Giant spin splitting through surface alloying

Theory of spin and orbital Edelstein effects

In systems with broken spatial inversion symmetry, such as surfaces, interfaces, or bulk systems lacking an inversion center, the application of a charge current can generate finite spin and orbital densities associated with a nonequilibrium magnetization, which is known as spin and orbital Edelstein effect (SEE and OEE), respectively. Early reports on this current-induced magnetization focus on two-dimensional Rashba systems, in which an in-plane nonequilibrium spin density is generated perpendicular to the applied charge current. However, until today, a large variety of materials have been theoretically predicted and experimentally demonstrated to exhibit a sizeable Edelstein effect, which comprises contributions from the spin as well as the orbital degrees of freedom, and whose associated magnetization may be out of plane, nonorthogonal, and even parallel to the applied charge current, depending on the system's particular symmetries. In this review, we give an overview on the most commonly used theoretical approaches for the discussion and prediction of the SEE and OEE. Further, we introduce a selection of the most intensely discussed materials exhibiting a finite Edelstein effect, and give a brief summary of common experimental techniques.

Noncollinear Electric Dipoles in a Polar Chiral Phase of CsSnBr3 Perovskite

Polar and chiral crystal symmetries confer a variety of potentially useful functionalities upon solids by coupling otherwise noninteracting mechanical, electronic, optical, and magnetic degrees of freedom. We describe two phases of the 3D perovskite, CsSnBr3, which emerge below 85 K due to the formation of Sn(II) lone pairs and their interaction with extant octahedral tilts. Phase II (77 K < T < 85 K, space group P21/m) exhibits ferroaxial order driven by a noncollinear pattern of lone pair-driven distortions within the plane normal to the unique octahedral tilt axis, preserving the inversion symmetry observed at higher temperatures. Phase I (T < 77 K, space group P21) additionally exhibits ferroelectric order due to distortions along the unique tilt axis, breaking both inversion and mirror symmetries. This polar and chiral phase exhibits second harmonic generation from the bulk and pronounced electrostriction and negative thermal expansion along the polar axis (Q22 ≈ 1.1 m4 C-2; αb = -7.8 × 10-5 K-1) through the onset of polarization. The structures of phases I and II were predicted by recursively following harmonic phonon instabilities to generate a tree of candidate structures and subsequently corroborated by synchrotron X-ray powder diffraction and polarized Raman and 81Br nuclear quadrupole resonance spectroscopies. Preliminary attempts to suppress unintentional hole doping to allow for ferroelectric switching are described. Together, the polar symmetry, small band gap, large spin-orbit splitting of Sn 5p orbitals, and predicted strain sensitivity of the symmetry-breaking distortions suggest bulk samples and epitaxial films of CsSnBr3 or its neighboring solid solutions as candidates for bulk Rashba effects.

The impact of Rashba spin-orbit coupling in charge-ordered systems

We study the impact of the Rashba spin-orbit coupling (RSOC) on the stability of charge-density wave (CDW) in systems with large electron-phonon coupling (EPC). Here, the EPC is considered in the framework of the Holstein model at the half-filled square lattice. We obtain the phase diagram of the Rashba-Holstein model using the Hartree-Fock mean-field theory, and identify the boundaries of the CDW and Rashba metal phases. We notice that the RSOC disfavors the CDW phase, driving the system to a correlated Rashba metal. Also, we employ a cluster perturbation theory (CPT) approach to investigate the phase diagram beyond the Hartree-Fock approximation. The quantum correlations captured by CPT indicate that the RSOC is even more detrimental to CDW than previously anticipated. That is, the Rashba metal region is observed to be expanded in comparison to the mean-field case. Additionally, we investigate pairing correlations, and the results further strengthen the identification of critical points.

Orbital Rashba Effect as a Platform for Robust Orbital Photocurrents

Orbital current has emerged over the past years as one of the key novel concepts in magnetotransport. Here, we demonstrate that laser pulses can be used to generate large and robust nonrelativistic orbital currents in systems where the inversion symmetry is broken by the orbital Rashba effect. By referring to model and first principles tools, we demonstrate that orbital Rashba effect, accompanied by crystal field splitting, can mediate robust orbital photocurrents without a need for spin-orbit interaction even in metallic systems. We show that such nonrelativistic orbital photocurrents are translated into derivative photocurrents of spin when relativistic effects are taken into account. We thus promote orbital photocurrents as a promising platform for optical generation of currents of angular momentum, and discuss their possible applications.

Probing Spin-Dependent Ballistic Charge Transport at Single-Nanometer Length Scales

The coherent transport of charge and spin is a key requirement of future devices for quantum computing and communication. Scattering at defects or impurities may significantly reduce the coherence of quantum-mechanical states, thereby affecting the device functionality. While numerous methods exist to experimentally assess charge transport, the real-space detection of a material's ballistic spin transport properties with nanometer resolution remains a challenge. Here we report on a novel approach that utilizes a combination of spin-polarized scanning tunneling microscopy (SP-STM) and the recently introduced molecular nanoprobe (MONA) technique. It relies on the local injection of spin-polarized charge carriers from a magnetic STM tip and their detection by a single surface-deposited phthalocyanine molecule via reversible electron-induced tautomerization events. Based on the particular electronic structure of the Rashba alloy BiAg2, which is governed by a spin-momentum-locked surface state, we prove that the current direction inverses upon tip magnetization reversal.

Phase biasing of a Josephson junction using Rashba-Edelstein effect

A charge-current-induced shift in the spin-locked Fermi surface leads to a non-equilibrium spin density at a Rashba interface, commonly known as the Rashba-Edelstein effect. Since this is an intrinsically interfacial property, direct detection of the spin moment is difficult. Here we demonstrate that a planar Josephson Junction, realized by placing two closely spaced superconducting electrodes over a Rashba interface, allows for a direct detection of the spin moment as an additional phase in the junction. Asymmetric Fraunhofer patterns obtained for Nb-(Pt/Cu)-Nb nano-junctions, due to the locking of Rashba-Edelstein spin moment to the flux quantum in the junction, provide clear signatures of this effect. This simple experiment offers a fresh perspective on direct detection of spin polarization induced by various spin-orbit effects. In addition, this platform also offers a magnetic-field-controlled phase biasing mechanism in conjunction with the Rashba-Edelstein spin-orbit effect for superconducting quantum circuits.

