Angle-resolved Inverse Photoemission Research Articles

L -gap surface resonance at Pt(111): Influence of atomic structure, d bands, and spin-orbit interaction

Pt(111) hosts a surface resonance with peculiar properties concerning energy vs momentum dispersion and spin texture. At variance with the free-electron-like behavior of the L-gap Shockley-type surface states on the fcc(111) surfaces of Au, Ag, and Cu, it splits into several branches with distinct spin polarization around the center of the surface Brillouin zone Γ¯. Theoretical predictions based on density-functional theory vary depending on the particular functionals used. To clarify this issue, we investigate the atomic structure of Pt(111) by low-energy electron diffraction and the unoccupied electronic structure by spin- and angle-resolved inverse photoemission. The experimental results are backed by theoretical studies using different functionals, which show that the characteristics of the surface band depend critically on the lattice constant. From the analysis of the energy-dependent low-energy electron diffraction intensities, we derive structural parameters of the Pt(111) surface relaxation with high accuracy. In addition, we give an unambiguous definition of the nonequivalent mirror-plane directions Γ¯M¯ and Γ¯M¯′ at fcc(111) surfaces, which is consistent with band-structure calculations and inverse-photoemission data. Concerning the surface resonance at the bottom of the L gap, we identified a delicate interplay of several contributions. Lattice constant, hybridization with d bands, and the influence of spin-orbit interaction are critical ingredients for understanding the peculiar energy dispersion and spin character of the unoccupied surface resonance. Published by the American Physical Society 2024

Interplay of spin–orbit and exchange interaction in a ferromagnet/heavy-metal hybrid system: Ni on W(110)

In a combined experimental and theoretical study, we investigate the interplay of spin–orbit interaction (SOI) and exchange interaction (XI) in the electronic structure of ultrathin Ni films on W(110). Using spin- and angle-resolved inverse photoemission, we observe that the size of the spin splitting of Ni-related exchange-split states differs for opposite magnetization directions. A quenched spin splitting for one of the magnetization directions reveals a contribution of SOI on an equal footing with XI. Using density-functional theory calculations, we explore the underlying mechanisms responsible for the experimentally observed coupling of SOI and XI. We find that a hybridization between adsorbate and substrate states, along with a high probability density of the respective states at the heavy W nuclei, cause the strong influence of SOI on the Ni-related exchange-split states.

Comment on "Spin- and angle-resolved inverse photoemission setup with spin orientation independent from electron incidence angle" [Rev. Sci. Instrum. 93, 093904 (2022)

The paper under discussion promises a spin- and angle-resolved inverse-photoemission (IPE) setup, where the spin-polarization direction of the electron beam used for excitation "can be tuned to any preferred direction" while "preserving the parallel beam condition." We support the idea to improve IPE setups by introducing a three-dimensional spin-polarization rotator, but we put the presented results to the test by comparing them with the literature results obtained by existing setups. Based on this comparison, we conclude that the presented proof-of-principle experiments miss the target in several aspects. Most importantly, the key experiment of tuning the spin-polarization direction under otherwise allegedly identical experimental conditions causes changes in the IPE spectra that are in conflict with existing experimental results and basic quantum-mechanical considerations. We propose experimental test measurements to identify and overcome the shortcomings.

Response to "Comment on 'Spin- and angle-resolved inverse photoemission setup with spin orientation independent from electron incidence angle'" [Rev. Sci. Instrum. 93, 093904 (2022)

We reply to the Comment by Donath et al. on our setup, which allows a total 3D control of the polarization direction of the electron beam in an inverse photoemission spectroscopy (IPES) experiment, a significant advance with respect to previous setups with partial polarization control. Donath et al. claim an incorrect operation of our setup after comparing their results, treated to enhance the spin asymmetry, with our spectra without the same treatment. They also equal spectra backgrounds instead of equaling peak intensities above the background. Thus, we compare our Cu(001) and Au(111) results with the literature. We reproduce previous results, including spin-up/spin-down spectral differences observed for Au and not observed for Cu. Also, spin-up/spin-down spectral differences appear at the expected reciprocal space regions. In the Comment, it is also stated that our tuning of the spin polarization misses the target because the spectra background changes when tuning the spin. We argue that the background change is irrelevant to IPES since the information is contained in peaks produced by primary electrons, those having conserved their energy in the inverse photoemission process. Second, our experiments agree with previous results from Donath et al. [Wissing et al., New J. Phys. 15, 105001 (2013)] and with a zero-order quantum-mechanical model of spins in vacuum. Deviations are explained by more realistic descriptions including the spin transmission through an interface. Consequently, the operation of our original setup is fully demonstrated. Our development corresponds to "the promising and rewarding angle-resolved IPES setup with the three-dimensional spin resolution," as indicated in the Comment, after our work.

