Heating a long-range ordered adsorbate phase beyond its stability temperature does not necessarily result in a disordered phase; it can also break up into heavily fluctuating ordered domains. Temporal and/or spatial averaging over these fluctuations may give the impression of both a wrong periodicity and false symmetry elements such as nonexisting glide planes or rotational axes of incorrect order. This can happen in real space and reciprocal space, and also below liquid-nitrogen temperature, so that the true nature of the phase might remain undetected. We demonstrate this scenario at the catalytically active Rh(100) surface covered by 1/2 monolayer of oxygen, using quantitative low-energy electron diffraction, variable-temperature scanning tunneling microscopy, and density functional theory. Using the example of CO adsorption, we show that local symmetry can have a decisive influence on the binding energy and thus the chemical reactivity.

We investigated the initial growth of TiTe_2 on Au(111) from sub-monolayer to multi-layer coverage by scanning tunneling microscopy (STM), low-energy electron diffraction intensity analysis (LEED-IV), and density functional theory (DFT). In the submonolayer regime we find a stable and well-ordered (5×√(3))_rect superstructure consisting of separated TiTe_2 molecules, whereby the Ti atoms substitute Au atoms of the first substrate layer as proven by LEED-IV. By adding further Ti and Te in a 1:2 ratio and proper annealing dealloying sets in and a homogeneous 1T-TiTe_2 monolayer film on an unreconstructed substrate is formed. The resulting moiré structure is close to a (4 × 4) superstructure w.r.t. Au(111) and has a slightly expanded in-plane lattice parameter compared to the 1T-TiTe_2 bulk value. With further stoichiometric deposition, thicker 1T-TiTe_2 films grow. Surprisingly, a five layer thick film exhibits an even larger lattice-parameter (1.5

We investigated the initial growth of TiTe2 on Au(111) from submonolayer to multilayer coverage by scanning tunneling microscopy (STM), low-energy electron diffraction intensity analysis (LEED-IV), and density functional theory. In the submonolayer regime, we find a stable and well-ordered (5 & times; 3)rect superstructure consisting of separated TiTe2 molecules, whereby the Ti atoms substitute Au atoms of the first substrate layer as proven by LEED-IV. By adding further Ti and Te in a 1:2 ratio and proper annealing dealloying sets in and a homogeneous 1T-TiTe2 monolayer film on an unreconstructed substrate is formed. The resulting moir & eacute; structure is close to a (4 & times; 4) superstructure with respect to Au(111) and has a slightly expanded in-plane lattice parameter compared to the 1T-TiTe2 bulk value. With further stoichiometric deposition, thicker 1T-TiTe2 films grow. Surprisingly, a five-layer thick film exhibits an even larger lattice parameter (1.5 % larger than the bulk value). All LEED-IV analyses are based on best-fit R factors of R 0.13.

As part of the Vienna package for Erlangen LEED, low-energy electron diffraction (ViPErLEED) project, computer programs have been developed for facile and user-friendly data extraction from movies of LEED images. The programs make use of some concepts from astronomical image processing and analysis. As a first step, flat-field and dark-frame corrections reduce the effects of inhomogeneities of the camera and screen. In a second step, for identifying all diffraction maxima ("spots"), it is sufficient to manually mark and label a single spot or very few spots. Then the program can automatically identify all other spots and determine the distortions of the image. This forms the basis for automatic spot tracking (i.e., following the spots as they move across the LEED screen) and intensity measurement. Even for complex structures with hundreds to a few thousand diffraction beams, this step takes less than a minute. The package also includes a program for further processing of these I(V ) curves (averaging of equivalent beams, manual and/or automatic selection, smoothing) as well as several utilities. The software is implemented as a set of plugins for the public-domain image processing program IMAGEJ and provided as an open-source package.

