Rashba-type Spin-orbit Interaction Research Articles

A circular photogalvanic effect in two-dimensional electron gas on the surface of SrTiO3

A spin-splitting state due to a Rashba-type spin–orbit interaction is investigated using two-dimensional electron gas (2DEG) at the surface of SrTiO3. The circular photogalvanic effect is utilized to detect the spin-splitting state. Both the polarization and incident light angle dependence of the measured photocurrent generated in the 2DEG unequivocally show the presence of surface spin splitting in the 2DEG, and variation of the carrier densities of the 2DEG provides further supporting evidence. This finding could pave the way for investigating spin textures and spin physics in two-dimensional carrier gas systems.

Reversible and Nonvolatile Manipulation of the Spin-Orbit Interaction in Ferroelectric Field-Effect Transistors Based on a Two-Dimensional Bismuth Oxychalcogenide

The spin-orbit interaction (SOI) offers a nonferromagnetic scheme to realize spin polarization through utilizing an electric field. Electrically tunable SOIs through electrostatic gates have been investigated; however, the relatively weak and volatile tunability limits their practical applications in spintronics. Here, we demonstrate the nonvolatile electric field control of the SOI via constructing ferroelectric Rashba architectures, i.e., two-dimensional ${\mathrm{Bi}}_{2}{\mathrm{O}}_{2}\mathrm{Se}/\mathrm{Pb}({\mathrm{Mg}}_{1/3}{\mathrm{Nb}}_{2/3}){\mathrm{O}}_{3}$-${\mathrm{PbTiO}}_{3}$ ferroelectric field-effect transistors. The experimentally observed weak antilocalization (WAL) cusp in ${\mathrm{Bi}}_{2}{\mathrm{O}}_{2}\mathrm{Se}$ films implies the Rashba-type SOI that arises from the asymmetric confinement potential. Significantly, taking advantage of the switchable ferroelectric polarization, the WAL-to-weak-localization-transition trend reveals the competition between spin relaxation and the dephasing process, and the variation of carrier density leads to a reversible and nonvolatile modulation of the spin-relaxation time and the spin-splitting energy of ${\mathrm{Bi}}_{2}{\mathrm{O}}_{2}\mathrm{Se}$ films by this ferroelectric gating. Our work provides a scheme to achieve nonvolatile control of the Rashba SOI with the utilization of ferroelectric remanent polarization.

Enhancement of the Rashba Effect in a Conducting SrTiO3 Surface by MoO3 Capping.

Systems having inherent structural asymmetry retain the Rashba-type spin-orbit interaction, which ties the spin and momentum of electrons in the band structure, leading to coupled spin and charge transport. One of the electrical manifestations of the Rashba spin-orbit interaction is nonreciprocal charge transport, which could be utilized for rectifying devices. Further tuning of the Rashba spin-orbit interaction allows additional functionalities in spin-orbitronic applications. In this work, we present our study of nonreciprocal charge transport in a conducting SrTiO3 (001) surface and its significant enhancement by a capping layer. The conductive strontium titanate SrTiO3 (STO) (001) surface was created through oxygen vacancies by Ar+ irradiation, and the nonreciprocal signal was probed by angle- and magnetic field-dependent second harmonic voltage measurement with an AC current. We observed robust directional transport in the Ar+-irradiated sample at low temperatures. The magnitude of the nonreciprocal signal is highly dependent on the irradiation time as it affects the depth of the conducting layer and the impact of the topmost conducting layer. Moreover, the nonreciprocal resistance was significantly enhanced by simply adding a MoO3 capping layer on the conductive STO surface. These results show a simple methodology for tuning and investigating the Rashba effect in a conductive STO surface, which could be adopted for various two-dimensional (2D) conducting layers for spin-orbitronic applications.

