Circular dichroism in hard X-ray photoelectron diffraction observed by time-of-flight momentum microscopy

X-ray photoelectron diffraction (XPD) is a powerful technique that yields detailed structural information of solids and thin films that complements electronic structure measurements. Among the strongholds of XPD we can identify dopant sites, track structural phase transitions, and perform holographic reconstruction. High-resolution imaging of k_ll-distributions (momentum microscopy) presents a new approach to core-level photoemission. It yields full-field k_x-k_y XPD patterns with unprecedented acquisition speed and richness in details. Here, we show that beyond the pure diffraction information, XPD patterns exhibit pronounced circular dichroism in the angular distribution (CDAD) with asymmetries up to 80%, alongside with rapid variations on a small k_ll-scale (0.1 Å^-1). Measurements with circularly-polarized hard X-rays (hν = 6 keV) for a number of core levels, including Si, Ge, Mo and W, prove that core-level CDAD is a general phenomenon that is independent of atomic number. The fine structure in CDAD is more pronounced compared to the corresponding intensity patterns. Additionally, they obey the same symmetry rules as found for atomic and molecular species, and valence bands. The CD is antisymmetric with respect to the mirror planes of the crystal, whose signatures are sharp zero lines. Calculations using both the Bloch-wave approach and one-step photoemission reveal the origin of the fine structure that represents the signature of Kikuchi diffraction. To disentangle the roles of photoexcitation and diffraction, XPD has been implemented into the Munich SPRKKR package to unify the one-step model of photoemission and multiple scattering theory.

Time-of-flight photoelectron momentum microscopy with 80-500 MHz photon sources: electron-optical pulse picker or bandpass pre-filter

The small time gaps of synchrotron radiation in conventional multi-bunch mode (100-500 MHz) or laser-based sources with high pulse rate (∼80 MHz) are prohibitive for time-of-flight (ToF) based photoelectron spectroscopy. Detectors with time resolution in the 100 ps range yield only 20-100 resolved time slices within the small time gap. Here we present two techniques of implementing efficient ToF recording at sources with high repetition rate. A fast electron-optical beam blanking unit with GHz bandwidth, integrated in a photoelectron momentum microscope, allows electron-optical `pulse-picking' with any desired repetition period. Aberration-free momentum distributions have been recorded at reduced pulse periods of 5 MHz (at MAX II) and 1.25 MHz (at BESSY II). The approach is compared with two alternative solutions: a bandpass pre-filter (here a hemispherical analyzer) or a parasitic four-bunch island-orbit pulse train, coexisting with the multi-bunch pattern on the main orbit. Chopping in the time domain or bandpass pre-selection in the energy domain can both enable efficient ToF spectroscopy and photoelectron momentum microscopy at 100-500 MHz synchrotrons, highly repetitive lasers or cavity-enhanced high-harmonic sources. The high photon flux of a UV-laser (80 MHz, <1 meV bandwidth) facilitates momentum microscopy with an energy resolution of 4.2 meV and an analyzed region-of-interest (ROI) down to <800 nm. In this novel approach to `sub-µm-ARPES' the ROI is defined by a small field aperture in an intermediate Gaussian image, regardless of the size of the photon spot.

Suppression of the vacuum space-charge effect in fs-photoemission by a retarding electrostatic front lens

The performance of time-resolved photoemission experiments at fs-pulsed photon sources is ultimately limited by the e-e Coulomb interaction, downgrading energy and momentum resolution. Here, we present an approach to effectively suppress space-charge artifacts in momentum microscopes and photoemission microscopes. A retarding electrostatic field generated by a special objective lens repels slow electrons, retaining the k-image of the fast photoelectrons. The suppression of space-charge effects scales with the ratio of the photoelectron velocities of fast and slow electrons. Fields in the range from -20 to -1100 V/mm for E_kin = 100 eV to 4 keV direct secondaries and pump-induced slow electrons back to the sample surface. Ray tracing simulations reveal that this happens within the first 40 to 3 μm above the sample surface for E_kin = 100 eV to 4 keV. An optimized front-lens design allows switching between the conventional accelerating and the new retarding mode. Time-resolved experiments at E_kin = 107 eV using fs extreme ultraviolet probe pulses from the free-electron laser FLASH reveal that the width of the Fermi edge increases by just 30 meV at an incident pump fluence of 22 mJ/cm² (retarding field -21 V/mm). For an accelerating field of +2 kV/mm and a pump fluence of only 5 mJ/cm², it increases by 0.5 eV (pump wavelength 1030 nm). At the given conditions, the suppression mode permits increasing the slow-electron yield by three to four orders of magnitude. The feasibility of the method at high energies is demonstrated without a pump beam at E_kin = 3830 eV using hard x rays from the storage ring PETRA III. The approach opens up a previously inaccessible regime of pump fluences for photoemission experiments.