Rashba effect: a chemical physicist's approach

Understanding the mechanisms underlying the emergence of giant spin splitting (GSS) is fundamental in the pursuit of more robust strategies for designing materials with desired spin splitting. This drive for material innovation continues to captivate a burgeoning community of early-career researchers with backgrounds in chemistry and material science. However, new to the field, they are often equipped only with the insight provided by the original Bychkov-Rashba model. Furthermore, daunted by the tight-binding perspective on the non-vanishing orbital angular momentum (OAM), they struggle to accurately account for the atomic spin-orbit interaction (SOI) in the formation of GSS. To address these challenges and equip young chemists with better-suited tools, this review aims to provide a more intuitive perspective on atomic interactions (orbital hybridization), structure symmetry, and atomic SOI in the formation of GSS. In pursuit of this goal, the review explores the Bychkov-Rashba model, its advantages, and limitations. Subsequently, it introduces the orbital framework, wherein GSS is modulated by atomic SOI and the interplay of OAM with the surface electrostatic field. Given the explicit dependence of both these factors on OAM, the review examines why OAM is typically quenched in crystal structures and how chemical bonds involving different orbital types can lead to its non-zero values in the presence of inversion symmetry breaking. Finally, with this chemistry-focused perspective, the review examines the rise of GSS in selected examples.

Giant Spin-Orbit Torque in Sputter-Deposited Bi Films

Bismuth (Bi) has the strongest spin-orbit coupling among non-radioactive elements and is thus a promising material for efficient charge-to-spin conversion. However, previous electrical detections have reported controversial results for the conversion efficiency. In this study, an optical detection of a spin-orbit torque is reported in a Bi/CoFeB bilayer with a polycrystalline texture of (012) and (003). Taking advantage of the optical detection, spin-orbit torque is accurately separated from the Oersted field and achieves a giant damping-like torque efficiency of +0.5, verifying efficient charge-to-spin conversion. This study also demonstrates a field-like torque efficiency of -0.1. For the mechanism of the charge-to-spin conversion, the bulk spin Hall effect and the interface Rashba-Edelstein effect are considered.

Large interlayer Dzyaloshinskii-Moriya interactions across Ag-layers

Seeking to enhance the strength of the interlayer Dzyaloshinskii-Moriya interaction (IL-DMI) through a combination of atomic and Rashba type spin-orbit coupling (SOC) we studied the strength and the thickness evolution of effective interlayer coupling in Co/Ag/Co trilayers by means of surface sensitive magneto-optical measurements that take advantage of the light penetration depth. Here, we report the observation of oscillatory, thickness-dependent chiral interaction between ferromagnetic layers. Despite the weakness of the Ag atomic SOC, the IL-DMI in our trilayers is orders of magnitude larger than that of known systems using heavy metals as a spacer except of recently reported -0.15 mJ/m2 in Co/Pt/Ru(t)/Pt/Co and varies between ≈ ±0.2 mJ/m2. In contrast to known multilayers Co/Ag/Co promotes in-plane chirality between magnetic layers. The strength of IL-DMI opens up new routes for design of three-dimensional chiral spin structures combining intra- and interlayer DMI and paves the way for enhancements of the DMI strength.

Advantages of Ferroelectrics as a Component of Heterostructures for Electronic Purposes: A DFT Insight

The main advantage of using ferroelectric materials as a component of complex heterostructures is the ability to tune various properties of the whole system by means of an external electric field. In particular, the electric field may change the polarization direction within the ferroelectric material and consequently affect the structural properties, which in turn affects the electronic and magnetic properties of the neighboring material. In addition, ferroelectrics allow the electrostriction phenomenon to proceed, which is promising and can be used to affect the magnetic states of the interface state in the heterostructure through a magnetic component. The interfacial phenomena are of great interest, as they provide extended functionality useful for next-generation electronic devices. Following the idea of utilizing ferroelectrics in heterostructural components in the present works, we consider 2DEG, the Rashba effect, the effect of magnetoelectric coupling, and magnetostriction in order to emphasize the advantages of such heterostructures as components of devices. For this purpose, model systems of LaMnO3/BaTiO3, La2CuO4/BaTiO3, Bi/BaTiO3, and Bi/PbTiO3, Fe/BaTiO3 heterostructures are investigated using density functional theory calculations.

Large-band-gap non-Dirac quantum spin Hall states and strong Rashba effect in functionalized thallene films

The quantum spin Hall state materials have recently attracted much attention owing to their potential applications in the design of spintronic devices. Based on density functional theory calculations and crystal field theory, we study electronic structures and topological properties of functionalized thallene films. Two different hydrogenation styles (Tl2H and Tl2H2) are considered, which can drastically vary the electronic and topological behaviors of the thallene. Due to the C3v symmetry of the two systems, the px and py orbitals at the Γ point have the non-Dirac band degeneracy. With spin-orbit coupling (SOC), topological nontrivial band gaps can be generated, giving rise to non-Dirac quantum spin Hall states in the two thallium hydride films. The nontrivial band gap for the monolayer Tl2H is very large (855 meV) due to the large on-site SOC of Tl px and py orbitals. The band gap in Tl2H2 is, however, small due to the band inversion between the Tl px/y and pz orbitals. It is worth noting that both the Tl2H and Tl2H2 monolayers exhibit strong Rashba spin splitting effects, especially for the monolayer Tl2H2 (αR = 2.52 eVÅ), rationalized well by the breaking of the structural inversion symmetry. The Rashba effect can be tuned sensitively by applying biaxial strain and external electric fields. Our findings provide an ideal platform for fabricating room-temperature spintronic and topological electronic devices.

In Situ Exfoliation Method of Large-Area 2D Materials

2D materials provide a rich platform to study novel physical phenomena arising from quantum confinement of charge carriers. Many of these phenomena are discovered by surface sensitive techniques, such as photoemission spectroscopy, that work in ultra-high vacuum (UHV). Success in experimental studies of 2D materials, however, inherently relies on producing adsorbate-free, large-area, high-quality samples. The method that yields 2D materials of highest quality is mechanical exfoliation from bulk-grown samples. However, as this technique is traditionally performed in a dedicated environment, the transfer of samples into vacuum requires surface cleaning that might diminish the quality of the samples. In this article, a simple method for in situ exfoliation directly in UHV is reported, which yields large-area, single-layered films. Multiple metallic and semiconducting transition metal dichalcogenides are exfoliated in situ onto Au, Ag, and Ge. The exfoliated flakes are found to be of sub-millimeter size with excellent crystallinity and purity, as supported by angle-resolved photoemission spectroscopy, atomic force microscopy, and low-energy electron diffraction. The approach is well-suited for air-sensitive 2D materials, enabling the study of a new suite of electronic properties. In addition, the exfoliation of surface alloys and the possibility of controlling the substrate-2D material twist angle is demonstrated.

