Experimental separation of Rashba and Dresselhaus spin splittings in semiconductor quantum wells

Controlling Magnetization in Ferromagnetic Semiconductors by Current-Induced Spin-Orbit Torque

In this paper, we review our work on the manipulation of magnetization in ferromagnetic semiconductors (FMSs) using electric-current-induced spin-orbit torque (SOT). Our review focuses on FMS layers from the (Ga,Mn)As zinc-blende family grown by molecular beam epitaxy. We describe the processes used to obtain spin polarization of the current that is required to achieve SOT, and we briefly discuss methods of specimen preparation and of measuring the state of magnetization. Using specific examples, we then discuss experiments for switching the magnetization in FMS layers with either out-of-plane or in-plane easy axes. We compare the efficiency of SOT manipulation in single-layer FMS structures to that observed in heavy-metal/ferromagnet bilayers that are commonly used in magnetization switching by SOT. We then provide examples of prototype devices made possible by manipulation of magnetization by SOT in FMSs, such as read-write devices. Finally, based on our experimental results, we discuss future directions which need to be explored to achieve practical magnetic memories and related applications based on SOT switching.

Controllable quantum scars induced by spin-orbit couplings in quantum dots

Spin-orbit couplings (SOCs), originating from the relativistic corrections in the Dirac equation, offer nonlinearity in the classical limit and are capable of driving chaotic dynamics. In a nanoscale quantum dot confined by a two-dimensional parabolic potential with SOCs, various quantum scar states emerge quasi-periodically in the eigenstates of the system, when the ratio of confinement energies in the two directions is nearly commensurable. The scars, displaying both quantum interference and classical trajectory features on the electron density, due to relativistic effects, serve as a bridge between the classical and quantum behaviors of the system. When the strengths of Rashba and Dresselhaus SOCs are identical, the chaos in the classical limit is eliminated as the classical Hamilton's equations become linear, leading to the disappearance of all quantum scar states. Importantly, the quantum scars induced by SOCs are robust against small perturbations of system parameters. With precise control achievable through external gating, the quantum scar induced by Rashba SOC is fully controllable and detectable.

Emerging Nonlinear Photocurrents in Lead Halide Perovskites for Spintronics

Lead halide perovskites (LHPs) containing organic parts are emerging optoelectronic materials with a wide range of applications thanks to their high optical absorption, carrier mobility, and easy preparation methods. They possess spin-dependent properties, such as strong spin-orbit coupling (SOC), and are promising for spintronics. The Rashba effect in LHPs can be manipulated by a magnetic field and a polarized light field. Considering the surfaces and interfaces of LHPs, light polarization-dependent optoelectronics of LHPs has attracted attention, especially in terms of spin-dependent photocurrents (SDPs). Currently, there are intense efforts being made in the identification and separation of SDPs and spin-to-charge interconversion in LHP. Here, we provide a comprehensive review of second-order nonlinear photocurrents in LHP in regard to spintronics. First, a detailed background on Rashba SOC and its related effects (including the inverse Rashba-Edelstein effect) is given. Subsequently, nonlinear photo-induced effects leading to SDPs are presented. Then, SDPs due to the photo-induced inverse spin Hall effect and the circular photogalvanic effect, together with photocurrent due to the photon drag effect, are compared. This is followed by the main focus of nonlinear photocurrents in LHPs containing organic parts, starting from fundamentals related to spin-dependent optoelectronics. Finally, we conclude with a brief summary and future prospects.

Tuning spin-orbit coupling and realizing inverse persistent spin helix by an extra above-barrier radiation in a GaAs/Al0.3Ga0.7As heterostructure

A persistent spin helix with equal strength of the Rashba and Dresselhaus spin-orbit coupling (SOC) is expected for future spintronic devices due to the suppression of spin relaxation. In this work we investigate the optical tuning of the Rashba and Dresselhaus SOC by monitoring the spin-galvanic effect (SGE) in a GaAs/Al_0.3Ga_0.7As two dimensional electron gas. An extra control light above the bandgap of the barrier is introduced to tune the SGE excited by a circularly polarized light below the bandgap of GaAs. We observe different tunability of the Rashba- and Dresselhaus-related SGE currents and extract the ratio of the Rashba and Dresselhaus coefficients. It decreases monotonously with the power of the control light and reaches a particular value of ∼-1, implying the formation of the inverse persistent spin helix state. By analyzing the optical tuning process phenomenologically and microscopically, we reveal greater optical tunability of the Rashba SOC than that of the Dresselhaus SOC.

Topological Superconductivity Based on Antisymmetric Spin-Orbit Coupling

Topological superconductivity (TSC) has drawn much attention for its fundamental interest and application in quantum computation. An outstanding challenge is the lack of intrinsic TSC materials with a p-wave pairing gap, which has led to the development of an effective p-wave theory of coupling s-wave gap with Rashba spin-orbit coupling (RSOC). However, the RSOC-strict mechanism and materials pose still both fundamental and practical limitations. Here, we generalize this theory to antisymmetric SOC (ASOC). Using k·p perturbation theory, we demonstrate that 2D crystals, with point groups of C₂, C₄, C₆, C_2v, C_4v, C_6v, D₂, D₄, D₆, S₄, or D_2d, can all facilitate the desired ASOC. Remarkably, this enables us to discover 314 TSC candidates by screening 2D material databases, which are further confirmed by first-principles calculations of Majorana boundary modes and the topological invariant of the superconducting gap. Our work fundamentally enriches TSC theory and greatly expands the classes of TSC materials for experimental exploration.