Fluctuation contribution to spin Hall effect in superconductors

We theoretically study the contribution of superconducting fluctuation to extrinsic spin Hall effects in two- and three-dimensional electron gas and intrinsic spin Hall effects in two-dimensional electron gas with Rashba-type spin-orbit interaction. The Aslamazov-Larkin, Density-of-States, Maki-Thompson terms have logarithmic divergence $\ln\epsilon$ in the limit $\epsilon=(T- T_{\mathrm{c}})/T_{\mathrm{c}} \rightarrow +0$ in two-dimensional systems for both extrinsic and intrinsic spin Hall effects except the Maki-Thompson terms in extrinsic effect, which are proportional to $(\epsilon-\gamma_\varphi)^{-1}\ln\epsilon$ with a cutoff $\gamma_\varphi$ in two-dimensional systems. We found that the fluctuation effects on the extrinsic spin Hall effect have an opposite sign to that in the normal state, while those on the intrinsic spin Hall effect have the same sign.

Selective enhancement of Kane Mele-type spin-orbit interaction in graphene

In order to enhance the spin orbit interaction (SOI) in graphene for seeking the dissipationless quantum spin Hall devices, unique Kane-Mele-type SOI and high mobility samples are desired. However, the common external modification of graphene often introduces “extrinsic” Rashba-type SOI, which will destroy the possible topological state, bring a certain degree of impurity scattering and reduce the sample mobility. Here we show that by the EDTA-Dy molecule dressing, the carrier mobility is even improved, and the quantum Hall plateaus are observed more clearly. The Kane-Mele type SOI is mimicked after dressing, which is evidenced by the suppressed weak localization at equal carrier densities and simultaneous Elliot-Yafet spin relaxation. This is attributed to the spin-flexural phonon coupling induced by the enhanced graphene ripples, as revealed by the in-plane magnetotransport measurement.

Synthetic Rashba spin-orbit system using a silicon metal-oxide semiconductor.

The spin-orbit interaction (SOI), mainly manifesting itself in heavy elements and compound materials, has been attracting much attention as a means of manipulating and/or converting a spin degree of freedom. Here, we show that a Si metal-oxide- semiconductor (MOS) heterostructure possesses Rashba-type SOI, although Si is a light element and has lattice inversion symmetry resulting in inherently negligible SOI in bulk form. When a strong gate electric field is applied to the Si MOS, we observe spin lifetime anisotropy of propagating spins in the Si through the formation of an emergent effective magnetic field due to the SOI. Furthermore, the Rashba parameter α in the system increases linearly up to 9.8 × 10-16 eV m for a gate electric field of 0.5 V nm-1; that is, it is gate tuneable and the spin splitting of 0.6 μeV is relatively large. Our finding establishes a family of spin-orbit systems.

Opposite current-induced spin polarizations in bulk-metallic Bi2Se3 and bulk-insulating Bi2Te2Se topological insulator thin flakes

One of the most fundamental and exotic properties of three-dimensional (3D) topological insulators (TIs) is spin-momentum locking (SML) of their topological surface states (TSSs), promising for potential applications in future spintronics. However, other possible conduction channels, such as a trivial two-dimensional electron gas (2DEG) with strong Rashba-type spin-orbit interaction (SOI) and bulk-conducting states that may possess a spin Hall effect (SHE), can coexist in 3D TIs, making determining the origin of the current-induced spin polarization (CISP) difficult. In this work, we directly compared the CISP between bulk-insulating ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{2}\mathrm{Se}$ (BTS221) and bulk-metallic ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ thin flakes using spin potentiometry. In the bulk-insulating BTS221, the observed CISP has a sign consistent with the expected helicity of the SML of the TSS, but an opposite sign to its calculated bulk spin Hall conductivity. However, compared to BTS221, an opposite CISP is observed in the bulk-metallic ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$, consistent with both the expectations of its Rashba-Edelstein effect of the band-bending induced 2DEG and bulk intrinsic spin Hall Effect (SHE). If one assumes a representative occupation of the Rashba band of $3\ifmmode\times\else\texttimes\fi{}{10}^{13}\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}2}$ in ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ with a relevant relaxation time of 100 fs, the contribution to the CISP could be more dominated by the bulk intrinsic SHE. Our results provide an electrical way to distinguish the TSS from other possible conducting channels in spin transport measurements on 3D TIs, and open ways for the potential applications in charge-spin conversion devices.

