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.

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.

Megahertz-rate ultrafast X-ray scattering and holographic imaging at the European XFEL.

The advent of X-ray free-electron lasers (XFELs) has revolutionized fundamental science, from atomic to condensed matter physics, from chemistry to biology, giving researchers access to X-rays with unprecedented brightness, coherence and pulse duration. All XFEL facilities built until recently provided X-ray pulses at a relatively low repetition rate, with limited data statistics. Here, results from the first megahertz-repetition-rate X-ray scattering experiments at the Spectroscopy and Coherent Scattering (SCS) instrument of the European XFEL are presented. The experimental capabilities that the SCS instrument offers, resulting from the operation at megahertz repetition rates and the availability of the novel DSSC 2D imaging detector, are illustrated. Time-resolved magnetic X-ray scattering and holographic imaging experiments in solid state samples were chosen as representative, providing an ideal test-bed for operation at megahertz rates. Our results are relevant and applicable to any other non-destructive XFEL experiments in the soft X-ray range.

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.

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.

Legal vs. Extra-Legal Responses to Public Health Emergencies.

There is a long-established claim that emergency action through the law is impossible, or bound to be ineffective. This article seeks to challenge this position by reference to the response of many European states to the Coronavirus pandemic and by drawing on Lon Fuller's theory of law. It argues that there are a number of reasons why a fragmentation of governance between ordinary, legal action and emergency, extra-legal action is neither necessary nor desirable in this specific context. In societies that are generally rule of law compliant governance according to formal legal principles is not only constraining, it also possesses the quality of a 'liberating limitation', creating the room for effective, sustainable action. Too little has been made of this positive dimension of the legal form as an instrument for emergency action.

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.

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.

Quantification of silver nanoparticle uptake and distribution within individual human macrophages by FIB/SEM slice and view.

BACKGROUND: Quantification of nanoparticle (NP) uptake in cells or tissues is very important for safety assessment. Often, electron microscopy based approaches are used for this purpose, which allow imaging at very high resolution. However, precise quantification of NP numbers in cells and tissues remains challenging. The aim of this study was to present a novel approach, that combines precise quantification of NPs in individual cells together with high resolution imaging of their intracellular distribution based on focused ion beam/ scanning electron microscopy (FIB/SEM) slice and view approaches. RESULTS: We quantified cellular uptake of 75 nm diameter citrate stabilized silver NPs (Ag 75 Cit) into an individual human macrophage derived from monocytic THP-1 cells using a FIB/SEM slice and view approach. Cells were treated with 10 µg/ml for 24 h. We investigated a single cell and found in total 3138 ± 722 silver NPs inside this cell. Most of the silver NPs were located in large agglomerates, only a few were found in clusters of fewer than five NPs. Furthermore, we cross-checked our results by using inductively coupled plasma mass spectrometry and could confirm the FIB/SEM results. CONCLUSIONS: Our approach based on FIB/SEM slice and view is currently the only one that allows the quantification of the absolute dose of silver NPs in individual cells and at the same time to assess their intracellular distribution at high resolution. We therefore propose to use FIB/SEM slice and view to systematically analyse the cellular uptake of various NPs as a function of size, concentration and incubation time.

Automatable sample fabrication process for pump-probe X-ray holographic imaging.

Soft X-ray holography is a recently developed imaging technique with sub-50 nm spatial resolution. Key advantages of this technique are magnetic and elemental sensitivity, compatibility with imaging at free electron laser facilities, and immunity to in-situ sample excitations and sample drift, which enables the reliable detection of relative changes between two images with a precision of a few nanometers. In X-ray holography, the main part of the experimental setup is integrated in the sample, which consequently requires a large number of fabrication steps. Here we present a generic design and an automatable fabrication process for samples suitable, and optimized for, efficient high resolution X-ray holographic dynamic imaging. The high efficiency of the design facilitates the acquisition of magnetic images in a few minutes and makes fully automatic image reconstruction possible.

Midterm results after subtrochanteric end-to-side valgization osteotomy in severe infantile coxa vara.

