Dichroic coherent diffractive imaging

Ultrafast X-ray Diffraction Probe of Coherent Spin-State Dynamics in Molecules

We propose an approach to probe coherent spin-state dynamics of molecules using circularly polarized hard X-ray pulses. For the dynamically aligned nitric oxide molecules in a coherent superposition spin-orbit coupled electronic state that can be prepared through stimulated Raman scattering, we demonstrate the capability of ultrafast X-ray diffraction to not only reveal the quantum beating of the coherent spin-state wave packet but also image the spatial spin density of the molecule. With a circularly polarized ultrafast X-ray diffraction signal, we show that the electronic density matrix can be retrieved. The spatiotemporal resolving power of ultrafast X-ray diffraction paves the way for tracking transient spatial wave function in molecular dynamics involving the spin degree of freedom.

Non-interferometric stand-alone single-shot holographic camera using reciprocal diffractive imaging

An ideal holographic camera measures the amplitude and phase of the light field so that the focus can be numerically adjusted after the acquisition, and depth information about an imaged object can be deduced. The performance of holographic cameras based on reference-assisted holography is significantly limited owing to their vulnerability to vibration and complex optical configurations. Non-interferometric holographic cameras can resolve these issues. However, existing methods require constraints on an object or measurement of multiple-intensity images. In this paper, we present a holographic image sensor that reconstructs the complex amplitude of scattered light from a single-intensity image using reciprocal diffractive imaging. We experimentally demonstrate holographic imaging of three-dimensional diffusive objects and suggest its potential applications by imaging a variety of samples under both static and dynamic conditions.

Post-acquisition upsampling method for scanning x-ray microscopy

A method of post-acquisition upsampling for scanning x-ray microscopy is developed in this study to improve the spatial resolution beyond the Nyquist frequency as determined by the intervals of a raster scan grid. The proposed method is applicable only when the probe beam size is not negligibly small compared with the pixels that constitute a raster micrograph-the Voronoi cells of a scan grid. The unconvoluted spatial variation in a photoresponse is estimated by solving a stochastic inverse problem at a higher resolution than that at which the data are acquired. This is followed by a rise in the spatial cutoff frequency due to a reduction in the noise floor. The practicability of the proposed method was verified by applying it to raster micrographs of x-ray absorption in Nd-Fe-B sintered magnets. The improvement thus achieved in spatial resolution was numerically demonstrated via spectral analysis by using the discrete Fourier transform. The authors also argue for a reasonable decimation scheme for the spatial sampling interval in relation to an ill-posed inverse problem and aliasing. The computer-assisted enhancement in the viability of scanning x-ray magnetic circular dichroism microscopy was illustrated by visualizing magnetic field-induced changes in domain patterns of the Nd₂Fe₁₄B main-phase.

Three-dimensional topological magnetic monopoles and their interactions in a ferromagnetic meta-lattice

Topological magnetic monopoles (TMMs), also known as hedgehogs or Bloch points, are three-dimensional (3D) non-local spin textures that are robust to thermal and quantum fluctuations due to the topology protection^1-4. Although TMMs have been observed in skyrmion lattices^1,5, spinor Bose-Einstein condensates^6,7, chiral magnets⁸, vortex rings^2,9 and vortex cores¹⁰, it has been difficult to directly measure the 3D magnetization vector field of TMMs and probe their interactions at the nanoscale. Here we report the creation of 138 stable TMMs at the specific sites of a ferromagnetic meta-lattice at room temperature. We further develop soft X-ray vector ptycho-tomography to determine the magnetization vector and emergent magnetic field of the TMMs with a 3D spatial resolution of 10 nm. This spatial resolution is comparable to the magnetic exchange length of transition metals¹¹, enabling us to probe monopole-monopole interactions. We find that the TMM and anti-TMM pairs are separated by 18.3 ± 1.6 nm, while the TMM and TMM, and anti-TMM and anti-TMM pairs are stabilized at comparatively longer distances of 36.1 ± 2.4 nm and 43.1 ± 2.0 nm, respectively. We also observe virtual TMMs created by magnetic voids in the meta-lattice. This work demonstrates that ferromagnetic meta-lattices could be used as a platform to create and investigate the interactions and dynamics of TMMs. Furthermore, we expect that soft X-ray vector ptycho-tomography can be broadly applied to quantitatively image 3D vector fields in magnetic and anisotropic materials at the nanoscale.

