Electron population dynamics in resonant non-linear x-ray absorption in nickel at a free-electron laser.

Free-electron lasers provide bright, ultrashort, and monochromatic x-ray pulses, enabling novel spectroscopic measurements not only with femtosecond temporal resolution: The high fluence of their x-ray pulses can also easily enter the regime of the non-linear x-ray-matter interaction. Entering this regime necessitates a rigorous analysis and reliable prediction of the relevant non-linear processes for future experiment designs. Here, we show non-linear changes in the L3-edge absorption of metallic nickel thin films, measured with fluences up to 60 J/cm2. We present a simple but predictive rate model that quantitatively describes spectral changes based on the evolution of electronic populations within the pulse duration. Despite its simplicity, the model reaches good agreement with experimental results over more than three orders of magnitude in fluence, while providing a straightforward understanding of the interplay of physical processes driving the non-linear changes. Our findings provide important insights for the design and evaluation of future high-fluence free-electron laser experiments and contribute to the understanding of non-linear electron dynamics in x-ray absorption processes in solids at the femtosecond timescale.

Versatile tabletop setup for picosecond time-resolved resonant soft-x-ray scattering and spectroscopy.

We present a laser-driven, bright, and broadband (50 to 1500 eV) soft-x-ray plasma source with <10 ps pulse duration. This source is employed in two complementary, laboratory-scale beamlines for time-resolved, magnetic resonant scattering and spectroscopy, as well as near-edge x-ray absorption fine-structure (NEXAFS) spectroscopy. In both beamlines, dedicated reflection zone plates (RZPs) are used as single optical elements to capture, disperse, and focus the soft x rays, reaching resolving powers up to E/ΔE > 1000, with hybrid RZPs at the NEXAFS beamline retaining a consistent E/ΔE > 500 throughout the full spectral range, allowing for time-efficient data acquisition. We demonstrate the versatility and performance of our setup by a selection of soft-x-ray spectroscopy and scattering experiments, which so far have not been possible on a laboratory scale. Excellent data quality, combined with experimental flexibility, renders our approach a true alternative to large-scale facilities, such as synchrotron-radiation sources and free-electron lasers.

Pump-probe x-ray microscopy of photo-induced magnetization dynamics at MHz repetition rates.

We present time-resolved scanning x-ray microscopy measurements with picosecond photo-excitation via a tailored infrared pump laser at a scanning transmission x-ray microscope. Specifically, we image the laser-induced demagnetization and remagnetization of thin ferrimagnetic GdFe films proceeding on a few nanoseconds timescale. Controlling the heat load on the sample via additional reflector and heatsink layers allows us to conduct destruction-free measurements at a repetition rate of 50 MHz. Near-field enhancement of the photo-excitation and controlled annealing effects lead to laterally heterogeneous magnetization dynamics which we trace with 30 nm spatial resolution. Our work opens new opportunities to study photo-induced dynamics on the nanometer scale, with access to picosecond to nanosecond time scales, which is of technological relevance, especially in the field of magnetism.

Coherent correlation imaging for resolving fluctuating states of matter.

Fluctuations and stochastic transitions are ubiquitous in nanometre-scale systems, especially in the presence of disorder. However, their direct observation has so far been impeded by a seemingly fundamental, signal-limited compromise between spatial and temporal resolution. Here we develop coherent correlation imaging (CCI) to overcome this dilemma. Our method begins by classifying recorded camera frames in Fourier space. Contrast and spatial resolution emerge by averaging selectively over same-state frames. Temporal resolution down to the acquisition time of a single frame arises independently from an exceptionally low misclassification rate, which we achieve by combining a correlation-based similarity metric1,2 with a modified, iterative hierarchical clustering algorithm3,4. We apply CCI to study previously inaccessible magnetic fluctuations in a highly degenerate magnetic stripe domain state with nanometre-scale resolution. We uncover an intricate network of transitions between more than 30 discrete states. Our spatiotemporal data enable us to reconstruct the pinning energy landscape and to thereby explain the dynamics observed on a microscopic level. CCI massively expands the potential of emerging high-coherence X-ray sources and paves the way for addressing large fundamental questions such as the contribution of pinning5-8 and topology9-12 in phase transitions and the role of spin and charge order fluctuations in high-temperature superconductivity13,14.

Real-time spatial characterization of micrometer-sized X-ray free-electron laser beams focused by bendable mirrors.