Current Understanding of Band-Edge Properties of Halide Perovskites: Urbach Tail, Rashba Splitting, and Exciton Binding Energy

The band-edge structure of halide perovskites, derived from the hybridization of atomic orbitals, plays a fundamental role in determining their optical and electronic properties. Several important concepts have been frequently discussed to describe the influence of band-edge structure on their optoelectronic properties, including Urbach tail, Rashba splitting, and exciton binding energy. In this Perspective, we provide a fundamental understanding of these concepts, with the focus on their dependence on composition, structure, or dimensionality. Subsequently, the implications for material optimization and device fabrication are discussed. Furthermore, we highlight the Rashba effect on the exciton fine structure in perovskite nanocrystals (PNCs), which explains the unique emissive properties. Finally, we discuss the potential influence of band-edge properties on the light emission process. We hope that this Perspective can inspire the investigation of band-edge properties of halide perovskites for light-emitting diodes, lasers, and spin electronics.

A Noble-Metal-Free Spintronic System with Proximity-Enhanced Ferromagnetic Topological Surface State of FeSi above Room Temperature

Strongly spin-orbit coupled states at metal interfaces, topological insulators, and 2D materials enable efficient electric control of spin states, offering great potential for spintronics. However, there are still materials challenges to overcome, including the integration into advanced silicon electronics and the scarce resources of constituent heavy elements of those materials. Through magneto-transport measurements and first-principles calculations, here robust spin-orbit coupling (SOC)-induced properties of a ferromagnetic topological surface state in FeSi and their controllability via hybridization with adjacent materials are demonstrated. In comparison to the case of its naturally oxidized surface, the ferromagnetic transition temperature is greatly increased beyond room temperature and the effective SOC strength is almost doubled at the surface in proximity to a wide-bandgap fluoride insulator. Those enhanced magnetic properties enable room-temperature magnetization switching, being applicable to spin-orbit torque based spintronic devices. Realization of strong SOC in the noble-metal-free silicon-based compound will accelerate spintronic applications.

Large Spin Hall Conductivity and Excellent Hydrogen Evolution Reaction Activity in Unconventional PtTe1.75 Monolayer

Two-dimensional (2D) materials have gained lots of attention due to the potential applications. In this work, we propose that based on first-principles calculations, the (2 × 2) patterned PtTe₂ monolayer with kagome lattice formed by the well-ordered Te vacancy (PtTe_1.75) hosts large and tunable spin Hall conductivity (SHC) and excellent hydrogen evolution reaction (HER) activity. The unconventional nature relies on the A1 @ 1b band representation of the highest valence band without spin-orbit coupling (SOC). The large SHC comes from the Rashba SOC in the noncentrosymmetric structure induced by the Te vacancy. Even though it has a metallic SOC band structure, the ℤ₂ invariant is well defined because of the existence of the direct bandgap and is computed to be nontrivial. The calculated SHC is as large as 1.25 × 10³ ℏ e (Ω cm)^-1 at the Fermi level (E_F ). By tuning the chemical potential from E_F - 0.3 to E_F + 0.3 eV, it varies rapidly and monotonically from -1.2 × 10³ to 3.1 × 1 0 3 ℏ e Ω   cm - 1 . In addition, we also find that the Te vacancy in the patterned monolayer can induce excellent HER activity. Our results not only offer a new idea to search 2D materials with large SHC, i.e., by introducing inversion-symmetry breaking vacancies in large SOC systems, but also provide a feasible system with tunable SHC (by applying gate voltage) and excellent HER activity.

MX family: an efficient platform for topological spintronics based on Rashba and Zeeman-like spin splittings

Taking various combinations of M = (Mo, W) and X = (C, S, Se) as examples, we propose that MX (M = transition metals, X = IV,V or VI elements) family can establish an excellent platform for both conventional and topological spintronics applications based on anisotropic Rashba-like and non-magnetic Zeeman-type spin splittings with electrically tunable nature. In particular, we observe sizeable Zeeman-like and Rashba-like spin splittings with an anisotropic nature. Meanwhile, they exhibit Rashba-like and topologically robust helical edge states when grown in ferroelectric and paraelectric phases, respectively. These MX monolayers are realized to be quantum valley Hall insulators due to valley contrasting Berry curvatures. The carriers in these MX monolayers can be selectively excited from opposite valleys depending on the polarity of circularly polarized light. The amplitude of the spin splitting can be further tuned by applying external means such as strain, electric field or alloy engineering. Furthermore, considering graphene sheet over the WC monolayer as a prototype example, we show that these MX monolayers can boost the relativistic effect by coupling with the systems exhibiting extremely weak spin-orbit coupling (SOC). Depending on the surface of WC monolayer in contact with the graphene sheet, graphene over WC monolayer passes through the transformation from the semiconducting junction to the Shotcky barrier-free contact. Finally, we reveal that these MX monolayers could also be grown on the substrates such as WS2(001)and GaTe (001) with type-II band alignment, where electron and hole become layer splitted across the interface. Our analysis should be fairly applied to other systems with strong SOC and an equivalent geometrical structure to the MX monolayers.

Direct visualization of Rashba-split bands and spin/orbital-charge interconversion at KTaO3 interfaces

Rashba interfaces have emerged as promising platforms for spin-charge interconversion through the direct and inverse Edelstein effects. Notably, oxide-based two-dimensional electron gases display a large and gate-tunable conversion efficiency, as determined by transport measurements. However, a direct visualization of the Rashba-split bands in oxide two-dimensional electron gases is lacking, which hampers an advanced understanding of their rich spin-orbit physics. Here, we investigate KTaO₃ two-dimensional electron gases and evidence their Rashba-split bands using angle resolved photoemission spectroscopy. Fitting the bands with a tight-binding Hamiltonian, we extract the effective Rashba coefficient and bring insight into the complex multiorbital nature of the band structure. Our calculations reveal unconventional spin and orbital textures, showing compensation effects from quasi-degenerate band pairs which strongly depend on in-plane anisotropy. We compute the band-resolved spin and orbital Edelstein effects, and predict interconversion efficiencies exceeding those of other oxide two-dimensional electron gases. Finally, we suggest design rules for Rashba systems to optimize spin-charge interconversion performance.