Imaging mesoscopic antiferromagnetic spin textures in the dilute limit from single-geometry resonant coherent x-ray diffraction

The detection and manipulation of antiferromagnetic domains and topological antiferromagnetic textures are of central interest to solid-state physics. A fundamental step is identifying tools to probe the mesoscopic texture of an antiferromagnetic order parameter. In this work, we demonstrate that Bragg coherent diffractive imaging can be extended to study the mesoscopic texture of an antiferromagnetic order parameter using resonant magnetic x-ray scattering. We study the onset of the antiferromagnet transition in PrNiO₃, focusing on a temperature regime in which the antiferromagnetic domains are dilute in the beam spot and the coherent diffraction pattern modulating the antiferromagnetic peak is greatly simplified. We demonstrate that it is possible to extract the arrangements and sizes of these domains from single diffraction patterns and show that the approach could be extended to a time-structured light source to study the motion of dilute domains or the motion of topological defects in an antiferromagnetic spin texture.

X-ray Spectroptychography

X-ray spectroptychography is an emerging method for the chemical microanalysis of advanced nanomaterials such as catalysts and batteries. This method builds upon established synchrotron X-ray microscopy and spectromicroscopy techniques with added spatial resolution from ptychography, an algorithmic imaging technique. This minireview will introduce the technique of X-ray spectroptychography, where ptychography is performed with variable photon energy, and discuss recent results and prospects for this method.

Methods of Coherent X-Ray Diffraction Imaging

Abstract

Methods of coherent X-ray diffraction imaging of the spatial structure of noncrystalline objects and nanocrystals (nanostructures) are considered. Particular attention is paid to the methods of scanning-based coherent diffraction imaging (ptychography), visualization based on coherent surface scattering with application of correlation spectroscopy approaches, and specific features of visualization using X-ray free-electron laser radiation. The corresponding data in the literature are analyzed to demonstrate the state of the art of the methods of coherent diffraction imaging and fields of their application.

Ultrafast high-harmonic nanoscopy of magnetization dynamics

Light-induced magnetization changes, such as all-optical switching, skyrmion nucleation, and intersite spin transfer, unfold on temporal and spatial scales down to femtoseconds and nanometers, respectively. Pump-probe spectroscopy and diffraction studies indicate that spatio-temporal dynamics may drastically affect the non-equilibrium magnetic evolution. Yet, direct real-space magnetic imaging on the relevant timescales has remained challenging. Here, we demonstrate ultrafast high-harmonic nanoscopy employing circularly polarized high-harmonic radiation for real-space imaging of femtosecond magnetization dynamics. We map quenched magnetic domains and localized spin structures in Co/Pd multilayers with a sub-wavelength spatial resolution down to 16 nm, and strobosocopically trace the local magnetization dynamics with 40 fs temporal resolution. Our compact experimental setup demonstrates the highest spatio-temporal resolution of magneto-optical imaging to date. Facilitating ultrafast imaging with high sensitivity to chiral and linear dichroism, we envisage a wide range of applications spanning magnetism, phase transitions, and carrier dynamics.

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.

High-Throughput 3D Ensemble Characterization of Individual Core-Shell Nanoparticles with X-ray Free Electron Laser Single-Particle Imaging

The structures as building blocks for designing functional nanomaterials have fueled the development of versatile nanoprobes to understand local structures of noncrystalline specimens. Progress in analyzing structures of individual specimens with atomic scale accuracy has been notable recently. In most cases, however, only a limited number of specimens are inspected lacking statistics to represent the systems with structural inhomogeneity. Here, by employing single-particle imaging with X-ray free electron lasers and algorithms for multiple-model 3D imaging, we succeeded in investigating several thousand specimens in a couple of hours and identified intrinsic heterogeneities with 3D structures. Quantitative analysis has unveiled 3D morphology, facet indices, and elastic strain. The 3D elastic energy distribution is further corroborated by molecular dynamics simulations to gain mechanical insight at the atomic level. This work establishes a route to high-throughput characterization of individual specimens in large ensembles, hence overcoming statistical deficiency while providing quantitative information at the nanoscale.

