A first-principles study on the Rashba effect in surface systems

Obtaining giant Rashba-Dresselhaus spin splitting in two-dimensional chiral metal-organic frameworks

Two-dimensional (2D) nonmagnetic semiconductors with large Rashba-Dresselhaus (R-D) spin splitting at valence or conduction bands are attractive for magnetic-field-free spintronic applications. However, so far, the number of 2D R-D inorganic semiconductors has been quite limited, and the factors that determine R-D spin splitting as well as rational design of giant spin splitting, remain unclear. For this purpose, by exploiting 2D chiral metal-organic frameworks (CMOFs) as a platform, we theoretically develop a three-step screening method to obtain a series of candidate 2D R-D semiconductors with valence band spin splitting up to 97.2 meV and corresponding R-D coupling constants up to 1.37 eV Å. Interestingly, the valence band spin texture is reversible by flipping the chirality of CMOFs. Furthermore, five keys for obtaining giant R-D spin splitting in 2D CMOFs are successfully identified: (i) chirality, (ii) large spin-orbit coupling, (iii) narrow band gap, (iv) valence and conduction bands having the same symmetry at the Γ point, and (v) strong ligand field.

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.

Spin-dependent band-gap formation for theL-gap surface state on the(22×3)reconstructed Au(111) surface

We elucidate how the free-electron-like energy dispersion of theL-gap surface state on a Au(111)-(1 × 1) surface is modified by the experimentally observed uniaxial reconstruction of the topmost atomic layer. For this purpose, we perform a first-principles embedded Green's function calculation for the(22×3)reconstructed semi-infinite Au(111) surface. The obtained band structure unfolded into the surface Brillouin zone of the (1 × 1) surface can be understood in terms of two spin-split parabolic bands centered at theΓ¯point, their umklapp-induced replicas centered at reciprocal lattice vectors of the superlattice (SL) with much weaker intensities, and mini band gaps at the crossing of two of them. More importantly, it is revealed that the band-gap size depends not only on the amplitude of the SL potential but also on mutual spin orientations of two crossing bands. Furthermore, we demonstrate that the band-gap size and the charge density distribution of the surface states are closely correlated with spatial profile of the SL potential.

What Dictates Rashba Splitting in 2D van der Waals Heterobilayers

Rashba spin-orbit coupling enables electric control of spin states, promising enormous advances from conventional charge-based computing. Until now, a general scheme or a descriptor to find an optimal system with isolated spin states with large tunable splitting is still lacking. Here, based on first-principles calculations, we explore the microscopic physicochemical mechanism responsible for the Rashba effect in 2D van der Waals heterobilayers. We find that the difference in the Born effective charge of atoms at the interface can be used as a single-layer descriptor to predict heteropairs with large Rashba splitting, thus reducing the scaling factor in materials search. Moreover, we discover that for most 2D materials, the routinely used Rashba parameter α_R is not a good gauge of the effect's strength. From our general scheme, MoTe₂|Tl₂O and MoTe₂|PtS₂, with spin splitting above 120 meV, Rashba energy E_R = 94 meV, and wavenumber difference 2k₀ = 0.36 Å^-1 ("effective" α_R > 1 eVÅ), emerge as the best candidates for spin transistors at room temperature.

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.

Deterministic Spin-Orbit Torque Switching by a Light-Metal Insertion

Spin-orbit torque (SOT) switching of magnetization is a promising emerging technology for nonvolatile spintronic memory and logic applications. However, deterministic switching of perpendicular magnetization with SOTs requires an additional symmetry breaking, which is typically provided by an external magnetic field, making it impractical for applications. In this work, we disclose that by the insertion of a slightly asymmetric light-metal layer at the heavy metal-ferromagnet interface of SOT heterostructures, current-induced out-of-plane effective magnetic fields are introduced that enable deterministic switching without an external magnetic field. We obtain uniform perpendicular magnetic anisotropy and switching current density despite the asymmetry of the light-metal layer, and we show the scalability of our approach by studying device sizes that differ by 2 orders of magnitude. Our work provides a practical route for utilization of SOTs for magnetization switching on the wafer scale and paves the way for the practical application of SOT-based technology.