Visualization of the Rashbasplit bands in oxide two-dimensional electron gases is lacking, which hampers understanding of their rich spin-orbit physics. Here, the authors investigate KTaO₃ two dimensional electron gases and their Rashba-split bands.

The Giant Spin-to-Charge Conversion of the Layered Rashba Material BiTeI

Rashba spin-orbit coupling (SOC) could facilitate an efficient interconversion between spin and charge currents. Among various systems, BiTeI holds one of the largest Rashba-type spin splittings. Unlike other Rashba systems (e.g., Bi/Ag and Bi₂Se₃), an experimental investigation of the spin-to-charge interconversion in BiTeI remains to be explored. Through performing an angle-resolved photoemission spectroscopy (ARPES) measurement, such a large Rashba-type spin splitting with a Rashba parameter α_R = 3.68 eV Å is directly identified. By studying the spin pumping effect in the BiTeI/NiFe bilayer, we reveal a very large inverse Rashba-Edelstein length λ_IREE ≈ 1.92 nm of BiTeI at room temperature. Furthermore, the λ_IREE monotonously increases to 5.00 nm at 60 K, indicating an enhanced Rashba SOC at low temperature. These results suggest that BiTeI films with the giant Rashba SOC are promising for achieving efficient spin-to-charge interconversion, which could be implemented for building low-power-consumption spin-orbitronic devices.

Coherent Picture on the Pure Spin Transport between Ag/Bi and Ferromagnets

In a joint effort of both experiments and first-principles calculations, we resolve a hotly debated controversy and provide a coherent picture on the pure spin transport between Ag/Bi and ferromagnets. We demonstrate a strong inverse Rashba-Edelstein effect (IREE) at the interface in between Ag/Bi with a ferromagnetic metal (FM) but not with a ferromagnetic insulator. This is in sharp contrast to the previously claimed IREE at Ag/Bi interface or inverse spin Hall effect dominated spin transport. A more than one order of magnitude modulation of IREE signal is realized for different Ag/Bi-FM interfaces, casting strong tunability and a new direction for searching efficient spintronics materials.

Magnetoelectric effects in Josephson junctions

The review is devoted to the fundamental aspects and characteristic features of the magnetoelectric effects, reported in the literature on Josephson junctions (JJs). The main focus of the review is on the manifestations of the direct and inverse magnetoelectric effects in various types of Josephson systems. They provide a coupling of the magnetization in superconductor/ferromagnet/superconductor JJs to the Josephson current. The direct magnetoelectric effect is a driving force of spin torques acting on the ferromagnet inside the JJ. Therefore it is of key importance for the electrical control of the magnetization. The inverse magnetoelectric effect accounts for the back action of the magnetization dynamics on the Josephson subsystem, in particular, making the JJ to be in the resistive state in the presence of the magnetization dynamics of any origin. The perspectives of the coupling of the magnetization in JJs with ferromagnetic interlayers to the Josephson current via the magnetoelectric effects are discussed.

Ab initiodescription of disorder effects in layered cathode active materials by the coherent potential approximation

Disorder effects in alloys are usually modeled by averaging various supercell calculations considering different positions of the alloy atoms. This approach, however, is only possible as long as the portion of the individual components of the alloy is sufficiently large. Herein, we present anab initiostudy considering the lithium insertion material Li_1-x[Ni_0.33Co_0.33Mn_0.33]O₂as model system to demonstrate the power of the coherent potential approximation within the Korringa-Kohn-Rostoker Green's function method. This approach enables the description of disorder effects within alloy systems of any composition. It is applied in this study to describe the (de-)intercalation of arbitrary amounts of lithium from the cathode active material. Moreover, we highlight that using either fully optimized structures or experimental lattice parameters and atomic positions both lead to comparable results. Our findings suggest that this approach is also suitable for modeling the electronic structure of state-of-the-art materials such as high-nickel alloys.

Thickness dependent band structure of-bismuthene grown on epitaxial graphene

Along with the great interest in two-dimensional elemental materials that has emerged in recent years, atomically thin layers of bismuth have attracted attention due to physical properties on account of a strong spin-orbit coupling. Thickness dependent electronic band structure must be explored over the whole Brillouin zone in order to further explore their topological electronic properties. The anisotropic band structures along zig-zag and armchair directions of α-bismuthene (α-Bi) were resolved using the two-dimensional mapping of angle-resolved photoemission spectra. An increase in the number of layers from 1- to 2-bilayers (BLs) shifts the top of a hole band onΓ¯-X¯1line to high wavenumber regions. Subsequently, an electron pocket onΓ¯-X¯1line and a hole pocket centred atΓ¯point appears in the 3 BL α-Bi. Gapless Dirac-cone features with a large anisotropy were clearly resolved onX¯2point in the 1-BL and 2-BL α-Bi, which can be attributed to the strong spin-orbit coupling and protection by the nonsymmorphic symmetry of the α-Bi lattice.

Precursors of Majorana modes and their length-dependent energy oscillations probed at both ends of atomic Shiba chains

Isolated Majorana modes (MMs) are highly non-local quantum states with non-Abelian exchange statistics, which localize at the two ends of finite-size 1D topological superconductors of sufficient length. Experimental evidence for MMs is so far based on the detection of several key signatures: for example, a conductance peak pinned to the Fermi energy or an oscillatory peak splitting in short 1D systems when the MMs overlap. However, most of these key signatures were probed only on one of the ends of the 1D system, and firm evidence for an MM requires the simultaneous detection of all the key signatures on both ends. Here we construct short atomic spin chains on a superconductor-also known as Shiba chains-up to a chain length of 45 atoms using tip-assisted atom manipulation in scanning tunnelling microscopy experiments. We observe zero-energy conductance peaks localized at both ends of the chain that simultaneously split off from the Fermi energy in an oscillatory fashion after altering the chain length. By fitting the parameters of a low-energy model to the data, we find that the peaks are consistent with precursors of MMs that evolve into isolated MMs protected by an estimated topological gap of 50 μeV in chains of at least 35 nm length, corresponding to 70 atoms.