Imaging three-dimensional magnetic systems with x-rays

Recent progress in nanofabrication and additive manufacturing have facilitated the building of nanometer-scale three-dimensional (3D) structures, that promise to lead to an emergence of new functionalities within a number of fields, compared to state-of-the-art two dimensional systems. In magnetism, the move to 3D systems offers the possibility for novel magnetic properties not available in planar systems, as well as enhanced performance, both of which are key for the development of new technological applications. In this review paper we will focus our attention on 3D magnetic systems and how their magnetic configuration can be retrieved using x-ray magnetic nanotomography. We will start with an introduction to magnetic materials, and their relevance to our everyday life, along with the growing impact that they will have in the coming years in, for example, reducing energy consumption. We will then briefly introduce common methods used to study magnetic materials, such as electron holography, neutron and x-ray imaging. In particular, we will focus on x-ray magnetic circular dichroism (XMCD) and how it can be used to image magnetic moment configurations. As a next step we will introduce tomography for 3D imaging, and how it can be adapted to study magnetic materials. Particular attention will be given to explaining the reconstruction algorithms that can be used to retrieve the magnetic moment configuration from the experimental data, as these represent one of the main challenges so far, as well as the different experimental geometries that are available. Recent experimental results will be used as specific examples to guide the reader through each step in order to make sure that the paper will be accessible for those interested in the topic that do not have a specialized background on magnetic imaging. Finally, we will describe the future prospects of such studies, identifying the current challenges facing the field, and how these can be tackled. In particular we will highlight the exciting possibilities offered by the next generation of synchrotron sources which will deliver diffraction limited beams, as well as with the extension of well-established methodologies currently implemented for the study of two-dimensional magnetic materials to achieve higher dimensional investigations.

Across the spectrum: integrating multidimensional metal analytics for in situ metallomic imaging

To know how much of a metal species is in a particular location within a biological context at any given time is essential for understanding the intricate roles of metals in biology and is the fundamental question upon which the field of metallomics was born. Simply put, seeing is powerful. With the combination of spectroscopy and microscopy, we can now see metals within complex biological matrices complemented by information about associated molecules and their structures. With the addition of mass spectrometry and particle beam based techniques, the field of view grows to cover greater sensitivities and spatial resolutions, addressing structural, functional and quantitative metallomic questions from the atomic level to whole body processes. In this perspective, I present a paradigm shift in the way we relate to and integrate current and developing metallomic analytics, highlighting both familiar and perhaps less well-known state of the art techniques for in situ metallomic imaging, specific biological applications, and their use in correlative studies. There is a genuine need to abandon scientific silos and, through the establishment of a metallomic scientific platform for further development of multidimensional analytics for in situ metallomic imaging, we have an incredible opportunity to enhance the field of metallomics and demonstrate how discovery research can be done more effectively.

Three-dimensional optical trapping and orientation of microparticles for coherent X-ray diffraction imaging

Optical trapping has been implemented in many areas of physics and biology as a noncontact sample manipulation technique to study the structure and dynamics of nano- and mesoscale objects. It provides a unique approach for manipulating microscopic objects without inducing undesired changes in structure. Combining optical trapping with hard X-ray microscopy techniques, such as coherent diffraction imaging and crystallography, provides a nonperturbing environment where electronic and structural dynamics of an individual particle in solution can be followed in situ. It was previously shown that optical trapping allows the manipulation of micrometer-sized objects for X-ray fluorescence imaging. However, questions remain over the ability of optical trapping to position objects for X-ray diffraction measurements, which have stringent requirements for angular stability. Our work demonstrates that dynamic holographic optical tweezers are capable of manipulating single micrometer-scale anisotropic particles in a microfluidic environment with the precision and stability required for X-ray Bragg diffraction experiments-thus functioning as an "optical goniometer." The methodology can be extended to a variety of X-ray experiments and the Bragg coherent diffractive imaging of individual particles in solution, as demonstrated here, will be markedly enhanced with the advent of brighter, coherent X-ray sources.

Imaging antiferromagnetic antiphase domain boundaries using magnetic Bragg diffraction phase contrast

Manipulating magnetic domains is essential for many technological applications. Recent breakthroughs in Antiferromagnetic Spintronics brought up novel concepts for electronic device development. Imaging antiferromagnetic domains is of key importance to this field. Unfortunately, some of the basic domain types, such as antiphase domains, cannot be imaged by conventional techniques. Herein, we present a new domain projection imaging technique based on the localization of domain boundaries by resonant magnetic diffraction of coherent X rays. Contrast arises from reduction of the scattered intensity at the domain boundaries due to destructive interference effects. We demonstrate this approach by imaging antiphase domains in a collinear antiferromagnet Fe₂Mo₃O₈, and observe evidence of domain wall interaction with a structural defect. This technique does not involve any numerical algorithms. It is fast, sensitive, produces large-scale images in a single-exposure measurement, and is applicable to a variety of magnetic domain types.

Imaging the antiferromagnetic (AFM) domains facilitates the understanding and design of AFM spintronics but is still challenging. Here the authors show an imaging approach for antiphase domains in AFM Fe₂Mo₃O₈ by resonantly scattered coherent soft X-rays, which is also applicable to collinear antiferromagnets.

