Spin-resolved photoemission of surface states of W(110)-(1 x 1)H

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.

Spin- and angle-resolved inverse photoemission setup with spin orientation independent from electron incidence angle

A new spin- and angle-resolved inverse photoemission setup with a low-energy electron source is presented. The spin-polarized electron source, with a compact design, can decouple the spin polarization vector from the electron beam propagation vector, allowing one to explore any spin orientation at any wavevector in angle-resolved inverse photoemission. The beam polarization can be tuned to any preferred direction with a shielded electron optical system, preserving the parallel beam condition. We demonstrate the performances of the setup by measurements on Cu(001) and Au(111). We estimate the energy resolution of the overall system at room temperature to be ∼170 meV from k_BT_eff of a Cu(001) Fermi level, allowing a direct comparison to photoemission. The spin-resolved operation of the setup has been demonstrated by measuring the Rashba splitting of the Au(111) Shockley surface state. The effective polarization of the electron beam is P = 30% ± 3%, and the wavevector resolution is Δk_F ≲ 0.06 Å^-1. Measurements on the Au(111) surface state demonstrate how the electron beam polarization direction can be tuned in the three spatial dimensions. The maximum of the spin asymmetry is reached when the electron beam polarization is aligned with the in-plane spin polarization of the Au(111) surface state.

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.

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.

Spin-orbit torque manipulated by fine-tuning of oxygen-induced orbital hybridization

Current-induced spin-orbit torques provide an effective way to manipulate magnetization in spintronic devices, promising for fast switching applications in nonvolatile memory and logic units. Recent studies have revealed that the spin-orbit torque is strongly altered by the oxidation of heterostructures with broken inversion symmetry. Although this finding opens a new field of metal-oxide spin-orbitronics, the role of the oxidation in the spin-orbit physics is still unclear. Here, we demonstrate a marked enhancement of the spin-orbit torque induced by a fine-tuning of oxygen-induced modification of orbital hybridization. This is evidenced by a concomitant enhancement of the interface spin-orbit torque, interface spin loss, and interface perpendicular magnetic anisotropy within a narrow range of the oxidation level of metallic heterostructures. This result reveals the crucial role of the atomic-scale effects in the generation of the spin-orbit torques, opening the door to atomic-level engineering of the spin-orbit physics.

Rashba-like spin splitting along three momentum directions in trigonal layered PtBi2

Spin-orbit coupling (SOC) has gained much attention for its rich physical phenomena and highly promising applications in spintronic devices. The Rashba-type SOC in systems with inversion symmetry breaking is particularly attractive for spintronics applications since it allows for flexible manipulation of spin current by external electric fields. Here, we report the discovery of a giant anisotropic Rashba-like spin splitting along three momentum directions (3D Rashba-like spin splitting) with a helical spin polarization around the M points in the Brillouin zone of trigonal layered PtBi₂. Due to its inversion asymmetry and reduced symmetry at the M point, Rashba-type as well as Dresselhaus-type SOC cooperatively yield a 3D spin splitting with α_R ≈ 4.36 eV Å in PtBi₂. The experimental realization of 3D Rashba-like spin splitting not only has fundamental interests but also paves the way to the future exploration of a new class of material with unprecedented functionalities for spintronics applications.

Rashba type spin splitting – relevant for spintronics applications - is driven by inversion symmetry breaking but could so far not be realized in all momentum directions in a crystal. Here, the authors report on PtBi₂ that exhibits Rashba spin splitting in all three momentum directions.

Circular-polarized-light-induced spin polarization characterized for the Dirac-cone surface state at W(110) with C2v symmetry

The C_2v surface symmetry of W(110) strongly influences a spin-orbit-induced Dirac-cone-like surface state and its characterization by spin- and angle-resolved photoelectron spectroscopy. In particular, using circular polarized light, a distinctive k-dependent spin texture is observed along the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\overline{{\boldsymbol{\Gamma }}{\boldsymbol{H}}}$$\end{document}ΓH¯ direction of the surface Brillouin zone. For all spin components P_x, P_y, and P_z, non-zero values are detected, while the initial-state spin polarization has only a P_y component due to mirror symmetry. The observed complex spin texture of the surface state is controlled by transition matrix element effects, which include orbital symmetries of the involved electron states as well as the geometry of the experimental set-up.

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.

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.