Rashba splitting in organic-inorganic lead-halide perovskites revealed through two-photon absorption spectroscopy

The Rashba splitting in hybrid organic-inorganic lead-halide perovskites (HOIP) is particularly promising and yet controversial, due to questions surrounding the presence or absence of inversion symmetry. Here we utilize two-photon absorption spectroscopy to study inversion symmetry breaking in different phases of these materials. This is an all-optical technique to observe and quantify the Rashba effect as it probes the bulk of the materials. In particular, we measure two-photon excitation spectra of the photoluminescence in 2D, 3D, and anionic mixed HOIP crystals, and show that an additional band above, but close to the optical gap is the signature of new two-photon transition channels that originate from the Rashba splitting. The inversion symmetry breaking is believed to arise from ionic impurities that induce local electric fields. The observation of the Rashba splitting in the bulk of HOIP has significant implications for the understanding of their spintronic and optoelectronic device properties.

Theory of unidirectional magnetoresistance and nonlinear Hall effect

We study the unidirectional magnetoresistance (UMR) and the nonlinear Hall effect (NLHE) in the ferromagnetic Rashba model. For this purpose we derive expressions to describe the response of the electric current quadratic in the applied electric field. We compare two different formalisms, namely the standard Keldysh nonequilibrium formalism and the Moyal-Keldysh formalism, to derive the nonlinear conductivities of UMR and NLHE. We find that both formalisms lead to identical numerical results when applied to the ferromagnetic Rashba model. The UMR and the NLHE nonlinear conductivities tend to be comparable in magnitude according to our calculations. Additionally, their dependencies on the Rashba parameter and on the quasiparticle broadening are similar. The nonlinear zero-frequency response considered here is several orders of magnitude higher than the one at optical frequencies that describes the photocurrent generation in the ferromagnetic Rashba model. Additionally, we compare our Keldysh nonequilibrium expression in the independent-particle approximation to literature expressions of the UMR that have been obtained within the constant relaxation time approximation of the Boltzmann formalism. We find that both formalisms converge to the same analytical formula in the limit of infinite relaxation time. However, remarkably, we find that the Boltzmann result does not correspond to the intraband term of the Keldysh expression. Instead, the Boltzmann result corresponds to the sum of the intraband term and an interband term that can be brought into the form of an effective intraband term due to thef-sum rule.

Coexisting unconventional Rashba- and Zeeman-type spin splitting in Pb-adsorbed monolayer WSe2

Based on first-principles calculations, the unconventional Rashba- and Zeeman-type spin splitting can simultaneously coexist in the Pb-adsorbed monolayer WSe₂system. The first two adsorption configurationst₁andt₂show remarkable features under the spin-orbit coupling, in which two split energy branches show same spin states at the left or right side of Γ, and the spin polarization is reversed for both Rashba band branches. For the second adsorption configuration, an energy gap was observed near the unconventional spin polarization caused by the repelled Rashba bands for avoid crossing, and this gap can produce non-dissipative spin current by applying the voltage. The results fort₂configuration with spin reversal show that the repel band gap and Rashba parameter can be effectively regulated within the biaxial strain range of -8% to 6%. By changing the adsorption distancedbetween Pb and the neighboring Se atom layer, the reduceddcaused the transfer from Rashba-type to Zeeman-type spin splitting. This predicted adsorption system would be promising for spintronic applications.

Berry curvature induced magnetotransport in 3D noncentrosymmetric metals

We study the magnetoelectric and magnetothermal transport properties of noncentrosymmetric metals using semiclassical Boltzmann transport formalism by incorporating the effects of Berry curvature (BC) and orbital magnetic moment (OMM). These effects impart quadratic-Bdependence to the magnetoelectric and magnetothermal conductivities, leading to intriguing phenomena such as planar Hall effect, negative magnetoresistance (MR), planar Nernst effect and negative Seebeck effect. The transport coefficients associated with these effects show the usual oscillatory behavior with respect to the angle between the applied electric field and magnetic field. The bands of noncentrosymmetric metals are split by Rashba spin-orbit coupling except at a band touching point (BTP). For Fermi energy below (above) the BTP, giant (diminished) negative MR is observed. This difference in the nature of MR is related to the magnitudes of the velocities, BC and OMM on the respective Fermi surfaces, where the OMM plays the dominant role. The absolute MR and planar Hall conductivity show a decreasing (increasing) trend with Rashba coupling parameter for Fermi energy below (above) the BTP.

Prediction of giant and ideal Rashba-type splitting in ordered alloy monolayers grown on a polar surface

A large and ideal Rashba-type spin-orbit splitting is desired for the applications of materials in spintronic devices and the detection of Majorana fermions in solids. Here, we propose an approach to achieve giant and ideal spin-orbit splittings through a combination of ordered surface alloying and interface engineering, that is, growing alloy monolayers on an insulating polar surface. We illustrate this unique strategy by means of first-principle calculations of buckled hexagonal monolayers of SbBi and PbBi supported on Al₂O₃(0001). Both systems display ideal Rashba-type states with giant spin-orbit splittings, characterized with energy offsets over 600 meV and momentum offsets over 0.3 Å⁻¹, respectively. Our study thus points to an effective way of tuning spin-orbit splitting in low-dimensional materials to draw immediate experimental interest.

Dynamic Spin-Triplet Order Induced by Alternating Electric Fields in Superconductor-Ferromagnet-Superconductor Josephson Junctions

Dynamic states offer extended possibilities to control the properties of quantum matter. Recent efforts are focused on studying the ordered states which appear exclusively under the time-dependent drives. Here, we demonstrate a class of systems which feature dynamic spin-triplet superconducting order stimulated by the alternating electric field. The effect is based on the interplay of ferromagnetism, interfacial spin-orbital coupling, and the condensate motion driven by the field, which converts hidden static p-wave order, produced by the joint action of the ferromagnetism and the spin-orbital coupling, into dynamic s-wave equal-spin-triplet correlations. We demonstrate that the critical current of Josephson junctions hosting these states is proportional to the electromagnetic power, supplied either by the external irradiation or by the ac current source. Based on these unusual properties we propose the scheme of a Josephson transistor which can be switched by the ac voltage and demonstrates an even-numbered sequence of Shapiro steps. Combining the photoactive Josephson junctions with recently discovered Josephson phase batteries we find photomagnetic SQUID devices which can generate spontaneous magnetic fields while being exposed to irradiation.