Spin-Hall conductivity and Hall angle in a two-dimensional system with impurities in the presence of spin–orbit interactions

We investigate the spin-torque-dependent Spin Hall phenomenon in a two-dimensional tight-binding system in the presence of Rashba and Dresselhaus spin–orbit interactions and random static impurities. We employ the Matsubara Green function techniques to calculate the relaxation time caused by the scattering of electrons by impurities. The longitudinal and transverse conductivities are next calculated with the help of the Kubo formalism. We have also calculated the spin Hall angle for the present model and studied its dependence on spin–orbit interactions and impurity strength. Finally, we explore the effect of interplay between the Rashba and Dresselhaus interactions on the spin-Hall effect.

Effect of Rashba and Dresselhaus spin-orbit coupling on supercurrent rectification and magnetochiral anisotropy of ballistic Josephson junctions

Simultaneous breaking of inversion- and time-reversal symmetry in Josephson junction (JJ) leads to a possible violation of theI(φ) = -I(-φ) equality for the current-phase relation. This is known as anomalous Josephson effect and it produces a phase shiftφ₀in sinusoidal current-phase relations. In ballistic JJs with non-sinusoidal current phase relation the observed phenomenology is much richer, including the supercurrent diode effect and the magnetochiral anisotropy (MCA) of Josephson inductance. In this work, we present measurements of both effects on arrays of JJs defined on epitaxial Al/InAs heterostructures. We show that the orientation of the current with respect to the lattice affects the MCA, possibly as the result of a finite Dresselhaus component. In addition, we show that the two-fold symmetry of the Josephson inductance reflects in the activation energy for phase slips.

Strain Effects on Rashba Spin-Orbit Coupling of 2D Hole Gases in GeSn/Ge Heterostructures

A demonstration of 2D hole gases in GeSn/Ge heterostructures with a mobility as high as 20 000 cm² V^-1 s^-1 is given. Both the Shubnikov-de Haas oscillations and integer quantum Hall effect are observed, indicating high sample quality. The Rashba spin-orbit coupling (SOC) is investigated via magneto-transport. Further, a transition from weak localization to weak anti-localization is observed, which shows the tunability of the SOC strength by gating. The magneto-transport data are fitted to the Hikami-Larkin-Nagaoka formula. The phase-coherence and spin-relaxation times, as well as spin-splitting energy and Rashba coefficient of the k-cubic term, are extracted. The analysis reveals that the effects of strain and confinement potential at a high fraction of Sn suppress the Rashba SOC caused by the GeSn/Ge heterostructures.

Effective velocities of polaron spin states in monolayer transition metal dichalcogenides

We propose a theoretical model for studying the effective velocities of polaron spin states in monolayer transition metal dichalcogenides (TMDS) on the substrate. It is found that the effective velocity of polaron shows the splitting with different magnitudes due to the Rashba spin-orbit coupling, which results in the reversed distribution of the effective velocities of polaron spin states. Moreover, the reversed points depend on the truncated wave-vector of optical phonon and can be modulated by the polarity of substrate and the internal distance between monolayer TMDS and substrate. These theoretical results enlighten some simple ways to distinguish and modulate the polaron spin states in two-dimensional heterostructures.

Anomalous circular photogalvanic effect in p-GaAs

The anomalous circular photogalvanic effect (ACPGE) is observed in p-GaAs with a thickness of 2 μm at room temperature, in which circularly polarized light is used to inject spin-polarized carriers and the spin diffusion can generate a macroscopic detectable charge current due to the inverse spin Hall effect. The normalized ACPGE signals show first increasing and then decreasing with increasing the doping concentration. The role of the doping impurities is discussed by both extrinsic and intrinsic models, and both can well explain the variation of ACPGE with the doping concentration.

Highly Efficient Electric-Field Control of Giant Rashba Spin-Orbit Coupling in Lattice-Matched InSb/CdTe Heterostructures

Spin-orbit coupling (SOC), the relativistic effect describing the interaction between the orbital and spin degrees of freedom, provides an effective way to tailor the spin/magnetic orders using electrical means. Here, we report the manipulation of the spin-orbit interaction in the lattice-matched InSb/CdTe heterostructures. Owing to the energy band bending at the heterointerface, the strong Rashba effect is introduced to drive the spin precession where pronounced weak antilocalization cusps are observed up to 100 K. With effective quantum confinement and suppressed bulk conduction, the SOC strength is found to be enhanced by 75% in the ultrathin InSb/CdTe film. Most importantly, we realize the electric-field control of the interfacial Rashba effect using a field-effect transistor structure and demonstrate the gate-tuning capability which is 1-2 orders of magnitude higher than other materials. The adoption of the InSb/CdTe integration strategy may set up a general framework for the design of strongly spin-orbit coupled systems that are essential for CMOS-compatible low-power spintronics.