Orbital-Driven Rashba Effect in a Binary Honeycomb Monolayer AgTe

The Rashba effect is fundamental to the physics of two-dimensional electron systems and underlies a variety of spintronic phenomena. It has been proposed that the formation of Rashba-type spin splittings originates microscopically from the existence of orbital angular momentum (OAM) in the Bloch wave functions. Here, we present detailed experimental evidence for this OAM-based origin of the Rashba effect by angle-resolved photoemission (ARPES) and two-photon photoemission experiments for a monolayer AgTe on Ag(111). Using quantitative low-energy electron diffraction analysis, we determine the structural parameters and the stacking of the honeycomb overlayer with picometer precision. Based on an orbital-symmetry analysis in ARPES and supported by first-principles calculations, we unequivocally relate the presence and absence of Rashba-type spin splittings in different bands of AgTe to the existence of OAM.

Clear variation of spin splitting by changing electron distribution at non-magnetic metal/Bi2O3 interfaces

Large spin splitting at Rashba interface, giving rise to strong spin-momentum locking, is essential for efficient spin-to-charge conversion. Recently, a Cu/Bismuth oxide (Bi₂O₃) interface has been found to exhibit an efficient spin-to-charge conversion similar to a Ag/Bi interface with large Rashba spin splitting. However, the guiding principle of designing the metal/oxide interface for the efficient conversion has not been clarified yet. Here we report strong non-magnetic (NM) material dependence of spin splitting at NM/Bi₂O₃ interfaces. We employed spin pumping technique to inject spin current into the interface and evaluated the magnitude of interfacial spin-to-charge conversion. We observed large modulation and sign change in conversion coefficient which corresponds to the variation of spin splitting. Our experimental results together with first-principles calculations indicate that such large variation is caused by material dependent electron distribution near the interface. The results suggest that control of interfacial electron distribution by tuning the difference in work function across the interface may be an effective way to tune the magnitude and sign of spin-to-charge conversion and Rashba parameter at interface.

Topologically Entangled Rashba-Split Shockley States on the Surface of Grey Arsenic

We discover a pair of spin-polarized surface bands on the (111) face of grey arsenic by using angle-resolved photoemission spectroscopy (ARPES). In the occupied side, the pair resembles typical nearly-free-electron Shockley states observed on noble-metal surfaces. However, pump-probe ARPES reveals that the spin-polarized pair traverses the bulk band gap and that the crossing of the pair at Γ[over ¯] is topologically unavoidable. First-principles calculations well reproduce the bands and their nontrivial topology; the calculations also support that the surface states are of Shockley type because they arise from a band inversion caused by crystal field. The results provide compelling evidence that topological Shockley states are realized on As(111).

Nonvortical Rashba Spin Structure on a Surface with C_{1h} Symmetry

A totally anisotropic peculiar Rashba-Bychkov (RB) splitting of electronic bands was found on the Tl/Si(110)-(1×1) surface with C_{1h} symmetry by angle- and spin-resolved photoelectron spectroscopy and first-principles theoretical calculation. The constant energy contour of the upper branch of the RB split band has a warped elliptical shape centered at a k point located between Γ[over ¯] and the edge of the surface Brillouin zone, i.e., at a point without time-reversal symmetry. The spin-polarization vector of this state is in-plane and points almost the same direction along the whole elliptic contour. This novel nonvortical RB spin structure is confirmed as a general phenomenon originating from the C_{1h} symmetry of the surface.