Flat-band conditions influenced by spin-orbit interaction in the presence of external magnetic field

We deduct conditions for the Hamiltonian coupling strengths necessary to achieve flat bands in polymers (i.e. a pentagon chain) considering many-body spin-orbit coupling and external magnetic field. We consider itinerant electrons on pentagon chains with first neighbour hoppings, on-site electron potentials and spin-flip first neighbour hoppings representing the Rashba type spin-orbit interaction (SOI). The external magnetic field is also present in the system via the Peierls phase factors. The band structure is obtained by solving the secular equation of the diagonalized one particle part of the Hamiltonian in k-space (momentum-space). The flat band conditions make the bands k-independent, providing a highly a degenerate state, which gives broad possibilities for applications. In our work we have shown how the SOI is able to relax the strict, rigid flat band conditions given by the Hamiltonian coupling strengths. The role of the external magnetic field was also investigated.

Theory of the inverse Faraday effect due to the Rashba spin–oribt interactions: roles of band dispersions and Fermi surfaces

We theoretically study the inverse Faraday effect, i.e., the optical induction of spin polarization with circularly polarized light, by particularly focusing on effects of band dispersions and Fermi surfaces in crystal systems with the spin–orbit interaction (SOI). By numerically solving the time-dependent Schrödinger equation of a tight-binding model with the Rashba-type SOI, we reproduce the light-induced spin polarization proportional to where E0 and ω are the electric-field amplitude and the angular frequency of light, respectively. This optical spin induction is attributed to dynamical magnetoelectric coupling between the light electric field and the electron spins mediated by the SOI. We elucidate that the magnitude and sign of the induced spin polarization sensitively depend on the electron filling. To understand these results, we construct an analytical theory based on the Floquet theorem. The theory successfully explains the dependencies on E0 and ω and ascribes the electron-filling dependence to a momentum-dependent effective magnetic field governed by the Fermi-surface geometry. Several candidate materials and experimental conditions relevant to our theory and model parameters are also discussed. Our findings will enable us to engineer the magneto-optical responses of matters via tuning the material parameters.

Engineering the spin–orbit interaction in surface conducting diamond with a solid-state gate dielectric

Hydrogen-terminated (H-terminated) diamond, when surface transfer doped, can support a sub-surface two-dimensional (2D) hole band that possesses a strong Rashba-type spin–orbit interaction. By incorporating a V2O5/Al2O3 bilayer gate dielectric in a diamond-based metal–oxide–semiconductor architecture, metallic surface conductivity can be maintained at low temperature, avoiding the carrier freeze out exhibited by devices with an Al2O3 gate dielectric alone. Hole densities of up to 2.5 × 1013 cm−2 are achieved by the electrostatic gating of the device, and the spin–orbit interaction strength can be tuned from 3.5 ± 0.5 meV to 8.4 ± 0.5 meV, with a concurrent reduction in the spin coherence length from 40 ± 1 nm to 27 ± 1 nm. The demonstration of a gated device architecture on the H-terminated that avoids the need to cycle the temperature, as is required for ionic liquid gating protocols, opens a pathway to engineering practical devices for the study and application of spin transport in diamond.

Strong spin-orbit interaction induced by transition metal oxides at the surface of hydrogen-terminated diamond

Hydrogen-terminated diamond possesses an intriguing p-type surface conductivity which is induced via thermodynamically driven electron transfer from the diamond surface into surface acceptors such as atmospheric adsorbates, a process called surface transfer doping. High electron affinity transition metal oxides (TMOs) including MoO3 and V2O5 have been shown to be highly effective solid-state surface acceptors for diamond, giving rise to a sub-surface two-dimensional (2D) hole layer with metallic conduction. In this work, low temperature magnetotransport is used as a tool to show the presence of a Rashba-type spin-orbit interaction with a high spin-orbit coupling of 19.9 meV for MoO3 doping and 22.9 meV for V2O5 doping, respectively, through the observation of a transition in the phase-coherent backscattering transport from weak localization to weak antilocalization at low temperature. Surface transfer doping of diamond with TMOs provides a 2D hole system with spin-orbit coupling that is over two times larger than that reported for diamond surfaces with atmospheric acceptors, opening up possibilities to study and engineer spin transport in a carbon material system.