The topological properties of Dp-wave superconductors in the mixed Rashba/Dresselhaus systems

We investigate the effect of mixing Rashba/Dresselhaus spin-orbit couplings (SOCs) on the topological properties of D + p-wave superconductors. It is known that the nodal D + p-wave Rashba superconductors become gapful under a Zeeman magnetic field. We extend this gap-generation mechanism to mixed Rashba/Dresselhaus systems and find that the induced energy gaps are strongly modified by the Dresselhaus component in the second quadrant of the Brillion zone (BZ). We further calculate the Chern number numerically and obtain the topological phase diagram. It is shown that the Dresselhaus SOCs have a negative effect on the topological properties; the topological nontrivial region withC= -4 in the phase diagram shrinks as the amplitude of the Dresselhaus component increases. In the Dresselhaus-dominated regime, the contributions of gapped nodes from different quadrants of the BZ cancel each other, resulting in zero Chern number in most of the phase diagram. The numerical results are well explained by an approximate analytical formula for Chern number.

Effective Manipulation of Spin Dynamics by Polarization Electric Field in InGaN/GaN Quantum Wells at Room Temperature

III-nitride wide bandgap semiconductors are favorable materials for developing room temperature spintronic devices. The effective manipulation of spin dynamics is a critical request to realize spin field-effect transistor (FET). In this work, the dependence of the spin relaxation time on external strain-induced polarization electric field is investigated in InGaN/GaN multiple quantum wells (MQWs) by time-resolved Kerr rotation spectroscopy. Owing to the almost canceled two different spin-orbit coupling (SOC), the spin relaxation time as long as 311 ps in the MQWs is obtained at room temperature, being much longer than that in bulk GaN. Furthermore, upon applying an external uniaxial strain, the spin relaxation time decreases sensitively, which originates from the breaking of the SU(2) symmetry. The extracted ratio of the SOC coefficients shows a linear dependence on the external strain, confirming the essential role of the polarization electric field. This effective manipulation of the spin relaxation time sheds light on GaN-based nonballistic spin FET working at room temperature.

Unique Spin Vortices and Topological Charges in Quantum Dots with Spin-orbit Couplings

Spin textures of one or two electrons in a quantum dot with Rashba or Dresselhaus spin-orbit couplings reveal several intriguing properties. We show here that even at the single-electron level stable spin vortices with tunable topological charges exist. These topological textures appear in the ground state of the dots. The textures are stabilized by time-reversal symmetry breaking and are robust against the eccentricity of the dot. The topological charge is directly related to the sign of the z component of the spin in a large dot, allowing a direct probe of its topological properties. This would clearly pave the way to possible future topological spintronics. The phenomenon of spin vortices persists for the interacting two-electron dot in the presence of a magnetic field.

Distinguishing Interface Magnetoresistance and Bulk Magnetoresistance through Rectification of Schottky Heterojunctions

High performance of many spintronic devices strongly depends on the spin-polarized electrical transport, especially the magnetoresistance (MR) in magnetic heterojunctions. However, it has been a great challenge to distinguish the bulk MR and interface MR by transport measurements because the bulk resistance and interface resistance formed a series circuit in magnetic heterojunctions. Here, a unique interface-sensitive rectification MR method is proposed to distinguish the interface MR and bulk MR of nonmagnetic In/GeO _x/n-Ge and magnetic Co/GeO _x/n-Ge diode-like heterojunctions. It is demonstrated that the low-field "butterfly" hysteresis loop observed only in the conventional MR curve originates from the anisotropic MR of ferromagnetic bulk Co layer, whereas the orbit-related large nonsaturating positive MR contains contributions from both the Schottky interface and bulk Ge substrate. This rectification MR method could be extended to magnetic heterojunctions with asymmetric potential barriers to realize a deeper understanding of the fundamental interface-related functionalities.

n-type Rashba spin splitting in a bilayer inorganic halide perovskite with external electric field

Here, we investigated the Rashba effect of the CsPbBr₃ bilayers under the external electric field (EEF) with first-principles calculations. For the PbBr₂ terminated bilayer, we found that only electrons experience the Rashba splitting under EEF, while holes do not. Such an n-type Rashba effect can be ascribed to the surface relaxation effect that reverses the positions of the top valence bands. The n-type Rashba parameter can be tuned monotonically to the maximum of 0.88 eV Å at EEF of 1.35 V nm^-1 at which the sequence of top valence bands recover to the bulk style. During this process the p-type spins will not survive in this 2D CsPbBr₃, that indeed reveals a new way for making advanced functional spintronic devices.

Spin-dependent magneto-thermopower of narrow-gap lead chalcogenide quantum wells

A semi-classical analysis of magneto-thermopower behaviour, namely, the Seebeck and Nernst effect (NE) in quantum wells of IV-VI lead salts with significant extrinsic Rashba spin-orbit coupling (RSOC) is performed in this report. In addition to the spin-dependent Seebeck effect that has been observed before, we also theoretically predict a similar spin-delineated behavior for its magneto-thermal analog, the spin-dependent NE. The choice of lead salts follows from a two-fold advantage they offer, in part, to their superior thermoelectric properties, especially PbTe, while their low band gaps and high spin-orbit coupling make them ideal candidates to study RSOC governed effects in nanostructures. The calculations show a larger longitudinal magneto-thermopower for the spin-up electrons while the transverse components are nearly identical. In contrast, for a magnetic field free case, the related power factor calculations reveal a significantly higher contribution from the spin-down ensemble and suffer a reduction with an increase in the electron density. We also discuss qualitatively the limitations of the semi-classical approach for the extreme case of a high magnetic field and allude to the observed thermopower behaviour when the quantum Hall regime is operational. Finally, techniques to modulate the thermopower are briefly outlined.