Unraveling Nanoscale Magnetic Ordering in Fe3O4 Nanoparticle Assemblies via X-rays

Understanding the correlations between magnetic nanoparticles is important for nanotechnologies, such as high-density magnetic recording and biomedical applications, where functionalized magnetic particles are used as contrast agents and for drug delivery. The ability to control the magnetic state of individual particles depends on the good knowledge of the magnetic correlations between particles when assembled. Inaccessible via standard magnetometry techniques, nanoscale magnetic ordering in self-assemblies of Fe3O4 nanoparticles is here unveiled via X-ray resonant magnetic scattering (XRMS). Measured throughout the magnetization process, the XRMS signal reveals size-dependent inter-particle magnetic correlations. Smaller (5 nm) particles show little magnetic correlations, even when packed close together, yielding to magnetic disorder in the absence of an external field, i.e., superparamagnetism. In contrast, larger (11 nm) particles tend to be more strongly correlated, yielding a mix of magnetic orders including ferromagnetic and anti-ferromagnetic orders. These magnetic correlations are present even when the particles are sparsely distributed.

Iterative phase retrieval in coherent diffractive imaging: practical issues

In this work, issues in phase retrieval in the coherent diffractive imaging (CDI) technique, from discussion on parameters for setting up a CDI experiment to evaluation of the goodness of the final reconstruction, are discussed. The distribution of objects under study by CDI often cannot be cross-validated by another imaging technique. It is therefore important to make sure that the developed CDI procedure delivers an artifact-free object reconstruction. Critical issues that can lead to artifacts are presented and recipes on how to avoid them are provided.

Imaging the magnetic structures of artificial quasicrystal magnets using resonant coherent diffraction of circularly polarized X-rays

Unraveling nanoscale spin structures has long been an important activity addressing various scientific interests, that are also readily adaptable to technological applications. This has invigorated the development of versatile nanoprobes suitable for imaging specimens under native conditions. Here we have demonstrated the resonant coherent diffraction of an artificial quasicrystal magnet with circularly polarized X-rays. The nanoscale magnetic structure was revealed from X-ray speckle patterns by comparing with micromagnetic simulations, as a step toward understanding the intricate relationship between the chemical and spin structures in an aperiodic quasicrystal lattice. Femtosecond X-ray pulses from free electron lasers are expected to immediately extend the current work to nanoscale structure investigations of ultrafast spin dynamics, surpassing the present spatio-temporal resolution.

In situ coherent diffractive imaging

Coherent diffractive imaging (CDI) has been widely applied in the physical and biological sciences using synchrotron radiation, X-ray free-electron laser, high harmonic generation, electrons, and optical lasers. One of CDI’s important applications is to probe dynamic phenomena with high spatiotemporal resolution. Here, we report the development of a general in situ CDI method for real-time imaging of dynamic processes in solution. By introducing a time-invariant overlapping region as real-space constraint, we simultaneously reconstructed a time series of complex exit wave of dynamic processes with robust and fast convergence. We validated this method using optical laser experiments and numerical simulations with coherent X-rays. Our numerical simulations further indicated that in situ CDI can potentially reduce radiation dose by more than an order of magnitude relative to conventional CDI. With further development, we envision in situ CDI could be applied to probe a range of dynamic phenomena in the future.

Coherent diffractive imaging (CDI) allows for high resolution imaging without lenses. Here, Lo et al. develop in situ CDI with real-time imaging and a corresponding low-dose requirement, with expected applications in the physical and life sciences.

Transverse Coherence Limited Coherent Diffraction Imaging using a Molybdenum Soft X-ray Laser Pumped at Moderate Pump Energies

Coherent diffraction imaging (CDI) in the extreme ultraviolet has become an important tool for nanoscale investigations. Laser-driven high harmonic generation (HHG) sources allow for lab scale applications such as cancer cell classification and phase-resolved surface studies. HHG sources exhibit excellent coherence but limited photon flux due poor conversion efficiency. In contrast, table-top soft X-ray lasers (SXRL) feature excellent temporal coherence and extraordinary high flux at limited transverse coherence. Here, the performance of a SXRL pumped at moderate pump energies is evaluated for CDI and compared to a HHG source. For CDI, a lower bound for the required mutual coherence factor of |μ₁₂| ≥ 0.75 is found by comparing a reconstruction with fixed support to a conventional characterization using double slits. A comparison of the captured diffraction signals suggests that SXRLs have the potential for imaging micron scale objects with sub-20 nm resolution in orders of magnitude shorter integration time compared to a conventional HHG source. Here, the low transverse coherence diameter limits the resolution to approximately 180 nm. The extraordinary high photon flux per laser shot, scalability towards higher repetition rate and capability of seeding with a high harmonic source opens a route for higher performance nanoscale imaging systems based on SXRLs.