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.

Large Rashba splitting, carrier mobility, and valley polarization in a 1T-SnS2/MoTe2 heterostructure

The structural and electronic properties of the 1T-SnS2/MoTe2 heterostructure were investigated based on density functional theory and Berry curvature calculations. Considering the strong spin-orbit coupling and space inversion asymmetry, large Rashba spin splitting of electronic bands appeared in this hybrid system. The Rashba coupling parameter αR in 1T-SnS2/MoTe2 reached 0.383 eV Å. Importantly, αR can be effectively tuned by biaxial strain. Moreover, our first-principles calculations show that the 1T-SnS2/MoTe2 heterostructure possesses a high carrier mobility of 5038.46 cm2 V-1 s-1. The Berry curvature and spin splitting were opposite at the K and K' valleys. Hence, the valleys and spins were simultaneously locked and polarized, and the valley and spin Hall effects simultaneously occurred.

Spin-to-Charge Conversion in Ag/Bi Bilayer Revisited

The spin-to-charge conversion of the Ag/Bi interface is studied in a device in which a spin current can be injected from either side selectively. The charge voltages generated by the two counterpropagating spin currents show opposite signs, that is consistent with the inverse spin Hall effect rather than the well-accepted inverse Rashba-Eldestein effect in the Ag/Bi bilayer. Femtosecond laser is further employed to generate the spin-current-induced terahertz signal in a Ag/Bi bilayer, which shows no evidence for the inverse Rashba-Eldestein effect, either. This work provides a clear-cut method to identify the spin-to-charge mechanism in a Rashba electronic state and delivers new understanding for the relevant spin-transport phenomena.

Transverse Transport in Two-Dimensional Relativistic Systems with Nontrivial Spin Textures

Using multiple scattering theory, we show that the generally accepted expression of transverse resistivity in magnetic systems that host skyrmions, given by the linear superposition of the ordinary, the anomalous, and the topological Hall effect, is incomplete and must be amended by an additional term, the "noncollinear" Hall effect (NHE). Its angular form is determined by the magnetic texture, the spin-orbit field of the electrons, and the underlying crystal structure, allowing us to disentangle the NHE from the various other Hall contributions. Its magnitude is proportional to the spin-orbit interaction strength. The NHE is an essential term required for decoding two- and three-dimensional spin textures from transport experiments.

Quasiparticle interference and quantum confinement in a correlated Rashba spin-split 2D electron liquid

Exploiting inversion symmetry breaking (ISB) in systems with strong spin-orbit coupling promises control of spin through electric fields-crucial to achieve miniaturization in spintronic devices. Delivering on this promise requires a two-dimensional electron gas with a spin precession length shorter than the spin coherence length and a large spin splitting so that spin manipulation can be achieved over length scales of nanometers. Recently, the transition metal oxide terminations of delafossite oxides were found to exhibit a large Rashba spin splitting dominated by ISB. In this limit, the Fermi surface exhibits the same spin texture as for weak ISB, but the orbital texture is completely different, raising questions about the effect on quasiparticle scattering. We demonstrate that the spin-orbital selection rules relevant for conventional Rashba system are obeyed as true spin selection rules in this correlated electron liquid and determine its spin coherence length from quasiparticle interference imaging.

Spin-orbit coupling induced splitting of Yu-Shiba-Rusinov states in antiferromagnetic dimers

Magnetic atoms coupled to the Cooper pairs of a superconductor induce Yu-Shiba-Rusinov states (in short Shiba states). In the presence of sufficiently strong spin-orbit coupling, the bands formed by hybridization of the Shiba states in ensembles of such atoms can support low-dimensional topological superconductivity with Majorana bound states localized on the ensembles’ edges. Yet, the role of spin-orbit coupling for the hybridization of Shiba states in dimers of magnetic atoms, the building blocks for such systems, is largely unexplored. Here, we reveal the evolution of hybridized multi-orbital Shiba states from a single Mn adatom to artificially constructed ferromagnetically and antiferromagnetically coupled Mn dimers placed on a Nb(110) surface. Upon dimer formation, the atomic Shiba orbitals split for both types of magnetic alignment. Our theoretical calculations attribute the unexpected splitting in antiferromagnetic dimers to spin-orbit coupling and broken inversion symmetry at the surface. Our observations point out the relevance of previously unconsidered factors on the formation of Shiba bands and their topological classification.

The influence of spin-orbit coupling on the hybridization of Shiba states in dimers of magnetic atoms on superconducting surfaces remains unexplored. Here, the authors reveal a splitting of atomic Shiba orbitals due to spin-orbit coupling and broken inversion symmetry in antiferromagnetically coupled Mn dimers placed on a Nb(110) surface.

Angle, Spin, and Depth Resolved Photoelectron Spectroscopy on Quantum Materials

The role of X-ray based electron spectroscopies in determining chemical, electronic, and magnetic properties of solids has been well-known for several decades. A powerful approach is angle-resolved photoelectron spectroscopy, whereby the kinetic energy and angle of photoelectrons emitted from a sample surface are measured. This provides a direct measurement of the electronic band structure of crystalline solids. Moreover, it yields powerful insights into the electronic interactions at play within a material and into the control of spin, charge, and orbital degrees of freedom, central pillars of future solid state science. With strong recent focus on research of lower-dimensional materials and modified electronic behavior at surfaces and interfaces, angle-resolved photoelectron spectroscopy has become a core technique in the study of quantum materials. In this review, we provide an introduction to the technique. Through examples from several topical materials systems, including topological insulators, transition metal dichalcogenides, and transition metal oxides, we highlight the types of information which can be obtained. We show how the combination of angle, spin, time, and depth-resolved experiments are able to reveal "hidden" spectral features, connected to semiconducting, metallic and magnetic properties of solids, as well as underlining the importance of dimensional effects in quantum materials.