Piezotronic Effect on Rashba Spin-Orbit Coupling in a ZnO/P3HT Nanowire Array Structure

A key concept in the emerging field of spintronics is the voltage-gate control of spin precession via the effective magnetic field generated by the Rashba spin-orbit coupling (SOC). Traditional external gate voltage usually needs a power supply, which can easily bring about background noise or lead to a short circuit in measurement, especially for nanoscale spintronic devices. Here, we present a study on the circular photogalvanic effect (CPGE) in a ZnO/P3HT nanowire array structure with the device excited under oblique incidence. We demonstrate that a strong Rashba SOC is induced by the structure inversion asymmetry of the ZnO/P3HT heterointerface. We show that the Rashba SOC can be effectively tuned by inner-crystal piezo-potential created inside the ZnO nanowires instead of an externally applied voltage. The piezo-potential can not only ensure the stability of future spin-devices under a static pressure or strain but also work without the need of extra energy; hence this room-temperature generation and piezotronic effect control of spin photocurrent demonstrate a potential application in large-scale flexible spintronics in piezoelectric nanowire systems.

Extraction of the Rashba spin-orbit coupling constant from scanning gate microscopy conductance maps for quantum point contacts

We study the possibility for the extraction of the Rashba spin-orbit coupling constant for a two-dimensional electron gas with the conductance microscopy technique. Due to the interplay between the effective magnetic field due to the Rashba spin-orbit coupling and the external magnetic field applied within the plane of confinement, the electron backscattering induced by a charged tip of an atomic force microscope located above the sample leads to the spin precession and spin mixing of the incident and reflected electron waves between the QPC and the tip-induced 2DEG depletion region. This mixing leads to a characteristic angle-dependent beating pattern visible in the conductance maps. We show that the structure of the Fermi level, bearing signatures of the spin-orbit coupling, can be extracted from the Fourier transform of the interference fringes in the conductance maps as a function of the magnetic field direction. We propose a simple analytical model which can be used to fit the experimental data in order to obtain the spin-orbit coupling constant.

Tuning of Rashba/Dresselhaus Spin Splittings by Inserting Ultra-Thin InAs Layers at Interfaces in Insulating GaAs/AlGaAs Quantum Wells

The ratio of Rashba and Dresselhaus spin splittings of the (001)-grown GaAs/AlGaAs quantum wells (QWs), investigated by the spin photocurrent spectra induced by circular photogalvanic effect (CPGE) at inter-band excitation, has been effectively tuned by changing the well width of QWs and by inserting a one-monolayer-thick InAs layer at interfaces of GaAs/AlGaAs QWs. Reflectance difference spectroscopy (RDS) is also employed to study the interface asymmetry of the QWs, whose results are in good agreement with that obtained by CPGE measurements. It is demonstrated that the inserted ultra-thin InAs layers will not only introduce structure inversion asymmetry (SIA), but also result in additional interface inversion asymmetry (IIA), whose effect is much stronger in QWs with smaller well width. It is also found that the inserted InAs layer brings in larger SIA than IIA. The origins of the additional SIA and IIA introduced by the inserted ultra-thin InAs layer have been discussed.

Helicity-dependent photocurrent induced by the in-plane transverse electric current in an InAs quantum well

We report the observation of a new type of helicity-dependent photocurrent induced by an in-plane transverse direct electric current in an InAs quantum well. The amplitude of the photocurrent depends linearly on the transverse current. Moreover, the observed incident azimuth-angle dependence of this photocurrent is different from that induced by the circular photogalvanic effect. This new photocurrent appears as a result of an asymmetrical carrier distribution in both the conduction and valence bands induced by the transverse current. The photoexcited carrier density created by interband transition processes is thus modulated and leads to the observed new azimuth-angle dependence. The observed efficient generation of the helicity-dependent photocurrent offers an effective approach to manipulate electron spins in two-dimensional semiconductor systems with the added advantage of electrical control of the spin-related photocurrent in spintronic applications.

Temperature dependence of spin photocurrent spectra induced by Rashba- and Dresselhaus-type circular photogalvanic effect at inter-band excitation in InGaAs/AlGaAs quantum wells

Spin photocurrent spectra induced by Rashba- and Dresselhaus-type circular photogalvanic effect (CPGE) at inter-band excitation have been experimentally investigated in InGaAs/AlGaAs quantum wells at a temperature range of 80 to 290 K. It is found that, the sign of Rashba-type current reverses at low temperatures, while that of Dresselhaus-type remains unchanged. The temperature dependence of ratio of Rashba and Dresselhaus spin-orbit coupling parameters, increasing from -6.7 to 17.9, is obtained, and the possible reasons are discussed. We also develop a model to extract the Rashba-type effective electric field at different temperatures. It is demonstrated that excitonic effect will significantly influence the Rashba-type CPGE, while it has little effect on Dresselhaus-type CPGE.