A real-time and accurate characterization of the X-ray beam size is essential to enable a large variety of different experiments at free-electron laser facilities. Typically, ablative imprints are employed to determine shape and size of µm-focused X-ray beams. The high accuracy of this state-of-the-art method comes at the expense of the time required to perform an ex-situ image analysis. In contrast, diffraction at a curved grating with suitably varying period and orientation forms a magnified image of the X-ray beam, which can be recorded by a 2D pixelated detector providing beam size and pointing jitter in real time. In this manuscript, we compare results obtained with both techniques, address their advantages and limitations, and demonstrate their excellent agreement. We present an extensive characterization of the FEL beam focused to ≈1 µm by two Kirkpatrick-Baez (KB) mirrors, along with optical metrology slope profiles demonstrating their exceptionally high quality. This work provides a systematic and comprehensive study of the accuracy provided by curved gratings in real-time imaging of X-ray beams at a free-electron laser facility. It is applied here to soft X-rays and can be extended to the hard X-ray range. Furthermore, curved gratings, in combination with a suitable detector, can provide spatial properties of µm-focused X-ray beams at MHz repetition rate.

Reference shape effects on Fourier transform holography.

Soft-x-ray holography which utilizes an optics mask fabricated in direct contact with the sample, is a widely applied x-ray microscopy method, in particular, for investigating magnetic samples. The optics mask splits the x-ray beam into a reference wave and a wave to illuminate the sample. The reconstruction quality in such a Fourier-transform holography experiment depends primarily on the characteristics of the reference wave, typically emerging from a small, high-aspect-ratio pinhole in the mask. In this paper, we study two commonly used reference geometries and investigate how their 3D structure affects the reconstruction within an x-ray Fourier holography experiment. Insight into these effects is obtained by imaging the exit waves from reference pinholes via high-resolution coherent diffraction imaging combined with three-dimensional multislice simulations of the x-ray propagation through the reference pinhole. The results were used to simulate Fourier-transform holography experiments to determine the spatial resolution and precise location of the reconstruction plane for different reference geometries. Based on our findings, we discuss the properties of the reference pinholes with view on application in soft-x-ray holography experiments.

Deterministic Generation and Guided Motion of Magnetic Skyrmions by Focused He+-Ion Irradiation.

Magnetic skyrmions are quasiparticles with nontrivial topology, envisioned to play a key role in next-generation data technology while simultaneously attracting fundamental research interest due to their emerging topological charge. In chiral magnetic multilayers, current-generated spin-orbit torques or ultrafast laser excitation can be used to nucleate isolated skyrmions on a picosecond time scale. Both methods, however, produce randomly arranged skyrmions, which inherently limits the precision on the location at which the skyrmions are nucleated. Here, we show that nanopatterning of the anisotropy landscape with a He+-ion beam creates well-defined skyrmion nucleation sites, thereby transforming the skyrmion localization into a deterministic process. This approach allows control of individual skyrmion nucleation as well as guided skyrmion motion with nanometer-scale precision, which is pivotal for both future fundamental studies of skyrmion dynamics and applications.

Quantitative hyperspectral coherent diffractive imaging spectroscopy of a solid-state phase transition in vanadium dioxide.

Solid-state systems can host a variety of thermodynamic phases that can be controlled with magnetic fields, strain, or laser excitation. Many phases that are believed to exhibit exotic properties only exist on the nanoscale, coexisting with other phases that make them challenging to study, as measurements require both nanometer spatial resolution and spectroscopic information, which are not easily accessible with traditional x-ray spectromicroscopy techniques. Here, we use coherent diffractive imaging spectroscopy (CDIS) to acquire quantitative hyperspectral images of the prototypical quantum material vanadium oxide across the vanadium L 2,3 and oxygen K x-ray absorption edges with nanometer-scale resolution. We extract the full complex refractive indices of the monoclinic insulating and rutile conducting phases of VO2 from a single sample and find no evidence for correlation-driven phase transitions. CDIS will enable quantitative full-field x-ray spectromicroscopy for studying phase separation in time-resolved experiments and other extreme sample environments where other methods cannot operate.

The patterning toolbox FIB-o-mat: Exploiting the full potential of focused helium ions for nanofabrication.

Focused beams of helium ions are a powerful tool for high-fidelity machining with spatial precision below 5 nm. Achieving such a high patterning precision over large areas and for different materials in a reproducible manner, however, is not trivial. Here, we introduce the Python toolbox FIB-o-mat for automated pattern creation and optimization, providing full flexibility to accomplish demanding patterning tasks. FIB-o-mat offers high-level pattern creation, enabling high-fidelity large-area patterning and systematic variations in geometry and raster settings. It also offers low-level beam path creation, providing full control over the beam movement and including sophisticated optimization tools. Three applications showcasing the potential of He ion beam nanofabrication for two-dimensional material systems and devices using FIB-o-mat are presented.