Current-Induced Spin Torques on Single GdFeCo Magnetic Layers

Spintronics exploit spin-orbit coupling (SOC) to generate spin currents, spin torques, and, in the absence of inversion symmetry, Rashba and Dzyaloshinskii-Moriya interactions. The widely used magnetic materials, based on 3d metals such as Fe and Co, possess a small SOC. To circumvent this shortcoming, the common practice has been to utilize the large SOC of nonmagnetic layers of 5d heavy metals (HMs), such as Pt, to generate spin currents and, in turn, exert spin torques on the magnetic layers. Here, a new class of material architectures is introduced, excluding nonmagnetic 5d HMs, for high-performance spintronics operations. Very strong current-induced torques exerted on single ferrimagnetic GdFeCo layers, due to the combination of large SOC of the Gd 5d states and inversion symmetry breaking mainly engineered by interfaces, are demonstrated. These "self-torques" are enhanced around the magnetization compensation temperature and can be tuned by adjusting the spin absorption outside the GdFeCo layer. In other measurements, the very large emission of spin current from GdFeCo, 80% (20%) of spin anomalous Hall effect (spin Hall effect) symmetry is determined. This material platform opens new perspectives to exert "self-torques" on single magnetic layers as well as to generate spin currents from a magnetic layer.

Rashba Effect and Raman Spectra of Tl2O/PtS2 Heterostructure

The possibility to achieve charge-to-spin conversion via Rashba spin-orbit effects provides stimulating opportunities toward the development of nanoscale spintronics. Here, we use first-principles calculations to study the electronic and spintronic properties of Tl₂O/PtS₂ heterostructure, for which we have confirmed the dynamical stability by its positive phonon frequencies. An unexpectedly high binding energy of -0.38 eV per unit cell depicts strong interlayer interactions between Tl₂O and PtS₂. Interestingly, we discover Rashba spin-splittings (with a large α _R value) in the valence band of Tl₂O stemming from interfacial spin-orbit effects caused by PtS₂. The role of van der Waals binding on the orbital rearrangements has been studied using the electron localization function and atomic orbital projections, which explains in detail the electronic dispersion near the Fermi level. Moreover, we explain the distinct band structure alignment in momentum space but separation in real space of Tl₂O/PtS₂ heterostructure. Since two-dimensional (2D) Tl₂O still awaits experimental confirmation, we calculate, for the first time, the Raman spectra of pristine Tl₂O and the Tl₂O/PtS₂ heterostructure and discuss peak positions corresponding to vibrational modes of the atoms. These findings offer a promising avenue to explore spin physics for potential spintronics applications via 2D heterostructures.

Initiating Ullmann-like coupling of Br2Py by a semimetal surface

Intensive efforts have been devoted to surface Ullmann-like coupling in recent years, due to its appealing success towards on-surface synthesis of tailor-made nanostructures. While attentions were mostly drawn on metallic substrates, however, Ullmann dehalogenation and coupling reaction on semimetal surfaces has been seldom addressed. Herein, we demonstrate the self-assembly of 2, 7-dibromopyrene (Br₂Py) and the well controllable dehalogenation reaction of Br₂Py on the Bi(111)–Ag substrate with a combination of scanning tunnelling microscopy (STM) and density functional theory calculations (DFT). By elaborately investigating the reaction path and formed organic nanostructures, it is revealed that the pristinely inert bismuth layer supported on the silver substrate can initiate Ullmann-like coupling in a desired manner by getting alloyed with Ag atoms underneath, while side products have not been discovered. By clarifying the pristine nature of Bi–Ag(111) and Ullmann-like reaction mechanisms, our report proposes an ideal template for thoroughly exploring dehalogenative coupling reaction mechanisms with atomic insights and on-surface synthesis of carbon-based architectures.

Ideal strength and strain engineering of the Rashba effect in two-dimensional BiTeBr

Strain engineering can lead to enhanced charge transfer and therefore, can effectively tune Rashba effect.

Rashba Effect in Functional Spintronic Devices

Exploiting spin transport increases the functionality of electronic devices and enables such devices to overcome physical limitations related to speed and power. Utilizing the Rashba effect at the interface of heterostructures provides promising opportunities toward the development of high-performance devices because it enables electrical control of the spin information. Herein, the focus is mainly on progress related to the two most compelling devices that exploit the Rashba effect: spin transistors and spin-orbit torque devices. For spin field-effect transistors, the gate-voltage manipulation of the Rashba effect and subsequent control of the spin precession are discussed, including for all-electric spin field-effect transistors. For spin-orbit torque devices, recent theories and experiments on interface-generated spin current are discussed. The future directions of manipulating the Rashba effect to realize fully integrated spin logic and memory devices are also discussed.

Orbital Angular Momentum Induced Spin Polarization of 2D Metallic Bands

The electrons in 2D systems with broken inversion symmetry are spin-polarized due to spin-orbit coupling and provide perfect targets for observing exotic spin-related fundamental phenomena. We observe a Fermi surface with a novel spin texture in the 2D metallic system formed by indium double layers on Si(111) and find that the primary origin of the spin-polarized electronic states of this system is the orbital angular momentum and not the so-called Rashba effect. The present results deepen the understanding of the physics arising from spin-orbit coupling in atomic-layered materials with consequences for spintronic devices and the physics of the superconducting state.

Simple Model for Corrugation in Surface Alloys Based on First-Principles Calculations

The structural stability of M/Ag(111)–3×3R30°  surface alloys is systematically investigated by using first-principles calculations, where M is a member of group III (B, Al, Ga, In, Tl), IV (C, Si, Ge, Sn, Pb), and V (N, P, As, Sb, Bi) elements. We focus on the corrugation parameter d which is determined by the height of the M atom from the Ag atom in the plane of the top-most atom, and the relation between atomic radii and corrugations in M/Ag(111) is obtained. The tendencies of the corrugation parameter d can be understood by using a simple hard spherical atomic model. We introduce a new type of atomic radii determined by the corrugation in surface alloys, surface alloy atomic radii, which can be useful for rapid predictions of the structures of surface alloys, not only for M/Ag (111)–3×3R30° systems but also for other surface alloys.

Phase transition and thermal stability of epitaxial PtSe2 nanolayer on Pt(111)

This work relates to direct synthesis of the two-dimensional (2D) transition metal dichalchogenide (TMD) PtSe₂ using an original method based on chemical deposition during immersion of a Pt(111) surface into aqueous Na₂Se solution. Annealing of the sample induces significant modifications in the structural and electronic properties of the resulting PtSe₂ film. We report systematic investigations of temperature dependent phase transitions by combining synchrotron based high-resolution X-ray photoemission (XPS), low temperature scanning tunnelling microscopy (LT-STM) and low energy electron diffraction (LEED). From the STM images, a phase transition from TMD 2H-PtSe₂ to Pt₂Se alloy monolayer structure is observed, in agreement with the LEED patterns showing a transition from (4 × 4) to (√3 × √3)R30° and then to a (2 × 2) superstructure. This progressive evolution of the surface reconstruction has been monitored by XPS through systematic de-convolution of the Pt4f and Se3d core level peaks at different temperatures. The present work provides an alternative method for the large scale fabrication of 2D transition metal dichalchogenide films.