Rapid high-resolution spin- and angle-resolved photoemission spectroscopy with pulsed laser source and time-of-flight spectrometer

A high-efficiency spin- and angle-resolved photoemission spectroscopy (spin-ARPES) spectrometer is coupled with a laboratory-based laser for rapid high-resolution measurements. The spectrometer combines time-of-flight (TOF) energy measurements with low-energy exchange scattering spin polarimetry for high detection efficiencies. Samples are irradiated with fourth harmonic photons generated from a cavity-dumped Ti:sapphire laser that provides high photon flux in a narrow bandwidth, with a pulse timing structure ideally matched to the needs of the TOF spectrometer. The overall efficiency of the combined system results in near-E(F) spin-resolved ARPES measurements with an unprecedented combination of energy resolution and acquisition speed. This allows high-resolution spin measurements with a large number of data points spanning multiple dimensions of interest (energy, momentum, photon polarization, etc.) and thus enables experiments not otherwise possible. The system is demonstrated with spin-resolved energy and momentum mapping of the L-gap Au(111) surface states, a prototypical Rashba system. The successful integration of the spectrometer with the pulsed laser system demonstrates its potential for simultaneous spin- and time-resolved ARPES with pump-probe based measurements.

Two-dimensional superconducting state of monolayer Pb films grown on GaAs(110) in a strong parallel magnetic field

Two-dimensional (2D) superconductivity was studied by magnetotransport measurements on single-atomic-layer Pb films on a cleaved GaAs(110) surface. The superconducting transition temperature shows only a weak dependence on the parallel magnetic field up to 14T, which is higher than the Pauli paramagnetic limit. Furthermore, the perpendicular-magnetic-field dependence of the sheet resistance is almost independent of the presence of the parallel field component. These results are explained in terms of an inhomogeneous superconducting state predicted for 2D metals with a large Rashba spin splitting.

Giant ambipolar Rashba effect in the semiconductor BiTeI

We observe a giant spin-orbit splitting in the bulk and surface states of the noncentrosymmetric semiconductor BiTeI. We show that the Fermi level can be placed in the valence or in the conduction band by controlling the surface termination. In both cases, it intersects spin-polarized bands, in the corresponding surface depletion and accumulation layers. The momentum splitting of these bands is not affected by adsorbate-induced changes in the surface potential. These findings demonstrate that two properties crucial for enabling semiconductor-based spin electronics-a large, robust spin splitting and ambipolar conduction-are present in this material.

Electronic structure study of ultrathin Ag(111) films modified by a Si(111) substrate and √3 × √3-Ag2Bi surface

Angle-resolved photoemission spectroscopy experiments show that the electronic structure of a Ag(111) film grown on Si(111) is markedly perturbed by the formation of a √3 × √3-Ag(2)Bi Rashba-type surface alloy. Four spin-split surface states, with different band dispersions and energy contours, intercept and hybridize selectively with the sp-derived quantum well states of the Ag layer. Detailed two-dimensional band mapping of the system was carried out and constant energy contours at different energies result in hexagonal-, star- and flower-like distortions of the quantum well states as a result of various interactions. Further wavy-like modulations of the electronic structure of the film are found to originate from umklapp reflections of the Ag film states according to the surface periodicity.

Ir(111) surface state with giant Rashba splitting persists under graphene in air

We reveal a giant Rashba effect (α(R)≈1.3  eV Å) on a surface state of Ir(111) by angle-resolved photoemission and by density functional theory. It is demonstrated that the existence of the surface state, its spin polarization, and the size of its Rashba-type spin-orbit splitting remain unaffected when Ir is covered with graphene. The graphene protection is, in turn, sufficient for the spin-split surface state to survive in ambient atmosphere. We discuss this result along with indications for a topological protection of the surface state.

Spin-polarized Dirac-cone-like surface state with d character at W(110)

The surface of W(110) exhibits a Dirac-cone-like state with d character within a spin-orbit-induced symmetry gap. As a function of the wave vector parallel to the surface, it shows a nearly massless energy dispersion and a pronounced spin polarization, which is antisymmetric with respect to the Brillouin zone center. In addition, the observed constant energy contours are strongly anisotropic for all energies. This discovery opens new pathways to the study of surface spin-density waves arising from a strong Fermi surface nesting as well as d-electron-based topological properties.

Enhancement of the Kondo effect through Rashba spin-orbit interactions

We study a one-orbital Anderson impurity in a two-dimensional electron bath with Rashba spin-orbit interactions in the Kondo regime. The spin SU(2) symmetry-breaking term couples the impurity to a two-band electron gas. A Schrieffer-Wolff transformation shows the existence of the Dzyaloshinsky-Moriya interaction away from the particle-hole symmetric impurity state. A renormalization group analysis reveals a two-channel Kondo model with ferro- and antiferromagnetic couplings. The parity-breaking Dzyaloshinsky-Moriya term renormalizes the antiferromagnetic Kondo coupling with an exponential enhancement of the Kondo temperature.