Tunneling Anomalous and Spin Hall Effects

We predict, theoretically, the existence of the anomalous Hall effect when a tunneling current flows through a tunnel junction in which only one of the electrodes is magnetic. The interfacial spin-orbit coupling present in the barrier region induces a spin-dependent momentum filtering in the directions perpendicular to the tunneling current, resulting in a skew tunneling even in the absence of impurities. This produces an anomalous Hall conductance and spin Hall currents in the nonmagnetic electrode when a bias voltage is applied across the tunneling heterojunction. If the barrier is composed of a noncentrosymmetric material, the anomalous Hall conductance and spin Hall currents become anisotropic with respect to both the magnetization and crystallographic directions, allowing us to separate this interfacial phenomenon from the bulk anomalous and spin Hall contributions. The proposed effect should be useful for proving and quantifying the interfacial spin-orbit fields in metallic and metal-semiconductor systems.

Orthogonal Cherenkov sound in spin-orbit coupled systems

Conventionally the Cherenkov sound is governed by orbital degrees of freedom and is excited by supersonic particles. Additionally, it usually has a forward nature with a conic geometry known as the Cherenkov cone whose axis is oriented along the supersonic particle motion. Here we predict Cherenkov sound of a unique nature entirely resulting from the electronic spin degree of freedom and demonstrate a fundamentally distinct Cherenkov effect originating from essentially subsonic electrons in two-dimensional gases with both Bychkov-Rashba and Dresselhaus spin-orbit interactions. Specifically, we show that the axis of the conventional forward Cherenkov cone gets a nontrivial quarter-turn and at the same time the sound distribution strongly localizes around this rotated axis being now orthogonal to the subsonic particle motion. Apart from its fundamentally appealing nature, the orthogonal Cherenkov sound could have applications in planar semiconductor technology combining spin and acoustic phenomena to develop, e.g., acoustic amplifiers or sound sources with a flexible spin dependent orientation of the sound propagation.

Long-range spin-triplet correlations and edge spin currents in diffusive spin-orbit coupled SNS hybrids with a single spin-active interface

Utilizing a SU(2) gauge symmetry technique in the quasiclassical diffusive regime, we theoretically study finite-sized two-dimensional intrinsic spin-orbit coupled superconductor/normal-metal/superconductor (S/N/S) hybrid structures with a single spin-active interface. We consider intrinsic spin-orbit interactions (ISOIs) that are confined within the N wire and absent in the s-wave superconducting electrodes (S). Using experimentally feasible parameters, we demonstrate that the coupling of the ISOIs and spin moment of the spin-active interface results in maximum singlet-triplet conversion and accumulation of spin current density at the corners of the N wire nearest the spin-active interface. By solely modulating the superconducting phase difference, we show how the opposing parities of the charge and spin currents provide an effective venue to experimentally examine pure edge spin currents not accompanied by charge currents. These effects occur in the absence of externally imposed fields and moreover are insensitive to the arbitrary orientations of the interface spin moment. The experimental implementation of these robust edge phenomena are also discussed.

Generation of Rashba spin-orbit coupling in CdSe nanowire by ionic liquid gate

Spintronic devices rely on the spin degree of freedom (DOF), and spin orbit coupling (SOC) is the key to manipulate spin DOF. Quasi-one-dimensional structures, possessing marked anisotropy gives more choice for the manipulation of the spin DOF since the concrete SOC form varies along with crystallographic directions. The anisotropy of the Dresselhaus SOC in cadmium selenide (CdSe) nanobelt and nanowire was studied by circular photogalvanic effect. It was demonstrated that the Dresselhaus SOC parameter is zero along the [0001] crystallographic direction, which suppresses the spin relaxation and increases the spin diffusion length, and thus is beneficial to the spin manipulation. To achieve a device structure with Rashba SOC presence and Dresselhaus SOC absence for manipulating the spin DOF, an ionic liquid gate was produced on a nanowire grown along the [0001] crystallographic direction, and the Rashba SOC was induced by gating, as expected.

Tunable ferroelectric polarization and its interplay with spin-orbit coupling in tin iodide perovskites

Ferroelectricity is a potentially crucial issue in halide perovskites, breakthrough materials in photovoltaic research. Using density functional theory simulations and symmetry analysis, we show that the lead-free perovskite iodide (FA)SnI3, containing the planar formamidinium cation FA, (NH2CHNH2)(+), is ferroelectric. In fact, the perpendicular arrangement of FA planes, leading to a 'weak' polarization, is energetically more stable than parallel arrangements of FA planes, being either antiferroelectric or 'strong' ferroelectric. Moreover, we show that the 'weak' and 'strong' ferroelectric states with the polar axis along different crystallographic directions are energetically competing. Therefore, at least at low temperatures, an electric field could stabilize different states with the polarization rotated by π/4, resulting in a highly tunable ferroelectricity appealing for multistate logic. Intriguingly, the relatively strong spin-orbit coupling in noncentrosymmetric (FA)SnI3 gives rise to a co-existence of Rashba and Dresselhaus effects and to a spin texture that can be induced, tuned and switched by an electric field controlling the ferroelectric state.