Low-energy electron diffraction (LEED) is a widely used technique in surface-science laboratories. Yet, it is rarely used to its full potential. The quantitative information about the surface structure, contained in the modulation of the intensities of the diffracted beams as a function of incident electron energy, LEED I(V), is underutilized. To acquire these data, only minor adjustments would be required in most experimental setups, but existing analysis software is cumbersome to use and often computationally inefficient. The ViPErLEED (Vienna package for Erlangen LEED) project lowers these barriers, introducing a combined solution for user-friendly data acquisition, extraction, and computational analysis. These parts are discussed in three separate publications. Here, the focus is on the computational part of ViPErLEED, which performs highly automated LEED-I(V) calculations and structural optimizations. Minimal user input is required, and the functionality is significantly enhanced compared to existing solutions. Computation is performed by embedding the existing Erlangen tensor-LEED package (). ViPErLEED manages additional parallelization, monitors convergence, and processes all input and output. This makes LEED I(V) more accessible to new users while minimizing the potential for errors and the manual labor. Added functionalities include intelligent structure-dependent defaults for most calculation parameters, automatic detection of bulk and surface symmetries and their relationship, automated search procedures that preserve the symmetry and speed up convergence, adjustments to the code to handle larger systems than before, as well as parallelization and optimization. Modern file formats are used as input and output, and there is a direct interface to the atomic simulation environment (ASE) package. The software is implemented primarily in (version ≥3.7) and provided as an open-source package (GNU GPLv3 or any later version). A structure determination of the α-Fe2O3(11¯02)−(1×1) surface is presented as an example for the application of the software. Published by the American Physical Society 2025

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

The determination of the configuration of atomic adsorbates on clean metal surfaces has been a key issue in surface science 60 years ago and still is today. We demonstrate that despite the prevalence of combined scanning tunneling microscopy and density functional theory studies of adsorbate systems the pitfalls are plentiful calling for accurate, reliable structure analyses that can be delivered by diffraction methods. We analyze and compare the ordered phases of Te on Ir(111), Ir(100), and Au(100) demonstrating the accuracy, the in-depth information and physical insight that can nowadays be obtained by quantitative low-energy electron diffraction structural analyses.

For the production of transition-metal dichalcogenides by molecular beam epitaxy, an understanding of the interaction between chalcogenide atoms and metal surfaces is of fundamental interest. Here, we describe the occurrence of stable surface telluride phases when reacting submonolayer amounts of tellurium with a Pt(111) surface. We find that when approaching a Te amount of 0.44 monolayers from below, a disordered Te adsorbate phase is converted into a long-range ordered Pt(111)-(3 x 3)-4Te surface telluride, which is stable against loss of Te up to 890 K. Adding further Te, heavy domain walls develop that condense into a well-ordered domain structure with (10 x 10) periodicity. It hosts 49 Te atoms per unit cell and is thermally stable up to 770 K. These two phases are the only existing Te-induced surface reconstructions in the submonolayer regime. The atomic structure of the two phases is determined using low-energy electron diffraction intensity analysis, scanning tunneling microscopy, and density functional theory. The resulting complex surface structures are revealed with picometer accuracy and a great agreement between the employed methods. In particular, the analysis of the (10 x 10) structure demonstrates the currently achievable state-of-the-art for low-energy electron diffraction structural analyses in terms of experimental surface preparation and data collection but also of computational methods, and it leads the way to building up a structural database for two-dimensional materials and their interfaces.

The Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction mediates collinear magnetic interactions via the conduction electrons of a nonmagnetic spacer, resulting in a ferro-or antiferromagnetic magnetization in magnetic multilayers. Recently it has been discovered that heavy nonmagnetic spacers are able to mediate an indirect magnetic coupling that is noncollinear and chiral. This Dzyaloshinskii-Moriya-enhanced RKKY interaction causes the emergence of a variety of interesting magnetic structures, such as skyrmions and spin spirals. Here, we show by spin-polarized scanning tunneling microscopy that the interchain coupling between manganese oxide chains on Ir(001) can reproducibly be switched from chiral to collinear antiferromagnetic by increasing the oxidation state of MnO2, while the reverse process can be induced by thermal reduction. The underlying structure-property relationship is revealed by low-energy electron diffraction intensity analysis. Density functional theory calculations suggest that the magnetic transition may be caused by a significant increase of the Heisenberg exchange which overrides the Dzyaloshinskii-Moriya interaction upon oxidation.