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.

Spin and angle resolved photoemission on non-magnetic low-dimensional systems

The electronic structure of non-magnetic low-dimensional materials can acquire a spin structure due to the breaking of the inversion symmetry at the surface or interface. This so-called Rashba effect is a prime candidate for the manipulation of the electron spin without using any magnetic fields. This is crucial for the emerging field of spintronics, where the spin of the electron instead of its charge is used to transport or store information. Spin and angle resolved photoemission is currently one of the main experimental methods to measure the spin resolved electronic structure, which contains all the relevant information for spintronics. In this review, the technique of spin and angle resolved photoemission will be explained and recent results on low-dimensional non-magnetic structures will be discussed.

Is there a rashba effect in graphene on 3d ferromagnets?

Graphene is considered a candidate material for spintronics. Recently, graphene grown on Ni(111) has been reported to show a Rashba effect which depends on the magnetization. By spin- and angle-resolved photoelectron spectroscopy, we investigate the preconditions for such an effect for graphene on Ni as well as on Co which has a approximately 3x larger 3d magnetic moment: (i) spin polarization or (ii) exchange splitting of graphene pi states in normal emission geometry, and (iii) Rashba-type spin-orbit splitting off normal. As none of these are found to be of considerable size, the reported effect is neither Rashba-type, nor due to the spin-orbit coupling, nor involving the electron spin.

Rashba-type spin-orbit splitting of quantum well states in ultrathin Pb films

A Rashba-type spin-orbit splitting is found for quantum well states formed in ultrathin Pb films on Si (111). The resulting momentum splitting is comparable to what is found for semiconductor heterostructures. The splitting shows no coverage dependency and the sign of the spin polarization is reversed compared to Rashba splitting in the Au(111) surface state. We explain our results by competing effects at the two boundaries of the Pb layer.

Quantum cavity for spin due to spin-orbit interaction at a metal boundary

A quantum cavity for spin is created using a tungsten crystal as substrate of high nuclear charge and breaking the structural inversion symmetry through deposition of a gold quantum film. Spin- and angle-resolved photoelectron spectroscopy shows directly that quantum-well states and the "matrioshka" or Russian nested doll Fermi surface of the gold film are spin polarized and spin-orbit split up to a thickness of at least nine atomic layers. Ferromagnetic materials or external magnetic fields are not required, and the quantum film does not need to possess a high atomic number as analogous results with silver show.

Complex quasiparticle band structure induced by electron-phonon interaction: band splitting in the 1x1H/W110 surface

We show that the self-consistent solution of the complex Dyson equation for the electron-phonon (EP) problem introduces many body effects which are often observed in photoemission experiments. The formalism is applied to the H covered W(110) surface, using first-principles results for the electronic and vibrational structure. We demonstrate that the measured spin-polarized surface band splitting [Phys. Rev. Lett. 84, 2925 (2000)10.1103/PhysRevLett.84.2925; 89, 216802 (2002)] can be traced back to different quasiparticle (QP) states induced by EP coupling. Despite the breakdown of the single QP picture, the spectral functions are very well represented by the predicted multiple QP structure.

Origin of spin-orbit splitting for monolayers of au and ag on w(110) and mo(110)

Spin-orbit coupling can give rise to spin-split electronic states without a ferromagnet or an external magnetic field. We create large spin-orbit splittings in a Au and Ag monolayer on W(110) and show that the size of the splitting does not depend on the atomic number of the Au or Ag overlayer but of the W substrate. Spin- and angle-resolved photoemission and Fermi-surface scans reveal that the overlayer states acquire spin polarization through spin-dependent overlayer-substrate hybridization.

Surface phase transition in H/W(110) induced by tuning the fermi surface nesting vector by hydrogen loading

At a hydrogen coverage of one monolayer, W(110) is known to exhibit a Fermi nesting in its electronic surface states with a nesting vector q{N} of 0.9 A{-1} along [001]. Here we show that additional H adsorption allows a controlled tuning of q{N}. As q{N} approaches the commensurate value of 1.0 A{-1}, its signature in inelastic He-atom scattering becomes more pronounced, finally disappearing as a surface charge density wave (CDW) develops and the surface symmetry changes from c(2 x 2) to a p(8 x 2) superstructure. The gradual change in q{N} is attributed to an energetic shift of the spin-polarized electronic surface states that eventually form the surface CDW.