Compact setup for spin-, time-, and angle-resolved photoemission spectroscopy

We present a compact setup for spin-, time-, and angle-resolved photoemission spectroscopy. A 10 kHz titanium sapphire laser system delivers pulses of 20 fs duration, which drive a high harmonic generation-based source for ultraviolet photons at 21 eV for photoemission. The same laser also excites the sample for pump-probe experiments. Emitted electrons pass through a hemispherical energy analyzer and a spin-filtering element. The latter is based on spin-polarized low-energy electron diffraction on an Au-passivated iridium crystal. The performance of the measurement system is discussed in terms of the resolution and efficiency of the spin filter, which are higher than those for Mott-based techniques.

Time- and momentum-resolved photoemission studies using time-of-flight momentum microscopy at a free-electron laser

Time-resolved photoemission with ultrafast pump and probe pulses is an emerging technique with wide application potential. Real-time recording of nonequilibrium electronic processes, transient states in chemical reactions, or the interplay of electronic and structural dynamics offers fascinating opportunities for future research. Combining valence-band and core-level spectroscopy with photoelectron diffraction for electronic, chemical, and structural analyses requires few 10 fs soft X-ray pulses with some 10 meV spectral resolution, which are currently available at high repetition rate free-electron lasers. We have constructed and optimized a versatile setup commissioned at FLASH/PG2 that combines free-electron laser capabilities together with a multidimensional recording scheme for photoemission studies. We use a full-field imaging momentum microscope with time-of-flight energy recording as the detector for mapping of 3D band structures in (k_x, k_y, E) parameter space with unprecedented efficiency. Our instrument can image full surface Brillouin zones with up to 7 Å^-1 diameter in a binding-energy range of several eV, resolving about 2.5 × 10⁵ data voxels simultaneously. Using the ultrafast excited state dynamics in the van der Waals semiconductor WSe₂ measured at photon energies of 36.5 eV and 109.5 eV, we demonstrate an experimental energy resolution of 130 meV, a momentum resolution of 0.06 Å^-1, and a system response function of 150 fs.

Spin-filtered time-of-flight k-space microscopy of Ir - Towards the "complete" photoemission experiment

The combination of momentum microscopy (high resolution imaging of the Fourier plane) with an imaging spin filter has recently set a benchmark in k-resolution and spin-detection efficiency. Here we show that the degree of parallelization can be further increased by time-of-flight energy recording. On the quest towards maximum information (in earlier work termed "complete" photoemission experiment) we have studied the prototypical high-Z fcc metal iridium. Large partial bandgaps and strong spin-orbit interaction lead to a sequence of spin-polarized surface resonances. Soft X-rays give access to the 4D spectral density function ρ (E_B,k_x,k_y,k_z) weighted by the photoemission cross section. The Fermi surface and all other energy isosurfaces, Fermi velocity distribution v_F(k_F), electron or hole conductivity, effective mass and inner potential can be obtained from the multi-dimensional array ρ by simple algorithms. Polarized light reveals the linear and circular dichroism texture in a simple manner and an imaging spin filter exposes the spin texture. One-step photoemission calculations are in fair agreement with experiment. Comparison of the Bloch spectral function with photoemission calculations uncovers that the observed high spin polarization of photoelectrons from bulk bands originates from the photoemission step and is not present in the initial state.

Hosting of surface states in spin-orbit induced projected bulk band gaps of W(1 1 0) and Ir(1 1 1)

Spin-momentum locking of surface states has attracted great interest in recent years due to envisioned technological applications in the field of spintronics. Normal metal surfaces like W(1 1 0) and Ir(1 1 1) show surface states with energy dispersions and spin-polarization textures, which are reminiscent of topologically non-trivial surface states. In order to understand this phenomenon the connection of bulk and surface states has to be explored. Using time-of-flight momentum microscopy with soft x-ray excitation, we present a comprehensive analysis of the bulk bands of W and Ir. Surface states are determined by the same method with photon excitation in the vacuum ultraviolet region. The superposition of both spectral densities reveals the hosting of surface states within the gap structure of bulk bands projected on the surface Brillouin zone. Quantitative differences in the extension of experimental and theoretical local band gaps indicate an underestimation of electron correlation effects in theory.