Metal-halide perovskite (MHP) thin films for next-generation solar cells are typically fabricated by wet -chemical synthesis in which surface properties such as the orientation of surface facets and their termination cannot be controlled. MHP device efficiencies depend critically on those surface properties. We demonstrate the epitaxial growth of several nanometer thick purely (001)-orientated films of CsPbBr3 and CsSnBr3 MHPs on Au(001) by molecular beam epitaxy. The epitaxial films are in a cubic phase aligned with the substrate. Their surfaces are singly terminated and can be modified for the first time. While the CsBr and PbBr2 surface terminations differ in terms of their atomic structure and defect content, the films are intrinsic semiconductors irrespective of the termination. The work function of the PbBr2-terminated surface is increased by 0.7 eV, which has drastic implications for the level alignment at MHP interfaces.

The Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction mediates collinear magnetic interactions via the conduction electrons of a non-magnetic spacer, resulting in a ferro- or antiferromagnetic magnetization in magnetic multilayers. The resulting spin-polarized charge transport effects have found numerous applications. Recently it has been discovered that heavy non-magnetic spacers are able to mediate an indirect magnetic coupling that is non-collinear and chiral. This Dzyaloshinskii-Moriya-enhanced RKKY (DME-RKKY) interaction causes the emergence of a variety of interesting magnetic structures, such as skyrmions and spin spirals. Applications using these magnetic quasi-particles require a thorough understanding and fine-tuning of the balance between the Dzyaloshinskii-Moriya interaction and other magnetic interactions, e.g., the exchange interaction and magnetic anisotropy contributions. Here, we show by spin-polarized scanning tunneling microscopy that the spin structure of manganese oxide chains on Ir(001) can reproducibly be switched from chiral to collinear antiferromagnetic interchain interactions by increasing the oxidation state of MnO$_2$ while the reverse process can be induced by thermal reduction. The underlying structural change is revealed by low-energy electron diffraction intensity data (LEED-IV) analysis. Density functional theory calculations suggest that the magnetic transition may be caused by a significant increase of the Heisenberg exchange upon oxidation.

We present a so far undetected submonolayer phase of copper telluride on Cu(111) with $\left(5 \times \sqrt{3}\right)_{\text{rect}}$ periodicity and coverage of 0.40 ML Tellurium (Te), which can be grown with perfect long-range order. It is structurally characterized by a combination of quantitative low-energy electron diffraction (LEED-IV), scanning tunneling microscopy (STM), and density functional theory (DFT). We find that Te induces the formation of four atom wide linear troughs within the Cu(111) surface filled up by two Te atoms per unit cell. Additionally, the interspace between the troughs is decorated by Cu$_2$Te$_2$ ad-chains sitting at hcp sites. All Te atoms exhibit the same local sixfold coordination: They occupy threefold hollow sites of the substrate and are one-sided attached to another three Cu atoms. The presented structural model is verified by a LEED-IV analysis with Pendry R-factor of R = 0.174 and quantitative agreement of structural parameters with DFT predictions. It also has by far the lowest energy of all models tested by DFT and simulated STM images agree perfectly with experiment. It turns out that the new $\left(5 \times \sqrt{3}\right)_{\text{rect}}$ phase is the most dense surface telluride phase possible on Cu(111) before bulk-like copper telluride starts to growth.