Spin-orbit torques in a Rashba honeycomb antiferromagnet

Recent experiments on switching antiferromagnetic domains by electric current pulses have attracted a lot of attention to spin-orbit torques in antiferromagnets. In this work, we employ the tight-binding model solver, kwant, to compute spin-orbit torques in a two-dimensional antiferromagnet on a honeycomb lattice with strong spin-orbit interaction of Rashba type. Our model combines spin-orbit interaction, local s-d-like exchange, and scattering of conduction electrons on on-site disorder potential to provide a microscopic mechanism for angular momentum relaxation. We consider two versions of the model: one with preserved and one with broken sublattice symmetry. A non-equilibrium staggered polarization, that is responsible for the so-called Neel spin-orbit torque, is shown to vanish identically in the symmetric model but may become finite if sublattice symmetry is broken. Similarly, anti-damping spin-orbit torques vanish in the symmetric model but become finite and anisotropic in a model with broken sublattice symmetry. As expected, anti-damping torques also reveal a sizable dependence on impurity concentration. Our numerical analysis also confirms symmetry classification of spin-orbit torques and strong torque anisotropy due to in-plane confinement of electron momenta.

Gate-Defined Quantum Dots in Ge/SiGe Quantum Wells as a Platform for Spin Qubits

In the field of semiconductor quantum dot spin qubits, there is growing interest in leveraging the unique properties of hole-carrier systems and their intrinsically strong spin-orbit coupling to engineer novel spin qubits. In contrast to the weak spin-orbit interaction found in Si, strong spin-orbit coupling in Ge may allow purely electrical spin control using the electric field component of a microwave drive signal applied to a confinement gate, without the need for additional components such as microwave stripline antennas or micromagnets. A crucial aspect in the search for alternative semiconductor qubit host materials is the need to maintain the advantages of existing platforms such as Si: low disorder, long coherence times, extensibility, and semiconductor foundry compatibility. Recent advances in semiconductor heterostructure growth have made available high quality, undoped Ge/SiGe quantum wells that can serve as hosts for hole spin qubits. These quantum wells consist of a pure strained Ge layer flanked by Ge-rich SiGe layers above and below, grown by reduced pressure chemical vapor deposition. Isotopic enrichment is possible if required. The heavy hole charge carriers are characterized by a small effective mass m* ~ 0.08m 0 (about 2.4x lighter than for electrons in Si), high mobility μ ≥ 1E5 cm2/Vs, and highly anisotropic g-factors. The small effective mass should allow relatively large and easily-coupled quantum dots. The next-nearest light hole band is theoretically predicted to be on the order of ~ 100 meV below the heavy hole band. The p-orbital character of the hole wavefunction may provide an advantage in minimizing contact hyperfine interactions with nonzero-spin lattice nuclei. There is both theoretical and experimental evidence of a cubic Rashba-type spin-orbit interaction in this material, whose large strength is manifest as a spin-orbit length on the order of 1 micrometer. An additional advantage over Si is that the two-dimensional band structure of Ge quantum wells does not feature valley states, which can present difficulties for qubit operations. Here, we will describe our ongoing efforts to prepare spin qubits in this platform, including development of gated device architectures, device tuning protocols, and charge-sensing capabilities. Initial work focused on single-layer gate layouts, in which lithographically-defined single and double quantum dots were demonstrated at dilution refrigerator temperatures. Charging energies of ~ 1.7 meV were observed. These devices featured a broad and shallow potential landscape, and only a small number of holes could be confined to a quantum dot. Although adjacent quantum dots could be coupled to one another, this coupling was not easily tuned using this gate design. These limitations in the confinement and control of quantum dots motivated the subsequent adoption of multilayer gate-stack architectures, similar to what has been demonstrated in Si. Our three-layer devices feature gate electrodes designed for accumulation of holes, local depletion to form quantum dots, and selective isolation/screening of electric fields. Device structures feature Ti/Pt gates, ALD oxide dielectrics, and implanted ohmic contacts. Symmetrically constructed devices comprise two gated channels for quantum dot confinement, one to be used as the quantum dot under study and the other operated as a local charge sensor. By monitoring the conductance of the charge sensor as the quantum dot is tuned, we can remotely determine the dot’s occupation number, in principle down to the last hole. Iterative cycles of device fabrication and measurement, combined with numerical modeling, have allowed continuous improvements to the device design. Early three-layer device designs suffered from poor isolation between the upper and lower mirror-symmetric device channels. Numerical modeling showed (and measurements have confirmed) that an additional isolation gate could allow improved autonomy of the two channels while maintaining their electrostatic coupling needed for charge sensing. Ongoing, simulation-informed work to fine-tune the device geometry, as well as efforts toward a qubit demonstration, will be discussed. This work was funded, in part, by the Laboratory Directed Research and Development Program and performed, in part, at the Center for Integrated Nanotechnologies, an Office of Science User Facility operated for the US Department of Energy (DOE) Office of Science. Sandia National Laboratories is a multi-mission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the US Department of Energy’s National Nuclear Security Administration under contract DE-NA-0003525. The views expressed in this article do not necessarily represent the views of the US Department of Energy or the United States Government. The work at NTU was supported by the Ministry of Science and Technology (107-2622-8-002-018-). Figure 1