Formation of Ideal Rashba States on Layered Semiconductor Surfaces Steered by Strain Engineering

Spin splitting of Rashba states in two-dimensional electron system provides a promising mechanism of spin manipulation for spintronics applications. However, Rashba states realized experimentally to date are often outnumbered by spin-degenerated substrate states at the same energy range, hindering their practical applications. Here, by density functional theory calculation, we show that Au one monolayer film deposition on a layered semiconductor surface β-InSe(0001) can possess "ideal" Rashba states with large spin splitting, which are completely situated inside the large band gap of the substrate. The position of the Rashba bands can be tuned over a wide range with respect to the substrate band edges by experimentally accessible strain. Furthermore, our nonequilibrium Green's function transport calculation shows that this system may give rise to the long-sought strong current modulation when made into a device of Datta-Das transistor. Similar systems may be identified with other metal ultrathin films and layered semiconductor substrates to realize ideal Rashba states.

Spin-orbit coupling at surfaces and 2D materials

Spin-orbit interaction gives rise to a splitting of surface states via the Rashba effect, and in topological insulators it leads to the existence of topological surface states. The resulting k(//) momentum separation between states with the opposite spin underlies a wide range of new phenomena at surfaces and interfaces, such as spin transfer, spin accumulation, spin-to-charge current conversion, which are interesting for fundamental science and may become the basis for a breakthrough in the spintronic technology. The present review summarizes recent theoretical and experimental efforts to reveal the microscopic structure and mechanisms of spin-orbit driven phenomena with the focus on angle and spin-resolved photoemission and scanning tunneling microscopy.

Rashba Spin-Orbit Coupling in Image Potential States

The search in two-dimensional condensed matter systems of Rashba-type spin-polarized electronic states is aimed by the possibility to control and manipulate the spin orientation. In this Letter, for the first time, we report on the experimental evidence of a Rashba-type spin splitting in the n=1 image potential state. The image potential state Rashba splitting here measured at the graphene/Ir(111) interface, as confirmed by theoretical considerations, can be detectable to any metal surface with a significant spin-orbit coupling.

Giant spin splitting of the two-dimensional electron gas at the surface of SrTiO3

Two-dimensional electron gases (2DEGs) forming at the interfaces of transition metal oxides exhibit a range of properties, including tunable insulator-superconductor-metal transitions, large magnetoresistance, coexisting ferromagnetism and superconductivity, and a spin splitting of a few meV (refs 10, 11). Strontium titanate (SrTiO3), the cornerstone of such oxide-based electronics, is a transparent, non-magnetic, wide-bandgap insulator in the bulk, and has recently been found to host a surface 2DEG (refs 12-15). The most strongly confined carriers within this 2DEG comprise two subbands, separated by an energy gap of 90 meV and forming concentric circular Fermi surfaces. Using spin- and angle-resolved photoemission spectroscopy (SARPES), we show that the electron spins in these subbands have opposite chiralities. Although the Rashba effect might be expected to give rise to such spin textures, the giant splitting of almost 100 meV at the Fermi level is far larger than anticipated. Moreover, in contrast to a simple Rashba system, the spin-polarized subbands are non-degenerate at the Brillouin zone centre. This degeneracy can be lifted by time-reversal symmetry breaking, implying the possible existence of magnetic order. These results show that confined electronic states at oxide surfaces can be endowed with novel, non-trivial properties that are both theoretically challenging to anticipate and promising for technological applications.

Rotating spin and giant splitting: unoccupied surface electronic structure of Tl/Si(111)

We present a combined experimental and theoretical study on the unoccupied surface electronic structure of the Tl/Si(111) surface. Spin- and angle-resolved inverse-photoemission measurements with sensitivity to both the in-plane and the out-of-plane polarization direction detect a spin-orbit-split surface state, which is well described by theoretical calculations. We demonstrate that the spin polarization vector rotates from the classical in-plane Rashba polarization direction around Γ[over ¯] to the direction perpendicular to the surface at the K[over ¯](K[over ¯]') points-a direct consequence of the symmetry of the 2D hexagonal system. A giant splitting in energy of about 0.6 eV is observed and attributed to the strong localization of the unoccupied surface state close to the heavy Tl atoms. This leads to completely out-of-plane spin-polarized valleys in the vicinity of the Fermi level. As the valley polarization is oppositely oriented at the K[over ¯] and K[over ¯]' points, backscattering should be strongly suppressed in this system.

