystal structure and the Rashba SOI [12,13] due to spatial inversion asymmetry (SIA).In low-dimensional systems, the Rashba SOI becomes more important because it is stronger at the heterointerface and can be controlled by an external electric field. Many of the pioneering studies on the SOI-induced phenomena mentioned above were performed in two-dimensional electron systems, where the Rashba SOI is described by the k-linear Rashba term. In the Hamiltonian, the k-linear Rashba term can be written aswhere σ AE ¼ 1=2ðσ x AE iσ y Þ denote combinations of Pauli spin matrices, k AE ¼ k x AE ik y , and k x , k y are the components of the in-plane wave vector k ∥ . The effective magnetic field Ω 1 ðk ∥ Þ acting on the transport carrier due to the k-linear Rashba term is illustrated in Fig. 1(a).Recently, a higher-order contribution of the Rashba SOI, the so-called k 3 (k-cubic) Rashba SOI, has received more attention [14,15]. The Hamiltonian for the k-cubic Rashba SOI is expressed asand the effective magnetic field Ω 3 ðk ∥ Þ in k space is illustrated in Fig. 1(b) [15]. There is a significant difference in the effective field symmetry between the k-linear and the k-cubic Rashba SOI with one and three rotations in k space, respectively. The k 3 symmetry of the SOI is an interesting subject because it influences all of the SOI-induced phenomena as opposed to the k-linear Rashba term. For example, in case of the spin Hall effect, the k-cubic Rashba term is predicted to give rise to a larger spin Hall conductivity [17][18][19].

We demonstrate electrical injection and detection of spin-polarized electrons in silicon (Si) using epitaxially grown Fe3Si/Si Schottky-tunnel-barrier contacts. By an insertion of a δ-doped n + -Si layer (∼ 10 19 cm −3 ) near the interface between a ferromagnetic Fe3Si contact and a Si channel (∼ 10 15 cm −3 ), we achieve a marked enhancement in the tunnel conductance for reverse-bias characteristics of the Fe3Si/Si Schottky diodes. Using laterally fabricated four-probe geometries with the modified Fe3Si/Si contacts, we detect nonlocal output signals which originate from the spin accumulation in a Si channel at low temperatures. PACS numbers:To solve critical issues caused by the scaling limit of complementary metal-oxide-semiconductor (CMOS) technologies, spin-based electronics (spintronics) has been studied.[1] For semiconductor spintronic applications, an electrical spin injection from a ferromagnet (FM) into a semiconductor (SC) and its detection are crucial techniques.Recently, methods for spin injection and/or detection in silicon (Si) were explored intensely [2,3,4,5,6,7] because Si has a long spin relaxation time and is compatible with the current industrial semiconductor technologies. Although electrical detections of spin transport in Si conduction channels were demonstrated by two research groups, [4,5] an insulating Al 2 O 3 tunnel barrier between FM and Si was utilized for efficient spin injection and/or detection. To realize gate-tunable spin devices, e.g., spin metal-oxidesemiconductor field effect transistors (spin MOSFET), [8] demonstrations of electrical spin injection and detection in Si conduction channels using Schottky tunnel-barrier contacts will become considerably important. [9,10] By low-temperature molecular beam epitaxy (LTMBE), we recently demonstrated highly epitaxial growth of a binary Heusler alloy Fe 3 Si on Si and obtained an atomically abrupt heterointerface. [11] In this letter, inserting a heavily doped n + -Si layer near the abrupt interface between Fe 3 Si and n-Si, we achieve an effective Shottky tunnel barrier for spin injection into Si. Using nonlocal signal measurements, we demonstrate electrical injection and detection of spin-polarized electrons in Si conduction channels though the Schottky-tunnel-barrier contacts.The n + -Si layer was formed on n-Si(111) (n ∼ 4.5 × 10 15 cm −3 ) by a combination of the Si solid-phase epitaxy with an Sb δ-doping process, [12] where the carrier * E-mail: hamaya@ed.kyushu-u.ac.jp † E-mail: miyao@ed.kyushu-u.ac.jp concentration of the n + -Si layer was ∼ 2.3 × 10 19 cm −3 , determined by Hall effect measurements, and ∼ 10-nmthick non-doped Si layer was grown on the Sb δ-doped layer. Ferromagnetic Fe 3 Si layers with a thickness of ∼ 50 nm were grown by LTMBE at 130 • C, as shown in our previous work.[11] The interface between Fe 3 Si and n + -Si was comparable to that shown in Ref. 11. To evaluate electrical properties of the Fe 3 Si/Si Schottky contacts, we firstly fabricated two different Schottky diodes (∼ 1 mm in diameter) with and w...