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 ∼170meV from kBTeff 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 ΔkF ≲ 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.

Rashba-split image-potential state and unoccupied surface electronic structure of Re(0001)

The influence of spin-orbit interaction on the unoccupied electronic structure of the Re(0001) surface is investigated by spin- and angle-resolved inverse photoemission and density-functional theory calculations. In the two high-symmetry azimuths $\overline{\mathrm{\ensuremath{\Gamma}}}\phantom{\rule{0.16em}{0ex}}\overline{\text{K}}$ and $\overline{\mathrm{\ensuremath{\Gamma}}}\phantom{\rule{0.16em}{0ex}}\overline{\text{M}}$, we identify transitions into $d$-derived bulk states as well as different types of surface states. The Rashba-type spin-split hole pocket around $\overline{\mathrm{\ensuremath{\Gamma}}}$ finds continuation in empty spin-split surface states for higher ${\mathbf{k}}_{\ensuremath{\parallel}}$, thereby forming $\mathsf{W}$-shaped states whose lower parts are partially occupied. A large energy gap below and above the vacuum energy around $\overline{\mathrm{\ensuremath{\Gamma}}}$ hosts image-potential-induced surface states. The $n=1$ member of the Rydberg-like series exhibits a free-electron-like $E({\mathbf{k}}_{\ensuremath{\parallel}})$ dispersion with an effective mass of ${m}^{*}/{m}_{e}=1.2\ifmmode\pm\else\textpm\fi{}0.1$. Careful spin-resolved measurements for several angles of electron incidence allow us to detect Rashba-type spin-dependent energy splittings of this state with a Rashba parameter of ${\ensuremath{\alpha}}_{\text{R}}=105\ifmmode\pm\else\textpm\fi{}33\phantom{\rule{0.16em}{0ex}}\text{meV}\phantom{\rule{0.16em}{0ex}}\AA{}$.

Rashba-split surface state and spin-dependent photon emission from Re(0001) at Γ¯

The unoccupied electronic structure of the Re(0001) surface is investigated by spin- and angle-resolved inverse photoemission, experimentally and theoretically. The work is focused on the states around the center of the surface Brillouin zone $\overline{\mathrm{\ensuremath{\Gamma}}}$, where a hole pocket of a surface state with Rashba-type spin splitting is detected. Furthermore, we observe spin-dependent photon emission from unpolarized surface and bulk states at $\overline{\mathrm{\ensuremath{\Gamma}}}$. The size and sign of the spin asymmetry depends on experimental parameters such as the direction of the electron spin polarization and the photon detection angle. Maximum (zero) spin asymmetry is detected if the electron spin polarization and the plane of photon emission are perpendicular (parallel). The effect is traced back to spin-orbit-induced hybridization of the involved states.

Rashba-type splitting of the Au(110) surface state: A combined inverse and direct photoemission study

The Shockley surface state located at $\overline{\mathrm{Y}}$ on the $(1\ifmmode\times\else\texttimes\fi{}2)$-reconstructed Au(110) surface is predicted to exhibit a Rashba-type spin splitting. Previous photoemission experiments searched for this splitting but it could not be resolved yet. In order to uncover a possible splitting, the unoccupied surface state on Au(110) is examined with spin- and angle-resolved inverse photoemission, whereas Na-covered Au(110) allows for investigation of the now occupied surface state by means of spin- and angle-resolved direct photoemission. Our data show clear spin splittings in the order of $100\phantom{\rule{0.16em}{0ex}}\mathrm{meV}$ with a sign reversal at $\overline{\mathrm{Y}}$ in the surface state's in-plane spin components which is characteristic for a Rashba-type behavior. Furthermore, we deduce an effective mass of ${m}^{*}=(0.27\ifmmode\pm\else\textpm\fi{}0.02){m}_{e}$ and a Rashba parameter of ${\ensuremath{\alpha}}_{R}=(0.46\ifmmode\pm\else\textpm\fi{}0.04)\phantom{\rule{0.16em}{0ex}}\mathrm{eV}\phantom{\rule{0.16em}{0ex}}\AA{}$ from direct photoemission measurements.

