Resolving Nonequilibrium Shape Variations among Millions of Gold Nanoparticles.

Nanoparticles, exhibiting functionally relevant structural heterogeneity, are at the forefront of cutting-edge research. Now, high-throughput single-particle imaging (SPI) with X-ray free-electron lasers (XFELs) creates opportunities for recovering the shape distributions of millions of particles that exhibit functionally relevant structural heterogeneity. To realize this potential, three challenges have to be overcome: (1) simultaneous parametrization of structural variability in real and reciprocal spaces; (2) efficiently inferring the latent parameters of each SPI measurement; (3) scaling up comparisons between 105 structural models and 106 XFEL-SPI measurements. Here, we describe how we overcame these three challenges to resolve the nonequilibrium shape distributions within millions of gold nanoparticles imaged at the European XFEL. These shape distributions allowed us to quantify the degree of asymmetry in these particles, discover a relatively stable "shape envelope" among nanoparticles, discern finite-size effects related to shape-controlling surfactants, and extrapolate nanoparticles' shapes to their idealized thermodynamic limit. Ultimately, these demonstrations show that XFEL SPI can help transform nanoparticle shape characterization from anecdotally interesting to statistically meaningful.

Controlling stable Bloch points with electric currents.

The Bloch point is a point singularity in the magnetisation configuration, where the magnetisation vanishes. It can exist as an equilibrium configuration and plays an important role in many magnetisation reversal processes. In the present work, we focus on manipulating Bloch points in a system that can host stable Bloch points-a two-layer FeGe nanostrip with opposite chirality of the two layers. We drive Bloch points using spin-transfer torques and find that Bloch points can move collectively without any Hall effect and report that Bloch points are repelled from the sample boundaries and each other. We study pinning of Bloch points at wedge-shaped constrictions (notches) in the nanostrip and demonstrate that arrays of Bloch points can be moved past a series of notches in a controlled manner by applying consecutive current pulses of different strength. Finally, we simulate a T-shaped geometry and demonstrate that a Bloch point can be moved along different paths by applying current between suitable strip ends.

Bloch points in nanostrips.

Complex magnetic materials hosting topologically non-trivial particle-like objects such as skyrmions are under intensive research and could fundamentally change the way we store and process data. One important class of materials are helimagnetic materials with Dzyaloshinskii-Moriya interaction. Recently, it was demonstrated that thin nanodisks consisting of two layers with opposite chirality can host a single stable Bloch point of two different types at the interface between the layers. Using micromagnetic simulations we show that FeGe nanostrips consisting of two layers with opposite chirality can host multiple coexisting Bloch points in an arbitrary combination of the two different types. We show that the number of Bloch points that can simultaneously coexist depends on the strip geometry and the type of the individual Bloch points. Our simulation results allow us to predict strip geometries suitable for an arbitrary number of Bloch points. We show an example of an 80-Bloch-point configuration verifying the prediction.

Nematically Templated Vortex Lattices in Superconducting FeSe.

New pathways to controlling the morphology of superconducting vortex lattices─and their subsequent dynamics─are required to guide and scale vortex world-lines into a computing platform. We have found that the nematic twin boundaries align superconducting vortices in the adjacent terraces due to the incommensurate potential between vortices surrounding twin boundaries and those trapped within them. With the varying density and morphology of twin boundaries, the vortex lattice assumes several distinct structural phases, including square, regular, and irregular one-dimensional lattices. Through concomitant analysis of vortex lattice models, we have inferred the characteristic energetics of the twin boundary potential and furthermore predicted the existence of geometric size effects as a function of increasing confinement by the twin boundaries. These findings extend the ideas of directed control over vortex lattices to intrinsic topological defects and their self-organized networks, which have direct implications for the future design and control of strain-based topological quantum computing architectures.

Photon-shot-noise-limited transient absorption soft X-ray spectroscopy at the European XFEL.

Femtosecond transient soft X-ray absorption spectroscopy (XAS) is a very promising technique that can be employed at X-ray free-electron lasers (FELs) to investigate out-of-equilibrium dynamics for material and energy research. Here, a dedicated setup for soft X-rays available at the Spectroscopy and Coherent Scattering (SCS) instrument at the European X-ray Free-Electron Laser (European XFEL) is presented. It consists of a beam-splitting off-axis zone plate (BOZ) used in transmission to create three copies of the incoming beam, which are used to measure the transmitted intensity through the excited and unexcited sample, as well as to monitor the incoming intensity. Since these three intensity signals are detected shot by shot and simultaneously, this setup allows normalized shot-by-shot analysis of the transmission. For photon detection, an imaging detector capable of recording up to 800 images at 4.5 MHz frame rate during the FEL burst is employed, and allows a photon-shot-noise-limited sensitivity to be approached. The setup and its capabilities are reviewed as well as the online and offline analysis tools provided to users.