We identify the dominant source for low-frequency spin qubit splitting noise in a highly isotopically-purified silicon device with an embedded nanomagnet and a spin echo decay time T echo 2 = 128 µs. The power spectral density (PSD) of the charge noise explains both, the clear transition from a 1/f 2-to a 1/f-dependence of the splitting noise PSD as well as the experimental observation of a decreasing time-ensemble spin dephasing time, from T Ã 2 % 20 µs, with increasing measurement time over several hours. Despite their strong hyperfine contact interaction, the few 73 Ge nuclei overlapping with the quantum dot in the barrier do not limit T Ã 2 , likely because their dynamics is frozen on a few hours measurement scale. We conclude that charge noise and the design of the gradient magnetic field are the key to further improve the qubit fidelity in isotopically purified 28 Si/SiGe.

Valley splitting is a key feature of silicon-based spin qubits. Quantum dots in Si/Si x Ge 1−x heterostructures reportedly suffer from a relatively low valley splitting, limiting the operation temperature and the scalability of such qubit devices. Here, we demonstrate a robust and large valley splitting exceeding 200 μeV in a gate-defined single quantum dot, hosted in molecular-beam-epitaxy-grown 28 Si/Si x Ge 1−x. The valley splitting is monotonically and reproducibly tunable up to 15% by gate voltages, originating from a 6-nm lateral displacement of the quantum dot. We observe static spin relaxation times T 1 > 1 s at low magnetic fields in our device containing an integrated nanomagnet. At higher magnetic fields, T 1 is limited by the valley hotspot and by phonon noise coupling to intrinsic and artificial spin-orbit coupling, including phonon bottlenecking.

We study the electrical detection of spin accumulation at a ferromagnet-silicon interface, which can be verified by measuring a Hanle effect in three-terminal lateral devices. The device structures used consist of a semiconducting Si channel and a Schottky tunnel contact. In a low currentbias region, the Hanle-effect curves are observed only under forward bias conditions. This can be considered that the electrical detectability at the forward-biased contact is higher than that at the reverse-biased contact. This is possible evidence for the detection of spin-polarized electrons created in a Si channel.

Using high-quality Fe3Si/n + -Ge Schottky-tunnel-barrier contacts, we study spin accumulation in an n-type germanium (n-Ge) channel. In the three-or two-terminal voltage measurements with low bias current conditions at 50 K, Hanle-effect signals are clearly detected only at a forward-biased contact. These are reliable evidence for electrical detection of the spin accumulation created in the n-Ge channel. The estimated spin lifetime in n-Ge at 50 K is one order of magnitude shorter than those in n-Si reported recently. The magnitude of the spin signals cannot be explained by the commonly used spin diffusion model. We discuss a possible origin of the difference between experimental data and theoretical values.

This paper reviews the recent progress in germanium (Ge) spintronics on the basis of the electrical spin injection from ferromagnets (FM), where Ge is a next generation semiconductor for applications such as CMOS and optical communication on the silicon platform. In general, four-terminal nonlocal voltage measurements in FM–Ge lateral spin-valve devices are important to discuss the spin transport and spin relaxation in n-Ge. First, to obtain relatively low contact resistance compared to the FM/MgO/Ge contacts, we introduce the formation of high-quality FM/Ge heterointerfaces with a phosphorus δ-doped Ge layer, where the atomic arrangement matching at the interface between the (1 1 1) surface of body-centered cubic FMs and Ge(1 1 1) is important. Next, we explain electrical detections of the spin transport in degenerate n-Ge. Owing to the Heusler alloy/Ge Schottky-tunnel barrier contacts, we obtain relatively large spin signals compared to those detected by using conventional CoFe contacts. Furthermore, we can experimentally determine the spin diffusion length and the spin lifetime in degenerate n-Ge by quantitatively analyzing the contact-distance dependence of the spin signals and the Hanle-effect curves. Since we can clarify the temperature dependence of the spin lifetime from 8 to 296 K, the spin relaxation mechanism in n-Ge can be understood as a consequence of the intervalley spin-flip scattering in the conduction band. We propose an advantage over GaAs systems by comparing the spin lifetimes between Ge and GaAs at around room temperature. Finally, we describe future prospects of Ge spintronics, including vertically fabricated device structures such as vertical spin MOSFETs and spin LEDs.

No abstract