Direct 3D mapping of the Fermi surface and Fermi velocity

We performed a full mapping of the bulk electronic structure including the Fermi surface and Fermi-velocity distribution v_F(k_F) of tungsten. The 4D spectral function ρ(E_B; k) in the entire bulk Brillouin zone and 6 eV binding-energy (E_B) interval was acquired in ∼3 h thanks to a new multidimensional photoemission data-recording technique (combining full-field k-microscopy with time-of-flight parallel energy recording) and the high brilliance of the soft X-rays used. A direct comparison of bulk and surface spectral functions (taken at low photon energies) reveals a time-reversal-invariant surface state in a local bandgap in the (110)-projected bulk band structure. The surface state connects hole and electron pockets that would otherwise be separated by an indirect local bandgap. We confirmed its Dirac-like spin texture by spin-filtered momentum imaging. The measured 4D data array enables extraction of the 3D dispersion of all bands, all energy isosurfaces, electron velocities, hole or electron conductivity, effective mass and inner potential by simple algorithms without approximations. The high-Z bcc metals with large spin-orbit-induced bandgaps are discussed as candidates for topologically non-trivial surface states.

Determination of surface and interface magnetic properties for the multiferroic heterostructure Co/BaTiO3 using spleed and arpes

Co/BaTiO3(0 0 1) is one of the most interesting multiferroic heterostructures as it combines different ferroic phases, setting this way the fundamentals for innovative technical applications. Various theoretical approaches have been applied to investigate the electronic and magnetic properties of Co/BaTiO3(0 0 1). Here we determine the magnetic properties of 3 ML Co/BaTiO3 by calculating spin-polarized electron diffraction as well as angle-resolved photoemission spectra, with both methods being well established as surface sensitive techniques. Furthermore, we discuss the impact of altering the BaTiO3 polarization on the spectra and ascribe the observed changes to characteristic details of the electronic structure.

Anomalous d-like surface resonances on Mo(110) analyzed by time-of-flight momentum microscopy

The electronic surface states on Mo(110) have been investigated using time-of-flight momentum microscopy with synchrotron radiation (hν=35 eV). This novel angle-resolved photoemission approach yields a simultaneous acquisition of the E-vs-k spectral function in the full surface Brillouin zone and several eV energy interval. (kx,ky,EB)-maps with 3.4 Å(-1) diameter reveal a rich structure of d-like surface resonances in the spin-orbit induced partial band gap. Calculations using the one-step model in its density matrix formulation predict an anomalous state with Dirac-like signature and Rashba spin texture crossing the bandgap at Γ¯ and EB=1.2 eV. The experiment shows that the linear dispersion persists away from the Γ¯-point in an extended energy- and k∥-range. Analogously to a similar state previously found on W(110) the dispersion is linear along H¯-Γ¯-H¯ and almost zero along N¯-Γ¯-N¯. The similarity is surprising since the spin-orbit interaction is 5 times smaller in Mo. A second point with unusual topology is found midway between Γ¯ and N¯. Band symmetries are probed by linear dichroism.

Imaging spin filter for electrons based on specular reflection from iridium (001)

As Stern-Gerlach type spin filters do not work with electrons, spin analysis of electron beams is accomplished by spin-dependent scattering processes based on spin-orbit or exchange interaction. Existing polarimeters are single-channel devices characterized by an inherently low figure of merit (FoM) of typically 10⁻⁴-10⁻³. This single-channel approach is not compatible with parallel imaging microscopes and also not with modern electron spectrometers that acquire a certain energy and angular interval simultaneously. We present a novel type of polarimeter that can transport a full image by making use of k-parallel conservation in low-energy electron diffraction. We studied specular reflection from Ir (001) because this spin-filter crystal provides a high analyzing power combined with a "lifetime" in UHV of a full day. One good working point is centered at 39 eV scattering energy with a broad maximum of 5 eV usable width. A second one at about 10 eV shows a narrower profile but much higher FoM. A relativistic layer-KKR SPLEED calculation shows good agreement with measurements.

Beyond the Heisenberg model: anisotropic exchange interaction between a Cu-tetraazaporphyrin monolayer and Fe3O4(100)

The exchange coupling of a single spin localized at the central ion of Cu-tetraazaporphyrin on a magnetite(100) surface has been studied using x-ray magnetic circular dichroism (XMCD). Sum rule analysis of the XMCD spectra results in Cu spin and orbital magnetic moments as a function of the applied external field at low temperatures (20 K). The exchange coupling is positive for magnetization direction perpendicular to the surface (ferromagnetic) while it is negative for in-plane magnetization direction (antiferromagnetic). We attribute the anisotropy of the Heisenberg exchange coupling to an orbitally dependent exchange Hamiltonian.