Interface-Induced Phenomena in Magnetism

This article reviews static and dynamic interfacial effects in magnetism, focusing on interfacially-driven magnetic effects and phenomena associated with spin-orbit coupling and intrinsic symmetry breaking at interfaces. It provides a historical background and literature survey, but focuses on recent progress, identifying the most exciting new scientific results and pointing to promising future research directions. It starts with an introduction and overview of how basic magnetic properties are affected by interfaces, then turns to a discussion of charge and spin transport through and near interfaces and how these can be used to control the properties of the magnetic layer. Important concepts include spin accumulation, spin currents, spin transfer torque, and spin pumping. An overview is provided to the current state of knowledge and existing review literature on interfacial effects such as exchange bias, exchange spring magnets, spin Hall effect, oxide heterostructures, and topological insulators. The article highlights recent discoveries of interface-induced magnetism and non-collinear spin textures, non-linear dynamics including spin torque transfer and magnetization reversal induced by interfaces, and interfacial effects in ultrafast magnetization processes.

Stability Limits and Defect Dynamics in Ag Nanoparticles Probed by Bragg Coherent Diffractive Imaging

Dissolution is critical to nanomaterial stability, especially for partially dealloyed nanoparticle catalysts. Unfortunately, highly active catalysts are often not stable in their reactive environments, preventing widespread application. Thus, focusing on the structure-stability relationship at the nanoscale is crucial and will likely play an important role in meeting grand challenges. Recent advances in imaging capability have come from electron, X-ray, and other techniques but tend to be limited to specific sample environments and/or two-dimensional images. Here, we report investigations into the defect-stability relationship of silver nanoparticles to voltage-induced electrochemical dissolution imaged in situ in three-dimensional detail by Bragg coherent diffractive imaging. We first determine the average dissolution kinetics by stationary probe rotating disk electrode in combination with inductively coupled plasma mass spectrometry, which allows in situ measurement of Ag⁺ ion formation. We then observe the dissolution and redeposition processes in single nanocrystals, providing unique insight about the role of surface strain, defects, and their coupling to the dissolution chemistry. The methods developed and the knowledge gained go well beyond a "simple" silver electrochemistry and are applicable to all electrocatalytic reactions where functional links between activity and stability are controlled by structure and defect dynamics.

Enhancing resolution in coherent x-ray diffraction imaging

Achieving a resolution near 1 nm is a critical issue in coherent x-ray diffraction imaging (CDI) for applications in materials and biology. Albeit with various advantages of CDI based on synchrotrons and newly developed x-ray free electron lasers, its applications would be limited without improving resolution well below 10 nm. Here, we review the issues and efforts in improving CDI resolution including various methods for resolution determination. Enhancing diffraction signal at large diffraction angles, with the aid of interference between neighboring strong scatterers or templates, is reviewed and discussed in terms of increasing signal-to-noise ratio. In addition, we discuss errors in image reconstruction algorithms-caused by the discreteness of the Fourier transformations involved-which degrade the spatial resolution, and suggest ways to correct them. We expect this review to be useful for applications of CDI in imaging weakly scattering soft matters using coherent x-ray sources including x-ray free electron lasers.

Measuring spectroscopy and magnetism of extracted and intracellular magnetosomes using soft X-ray ptychography

Characterizing the chemistry and magnetism of magnetotactic bacteria (MTB) is an important aspect of understanding the biomineralization mechanism and function of the chains of magnetosomes (Fe₃O₄ nanoparticles) found in such species. Images and X-ray absorption spectra (XAS) of magnetosomes extracted from, and magnetosomes in, whole Magnetovibrio blakemorei strain MV-1 cells have been recorded using soft X-ray ptychography at the Fe 2p edge. A spatial resolution of 7 nm is demonstrated. Precursor-like and immature magnetosome phases in a whole MV-1 cell were visualized, and their Fe 2p spectra were measured. Based on these results, a model for the pathway of magnetosome biomineralization for MV-1 is proposed. Fe 2p X-ray magnetic circular dichroism (XMCD) spectra have been derived from ptychography image sequences recorded using left and right circular polarization. The shape of the XAS and XMCD signals in the ptychographic absorption spectra of both sample types is identical to the shape and signals measured with conventional bright-field scanning transmission X-ray microscope. A weaker and inverted XMCD signal was observed in the ptychographic phase spectra of the extracted magnetosomes. The XMCD ptychographic phase spectrum of the intracellular magnetosomes differed from the ptychographic phase spectrum of the extracted magnetosomes. These results demonstrate that spectro-ptychography offers a superior means of characterizing the chemical and magnetic properties of MTB at the individual magnetosome level.