Several‐nanometer‐thick, closed, and epitaxial cobalt(II) oxide films with wurtzite crystal structure (w‐CoO) are grown on Au(111) and their structural and electronic properties analyzed. The structural quality of the oriented, oxygen‐terminated, and unreconstructed films allow the application of surface‐science methods to unravel the properties of this unusual polymorph of CoO and may pave the way for future thin‐film applications. An experimental structural analysis by low‐energy electron diffraction (LEED‐IV) is presented with an excellent agreement between measured and calculated intensity spectra expressed by a Pendry R‐factor of and few‐picometer error bounds in the parameter values. Using scanning tunneling spectroscopy (STS) the bandgap of the semiconducting films is found to be 1.4 ± 0.2 eV. Ultraviolet photoelectron spectroscopy (UPS) confirms the presence of a gap and the position of the Fermi level ( E F ). The structural results of density functional theory calculations using (hybrid) functionals to treat electron correlations and van der Waals forces agree well with the experimentally determined structure of the antiferromagnetic w‐CoO films. In contrast to generalized gradient approximation (GGA)+U calculations, the Heyd–Scuseria–Ernzerhof hybrid functional reproduces the semiconducting nature correctly and predicts surface states in the gap which might pin E F in agreement with STS and UPS.

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.

The surface atomic and electronic structure after deposition of 1/3 monolayer (ML) Te on Cu(111) was determined using a combination of low-energy electron diffraction (LEED), scanning tunneling microscopy and spectroscopy (STM/STS), angle-resolved single and two-photon photoelectron spectroscopy (ARPES /AR-2PPE) and density functional theory (DFT) calculations. Contrary to the current state in literature Te does not create a two-dimensional surface alloy but forms Cu$_2$Te$_2$ adsorbate chains in a $\left(2\sqrt{3} \times \sqrt{3}\right)\textrm{R30}^\circ$ superstructure. We establish this by a high-precision LEED-IV structural analysis with Pendry $R$ factor of $R = 0.099$ and corroborating DFT and STM results. The electronic structure of the surface phase is dominated by an anisotropic downward dispersing state at the Fermi energy $E_F$ and a more isotropic upward dispersing unoccupied state at $E-E_F = + 1.43\,\textrm{eV}$. Both states coexist with bulk states of the projected band structure and are therefore surface resonances.

By quantitative low-energy electron diffraction (LEED) we investigate the extensively studied commensurate charge density wave (CDW) phase of trigonal tantalum disulphide (1T-TaS2), which develops at low temperatures with a (root 13 x root 13)R13.9 degrees periodicity. A full-dynamical analysis of the energy dependence of diffraction spot intensities reveals the entire crystallographic surface structure, i.e., the detailed atomic positions within the outermost two trilayers consisting of 78 atoms as well as the CDW stacking. The analysis is based on an unusually large data set consisting of spectra for 128 inequivalent beams taken in the energy range 20-250 eV and an excellent fit quality expressed by a best-fit Pendry R factor of R = 0.110. The LEED intensity analysis reveals that the well-accepted model of star-of-David-shaped clusters of Ta atoms for the bulk structure also holds for the outermost two TaS2 trilayers. Specifically, in both layers the clusters of Ta atoms contract laterally by up to 0.25 angstrom and also slightly rotate within the superstructure cell, causing respective distortions as well as heavy bucklings (up to 0.23 angstrom) in the adjacent sulfur layers. Most importantly, our analysis finds that the CDWs of the first and second trilayers are vertically aligned, while there is a lateral shift of two units of the basic hexagonal lattice (6.71 angstrom) between the second and third trilayers. The results may contribute to a better understanding of the intricate electronic structure of the reference compound 1T-TaS2 and guide the way to the analysis of complex structures in similar quantum materials.

Layered materials forming charge-density-wave (CDW) states exhibit an intriguing interplay between crystallographic structure and electronic properties. Using quantitative low-energy electron diffraction, the authors determine with picometer accuracy the complex surface structure of the transition-metal dichalcogenide 1$T$-TaS${}_{2}$ in its commensurate CDW phase. The key findings are the vertical CDW stacking between first and second trilayer and the broken inversion symmetry in the first S-Ta-S trilayer, due to an expansion of the topmost S layer.