Direct determination of spin-orbit interaction coefficients and realization of the persistent spin helix symmetry

The spin-orbit interaction plays a crucial role in diverse fields of condensed matter, including the investigation of Majorana fermions, topological insulators, quantum information and spintronics. In III-V zinc-blende semiconductor heterostructures, two types of spin-orbit interaction--Rashba and Dresselhaus--act on the electron spin as effective magnetic fields with different directions. They are characterized by coefficients α and β, respectively. When α is equal to β, the so-called persistent spin helix symmetry is realized. In this condition, invariance with respect to spin rotations is achieved even in the presence of the spin-orbit interaction, implying strongly enhanced spin lifetimes for spatially periodic spin modes. Existing methods to evaluate α/β require fitting analyses that often include ambiguity in the parameters used. Here, we experimentally demonstrate a simple and fitting parameter-free technique to determine α/β and to deduce the absolute values of α and β. The method is based on the detection of the effective magnetic field direction and the strength induced by the two spin-orbit interactions. Moreover, we observe the persistent spin helix symmetry by gate tuning.

Gate control of the electron spin-diffusion length in semiconductor quantum wells

The spin diffusion length is a key parameter to describe the transport properties of spin polarized electrons in solids. Electrical spin injection in semiconductor structures, a major issue in spintronics, critically depends on this spin diffusion length. Gate control of the spin diffusion length could be of great importance for the operation of devices based on the electric field manipulation and transport of electron spin. Here we demonstrate that the spin diffusion length in a GaAs quantum well can be electrically controlled. Through the measurement of the spin diffusion coefficient by spin grating spectroscopy and of the spin relaxation time by time-resolved optical orientation experiments, we show that the diffusion length can be increased by more than 200% with an applied gate voltage of 5 V. These experiments allow at the same time the direct simultaneous measurements of both the Rashba and Dresselhaus spin-orbit splittings.

Spin photocurrent spectra induced by Rashba- and Dresselhaus-type circular photogalvanic effect at inter-band excitation in InGaAs/GaAs/AlGaAs step quantum wells

: Spin photocurrent spectra induced by Rashba- and Dresselhaus-type circular photogalvanic effect (CPGE) at inter-band excitation have been experimentally investigated in InGaAs/GaAs/AlGaAs step quantum wells (QWs) at room temperature. The Rashba- and Dresselhaus-induced CPGE spectra are quite similar with each other during the spectral region corresponding to the transition of the excitonic state 1H1E (the first valence subband of heavy hole to the first conduction subband of electrons). The ratio of Rashba- and Dresselhaus-induced CPGE current for the transition 1H1E is estimated to be 8.8±0.1, much larger than that obtained in symmetric QWs (4.95). Compared to symmetric QWs, the reduced well width enhances the Dresselhaus-type spin splitting, but the Rashba-type spin splitting increases more rapidly in the step QWs. Since the degree of the segregation effect of indium atoms and the intensity of build-in field in the step QWs are comparable to those in symmetric QWs, as proved by reflectance difference and photoreflectance spectra, respectively, the larger Rashba-type spin splitting is mainly induced by the additional interface introduced by step structures.

Dynamical self-quenching of spin pumping into double quantum dots

Nuclear spin polarization can be pumped into spin-blockaded quantum dots by multiple Landau-Zener passages through singlet-triplet anticrossings. By numerical simulations of realistic systems with 10(7) nuclear spins during 10(5) sweeps, we uncover a mechanism of dynamical self-quenching which results in a fast saturation of the nuclear polarization under stationary pumping. This is caused by screening the random field of the nuclear spins. For moderate spin-orbit coupling, self-quenching persists but its patterns are modified. Our finding explains low polarization levels achieved experimentally and calls for developing new protocols that break the self-quenching limitations.

Electric field-driven coherent spin reorientation of optically generated electron spin packets in InGaAs

Full electric-field control of spin orientations is one of the key tasks in semiconductor spintronics. We demonstrate that electric-field pulses can be utilized for phase-coherent ±π spin rotation of optically generated electron spin packets in InGaAs epilayers detected by time-resolved Faraday rotation. Through spin-orbit interaction, the electric-field pulses act as local magnetic field pulses. By the temporal control of the local magnetic field pulses, we can turn on and off electron spin precession and thereby rotate the spin direction into arbitrary orientations in a two-dimensional plane. Furthermore, we demonstrate a spin-echo-type spin drift experiment and find an unexpected partial spin rephasing, which is evident by a doubling of the spin dephasing time.

Experimental evidence of cubic Rashba effect in an inversion-symmetric oxide

We present evidence of cubic Rashba spin splitting in a quasi-two-dimensional electron gas formed at a surface of (001) SrTiO3 single crystal from the weak localization or antilocalization (WAL) analysis of the low-temperature magnetoresistance. Our WAL data were well fitted by the model assuming mj=±3/2 for the spin-split pair, in which 2π rotation of the electron wave vector k∥ in the kx-ky plane accompanies 6π rotation of the spin quantization axis. This finding pertains to the p symmetry of the t2g electronic band derived from d electrons in SrTiO3, which provides insights into the surface electronic state of (001) SrTiO3.

