A detailed account of the dependence of X-ray absorption spectra (XAS) on polarisation and light beam directions is given. Anisotropic XAS measured on single crystals, layered compounds, polymers and oriented powders are tabulated. The X-ray absorption cross section by non-magnetic samples is derived, including electric dipole and quadrupole contributions. Orders of magnitude are found for magnetic dipole and electric dipole-octupole terms. Using a spherical tensor expansion of the absorption cross section, simple analytical formulae are given for the angular dependence of the electric dipole and quadrupole contributions to XAS for all crystal point groups. These formulae are valid down to the edge and include many-body effects. The are applied to two experimental examples, the iron K-edge in haematite and the copper K-edge in CuCl42-. For the latter case, spherical tensor components are interpreted in terms of molecular orbitals. The influence of unpolarised and circularly polarised X-rays is discussed, as well as various experimental problems met in angle-resolved XAS. In an appendix, the quadrupole contribution to angular XAS is derived within the multiple-scattering formalism, along with closed expressions for the dipole and quadrupole spherical tensor components.

https://iopscience.iop.org/article/10.1088/0953-8984/2/3/018/pdf

Angular dependence of X-ray absorption spectra

The structure of a surface influences many of its important properties. For example, the chemical, electronic, and vibrational properties of surfaces are affected by small changes (i.e., 0.01 to 0.05 A) in the surface bond lengths. The surfaces of most semiconductors and of some noble metals are reconstructed, producing new and important properties of the surface region. Indeed, modern surface science is anchored on the ability of novel microscopic and spectroscopic techniques to yield quantitative information about surface structure.

The Structure of Surfaces

Photoelectron diffraction is the name given to the phenomenon resulting from the coherent interference of the directly emitted component of an electron wavefield, emerging from an atom as a result of core level photoemission, with other components elastically scattered by surrounding atoms. Experimental characterization of this effect provides information which can be used to provide quantitative determinations of the structure of surfaces, and particularly of adsorbed species on surfaces, in an element-specific fashion. Since the initial. Demonstration of the phenomenon in the late 1970s, an extensive methodology for surface structure determination has been developed. In this review the background physics of the process, and the development of the technique is described. A brief discussion of the high energy forward scattering version of the technique (X-ray photoelectron diffraction-XPD), which utilizes zero-order diffraction effects, is included, but the most of the review is concerned with the lower energy backscattering method more relevant to the determination of detailed adsorption sites on surfaces. In addition to the general theoretical, experimental and methodology background, a number of the more recent developments are described including use of 'direct inversion' methods for (approximate) structure determination, including a survey of photoelectron holography, and the realization of chemical shift photoelectron diffraction to allow structure determinations of surfaces including atoms of one element in more than one inequivalent site. All of the developments are illustrated with specific examples, mainly of molecular and atomic adsorbates on metal surfaces.

https://iopscience.iop.org/article/10.1088/0034-4885/57/10/003/pdf

Adsorbate structure determination on surfaces using photoelectron diffraction

Adsorbate-induced restructuring of surfaces

Angle-resolved photoemission spectroscopy (ARPES) has emerged as a leading experimental probe for studying the complex phenomena in quantum materials, a subject of increasing importance The power of this technique stems from the directness and the richness of the momentum-resolved information it can provide, such as band dispersion, Fermi surface topology, and electron self-energy Over the past decade, the significantly improved energy and momentum resolution and carefully matched experiments have turned this technique into a sophisticated tool in characterizing the electronic structure of complex materials This revolution is mostly evident in the study of cuprate high-temperature superconductors More recently, this technique has played a critical role in advancing our understanding of the newly discovered iron-based superconductors and topological insulators In this paper we review some of the recent ARPES results and discuss the future perspective in this rapidly developing field

Angle-Resolved Photoemission Studies of Quantum Materials

Angle-resolved photoemission extended fine structure from adsorbate core levels yields complete, accurate surface structures without resort to trial-and-error comparisons to theory. Scattering peaks from individual substrate atoms were observed with use of $\mathrm{S}(1s)$ photoemission from $c(2\ifmmode\times\else\texttimes\fi{}2)\mathrm{S}/\mathrm{Ni}(001)$ and $p(2\ifmmode\times\else\texttimes\fi{}2)\mathrm{S}/\mathrm{Cu}(001)$, along [011]. Fourfold-hollow site geometries were found for both systems, with interatomic distances of $R(\mathrm{S}\ensuremath{-}\mathrm{N}\mathrm{i})=2.24(3)$ \AA{} and $R(\mathrm{S}\ensuremath{-}\mathrm{C}\mathrm{u})=2.28(3)$ \AA{}.