Visualizing the multifractal wave functions of a disordered two-dimensional electron gas

The wavefunctions of a disordered two-dimensional electron gas at the quantum-critical Anderson transition are predicted to exhibit multifractal scaling in their real space amplitude. We experimentally investigate the appearance of these characteristics in the spatially resolved local density of states of a two-dimensional mixed surface alloy Bi_xPb_{1-x}/Ag(111), by combining high-resolution scanning tunneling microscopy with spin and angle-resolved inverse-photoemission experiments. Our detailed knowledge of the surface alloy electronic band structure, the exact lattice structure and the atomically resolved local density of states enables us to construct a realistic Anderson tight binding model of the mixed surface alloy, and to directly compare the measured local density of states characteristics with those from our model calculations. The statistical analyses of these two-dimensional local density of states maps reveal their log-normal distributions and multifractal scaling characteristics of the underlying wavefunctions with a finite anomalous scaling exponent. Finally, our experimental results confirm theoretical predictions of an exact scaling symmetry for Anderson quantum phase transitions in the Wigner-Dyson classes.

Empty electron states in cobalt-intercalated graphene.

The dispersion of the electronic states of epitaxial graphene (Gr) depends significantly on the strength of the bonding with the underlying substrate. We report on empty electron states in cobalt-intercalated Gr grown on Ir(111), studied by angle-resolved inverse photoemission spectroscopy and x-ray absorption spectroscopy, complemented with density functional theory calculations. The weakly bonded Gr on Ir preserves the peculiar spectroscopic features of the Gr band structure, and the empty spectral densities are almost unperturbed. Upon intercalation of a Co layer, the electronic response of the interface changes, with an intermixing of the Gr π* bands and Co d states, which breaks the symmetry of π/σ states, and a downshift of the upper part of the Gr Dirac cone. Similarly, the image potential of Ir(111) is unaltered by the Gr layer, while a downward shift is induced upon Co intercalation, as unveiled by the image state energy dispersion mapped in a large region of the surface Brillouin zone.

Coincidence angle-resolved photoemission spectroscopy: Proposal for detection of two-particle correlations

The angle-resolved photoemission spectroscopy (ARPES) is one powerful experimental technique to study the electronic structure of materials. As many electron materials show unusual many-body correlations, the technique to detect directly these many-body correlations will play important roles in the study of their many-body physics. In this article, we propose a technique to detect directly the two-particle correlations, a coincidence ARPES (cARPES) where two incident photons excite two respective photoelectrons which are detected in coincidence. While the one-photon-absorption and one-photoelectron-emission ARPES provides the single-particle spectrum function, the proposed cARPES with two-photon absorption and two-photoelectron emission is relevant to a two-particle Bethe-Salpeter wave function. Examples of the coincidence detection probability of the cARPES for a free Fermi gas and a Bardeen-Cooper-Schrieffer (BCS) superconducting state are studied in detail. We also propose another two experimental techniques, a coincidence angle-resolved photoemission and inverse-photoemission spectroscopy (cARP/IPES) and a coincidence angle-resolved inverse-photoemission spectroscopy (cARIPES). As all of these proposed coincidence techniques can provide the two-particle frequency Bethe-Salpeter wave functions, they can show the momentum and energy dependent two-particle dynamical physics of the material electrons in the particle-particle or particle-hole channel. Thus, they can be introduced to study the Cooper-pair physics in the superconductor, the itinerant magnetism in the metallic ferromagnet/antiferromagnet, and the particle-hole pair physics in the metallic nematic state. Moreover, as the two-particle Bethe-Salpeter wave functions also involve the inner-pair dynamical physics, these proposed coincidence techniques can be used to study the inner-pair time-retarded physics.