BACKGROUND: For the treatment of the severe infantile coxa vara it is mandatory for the orthopaedic surgeon to observe the mechanobiology of the growing hip before and after the surgical intervention. We hereby would like to present our experiences with the subtrochanteric end-to-side valgization osteotomy and to compare the procedure with the alternatively used Y-shaped osteotomy as described by Pauwels. METHODS: Thirteen patients (20 hips) who had undergone subtrochanteric end-to-side valgization were followed for a mean 6.2 years (range, 0.8 to 12.8 y). At the time of surgery the mean age was 7.1 years (range, 2.0 to 13.3 y), last follow-up examination was performed at a mean of 13.4 years of age (range, 5.1 to 18.3 y). The deformities were etiologically based on 5 entities: congenital coxa vara (n=1), osteochondrodysplasias (n=12), postosteomyelitic coxa vara (n=5), and avascular femoral head necrosis in the course of congenital dysplasia of the hip (n=2). The follow-up rate was 100%.In addition, we analyzed a total of 93 pelvic radiographies with a total of 139 hip joints. Thirty angles and distances were assessed according to parameters described in the literature. RESULTS: Although preoperatively 12 patients presented with a positive Trendelenburg's sign, it was only present postoperatively in 2 patients. Duchenne's limp reduced from 10 to 1. All of the 15 preoperatively apparent nonunions could be healed by means of surgery. Two hips redeveloped pathologically lowered collodiaphyseal angles postoperatively, one of which had to undergo revision surgery. Preoperatively 15 out of 20 patients (75%) showed nonunions all of which healed after surgery. No recurrence could be seen at the time of the last follow-up.The following angles were assessed on plain radiographies of the pelvis preoperatively and directly postoperatively as well as on the last follow-up at a mean of 85 months: CCD-angle 98 degrees/156 degrees/144 degrees, EY-angle 55 degrees/5 degrees/15.7 degrees, AY-angle 32 degrees/75 degrees/66 degrees, CE-angle 20 degrees/25 degrees/18 degrees, AC-angle 20 degrees/18 degrees/20 degrees. The articulotrochanteric distance was 5 mm/26 mm/14 mm. CONCLUSIONS: The subtrochanteric end-to-side valgization osteotomy showed to be highly effective in the management of the infantile coxa vara, improving the clinical impairment of the patients postoperatively. All of the preoperatively present nonunions showed osseous consolidation at follow-up examination. Only minor revarization tendencies could be found. The procedure is technically less demanding, safer and more efficient regarding the lengthening of the affected limb in comparison to the Y-shaped intertrochanteric osteotomy as described by Pauwels. LEVEL OF EVIDENCE: Case-control study (EBM-level III).

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.

Method for single-shot coherent diffractive imaging of magnetic domains.

In preparation for real space studies of magnetic domains in a pump-probe setup at free-electron laser sources, it is necessary to develop an imaging method compatible with the linearly polarized radiation available at these sources. We present results from a prototype experiment performed at the synchrotron source BESSY II, using a modification of existing phase retrieval techniques. Our results show that it is possible to image magnetic domains in real space using linear polarized light, and we introduce the concept of a reliability map of our reconstructions using Gabor transforms.

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.

Magnetic imaging at linearly polarized x-ray sources.

We present a method for high-resolution magnetic imaging at linearly polarized partially coherent x-ray sources. The magnetic imaging was realized via Fourier transform holography. In order to achieve elliptical x-ray polarization, three different filters were designed based on the x-ray magnetic circular dichroism effect. We present proof-of-principle images of magnetic nanostructures and discuss the application of the method for future experiments at free-electron laser sources.

Wavefield back-propagation in high-resolution X-ray holography with a movable field of view.

Mask-based Fourier transform holography is used to record images of biological objects with 2.2 nm X-ray wavelength. The holography mask and the object are decoupled from each other which allows us to move the field of view over a large area over the sample. Due to the separation of the mask and the sample on different X-ray windows, a gap between both windows in the micrometer range typically exists. Using standard Fourier transform holography, focussed images of the sample can directly be reconstructed only for gap distances within the setup's depth of field. Here, we image diatoms as function of the gap distance and demonstrate the possibility to recover focussed images via a wavefield back-propagation technique. The limitations of our approach with respect to large separations are mainly associated with deviations from flat-field illumination of the object.

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.

Holographic soft X-ray omni-microscopy of biological specimens.

Mask-based digital soft X-ray Fourier transform holography using coherent synchrotron radiation is applied to image diatoms and freeze-dried 3T3 fibroblast cells. At soft X-ray wavelengths between 4 nm and 8 nm we achieve spatial resolutions down to 450 nm over a 33.5 microm field of view. As holography records amplitude and phase of the scattered wavefield, images with different contrast mechanisms can be generated a posteriori by numerical processing of the holographic data ("omni-microscopy"). We present Zernike phase contrast, Schlieren phase contrast, differential interference and gradient contrast images based on amplitude and phase information. We discuss the potential of this approach for destructive single-shot imaging beyond dose limitations of biological samples at coherent femtosecond-pulsed X-ray sources.