Confinement of Skyrmions in Nanoscale FeGe Device-like Structures.

Skyrmion-based devices have been proposed as a promising solution for low-energy data storage. These devices include racetrack or logic structures and require skyrmions to be confined in regions with dimensions comparable to the size of a single skyrmion. Here we examine skyrmions in FeGe device shapes using Lorentz transmission electron microscopy to reveal the consequences of skyrmion confinement in a device-like structure. Dumbbell-shaped elements were created by focused ion beam milling to provide regions where single skyrmions are confined adjacent to areas containing a skyrmion lattice. Simple block shapes of equivalent dimensions were also prepared to allow a direct comparison with skyrmion formation in a less complex, yet still confined, device geometry. The impact of applying a magnetic field and varying the temperature on the formation of skyrmions within the shapes was examined. This revealed that it is not just confinement within a small device structure that controls the position and number of skyrmions but that a complex device geometry changes the skyrmion behavior, including allowing skyrmions to form at lower applied magnetic fields than in simple shapes. The impact of edges in complex shapes is observed to be significant in changing the behavior of the magnetic textures formed. This could allow methods to be developed to control both the position and number of skyrmions within device structures.

Unsupervised learning approaches to characterizing heterogeneous samples using X-ray single-particle imaging.

One of the outstanding analytical problems in X-ray single-particle imaging (SPI) is the classification of structural heterogeneity, which is especially difficult given the low signal-to-noise ratios of individual patterns and the fact that even identical objects can yield patterns that vary greatly when orientation is taken into consideration. Proposed here are two methods which explicitly account for this orientation-induced variation and can robustly determine the structural landscape of a sample ensemble. The first, termed common-line principal component analysis (PCA), provides a rough classification which is essentially parameter free and can be run automatically on any SPI dataset. The second method, utilizing variation auto-encoders (VAEs), can generate 3D structures of the objects at any point in the structural landscape. Both these methods are implemented in combination with the noise-tolerant expand-maximize-compress (EMC) algorithm and its utility is demonstrated by applying it to an experimental dataset from gold nanoparticles with only a few thousand photons per pattern. Both discrete structural classes and continuous deformations are recovered. These developments diverge from previous approaches of extracting reproducible subsets of patterns from a dataset and open up the possibility of moving beyond the study of homogeneous sample sets to addressing open questions on topics such as nanocrystal growth and dynamics, as well as phase transitions which have not been externally triggered.

Author Correction: Membrane protein megahertz crystallography at the European XFEL.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Evaluation of serial crystallographic structure determination within megahertz pulse trains.

The new European X-ray Free-Electron Laser (European XFEL) is the first X-ray free-electron laser capable of delivering intense X-ray pulses with a megahertz interpulse spacing in a wavelength range suitable for atomic resolution structure determination. An outstanding but crucial question is whether the use of a pulse repetition rate nearly four orders of magnitude higher than previously possible results in unwanted structural changes due to either radiation damage or systematic effects on data quality. Here, separate structures from the first and subsequent pulses in the European XFEL pulse train were determined, showing that there is essentially no difference between structures determined from different pulses under currently available operating conditions at the European XFEL.

Membrane protein megahertz crystallography at the European XFEL.

The world's first superconducting megahertz repetition rate hard X-ray free-electron laser (XFEL), the European XFEL, began operation in 2017, featuring a unique pulse train structure with 886 ns between pulses. With its rapid pulse rate, the European XFEL may alleviate some of the increasing demand for XFEL beamtime, particularly for membrane protein serial femtosecond crystallography (SFX), leveraging orders-of-magnitude faster data collection. Here, we report the first membrane protein megahertz SFX experiment, where we determined a 2.9 Å-resolution SFX structure of the large membrane protein complex, Photosystem I, a > 1 MDa complex containing 36 protein subunits and 381 cofactors. We address challenges to megahertz SFX for membrane protein complexes, including growth of large quantities of crystals and the large molecular and unit cell size that influence data collection and analysis. The results imply that megahertz crystallography could have an important impact on structure determination of large protein complexes with XFELs.

The Karabo distributed control system.