Spin dynamics of hot excitons in diluted magnetic semiconductors with spin-orbit interaction

We explore the impact of a Rashba-type spin-orbit interaction in the conduction band on the spin dynamics of hot excitons in diluted magnetic semiconductor quantum wells. In materials with strong spin-orbit coupling, we identify parameter regimes where spin-orbit effects greatly accelerate the spin decay and even change the dynamics qualitatively in the form of damped oscillations. Furthermore, we show that the application of a small external magnetic field can be used to either mitigate the influence of spin-orbit coupling or entirely remove its effects for fields above a material-dependent threshold.

Gate-Defined Quantum Dots in Ge/SiGe Quantum Wells as a Platform for Spin Qubits

In the field of semiconductor quantum dot spin qubits, there is growing interest in leveraging the unique properties of hole-carrier systems and their intrinsically strong spin-orbit coupling to engineer novel qubits. Recent advances in semiconductor heterostructure growth have made available high quality, undoped Ge/SiGe quantum wells, consisting of a pure strained Ge layer flanked by Ge-rich SiGe layers above and below. These quantum wells feature heavy hole carriers and a cubic Rashba-type spin-orbit interaction. Here, we describe progress toward realizing spin qubits in this platform, including development of multi-metal-layer gated device architectures, device tuning protocols, and charge-sensing capabilities. Iterative improvement of a three-layer metal gate architecture has significantly enhanced device performance over that achieved using an earlier single-layer gate design. We discuss ongoing, simulation-informed work to fine-tune the device geometry, as well as efforts toward a single-spin qubit demonstration.

Asymmetric and Symmetric Exchange in a Generalized 2D Rashba Ferromagnet.

Dzyaloshinskii-Moriya interaction (DMI) is investigated in a 2D ferromagnet (FM) with spin-orbit interaction of Rashba type at finite temperatures. The FM is described in the continuum limit by an effective s-d model with arbitrary dependence of spin-orbit coupling (SOC) and kinetic energy of itinerant electrons on the absolute value of momentum. In the limit of weak SOC, we derive a general expression for the DMI constant D from a microscopic analysis of the electronic grand potential. We compare D with the exchange stiffness A and show that, to the leading order in small SOC strength α_{R}, the conventional relation D=(4mα_{R}/ℏ)A, in general, does not hold beyond the Bychkov-Rashba model. Moreover, in this model, both A and D vanish at zero temperature in the metal regime (i.e., when two spin sub-bands are partly occupied). For nonparabolic bands or nonlinear Rashba coupling, these coefficients are finite and acquire a nontrivial dependence on the chemical potential that demonstrates the possibility to control the size and chirality of magnetic textures by adjusting a gate voltage.