Fermi nesting between atomic wires with strong spin-orbit coupling

The mutual interplay between superlattice structures, band filling factors, and spin-orbit coupling results in a highly correlated electronic spin and charge state found for an array of atomic Pb wires grown on Si(557). By means of spin- and angle-resolved photoemission spectroscopy, the spin texture close to the Fermi surface was found to be alternating and equidistant; thus, Fermi nesting occurs in between bands with the same spin helicity, giving rise to spin-polarized charge-density waves in the direction across the wires. An out-of-phase superposition of both Rashba channels is manifested by an extraordinary large Rashba splitting of Δk0=0.2  Å(-1)=g/2, where g is a reciprocal lattice vector defined by the interwire distance and fits into the model of spin-density waves in antiferromagnetically ordered chain structures. The implications towards spin-polarized transport along the wires will be discussed.

Spin-orbit-induced photoelectron spin polarization in angle-resolved photoemission from both atomic and condensed matter targets

The existence of highly spin polarized photoelectrons emitted from non-magnetic solids as well as from unpolarized atoms and molecules has been found to be very common in many studies over the past 40 years. This so-called Fano effect is based upon the influence of the spin-orbit interaction in the photoionization or the photoemission process. In a non-angle-resolved photoemission experiment, circularly polarized radiation has to be used to create spin polarized photoelectrons, while in angle-resolved photoemission even unpolarized or linearly polarized radiation is sufficient to get a high spin polarization. In past years the Rashba effect has become very important in the angle-resolved photoemission of solid surfaces, also with an observed high photoelectron spin polarization. It is the purpose of the present topical review to cross-compare the spin polarization experimentally found in angle-resolved photoelectron emission spectroscopy of condensed matter with that of free atoms, to compare it with the Rashba effect and topological insulators to describe the influence and the importance of the spin-orbit interaction and to show and disentangle the matrix element and phase shift effects therein.The relationship between the energy dispersion of these phase shifts and the emission delay of photoelectron emission in attosecond-resolved photoemission is also discussed. Furthermore the influence of chiral structures of the photo-effect target on the spin polarization, the interferences of different spin components in coherent superpositions in photoemission and a cross-comparison of spin polarization in photoemission from non-magnetic solids with XMCD on magnetic materials are presented; these are all based upon the influence of the spin-orbit interaction in angle-resolved photoemission.

Effect of atomic impurities on the helical surface states of the topological insulator Bi2Te3

The effect of atomic impurities including N, O, Na, Ti and Co on the surface states of the topological insulator (TI) Bi(2)Te(3) is studied using pseudopotential first principles methods. The robustness of the TI surface states is particularly investigated against magnetic and non-magnetic atomic adsorption by calculating the electronic band structure, charge transfer, and magnetic moments. Interestingly, it is found that a non-magnetic nitrogen atom has produced a residual magnetic moment and opens a gap in the surface states whereas Na and O atoms preserve the Dirac-like dispersion. The charge transfer from the adatoms produces an electric dipole field that causes Rashba splitting in the surface bands. For atomic impurities with 3d orbitals (Ti and Co), the TI surface states are destroyed and two spin-resolved resonance peaks are developed near the Fermi level in the DOS.