LEED, STM and XPS techniques were used to systematically study a temperature-dependent phase transition on a PtSe₂ film grown on the surface of Pt(111) by a chemical deposition method.

Control of Spin-Orbit Torques by Interface Engineering in Topological Insulator Heterostructures

(Bi_1-xSb_x)₂Te₃ topological insulators (TIs) are gathering increasing attention owing to their large charge-to-spin conversion efficiency and the ensuing spin-orbit torques (SOTs) that can be used to manipulate the magnetization of a ferromagnet (FM). The origin of the torques, however, remains elusive, while the implications of hybridized states and the strong material intermixing at the TI/FM interface are essentially unexplored. By combining interface chemical analysis and spin-transfer ferromagnetic resonance (ST-FMR) measurements, we demonstrate that intermixing plays a critical role in the generation of SOTs. By inserting a suitable normal metal spacer, material intermixing is reduced and the TI properties at the interface are largely improved, resulting in strong variations in the nature of the SOTs. A dramatic enhancement of a field-like torque, opposing and surpassing the Oersted-field torque, is observed, which can be attributed to the non-equilibrium spin density in Rashba-split surface bands and to the suppression of spin memory loss. These phenomena can play a relevant role at other interfaces, such as those comprising transition metal dichalcogenides.

Probing the Electronic Structure of Hybrid Perovskites in the Orientationally Disordered Cubic Phase

Hybrid organic-inorganic lead halide perovskites are projected as new generation photovoltaic and optoelectronic materials with improved efficiencies. However, their electronic structure so far remains poorly understood, particularly in the orientationally disordered cubic phase. We performed electronic structure investigations using angle-resolved photoemission spectroscopy on two prototypical samples (MAPbBr₃ and MAPbCl₃) in their cubic phase, and the results are compared with the calculations within two theoretical models where MA⁺ is orientationally (1) disordered (MA⁺ ion is replaced by spherically symmetric Cs⁺ ion) and (2) ordered (MA oriented along (100) direction) but keeping the symmetry of the unit cell cubic. Degeneracy of the valence bands and behavior of constant energy contours are consistent with model 1, which supports strongly the disordered nature of the orientation of the MA⁺ ions in the cubic phase. Band structure calculations also reveal that spin-orbit coupling induced Rashba splitting is suppressed by the orientational disorder.

Scanning tunneling spectroscopy studies of topological materials

Topological materials have become promising materials for next-generation devices by utilizing their exotic electronic states. Their exotic states caused by spin-orbital coupling usually locate on the surfaces or at the edges. Scanning tunneling spectroscopy (STS) is a powerful tool to reveal the local electronic structures of condensed matters. Therefore, STS provides us with an almost perfect method to access the exotic states of topological materials. In this topical review, we report the current investigations by several methods based on the STS technique for layered topological material from transition metal dichalcogenide Weyl semimetals (WTe₂ and MoTe₂) to two dimensional topological insulators (layered bismuth and silicene). The electronic characteristics of these layered topological materials are experimentally identified.

Two-Dimensional Rare Earth-Gold Intermetallic Compounds on Au(111) by Surface Alloying

Surface alloying is a straightforward route to control and modify the structure and electronic properties of surfaces. Here, we present a systematic study on the structural and electronic properties of three novel rare earth-based intermetallic compounds, namely, ReAu₂ (Re = Tb, Ho, and Er), on Au(111) via directly depositing rare earth metals onto the hot Au(111) surface. Scanning tunneling microscopy/spectroscopy measurements reveal very similar atomic structures and electronic properties, e.g., electronic states and surface work functions, for all these intermetallic compound systems because of the physical and chemical similarities between these rare earth elements. Further, these electronic properties are periodically modulated by the moiré structures caused by the lattice mismatches between ReAu₂ and Au(111). These periodically modulated surfaces could serve as templates for the self-assembly of nanostructures. In addition, these two-dimensional rare earth-based intermetallic compounds provide platforms to investigate rare earth-related catalysis, magnetisms, etc. in the lower dimensions.

Giant Rashba splitting in one-dimensional atomic tellurium chains

The search for a one-dimensional (1D) system with purely 1D bands and strong Rashba spin splitting is essential for the realization of Majorana fermions and spin transport but presents a fundamental challenge to date. Herein, using first-principles calculations, we demonstrated that atomic Tellurium (Te) chains exhibit purely 1D bands and giant Rashba spin splitting, and their splitting parameters depend strongly on strain and structure distortion. This phenomenon stems from the helical structure of atomic Te chains, which can not only sustain significant strain but also realize the synergy of orbital angular momentum and in-chain potential gradient in enhancing spin splitting. The structure distortion of stretched helical Te chains is critical to execute this synergy, generating a large Rashba spin splitting among the known systems. Our findings proposed a potential 1D giant Rashba splitting system for exploring spintronics and Majorana fermions, and provide routes for engineering spin splitting in other materials.

A 2D Rashba electron gas with large spin splitting in Janus structures of SnPbO2

For realizing two-dimensional (2D) spintronic devices, controllable manipulation of different spin channels is needed. In order to achieve this goal, the materials should have well-separated spin energies induced by spin-orbit coupling (SOC). However, a negligible SOC effect in 2D SnO limits its application in this prospect. Herein, we demonstrate that the stable Janus structure of SnPbO₂ can exhibit large spin splitting (67 meV) at the valence band maximum (VBM) due to the breakdown of inverse symmetry. This spin splitting is larger than the thermal fluctuation at room temperature as well as some other 2D systems. In addition, the splitting can be further enhanced by strains (82 meV) or hole doping (147 meV). More importantly, there are no other electronic states except for the Rashba states at the VBM, which make it ideal for practical applications. Our study provides alternative ways to regulate the electronic structure of SnO and the feasibility for spin manipulation in this interesting 2D system.