Advances and challenges in cryo ptychography at the Advanced Photon Source

Ptychography has emerged as a nondestructive tool to quantitatively study extended samples at a high spatial resolution. In this manuscript, we report on recent developments from our team. We have combined cryo ptychography and fluorescence microscopy to provide simultaneous views of ultrastructure and elemental composition, we have developed multi-GPU parallel computation to speed up ptychographic reconstructions, and we have implemented fly-scan ptychography to allow for faster data acquisition. We conclude with a discussion of future challenges in high-resolution 3D ptychography.

Bright circularly polarized soft X-ray high harmonics for X-ray magnetic circular dichroism

We demonstrate, to our knowledge, the first bright circularly polarized high-harmonic beams in the soft X-ray region of the electromagnetic spectrum, and use them to implement X-ray magnetic circular dichroism measurements in a tabletop-scale setup. Using counterrotating circularly polarized laser fields at 1.3 and 0.79 µm, we generate circularly polarized harmonics with photon energies exceeding 160 eV. The harmonic spectra emerge as a sequence of closely spaced pairs of left and right circularly polarized peaks, with energies determined by conservation of energy and spin angular momentum. We explain the single-atom and macroscopic physics by identifying the dominant electron quantum trajectories and optimal phase-matching conditions. The first advanced phase-matched propagation simulations for circularly polarized harmonics reveal the influence of the finite phase-matching temporal window on the spectrum, as well as the unique polarization-shaped attosecond pulse train. Finally, we use, to our knowledge, the first tabletop X-ray magnetic circular dichroism measurements at the N4,5 absorption edges of Gd to validate the high degree of circularity, brightness, and stability of this light source. These results demonstrate the feasibility of manipulating the polarization, spectrum, and temporal shape of high harmonics in the soft X-ray region by manipulating the driving laser waveform.

Ptychography in anisotropic media

This letter describes ptychography in the context of polarized light probing anisotropic specimen (i.e., showing properties of birefringence and/or diattenuation). We established an optimization strategy using a vectorial formalism. We propose a measurement scheme using a set of linearly polarized probes and linear polarization analyzers, which allows the retrieval of the full anisotropy map of the specimen.

Coherent diffractive imaging: towards achieving atomic resolution

The next generation of X-ray sources will feature highly brilliant X-ray beams that will enable the imaging of local nanoscale structures with unprecedented resolution. A general formalism to predict the achievable spatial resolution in coherent diffractive imaging, based solely on diffracted intensities, is provided. The coherent dose necessary to reach atomic resolution depends significantly on the atomic scale structure, where disordered or amorphous materials require roughly three orders of magnitude lower dose compared with the expected scaling of uniform density materials. Additionally, dose reduction for crystalline materials are predicted at certain resolutions based only on their unit-cell dimensions and structure factors.

X-rays and magnetism

Magnetism is among the most active and attractive areas in modern solid state physics because of intriguing phenomena interesting to fundamental research and a manifold of technological applications. State-of-the-art synthesis of advanced magnetic materials, e.g. in hybrid structures paves the way to new functionalities. To characterize modern magnetic materials and the associated magnetic phenomena, polarized x-rays have emerged as unique probes due to their specific interaction with magnetic materials. A large variety of spectroscopic and microscopic techniques have been developed to quantify in an element, valence and site-sensitive way properties of ferro-, ferri-, and antiferromagnetic systems, such as spin and orbital moments, and to image nanoscale spin textures and their dynamics with sub-ns time and almost 10 nm spatial resolution. The enormous intensity of x-rays and their degree of coherence at next generation x-ray facilities will open the fsec time window to magnetic studies addressing fundamental time scales in magnetism with nanometer spatial resolution. This review will give an introduction into contemporary topics of nanoscale magnetic materials and provide an overview of analytical spectroscopy and microscopy tools based on x-ray dichroism effects. Selected examples of current research will demonstrate the potential and future directions of these techniques.

Beyond crystallography: diffractive imaging using coherent x-ray light sources

X-ray crystallography has been central to the development of many fields of science over the past century. It has now matured to a point that as long as good-quality crystals are available, their atomic structure can be routinely determined in three dimensions. However, many samples in physics, chemistry, materials science, nanoscience, geology, and biology are noncrystalline, and thus their three-dimensional structures are not accessible by traditional x-ray crystallography. Overcoming this hurdle has required the development of new coherent imaging methods to harness new coherent x-ray light sources. Here we review the revolutionary advances that are transforming x-ray sources and imaging in the 21st century.

