Exploring the Fundamental Spatial Limits of Magnetic All-Optical Switching.

All-optical switching (AOS) results in ultrafast and deterministic magnetization reversal upon single laser pulse excitation, potentially supporting faster and more energy-efficient data storage. To explore the fundamental limits of achievable bit densities in AOS, we have used soft X-ray transient grating spectroscopy to study the ultrafast magnetic response of a GdFe alloy after a spatially structured excitation with a periodicity of 17 nm. The ultrafast spatial evolution of the magnetization in combination with atomistic spin dynamics and microscopic temperature model calculations allows us to derive a detailed phase diagram of AOS as a function of both the absorbed energy density and the nanoscale excitation period. Our results suggest that the minimum size for AOS in GdFe alloys, induced by a nanoscale periodic excitation, is around 25 nm and that this limit is governed by ultrafast lateral electron diffusion and by the threshold for optical damage.

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.

The COMIX polarimeter: a compact device for XUV polarization analysis.

We report on the characterization of a novel extreme-ultraviolet polarimeter based on conical mirrors to simultaneously detect all the components of the electric field vector for extreme-ultraviolet radiation in the 45-90 eV energy range. The device has been characterized using a variable polarization source at the Elettra synchrotron, showing good performance in the ability to determine the radiation polarization. Furthermore, as a possible application of the device, Faraday spectroscopy and time-resolved experiments have been performed at the Fe M2,3-edge on an FeGd ferrimagnetic thin film using the FERMI free-electron laser source. The instrument is shown to be able to detect the small angular variation induced by an optical external stimulus on the polarization state of the light after interaction with magnetic thin film, making the device an appealing tool for magnetization dynamics research.

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.

All-Optical Switching on the Nanometer Scale Excited and Probed with Femtosecond Extreme Ultraviolet Pulses.

Ultrafast control of magnetization on the nanometer length scale, in particular all-optical switching, is key to putting ultrafast magnetism on the path toward future technological application in data storage technology. However, magnetization manipulation with light on this length scale is challenging due to the wavelength limitations of optical radiation. Here, we excite transient magnetic gratings in a GdFe alloy with a periodicity of 87 nm by the interference of two coherent femtosecond light pulses in the extreme ultraviolet spectral range. The subsequent ultrafast evolution of the magnetization pattern is probed by diffraction of a third, time-delayed pulse tuned to the Gd N-edge at a wavelength of 8.3 nm. By examining the simultaneously recorded first and second order diffractions and by performing reference real-space measurements with a wide-field magneto-optical microscope with femtosecond time resolution, we can conclusively demonstrate the ultrafast emergence of all-optical switching on the nanometer length scale.

Probing electron and hole colocalization by resonant four-wave mixing spectroscopy in the extreme ultraviolet.

Extending nonlinear spectroscopic techniques into the x-ray domain promises unique insight into photoexcited charge dynamics, which are of fundamental and applied interest. We report on the observation of a third-order nonlinear process in lithium fluoride (LiF) at a free-electron laser. Exploring the yield of four-wave mixing (FWM) in resonance with transitions to strongly localized core exciton states versus delocalized Bloch states, we find resonant FWM to be a sensitive probe for the degree of charge localization: Substantial sum- and difference-frequency generation is observed exclusively when in a one- or three-photon resonance with a LiF core exciton, with a dipole forbidden transition affecting details of the nonlinear response. Our reflective geometry-based approach to detect FWM signals enables the study of a wide variety of condensed matter sample systems, provides atomic selectivity via resonant transitions, and can be easily scaled to shorter wavelengths at free-electron x-ray lasers.

Nonequilibrium sub-10 nm spin-wave soliton formation in FePt nanoparticles.

Magnetic nanoparticles such as FePt in the L10 phase are the bedrock of our current data storage technology. As the grains become smaller to keep up with technological demands, the superparamagnetic limit calls for materials with higher magnetocrystalline anisotropy. This, in turn, reduces the magnetic exchange length to just a few nanometers, enabling magnetic structures to be induced within the nanoparticles. Here, we describe the existence of spin-wave solitons, dynamic localized bound states of spin-wave excitations, in FePt nanoparticles. We show with time-resolved x-ray diffraction and micromagnetic modeling that spin-wave solitons of sub-10 nm sizes form out of the demagnetized state following femtosecond laser excitation. The measured soliton spin precession frequency of 0.1 THz positions this system as a platform to develop novel miniature devices.

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.

Enabling time-resolved 2D spatial-coherence measurements using the Fourier-analysis method with an integrated curved-grating beam monitor.

Direct 2D spatial-coherence measurements are increasingly gaining importance at synchrotron beamlines, especially due to present and future upgrades of synchrotron facilities to diffraction-limited storage rings. We present a method to determine the 2D spatial coherence of synchrotron radiation in a direct and particularly simple way by using the Fourier-analysis method in conjunction with curved gratings. Direct photon-beam monitoring provided by a curved grating circumvents the otherwise necessary separate determination of the illuminating intensity distribution required for the Fourier-analysis method. Hence, combining these two methods allows for time-resolved spatial-coherence measurements. As a consequence, spatial-coherence degradation effects caused by beamline optics vibrations, which is one of the key issues of state-of-the-art X-ray imaging and scattering beamlines, can be identified and analyzed.

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.

27 W 2.1 µm OPCPA system for coherent soft X-ray generation operating at 10 kHz.

We developed a high power optical parametric chirped-pulse amplification (OPCPA) system at 2.1 µm harnessing a 500 W Yb:YAG thin disk laser as the only pump and signal generation source. The OPCPA system operates at 10 kHz with a single pulse energy of up to 2.7 mJ and pulse duration of 30 fs. The maximum average output power of 27 W sets a new record for an OPCPA system in the 2 µm wavelength region. The soft X-ray continuum generated through high harmonic generation with this driver laser can extend to around 0.55 keV, thus covering the entire water window (284 eV - 543 eV). With a repetition rate still enabling pump-probe experiments on solid samples, the system can be used for many applications.

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.