Spin resolved photoelectron spectroscopy of Fe(3)O(4): the case against half-metallicity

Many materials have been theoretically predicted to be half-metallic, and hence suitable for use as pure spin sources in spintronic devices. Yet to date, remarkably few of these predictions have been experimentally verified. We have used spin polarized photoelectron spectroscopy to study one candidate half-metallic system, Fe(3)O(4). Such experiments are normally hampered by difficulties in producing clean stoichiometric surfaces with a polarization that is truly representative of that of the bulk. However, by utilizing higher photon energies than have traditionally been used for such experiments, we can study polarization in 'as received' samples, essentially 'looking through' the disrupted surface. High quality, strain relieved, ex situ prepared Fe(3)O(4) films have been thoroughly characterized by diffraction, transport and magnetometry studies of their crystallographic, electronic and magnetic properties. The spectroscopic results are found to agree fairly closely with previously published experimental data on in situ grown thin films and cleaved single crystals. However, despite the higher photoelectron kinetic energies of the experiment, it has not been possible to observe 100% polarization at the Fermi level. Hence, our data do not support the claim of true half-metallicity for Fe(3)O(4).

Giant spin splitting through surface alloying

The long-range ordered surface alloy Bi/Ag(111) is found to exhibit a giant spin splitting of its surface electronic structure due to spin-orbit coupling, as is determined by angle-resolved photoelectron spectroscopy. First-principles electronic structure calculations fully confirm the experimental findings. The effect is brought about by a strong in-plane gradient of the crystal potential in the surface layer, in interplay with the structural asymmetry due to the surface-potential barrier. As a result, the spin polarization of the surface states is considerably rotated out of the surface plane.

Experimental evidence for spin-split bands in a one-dimensional chain structure

Gold atom chains on vicinal Si(111) surfaces exhibit an unusual doublet of half-filled bands, whose origin has remained uncertain. The splitting is identified by angle-resolved photoemission as a spin splitting induced by the spin-orbit interaction (Rashba effect), in agreement with a theoretical prediction by Sánchez-Portal, Riikonen, and Martin. This interaction leads to a characteristic pattern of avoided band crossings at a superlattice zone boundary. Two out of four crossings are avoided, with a minigap E_{G}=85 meV and a k offset of 0.05 A;{-1}.

Role of spin-orbit coupling and hybridization effects in the electronic structure of ultrathin Bi films

The electronic structure of Bi(001) ultrathin films (thickness > or =7 bilayers) on Si(111)-7x7 was studied by angle-resolved photoemission spectroscopy and first-principles calculations. In contrast with the semimetallic nature of bulk Bi, both the experiment and theory demonstrate the metallic character of the films with the Fermi surface formed by spin-orbit-split surface states (SSs) showing little thickness dependence. Below the Fermi level, we clearly detected quantum well states (QWSs) at the M point, which were surprisingly found to be non-spin-orbit split; the films are "electronically symmetric" despite the obvious structural nonequivalence of the top and bottom interfaces. We found that the SSs hybridize with the QWSs near M and lose their spin-orbit-split character.

Photoemission of a quantum cavity with a nonmagnetic spin separator

Quantum well states are a consequence of confinement in a quantum cavity. In this study we investigate with photoemission the influence of the interface electronic structure on the quantum well state energy dispersion in ultrathin Mg(0001) films on W(110). Coupling between the sp-derived quantum well states and the substrate across the interface becomes manifest in a deviation from free electronlike dispersion behavior. Most importantly, we observe a marked level splitting, which is interpreted as due to the Rashba effect at the interface. Such an interfacial electron beam splitting on materials with strong spin-orbit coupling is an essential ingredient for novel spintronic devices. The combination of a quantum cavity with a heavy, electron reflecting substrate reveals spin-splitting effects in ultrathin films without conventional magnetism being involved.

Surface state scattering at a buried interface

The free-electron-like surface state of Mg(0001) is strongly modified in thin films grown on W(110). The long bulk penetration length of its wave function makes it sensitive to the reflective properties of the buried interface, and hence to the complex electronic structure of the substrate. In particular we find a many-fold splitting of the Mg surface band by entering a wide projected band gap of W(110). There is a strong thickness-dependent two-band splitting, which is a clear signature of the formation of a surface-interface resonant state. An additional split-off from these two surface bands is explained by the substrate induced spin-orbit interaction.

Strong spin-orbit splitting on bi surfaces

Using first-principles calculations and angle-resolved photoemission, we show that the spin-orbit interaction leads to a strong splitting of the surface-state bands on low-index surfaces of Bi. The dispersion of the states and the corresponding Fermi surfaces are profoundly modified in the whole surface Brillouin zone. We discuss the implications of these findings with respect to a proposed surface charge density wave on Bi(111) as well as to the surface screening, surface spin-density waves, electron (hole) dynamics in surface states, and to possible applications to the spintronics.