Multipurpose end-station for coherent diffraction imaging and scattering at FERMI@Elettra free-electron laser facility

The Diffraction and Projection Imaging (DiProI) beamline at FERMI, the Elettra free-electron laser (FEL), hosts a multi-purpose station that has been opened to users since the end of 2012. This paper describes the core capabilities of the station, designed to make use of the unique features of the FERMI-FEL for performing a wide range of static and dynamic scattering experiments. The various schemes for time-resolved experiments, employing both soft X-ray FEL and seed laser IR radiation are presented by using selected recent results. The ongoing upgrade is adding a reflection geometry setup for scattering experiments, expanding the application fields by providing both high lateral and depth resolution.

In situ strain evolution during a disconnection event in a battery nanoparticle

Disconnection of active material is a leading cause of battery degradation. X-ray imaging suggests the formation of an interphase layer on a cathode nanoparticle leads to disconnection.

Fresnel coherent diffractive imaging of elemental distributions in nanoscale binary compounds

We report quantitative determination of elemental distribution in binary compounds with nano meter scale spatial resolution using x-ray Fresnel coherent diffractive imaging (FCDI). We show that the quantitative magnitude and phase values of the x-ray wave exiting an object determined by FCDI can be utilized to obtain full-field atomic density maps of each element independently. The proposed method was demonstrated by reconstructing the density maps of Pt and NiO in a Pt-NiO binary compound with about 18 nm spatial resolution.

High-resolution multislice x-ray ptychography of extended thick objects

We report the first demonstration of hard x-ray ptychography using a multislice approach, which can solve the problem of the limited spatial resolution under the projection approximation. We measured ptychographic diffraction patterns of a two-layered object with a 105  μm gap using 7 keV focused coherent x rays. We successfully reconstructed the phase map of each layer at ∼50  nm resolution using a multislice approach, while the resolution was worse than ∼192  nm under the projection approximation. The present method has the potential to enable the three-dimensional high-resolution observation of extended thick specimens in materials science and biology.

Ptychographic overlap constraint errors and the limits of their numerical recovery using conjugate gradient descent methods

Ptychographic coherent x-ray diffractive imaging is a form of scanning microscopy that does not require optics to image a sample. A series of scanned coherent diffraction patterns recorded from multiple overlapping illuminated regions on the sample are inverted numerically to retrieve its image. The technique recovers the phase lost by detecting the diffraction patterns by using experimentally known constraints, in this case the measured diffraction intensities and the assumed scan positions on the sample. The spatial resolution of the recovered image of the sample is limited by the angular extent over which the diffraction patterns are recorded and how well these constraints are known. Here, we explore how reconstruction quality degrades with uncertainties in the scan positions. We show experimentally that large errors in the assumed scan positions on the sample can be numerically determined and corrected using conjugate gradient descent methods. We also explore in simulations the limits, based on the signal to noise of the diffraction patterns and amount of overlap between adjacent scan positions, of just how large these errors can be and still be rendered tractable by this method.

Soft X-ray spectromicroscopy using ptychography with randomly phased illumination

Ptychography is a form of scanning diffractive imaging that can successfully retrieve the modulus and phase of both the sample transmission function and the illuminating probe. An experimental difficulty commonly encountered in diffractive imaging is the large dynamic range of the diffraction data. Here we report a novel ptychographic experiment using a randomly phased X-ray probe to considerably reduce the dynamic range of the recorded diffraction patterns. Images can be reconstructed reliably and robustly from this setup, even when scatter from the specimen is weak. A series of ptychographic reconstructions at X-ray energies around the L absorption edge of iron demonstrates the advantages of this method for soft X-ray spectromicroscopy, which can readily provide chemical sensitivity without the need for optical refocusing. In particular, the phase signal is in perfect registration with the modulus signal and provides complementary information that can be more sensitive to changes in the local chemical environment.

Full field tabletop EUV coherent diffractive imaging in a transmission geometry

We demonstrate the first general tabletop EUV coherent microscope that can image extended, non-isolated, non-periodic, objects. By implementing keyhole coherent diffractive imaging with curved mirrors and a tabletop high harmonic source, we achieve improved efficiency of the imaging system as well as more uniform illumination at the sample, when compared with what is possible using Fresnel zone plates. Moreover, we show that the unscattered light from a semi-transparent sample can be used as a holographic reference wave, allowing quantitative information about the thickness of the sample to be extracted from the retrieved image. Finally, we show that excellent tabletop image fidelity is achieved by comparing the retrieved images with scanning electron and atomic force microscopy images, and show superior capabilities in some cases.