Breaking time-reversal symmetry at the M¯ point: Spin signal from a surface state on Tl/Ge(111)

We detected and analyzed a spin-dependent intensity asymmetry for spin-degenerate surface states at the $\overline{\mathrm{M}}$ point in the unoccupied electronic structure of Tl/Ge(111). Approximating the initial state by a plane wave, we calculated the inverse-photoemission process and obtained good agreement with the experimental data. Our model reveals that this spin asymmetry at a point of time-reversal invariant momentum (TRIM) is of different origin than other effects discussed in the literature, which are based on the light detection geometry, photon energy, and experimental probing depth of the electrons. Instead, the spin asymmetry in this nonmagnetic material with spin-orbit interaction is caused by breaking the initial-state time-reversal symmetry in the experiment. The effect is of general nature and can occur in spin- and angle-resolved inverse photoemission as well as photoemission at TRIM points.

Unoccupied electronic states of Ru(0001)

This report presents a combined theoretical and experimental description of the unoccupied electronic states of Ru(0001), along the Γ̅M̅ high symmetry direction of the Brillouin zone. A direct comparison between angle-resolved inverse photoemission spectroscopy and ab initio calculations of the 3-dimensional (3D) electronic structure of Ru(0001) have been used to determine the energy dispersion and the identification of different states and surface resonances. Both, measurements and calculations, complement previous reports regarding the electronic structure of Ru.

Spin-polarized surface electronic structure of Ta(110): Similarities and differences to W(110)

Tantalum and tungsten, direct neighbors in the periodic table, exhibit a very similar electronic structure. Compared with tungsten, however, the bands of tantalum are less occupied due to the lack of one electron. As a consequence, an exceptional Dirac-cone-like surface state, observed below the Fermi level for W(110), may appear above the Fermi level for Ta(110). To prove this conjecture, we investigate the unoccupied surface electronic structure of Ta(110) by spin- and angle-resolved inverse photoemission and electronic-structure calculations. Surprisingly, our results do not show the expected Dirac-cone-like surface state. Instead, spin-polarized unoccupied surface bands are identified, which have no equivalent in W(110). These findings are explained by the difference in the energetic positions of the surface states relative to the bulk states for Ta(110) and W(110) caused by the different lattice constants.

Spin texture with a twist in momentum space for Tl/Si(111)

The electronic structure and spin texture around the $\overline{\mathrm{M}}$ point of $\mathrm{Tl}/\mathrm{Si}(111)\text{\ensuremath{-}}(1\ifmmode\times\else\texttimes\fi{}1)$ is investigated with spin- and angle-resolved inverse photoemission and density-functional theory. The $\mathrm{Tl}/\mathrm{Si}(111)\text{\ensuremath{-}}(1\ifmmode\times\else\texttimes\fi{}1)$ surface exhibits a surface-derived unoccupied state, which extends over the complete surface Brillouin zone. It is known for its giant spin-orbit-induced splitting and unique symmetry- and spin-orbit-induced spin landscape: a rotating spin pattern in momentum space along $\overline{\mathrm{\ensuremath{\Gamma}}}\overline{\mathrm{K}}$ and pure in-plane spin polarization along $\overline{\mathrm{\ensuremath{\Gamma}}}\overline{\mathrm{M}}$. Our results demonstrate how the $\overline{\mathrm{M}}$ point is encircled by this state. Its spin texture shows a peculiar twist, which reflects the ${C}_{1h}$ symmetry of the $\overline{\mathrm{M}}$ point.

Spin-dependent size of interband hybridization gap: The interplay of adlayer and substrate states in Pb/Cu(111)

An interband hybridization gap with spin-dependent size was detected in a low-dimensional electron system influenced by strong spin-orbit coupling. Energy gaps between hybridizing states are distinctly influenced by strong spin-orbit coupling. If the size of these gaps depends on the spin direction of the states, this may lead to fully spin-polarized valleylike structures. As a model system to study the hybridization mechanism behind such valleys, we investigate the unoccupied electronic band structure of Pb/Cu(111) by spin- and angle-resolved inverse photoemission in combination with first-principles calculations. Here, we find a hybridization gap with a splitting of about 200 meV for the one and even larger than 500 meV for the other spin direction. We develop an effective two-band tight-binding model and demonstrate that the interplay of adlayer and substrate states is crucial to induce a sizable spin-orbit coupling and hybridization strength to the interacting states.