Theory of g-factor enhancement in narrow-gap quantum well heterostructures

We report on the study of the exchange enhancement of the g-factor in the two-dimensional (2D) electron gas in n-type narrow-gap semiconductor heterostructures. Our approach is based on the eight-band k⋅p Hamiltonian and takes into account the band nonparabolicity, the lattice deformation, the spin-orbit coupling and the Landau level broadening in the δ-correlated random potential model. Using the 'screened' Hartree-Fock approximation we demonstrate that the exchange g-factor enhancement not only shows maxima at odd values of Landau level filling factors but, due to the conduction band nonparabolicity, persists at even filling factor values as well. The magnitude of the exchange enhancement, the amplitude and the shape of the g-factor oscillations are determined by both the screening of the electron-electron interaction and the Landau level width. The 'enhanced' g-factor values calculated for the 2D electron gas in InAs/AlSb quantum well heterostructures are compared with our earlier experimental data and with those obtained by Mendez et al (1993 Phys. Rev. B 47 13937) in magnetic fields up to 30 T.

Current-induced spin-orbit torques

The ability to reverse the magnetization of nanomagnets by current injection has attracted increased attention ever since the spin-transfer torque mechanism was predicted in 1996. In this paper, we review the basic theoretical and experimental arguments supporting a novel current-induced spin torque mechanism taking place in ferromagnetic (FM) materials. This effect, hereafter named spin-orbit (SO) torque, is produced by the flow of an electric current in a crystalline structure lacking inversion symmetry, which transfers orbital angular momentum from the lattice to the spin system owing to the combined action of SO and exchange coupling. SO torques are found to be prominent in both FM metal and semiconducting systems, allowing for great flexibility in adjusting their orientation and magnitude by proper material engineering. Further directions of research in this field are briefly outlined.

Crystallographic plane tuning of magnetoplasmon excitations in two-dimensional electron gas systems

We investigate theoretically the magnetoplasmon spectrum of two-dimensional electron gas systems grown along different crystallographic directions, which are modulated by both the Dresselhaus spin-orbit interaction (DSOI) and the Rashba spin-orbit interaction (RSOI). Because the DSOI depends on the crystallographic orientation, the magnetoplasmon spectrum in the presence of the DSOI shows distinct features for different crystallographic planes. For some high-index planes, such as (140) and (114), the magnetoplasmon spectrum is anisotropic even under the pure-DSOI modulation, which is different from the isotropic behavior for the high-symmetry (001) plane. The coexistence of the DSOI and the RSOI leads to more drastic variations of the anisotropic magnetoplasmon spectrum in different crystallographic planes, which are revealed from the splittings of the collective excitation modes and the intensity of the spin density excitation at the anticrossing center of the splittings.

Acoustically induced spin-orbit interactions revealed by two-dimensional imaging of spin transport in GaAs

Magneto-optic Kerr microscopy was employed to investigate the spin-orbit interactions of electrons traveling in semiconductor quantum wells using surface acoustic waves (SAWs). Two-dimensional images of the spin flow induced by SAWs exhibit anisotropic spin precession behaviors caused by the coexistence of different types of spin-orbit interactions. The dependence of spin-orbit effective magnetic fields on SAW intensity indicates the existence of acoustically controllable spin-orbit interactions resulting from the strain and Rashba contributions induced by the SAWs.

Spin-orbit interaction induced anisotropic property in interacting quantum wires

: We investigate theoretically the ground state and transport property of electrons in interacting quantum wires (QWs) oriented along different crystallographic directions in (001) and (110) planes in the presence of the Rashba spin-orbit interaction (RSOI) and Dresselhaus SOI (DSOI). The electron ground state can cross over different phases, e.g., spin density wave, charge density wave, singlet superconductivity, and metamagnetism, by changing the strengths of the SOIs and the crystallographic orientation of the QW. The interplay between the SOIs and Coulomb interaction leads to the anisotropic dc transport property of QW which provides us a possible way to detect the strengths of the RSOI and DSOI.PACS numbers: 73.63.Nm, 71.10.Pm, 73.23.-b, 71.70.Ej.

Crystallographic plane tuning of charge and spin transport in semiconductor quantum wires

We investigate theoretically the charge and spin transport in quantum wires grown along different crystallographic planes in the presence of the Rashba spin-orbit interaction (RSOI) and the Dresselhaus spin-orbit interaction (DSOI). We find that changing the crystallographic planes leads to a variation of the anisotropy of the conductance due to a different interplay between the RSOI and DSOI, since the DSOI is induced by bulk inversion asymmetry, which is determined by crystallographic plane. This interplay depends sensitively on the crystallographic planes, and consequently leads to the anisotropic charge and spin transport in quantum wires embedded in different crystallographic planes.

Gate-controlled spin-orbit interaction in a parabolic GaAs/AlGaAs quantum well

We study the tunability of the spin-orbit interaction in a two-dimensional electron gas with a front and a back gate electrode by monitoring the spin precession frequency of drifting electrons using time-resolved Kerr rotation. The Rashba spin splitting can be tuned by the gate biases, while we find a small Dresselhaus splitting that depends only weakly on the gating. We determine the absolute values and signs of the two components and show that for zero Rashba spin splitting the anisotropy of the spin-dephasing rate vanishes.

All-electrical detection of the relative strength of Rashba and Dresselhaus spin-orbit interaction in quantum wires

We propose a method to determine the relative strength of Rashba and Dresselhaus spin-orbit interaction from transport measurements without the need of fitting parameters. To this end, we make use of the conductance anisotropy in narrow quantum wires with respect to the directions of an in-plane magnetic field, the quantum wire, and the crystal orientation. We support our proposal by numerical calculations of the conductance of quantum wires based on the Landauer formalism which show the applicability of the method to a wide range of parameters.