Temperature Dependence of Anomalous Hall Conductivity in Rashba-type Ferromagnets

The applicability and usefulness of Rashba model have been extended by recent observations in the field of spintronics, such as the spin-orbit torque at the junction interfaces between ferromagnetic (FM) metals and non-magnetic (NM) metals and the perpendicular anomalous magnetoresistance (AMR) in heterostructures such as FI/NM or FM/NI (I denotes an insulator). In particular, the observations of the perpendicular AMR effect stimulate further interest in the Rashba-type spin-orbit interaction (SOI) at interfaces. Thus, the Rashba model with exchange splitting (EXS) is considered not only to play as an effective model for the physical understanding but also to reflect actual bi-layer systems in current spintronics devices. In the present work, we have first investigated the temperature dependence of anomalous Hall conductivity (AHC) of Rashba-type ferromagnets considered effects of spin fluctuations within the disordered local moment (DLM) scheme. The most distinctive feature that we observed is that intrinsic AHC increases with increasing temperature. This can be understood from the aspect of spin chirality, which indicates that the AHC increases with decreasing EXS when the SOI is much smaller than the EXS. The extrinsic part of the Fermi surface term also increases with increasing temperature and has a large contribution, comparable to that of the intrinsic part. Although, such a behaviour has not yet been observed experimentally, we suggest that the physical picture found in this work might lurk in an anomalous Hall effects in Rashbe-type ferromagnets.

Effect of Rashba Spin–Orbit Interaction on the Stability of Spin-Vortex-Induced Loop Current in Hole-Doped Cuprate Superconductors: A Scenario for the Appearance of Magnetic Field Enhanced Charge Order and Fermi Surface Reconstruction

Rashba type spin–orbit interaction is included in the model Hamiltonian for the spin-vortex-induced loop current (SVILC) mechanism of superconductivity for hole doped cuprate superconductors and it...

Effect of Rashba type spin–orbit interaction on the electronic spectrum of graphene in the presence of a hydrogenic impurity

The effect of Rashba spin–orbit interaction on the electronic spectrum of gapped graphene with a hydrogenic impurity in the presence of topological defects is analyzed analytically. Degenerate perturbation theory is used to investigate the dependence of electronic spectrum of gapped graphene on the strengths of impurity and Rashba spin–orbit coupling. The results show that, as the strength of Rashba spin–orbit coupling increases, pseudo-Zeeman splitting of energy levels induced by topological defects is enhanced. Therefore, it is possible to tune this pseudo-Zeeman splitting through the strength of Rashba spin–orbit coupling and of the strength of hydrogenic impurity.

Effect of disorder on superconductivity and Rashba spin-orbit coupling in LaAlO3 / SrTiO3 interfaces

A rather unique feature of the two-dimensional electron gas formed at the interface between the two insulators ${\mathrm{LaAlO}}_{3}$ and ${\mathrm{SrTiO}}_{3}$ is to host both gate-tunable superconductivity and strong spin-orbit coupling. In the present work, we use the disorder generated by Cr substitution of Al atoms in ${\mathrm{LaAlO}}_{3}$ as a tool to explore the nature of superconductivity and spin-orbit coupling in these interfaces. We analyze the transport properties of three different samples whose only relevant difference is their elastic scattering time ${\ensuremath{\tau}}_{e}$. A reduction of the superconducting ${T}_{c}$ is observed with Cr doping consistent with an increase of electron-electron interaction in the presence of disorder. In addition, the evolution of spin-orbit coupling with gate voltage and Cr doping evidences a Dyakonov-Perel mechanism of spin relaxation (${\ensuremath{\tau}}_{\mathrm{SO}}\ensuremath{\propto}{\ensuremath{\tau}}_{e}^{\ensuremath{-}1}$) in the presence of a Rashba-type spin-orbit interaction.