Resonant elastic soft x-ray scattering

Resonant (elastic) soft x-ray scattering (RSXS) offers a unique element, site and valence specific probe to study spatial modulations of charge, spin and orbital degrees of freedom in solids on the nanoscopic length scale. It is not only used to investigate single-crystalline materials. This method also enables one to examine electronic ordering phenomena in thin films and to zoom into electronic properties emerging at buried interfaces in artificial heterostructures. During the last 20 years, this technique, which combines x-ray scattering with x-ray absorption spectroscopy, has developed into a powerful probe to study electronic ordering phenomena in complex materials and furthermore delivers important information on the electronic structure of condensed matter. This review provides an introduction to the technique, covers the progress in experimental equipment, and gives a survey on recent RSXS studies of ordering in correlated electron systems and at interfaces.

Invited article: Coherent imaging using seeded free-electron laser pulses with variable polarization: first results and research opportunities

FERMI@Elettra, the first vacuum ultraviolet and soft X-ray free-electron laser (FEL) using by default a "seeded" scheme, became operational in 2011 and has been opened to users since December 2012. The parameters of the seeded FERMI FEL pulses and, in particular, the superior control of emitted radiation in terms of spectral purity and stability meet the stringent requirements for single-shot and resonant coherent diffraction imaging (CDI) experiments. The advantages of the intense seeded FERMI pulses with variable polarization have been demonstrated with the first experiments performed using the multipurpose experimental station operated at the diffraction and projection imaging (DiProI) beamline. The results reported here were obtained with fixed non-periodic targets during the commissioning period in 2012 using 20-32 nm wavelength range. They demonstrate that the performance of the FERMI FEL source and the experimental station meets the requirements of CDI, holography, and resonant magnetic scattering in both multi- and single-shot modes. Moreover, we present the first magnetic scattering experiments employing the fully circularly polarized FERMI pulses. The ongoing developments aim at pushing the lateral resolution by using shorter wavelengths provided by double-stage cascaded FERMI FEL-2 and probing ultrafast dynamic processes using different pump-probe schemes, including jitter-free seed laser pump or FEL-pump∕FEL-probe with two color FEL pulses generated by the same electron bunch.

Effects of missing low-frequency information on ptychographic and plane-wave coherent diffraction imaging

In coherent diffractive imaging (CDI) experiments, a beamstop (BS) is commonly used to extend the exposure time of the charge-coupled detector and obtain high-angle diffraction signals. However, the negative effect of a large BS is also evident, causing low-frequency signals to be missed and making CDI reconstruction unstable or causing it to fail. We performed a systematic simulation investigation of the effects of BSs on the quality of reconstructed images from both plane-wave and ptychographic CDI (PCDI). For the same imaging quality, we found that ptychography can tolerate BSs that are at least 20 times larger than those for plane-wave CDI. For PCDI, a larger overlap ratio and a smaller illumination spot can significantly increase the imaging robustness to the negative influence of BSs. Our results provide guidelines for the usage of BSs in CDI, especially in PCDI experiments, which can help to further improve the spatial resolution of PCDI.

High numerical aperture reflection mode coherent diffraction microscopy using off-axis apertured illumination

We extend coherent diffraction imaging (CDI) to a high numerical aperture reflection mode geometry for the first time. We derive a coordinate transform that allows us to rewrite the recorded far-field scatter pattern from a tilted object as a uniformly spaced Fourier transform. Using this approach, FFTs in standard iterative phase retrieval algorithms can be used to significantly speed up the image reconstruction times. Moreover, we avoid the isolated sample requirement by imaging a pinhole onto the specimen, in a technique termed apertured illumination CDI. By combining the new coordinate transformation with apertured illumination CDI, we demonstrate rapid high numerical aperture imaging of samples illuminated by visible laser light. Finally, we demonstrate future promise for this technique by using high harmonic beams for high numerical aperture reflection mode imaging.

An instrument for 3D x-ray nano-imaging

We present an instrument dedicated to 3D scanning x-ray microscopy, allowing a sample to be precisely scanned through a beam while the angle of x-ray incidence can be changed. The position of the sample is controlled with respect to the beam-defining optics by laser interferometry. The instrument achieves a position stability better than 10 nm standard deviation. The instrument performance is assessed using scanning x-ray diffraction microscopy and we demonstrate a resolution of 18 nm in 2D imaging of a lithographic test pattern while the beam was defined by a pinhole of 3 μm in diameter. In 3D on a test object of copper interconnects of a microprocessor, a resolution of 53 nm is achieved.

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.