Proposal for direct measurement of a pure spin current by a polarized light beam

The photon helicity may be mapped to a spin-1/2, whereby we put forward an intrinsic interaction between a polarized light beam as a "photon spin current" and a pure spin current in a semiconductor, which arises from the spin-orbit coupling in valence bands as a pure relativity effect without involving the Rashba or the Dresselhaus effect due to inversion asymmetries. The interaction leads to linear and circular optical birefringence, which are similar to the Voigt effect and the Faraday rotation in magneto-optics but nevertheless involve no net magnetization. The birefringence effects provide a direct, nondemolition measurement of pure spin currents.

Tunneling anisotropic magnetoresistance and spin-orbit coupling in Fe/GaAs/Au tunnel junctions

We report the observation of tunneling anisotropic magnetoresistance effect in the epitaxial metal-semiconductor system Fe/GaAs/Au. The observed twofold anisotropy of the resistance can be switched by reversing the bias voltage, suggesting that the effect originates from the interference of the spin-orbit coupling at the interfaces. Corresponding model calculations reproduce the experimental findings very well.

Semiconductor spintronics

Spintronics refers commonly to phenomena in which the spin of electrons in a solid state environment plays the determining role. In a more narrow sense spintronics is an emerging research field of electronics: spintronics devices are based on a spin control of electronics, or on an electrical and optical control of spin or magnetism. While metal spintronics has already found its niche in the computer industry—giant magnetoresistance systems are used as hard disk read heads—semiconductor spintronics is yet to demonstrate its full potential. This review presents selected themes of semiconductor spintronics, introducing important concepts in spin transport, spin injection, Silsbee-Johnson spin-charge coupling, and spin-dependent tunneling, as well as spin relaxation and spin dynamics. The most fundamental spin-dependent interaction in nonmagnetic semiconductors is spin-orbit coupling. Depending on the crystal symmetries of the material, as well as on the structural properties of semiconductor based heterostructures, the spin-orbit coupling takes on different functional forms, giving a nice playground of effective spin-orbit Hamiltonians. The effective Hamiltonians for the most relevant classes of materials and heterostructures are derived here from realistic electronic band structure descriptions. Most semiconductor device systems are still theoretical concepts, waiting for experimental demonstrations. A review of selected proposed, and a few demonstrated devices is presented, with detailed description of two important classes: magnetic resonant tunnel structures and bipolar magnetic diodes and transistors. In view of the importance of ferromagnetic semiconductor materials, a brief discussion of diluted magnetic semiconductors is included. In most cases the presentation is of tutorial style, introducing the essential theoretical formalism at an accessible level, with case-study-like illustrations of actual experimental results, as well as with brief reviews of relevant recent achievements in the field.

Suppression of spin relaxation in submicron InGaAs wires

We investigate electron-spin dynamics in narrow two-dimensional n-InGaAs channels as a function of the channel width. The spin relaxation times increase with decreasing channel width, in accordance with recent theoretical predictions based on the dimensionally constrained D'yakonov-Perel' mechanism. Surprisingly, the suppression of the relaxation rate, which is anticipated for the one-dimensional limit, is observed for widths that are an order of magnitude larger than the electron mean free path. We find the spin precession length and the channel width to be the relevant length scales for interpreting these results.

Spin relaxation by transient monopolar and bipolar optical orientation

We have used two-color time-resolved spectroscopy to measure the relaxation of electron spin polarizations in a bulk semiconductor. The circularly polarized pump beam induces a polarization either by direct excitation from the valence band, or by free-carrier (Drude) absorption when tuned to an energy below the band gap. We find that the spin relaxation time, measured with picosecond time resolution by resonant induced Faraday rotation in both cases, increases in the presence of photogenerated holes. In the case of the material chosen, n-InSb, the increase was from 14 to 38 ps.

Spin relaxation and decoherence of holes in quantum dots

We investigate heavy-hole spin relaxation and decoherence in quantum dots in perpendicular magnetic fields. We show that at low temperatures the spin decoherence time is 2 times longer than the spin relaxation time. We find that the spin relaxation time for heavy holes can be comparable to or even longer than that for electrons in strongly two-dimensional quantum dots. We discuss the difference in the magnetic-field dependence of the spin relaxation rate due to Rashba or Dresselhaus spin-orbit coupling for systems with positive (i.e., GaAs quantum dots) or negative (i.e., InAs quantum dots) g factor.

Spin-orbit coupling and anisotropy of spin splitting in quantum dots

In lateral quantum dots, the combined effect of both Dresselhaus and Bychkov-Rashba spin-orbit coupling is equivalent to an effective magnetic field +/- B(SO) which has the opposite sign for s(z)= +/- 1/2 spin electrons. When the external magnetic field is perpendicular to the planar structure, the field B(SO) generates an additional splitting for electron states as compared to the spin splitting in the in-plane field orientation. The anisotropy of spin splitting has been measured and then analyzed in terms of spin-orbit coupling in several AlGaAs/GaAs quantum dots by means of resonant tunneling spectroscopy. From the measured values and sign of the anisotropy we are able to determine the dominating spin-orbit coupling mechanism.