Tuning the spin signal from a highly symmetric unpolarized electronic state

A remarkably large spin signal is observed on nonmagnetic W(110) for a highly symmetric unoccupied state with no intrinsic spin polarization. The magnitude and, more importantly, the sign of this spin signal, measured by spin- and angle-resolved inverse photoemission for normal electron incidence, can be tuned in a user-defined manner by variation of the photon-detection angle and/or by rotating the spin-polarization direction of the incident electrons. Using calculations of the orbitally decomposed spectral densities, this effect is traced back to a mixing of different symmetries within the respective state. This explanation is underlined by the behavior of a second electronic state of pure symmetry, which does not show such a spin signal. In general, the spin signals of electronic states are not only influenced by their intrinsic spin polarization but also by the choice of symmetry-breaking experimental parameters in combination with the particular orbital characters of the states under investigation. The latter permits one to tune the spin signal in magnitude and sign.

Thin line of a Rashba-type spin texture: Unoccupied surface resonance of Tl/Si(111) alongΓ¯M¯

The Tl/Si(111)-$(1\ifmmode\times\else\texttimes\fi{}1)$ surface features outstanding properties with a unique spin pattern in momentum space. Along $\overline{\ensuremath{\Gamma}}\overline{K}$ $(\overline{\ensuremath{\Gamma}}{\overline{K}}^{\ensuremath{'}})$, surface states with rotating spin had been observed. Here, the focus is put on the unoccupied surface electronic structure along the $\overline{\ensuremath{\Gamma}}\overline{M}$ high-symmetry direction. Spin- and angle-resolved inverse-photoemission experiments with sensitivity to the in-plane and out-of-plane components of the spin-polarization vector are conducted with the help of our recently developed rotatable spin-polarized electron source (ROSE). In agreement with our theoretical findings, we identify a surface resonance with giant spin-orbit-induced spin splitting, which exhibits an exclusive Rashba-type spin texture, i.e., a pure in-plane spin polarization perpendicular to $\overline{\ensuremath{\Gamma}}\overline{M}$, in compliance with the mirror-plane symmetry of the $\overline{\ensuremath{\Gamma}}\overline{M}$ direction. Notably, for slight deviations from the high-symmetry line, this constraint is lifted and additional spin-polarization components emerge. This highlights the importance of a correct alignment of the experiment when investigating samples with spin textures that are more complex than in simple Rashba systems or in ferromagnets.

Ambiguity of experimental spin information from states with mixed orbital symmetries.

The spin texture of the unoccupied bands of the surface alloy Bi/Ag(111) is investigated with spin- and angle-resolved inverse photoemission and first-principles calculations. Surprisingly, the measured spin character does not always reflect the calculated spin texture of the bands. With the help of photoemission calculations within the one-step model, however, the discrepancy is traced back to the influence of the orbital symmetry of the respective states in combination with the experimental geometry. In particular, the calculations show that the spin texture of a surface band with mixed orbital symmetries may neither be recovered with s- nor p- nor unpolarized light. In general, spin information from direct or inverse photoemission experiments on electronic states with mixed orbital symmetries at spin-orbit-influenced surfaces has to be taken with a pinch of salt, while it remains reliable for states with pure symmetry.

Nitrogen-doping processes of graphene by a versatile plasma-based method

We present controllable processes to fabricate nitrogen-doped graphene with different doping configurations, in particular pyridinic- or graphitic-nitrogen-rich graphene. Nitrogen-doping is realized by in situ post-growth doping of monolayer graphene on SiC(0001) using a tunable hybrid plasma source, which exposes the graphene to a stream of ions and/or to a neutral flow of thermalized species from a precursor nitrogen gas. Using angle-resolved inverse photoemission spectroscopy (ARIPES), we determine the doping level of the graphene through the analysis of the π∗ states dispersion. At a dose of about 1×1015ionscm−2 and an energy of ∼35eV, the Fermi level of the nitrogen-doped graphene is brought 0.4eV above its value for the pristine graphene monolayer on SiC(0001). This n-type doping is attributed to a 8.7 at.% graphitic-nitrogen as revealed by the core level spectroscopy (XPS). In contrast, exposure to a beam of thermalized nitrogen atoms mainly induces pyridinic-like nitrogen doping of graphene. It is thus possible to control the predominant bonding configuration of the doping nitrogen by choosing either a thermalized atom or a low-energy ion source.