Superconducting and ferromagnetic phases in SrTiO3/LaAlO3 oxide interface structures: possibility of finite momentum pairing

We introduce a model to explain the observed ferromagnetism and superconductivity in LAO/STO oxide interface structures. Because of the polar catastrophe mechanism, 1/2 charge per unit cell is transferred to the interface layer. We argue that this charge localizes and orders ferromagnetically via exchange with the conduction electrons. Ordinarily, this ferromagnetism would destroy superconductivity, but, due to strong spin-orbit coupling near the interface, the magnetism and superconductivity can coexist by forming a Fulde-Ferrell-Larkin-Ovchinikov-type condensate of Cooper pairs at finite momentum, which is surprisingly robust in the presence of strong disorder.

Rashba spin-splitting control at the surface of the topological insulator Bi2Se3

The electronic structure of Bi(2)Se(3) is studied by angle-resolved photoemission and density functional theory. We show that the instability of the surface electronic properties, observed even in ultrahigh-vacuum conditions, can be overcome via in situ potassium deposition. In addition to accurately setting the carrier concentration, new Rashba-like spin-polarized states are induced, with a tunable, reversible, and highly stable spin splitting. Ab initio slab calculations reveal that these Rashba states are derived from 5-quintuple-layer quantum-well states. While the K-induced potential gradient enhances the spin splitting, this may be present on pristine surfaces due to the symmetry breaking of the vacuum-solid interface.

Gapless interface states between topological insulators with opposite Dirac velocities

The Dirac cone on a surface of a topological insulator shows linear dispersion analogous to optics and its velocity depends on materials. We consider a junction of two topological insulators with different velocities, and calculate the reflectance and transmittance. We find that they reflect the backscattering-free nature of the helical surface states. When the two velocities have opposite signs, both transmission and reflection are prohibited for normal incidence, when a mirror symmetry normal to the junction is preserved. In this case we show that there necessarily exist gapless states at the interface between the two topological insulators. Their existence is protected by mirror symmetry, and they have characteristic dispersions depending on the symmetry of the system.

Orbital-angular-momentum based origin of Rashba-type surface band splitting

We propose that the existence of local orbital angular momentum (OAM) on the surfaces of high-Z materials plays a crucial role in the formation of Rashba-type surface band splitting. Local OAM state in a Bloch wave function produces an asymmetric charge distribution (electric dipole). The surface-normal electric field then aligns the electric dipole and results in chiral OAM states and the relevant Rashba-type splitting. Therefore, the band splitting originates from electric dipole interaction, not from the relativistic Zeeman splitting as proposed in the original Rashba picture. The characteristic spin chiral structure of Rashba states is formed through the spin-orbit coupling and thus is a secondary effect to the chiral OAM. Results from first-principles calculations on a single Bi layer under an external electric field verify the key predictions of the new model.

Large Rashba spin splitting of a metallic surface-state band on a semiconductor surface

The generation of spin-polarized electrons at room temperature is an essential step in developing semiconductor spintronic applications. To this end, we studied the electronic states of a Ge(111) surface, covered with a lead monolayer at a fractional coverage of 4/3, by angle-resolved photoelectron spectroscopy (ARPES), spin-resolved ARPES and first-principles electronic structure calculation. We demonstrate that a metallic surface-state band with a dominant Pb 6p character exhibits a large Rashba spin splitting of 200 meV and an effective mass of 0.028 m(e) at the Fermi level. This finding provides a material basis for the novel field of spin transport/accumulation on semiconductor surfaces. Charge density analysis of the surface state indicated that large spin splitting was induced by asymmetric charge distribution in close proximity to the nuclei of Pb atoms.

Finite electric field effects in the large perpendicular magnetic anisotropy surface Pt/Fe/Pt(001): a first-principles study

We investigate crystalline magnetic anisotropy in the electric field (EF) for the FePt surface which has a large perpendicular anisotropy, by means of the first-principles approach. Anisotropy is reduced linearly with respect to the inward EF, associated with the induced spin density around the Fe layer. Although the magnetic anisotropy energy (MAE) density reveals large variation around the atoms, the intrinsic contribution to the MAE is found to mainly come from the Fe layer. The surface without the capping Pt layer also shows similar linear dependence.