Observation of fluctuation-mediated picosecond nucleation of a topological phase.

Topological states of matter exhibit fascinating physics combined with an intrinsic stability. A key challenge is the fast creation of topological phases, which requires massive reorientation of charge or spin degrees of freedom. Here we report the picosecond emergence of an extended topological phase that comprises many magnetic skyrmions. The nucleation of this phase, followed in real time via single-shot soft X-ray scattering after infrared laser excitation, is mediated by a transient topological fluctuation state. This state is enabled by the presence of a time-reversal symmetry-breaking perpendicular magnetic field and exists for less than 300 ps. Atomistic simulations indicate that the fluctuation state largely reduces the topological energy barrier and thereby enables the observed rapid and homogeneous nucleation of the skyrmion phase. These observations provide fundamental insights into the nature of topological phase transitions, and suggest a path towards ultrafast topological switching in a wide variety of materials through intermediate fluctuating states.

A tabletop setup for ultrafast helicity-dependent and element-specific absorption spectroscopy and scattering in the extreme ultraviolet spectral range.

Further advances in the field of ultrafast magnetization dynamics require experimental tools to measure the spin and electron dynamics with element-specificity and femtosecond temporal resolution. We present a new laboratory setup for two complementary experiments with light in the extreme ultraviolet (XUV) spectral range. One experiment is designed for polarization-dependent transient spectroscopy, particularly for simultaneous measurements of magnetic circular dichroism (MCD) at the 3p resonances of the 3d transition metals Fe, Co, and Ni. The second instrument is designed for resonant small-angle scattering experiments with monochromatic light allowing us to monitor spin dynamics with spatial information on the nanometer scale. We combine a high harmonic generation (HHG) source with a phase shifter to obtain XUV pulses with variable polarization and a flux of about (3 ± 1) × 1010 photons/s/harmonic at 60 eV at the source. A dedicated reference spectrometer effectively reduces the intensity fluctuations of the HHG spectrum to below 0.12% rms. We demonstrate the capabilities of the setup by capturing the energy- and polarization-dependent absorption of a thin Co film as well as the time-resolved small-angle scattering in a magnetic-domain network of a Co/Pt multilayer. The new laboratory setup allows systematic studies of optically induced spin and electron dynamics with element-specificity, particularly with MCD as the contrast mechanism with femtosecond temporal resolution and an unprecedented signal-to-noise ratio.

Ultrafast Demagnetization Dominates Fluence Dependence of Magnetic Scattering at Co M Edges.

We systematically study the fluence dependence of the resonant scattering cross-section from magnetic domains in Co/Pd-based multilayers. Samples are probed with single extreme ultraviolet (XUV) pulses of femtosecond duration tuned to the Co M_{3,2} absorption resonances using the FERMI@Elettra free-electron laser. We report quantitative data over 3 orders of magnitude in fluence, covering 16 mJ/cm^{2}/pulse to 10 000 mJ/cm^{2}/pulse with pulse lengths of 70 fs and 120 fs. A progressive quenching of the diffraction cross-section with fluence is observed. Compression of the same pulse energy into a shorter pulse-implying an increased XUV peak electric field-results in a reduced quenching of the resonant diffraction at the Co M_{3,2} edge. We conclude that the quenching effect observed for resonant scattering involving the short-lived Co 3p core vacancies is noncoherent in nature. This finding is in contrast to previous reports investigating resonant scattering involving the longer-lived Co 2p states, where stimulated emission has been found to be important. A phenomenological model based on XUV-induced ultrafast demagnetization is able to reproduce our entire set of experimental data and is found to be consistent with independent magneto-optical measurements of the demagnetization dynamics on the same samples.

Achieving diffraction-limited resolution in soft-X-ray Fourier-transform holography.

The spatial resolution of microscopic images acquired via X-ray Fourier-transform holography is limited by the source size of the reference wave and by the numerical aperture of the detector. We analyze the interplay between both influences and show how they are matched in practice. We further identify, how high spatial frequencies translate to imaging artifacts in holographic reconstructions where mainly the reference beam limits the spatial resolution. As a solution, three methods are introduced based on numerical post-processing of the reconstruction. The methods comprise apodization of the hologram, refocusing via wave propagation, and deconvolution using the transfer function of the imaging system. In particular for the latter two, we demonstrate that image details smaller than the source size of the reference beam can be recovered up to the diffraction limit of the hologram. Our findings motivate the intentional application of a large reference-wave source enhancing the image contrast in applications with low photon numbers such as single-shot experiments at free-electron lasers or imaging at laboratory sources.