/pdf/direct-surface-structure-determination-with-photoelectron-s7r6hgns6u.pdf

Direct surface structure determination with photoelectron diffraction

We present a theory for photoelectron scattering in the 100--1000 eV energy range designed to simulate experimental measurements of angle-resolved photoemission extended fine structure (ARPEFS) from ordered surfaces. The zero-order problem of photoabsorption in the solid is treated first, followed by a scattering problem which incorporates the scattering ion cores in a perturbation series (cluster expansion). The dynamics of core-hole relaxation are discussed, but the dynamical effects are shown to be small. The Taylor-series magnetic-quantum-number expansion is used for the curved-wave, multiple-scattering equations. We argue that a velocity-dependent surface barrier gives primarily an inner potential shift, with no clear evidence for surface electron refraction. Analytic formulas for aperture integration are derived and thermal averaging in a correlated Debye model is extended to multiple scattering. Reasonable values for nonstructural parameters in the theory are shown to give very good simulations of the experimental ARPEFS measurements from c(2\ifmmode\times\else\texttimes\fi{}2)S/Ni(001) in contrast to previous theoretical calculations. We find, in agreement with full multiple-scattering calculations, that forward focusing is a fundamental feature of ARPEFS and that curved-wave corrections are essential for quantitative results. Since the scattering path-length difference is not appreciably altered by forward scattering, the ARPEFS oscillation frequency is equal to the geometrical path-length difference plus a small potential phase shift, but the amplitude and constant phase of the oscillations cannot be predicted by theories based upon single-scattering or plane-wave approximations.

/pdf/theory-of-angle-resolved-photoemission-extended-fine-2y7h1gvcu1.pdf

Theory of angle-resolved photoemission extended fine structure

Five approximate models for describing the scattering of spherical waves by central potentials are explored. The point-scattering model introduced by Lee and Pendry [Phys. Rev. B 11, 2795 (1975)] allows a short-range potential to be close to the source; a new homogeneous-wave model lifts the restriction on the potential diameter, but requires asymptotic incident waves. The popular plane-wave model requires both an infinitesimal-diameter potential and incident waves at their asymptotic limit. For realistic potentials at near-neighbor separations, none of these models is adequate: Even a hybrid model combining features of the point-scattering and homogeneous-wave methods does not allow for amplitude variation across the potential. The fifth small-atom model is based on a Taylor-series, magnetic-quantum-number expansion of the addition theorem for screened spherical waves. This Taylor-series approximation has the homogeneous-wave model as its zeroth-order term and the exact spherical-wave scattering process as its limit. Multiple-scattering equations for angle-resolved photoemission extended fine structure (ARPEFS) are derived and the effectiveness of these approximations is compared. We demonstrate that while the plane-wave model is reasonably accurate for near-180\ifmmode^\circ\else\textdegree\fi{} backscattering, small-angle scattering requires the curved-wave-front corrections available in the Taylor-series-expansion method.

/pdf/small-atom-approximations-for-photoelectron-scattering-in-3f51cvrpfe.pdf

Small-atom approximations for photoelectron scattering in the intermediate-energy range.

We derive new, simplified formulas for the scattering of l=1 spherical waves from central potentials, as a basis for discussing curved-wave-front corrections to single-scattering plane-wave models for angle-resolved photoemission extended fine structure and extended x-ray-absorption fine structure. A differential form for the expansion of the screened spherical wave replaces the usual Gaunt-integral form to facilitate the summation over equivalent magnetic sublevels in the scattered wave. Spherical-wave scattering factors are defined and interpreted as corrections to the plane-wave scattering factor. We argue and demonstrate by example that the remarkable success of plane-wave models does not result from reaching the spherical-wave asymptotic limit; instead, successive partial-wave corrections cancel for backscattering at high energy. The new scattering formulas allow curved-wave-front numerical calculations to be performed with little more effort than with plane-wave formulas.

/pdf/curved-wave-front-corrections-for-photoelectron-scattering-4vse5q8iwk.pdf

Curved-wave-front corrections for photoelectron scattering

Measurements of the extended fine structure in the photoemission intensity from the S(1s) core level were performed for a c(2\ifmmode\times\else\texttimes\fi{}2) overlayer of S on Ni(011). Four experimental geometries were employed, making this the most complete angle-resolved-photoemission extended-fine-structure (ARPEFS) study to date. Surface structural information was extracted from the ARPEFS using a combination of Fourier-transform techniques and comparisons to multiple-scattering calculations. The results of this analysis are in excellent agreement with previous studies of this system indicating that S adsorbs in a rectangular hollow site 2.20\ifmmode\pm\else\textpm\fi{}0.02 A\r{} above a second-layer Ni atom. We further present evidence for a buckling of the second Ni layer, giving an expansion in the separation between the first Ni layer and the second-layer Ni atoms covered by S atoms of 11% from the bulk value, while second-layer Ni atoms not covered in the c(2\ifmmode\times\else\texttimes\fi{}2) structure assume essentially bulk positions. We also examine in detail the effects of multiple scattering on the extraction of this structural information from ARPEFS and present results for surfaces with S coverages greater than 1/2 monolayer.

J.J. Barton

Papers

Direct surface structure determination with photoelectron diffraction

Theory of angle-resolved photoemission extended fine structure

Small-atom approximations for photoelectron scattering in the intermediate-energy range.

Curved-wave-front corrections for photoelectron scattering

Angle-resolved-photoemission extended-fine-structure spectroscopy investigation of c(2 x 2) S/Ni(011).