Spin texture of time-reversal symmetry invariant surface states on W(110)

Spanning Fermi arcs in a two-dimensional magnet

The discovery of topological states of matter has led to a revolution in materials research. When external or intrinsic parameters break symmetries, global properties of topological materials change drastically. A paramount example is the emergence of Weyl nodes under broken inversion symmetry. While a rich variety of non-trivial quantum phases could in principle also originate from broken time-reversal symmetry, realizing systems that combine magnetism with complex topological properties is remarkably elusive. Here, we demonstrate that giant open Fermi arcs are created at the surface of ultrathin hybrid magnets where the Fermi-surface topology is substantially modified by hybridization with a heavy-metal substrate. The interplay between magnetism and topology allows us to control the shape and the location of the Fermi arcs by tuning the magnetization direction. The hybridization points in the Fermi surface can be attributed to a non-trivial mixed topology and induce hot-spots in the Berry curvature, dominating spin and charge transport as well as magneto-electric coupling effects.

It has been predicted that elemental Iron, with low dimensionality, will be a topological metal hosting Weyl nodes. Here, Chen et al. grow iron on tungsten, a heavy metal with a strong spin-orbit interaction, and using momentum microscopy, show the emergence of giant open Fermi arcs which can be shaped by varying the magnetization of the iron.

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.

Single-hemisphere photoelectron momentum microscope with time-of-flight recording

Photoelectron momentum microscopy is an emerging powerful method for angle-resolved photoelectron spectroscopy (ARPES), especially in combination with imaging spin filters. These instruments record k_x-k_y images, typically exceeding a full Brillouin zone. As energy filters, double-hemispherical or time-of-flight (ToF) devices are in use. Here, we present a new approach for momentum mapping of the full half-space, based on a large single hemispherical analyzer (path radius of 225 mm). Excitation by an unfocused He lamp yielded an energy resolution of 7.7 meV. The performance is demonstrated by k-imaging of quantum-well states in Au and Xe multilayers. The α²-aberration term (α, entrance angle in the dispersive plane) and the transit-time spread of the electrons in the spherical field are studied in a large pass-energy (6 eV-660 eV) and angular range (α up to ±7°). It is discussed how the method circumvents the preconditions of previous theoretical work on the resolution limitation due to the α²-term and the transit-time spread, being detrimental for time-resolved experiments. Thanks to k-resolved detection, both effects can be corrected numerically. We introduce a dispersive-plus-ToF hybrid mode of operation, with an imaging ToF analyzer behind the exit slit of the hemisphere. This instrument captures 3D data arrays I (E_B, k_x, k_y), yielding a gain up to N² in recording efficiency (N being the number of resolved time slices). A key application will be ARPES at sources with high pulse rates such as synchrotrons with 500 MHz time structure.

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.

Early Stages of Ultrafast Spin Dynamics in a 3d Ferromagnet

Prior to the development of pulsed lasers, one assigned a single local temperature to the lattice, the electron gas, and the spins. With the availability of ultrafast laser sources, one can now drive the temperature of these reservoirs out of equilibrium. Thus, the solid shows new internal degrees of freedom characterized by individual temperatures of the electron gas T_{e}, the lattice T_{l} and the spins T_{s}. We demonstrate an analogous behavior in the spin polarization of a ferromagnet in an ultrafast demagnetization experiment: At the Fermi energy, the polarization is reduced faster than at deeper in the valence band. Therefore, on the femtosecond time scale, the magnetization as a macroscopic quantity does not provide the full picture of the spin dynamics: The spin polarization separates into different parts similar to how the single temperature paradigm changed with the development of ultrafast lasers.

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.