Singleshot polychromatic coherent diffractive imaging with a high-order harmonic source.

Singleshot polychromatic coherent diffractive imaging is performed with a high-intensity high-order harmonic generation source. The coherence properties are analyzed and several reconstructions show the shot-to-shot fluctuations of the incident beam wavefront. The method is based on a multi-step approach. First, the spectrum is extracted from double-slit diffraction data. The spectrum is used as input to extract the monochromatic sample diffraction pattern, then phase retrieval is performed on the quasi-monochromatic data to obtain the sample's exit surface wave. Reconstructions based on guided error reduction (ER) and alternating direction method of multipliers (ADMM) are compared. ADMM allows additional penalty terms to be included in the cost functional to promote sparsity within the reconstruction.

Fast current-driven domain walls and small skyrmions in a compensated ferrimagnet.

Spintronics is a research field that aims to understand and control spins on the nanoscale and should enable next-generation data storage and manipulation. One technological and scientific key challenge is to stabilize small spin textures and to move them efficiently with high velocities. For a long time, research focused on ferromagnetic materials, but ferromagnets show fundamental limits for speed and size. Here, we circumvent these limits using compensated ferrimagnets. Using ferrimagnetic Pt/Gd44Co56/TaOx films with a sizeable Dzyaloshinskii-Moriya interaction, we realize a current-driven domain wall motion with a speed of 1.3 km s-1 near the angular momentum compensation temperature (TA) and room-temperature-stable skyrmions with minimum diameters close to 10 nm near the magnetic compensation temperature (TM). Both the size and dynamics of the ferrimagnet are in excellent agreement with a simplified effective ferromagnet theory. Our work shows that high-speed, high-density spintronics devices based on current-driven spin textures can be realized using materials in which TA and TM are close together.

Imaging Nanometer Phase Coexistence at Defects During the Insulator-Metal Phase Transformation in VO2 Thin Films by Resonant Soft X-ray Holography.

We use resonant soft X-ray holography to image the insulator-metal phase transition in vanadium dioxide with element and polarization specificity and nanometer spatial resolution. We observe that nanoscale inhomogeneity in the film results in spatial-dependent transition pathways between the insulating and metallic states. Additional nanoscale phases form in the vicinity of defects which are not apparent in the initial or final states of the system, which would be missed in area-integrated X-ray absorption measurements. These intermediate phases are vital to understand the phase transition in VO2, and our results demonstrate how resonant imaging can be used to understand the electronic properties of phase-separated correlated materials obtained by X-ray absorption.

In situ single-shot diffractive fluence mapping for X-ray free-electron laser pulses.

Free-electron lasers (FELs) in the extreme ultraviolet (XUV) and X-ray regime opened up the possibility for experiments at high power densities, in particular allowing for fluence-dependent absorption and scattering experiments to reveal non-linear light-matter interactions at ever shorter wavelengths. Findings of such non-linear effects are met with tremendous interest, but prove difficult to understand and model due to the inherent shot-to-shot fluctuations in photon intensity and the often structured, non-Gaussian spatial intensity profile of a focused FEL beam. Presently, the focused beam is characterized and optimized separately from the actual experiment. Here, we present the simultaneous measurement of XUV diffraction signals from solid samples in tandem with the corresponding single-shot spatial fluence distribution on the actual sample. Our in situ characterization scheme enables direct monitoring of the sample illumination, providing a basis to optimize and quantitatively understand FEL experiments.

A general approach to obtain soft x-ray transparency for thin films grown on bulk substrates.

We present a general approach to thin bulk samples to transparency for experiments in the soft x-ray and extreme ultraviolet spectral range. The method relies on mechanical grinding followed by focused-ion-beam milling. It results in a uniformly thin area of high surface quality, suitable for nanoscale imaging in transmission. In a proof-of-principle experiment, nanoscale magnetic bits on a commercial hard drive glass disk are imaged with a spatial resolution below 30 nm by soft x-ray spectro-holography. Furthermore, we demonstrate imaging of a lithographically patterned test object via absorption contrast. Our approach is suitable for both amorphous and crystalline substrates and has been tested for a variety of common epitaxy growth substrates. Lateral thinning areas in excess of 100 µm2 and a remaining substrate thickness as thin as 150 nm are easily achievable. Our approach allows preserving a previously grown thin film, and from nanofocus electron diffraction, we find no evidence for morphological changes induced by the process, in agreement with numerical simulations of the ion implantation depth distributon. We expect our method to be widely applicable and especially useful for nanoscale imaging of epitaxial thin films.