The Karabo distributed control system has been developed to address the challenging requirements of the European X-ray Free Electron Laser facility, including complex and custom-made hardware, high data rates and volumes, and close integration of data analysis for distributed processing and rapid feedback. Karabo is a pluggable, distributed application management system forming a supervisory control and data acquisition environment as part of a distributed control system. Karabo provides integrated control of hardware, monitoring, data acquisition and data analysis on distributed hardware, allowing rapid control feedback based on complex algorithms. Services exist for access control, data logging, configuration management and situational awareness through alarm indicators. The flexible framework enables quick response to the changing requirements in control and analysis, and provides an efficient environment for development, and a single interface to make all changes immediately available to operators and experimentalists.

Stable and manipulable Bloch point.

The prediction of magnetic skyrmions being used to change the way we store and process data has led to materials with Dzyaloshinskii-Moriya interaction coming into the focus of intensive research. So far, studies have looked mostly at magnetic systems composed of materials with single chirality. In a search for potential future spintronic devices, combination of materials with different chirality into a single system may represent an important new avenue for research. Using finite element micromagnetic simulations, we study an FeGe disk with two layers of different chirality. We show that for particular thicknesses of layers, a stable Bloch point emerges at the interface between two layers. In addition, we demonstrate that the system undergoes hysteretic behaviour and that two different types of Bloch point exist. These 'head-to-head' and 'tail-to-tail' Bloch point configurations can, with the application of an external magnetic field, be switched between. Finally, by investigating the time evolution of the magnetisation field, we reveal the creation mechanism of the Bloch point. Our results introduce a stable and manipulable Bloch point to the collection of particle-like state candidates for the development of future spintronic devices.

MHz data collection of a microcrystalline mixture of different jack bean proteins.

We provide a detailed description of a serial femtosecond crystallography (SFX) dataset collected at the European X-ray free-electron laser facility (EuXFEL). The EuXFEL is the first high repetition rate XFEL delivering MHz X-ray pulse trains at 10 Hz. The short spacing (<1 µs) between pulses requires fast flowing microjets for sample injection and high frame rate detectors. A data set was recorded of a microcrystalline mixture of at least three different jack bean proteins (urease, concanavalin A, concanavalin B). A one megapixel Adaptive Gain Integrating Pixel Detector (AGIPD) was used which has not only a high frame rate but also a large dynamic range. This dataset is publicly available through the Coherent X-ray Imaging Data Bank (CXIDB) as a resource for algorithm development and for data analysis training for prospective XFEL users.

Do Images of Biskyrmions Show Type-II Bubbles?

The intense research effort investigating magnetic skyrmions and their applications for spintronics has yielded reports of more exotic objects including the biskyrmion, which consists of a bound pair of counter-rotating vortices of magnetization. Biskyrmions have been identified only from transmission electron microscopy images and have not been observed by other techniques, nor seen in simulations carried out under realistic conditions. Here, quantitative Lorentz transmission electron microscopy, X-ray holography, and micromagnetic simulations are combined to search for biskyrmions in MnNiGa, a material in which they have been reported. Only type-I and type-II magnetic bubbles are found and images purported to show biskyrmions can be explained as type-II bubbles viewed at an angle to their axes. It is not the magnetization but the magnetic flux density resulting from this object that forms the counter-rotating vortices.

Megahertz serial crystallography.

The new European X-ray Free-Electron Laser is the first X-ray free-electron laser capable of delivering X-ray pulses with a megahertz inter-pulse spacing, more than four orders of magnitude higher than previously possible. However, to date, it has been unclear whether it would indeed be possible to measure high-quality diffraction data at megahertz pulse repetition rates. Here, we show that high-quality structures can indeed be obtained using currently available operating conditions at the European XFEL. We present two complete data sets, one from the well-known model system lysozyme and the other from a so far unknown complex of a ß-lactamase from K. pneumoniae involved in antibiotic resistance. This result opens up megahertz serial femtosecond crystallography (SFX) as a tool for reliable structure determination, substrate screening and the efficient measurement of the evolution and dynamics of molecular structures using megahertz repetition rate pulses available at this new class of X-ray laser source.

Megahertz data collection from protein microcrystals at an X-ray free-electron laser.

X-ray free-electron lasers (XFELs) enable novel experiments because of their high peak brilliance and femtosecond pulse duration. However, non-superconducting XFELs offer repetition rates of only 10-120 Hz, placing significant demands on beam time and sample consumption. We describe serial femtosecond crystallography experiments performed at the European XFEL, the first MHz repetition rate XFEL, delivering 1.128 MHz X-ray pulse trains at 10 Hz. Given the short spacing between pulses, damage caused by shock waves launched by one XFEL pulse on sample probed by subsequent pulses is a concern. To investigate this issue, we collected data from lysozyme microcrystals, exposed to a ~15 µm XFEL beam. Under these conditions, data quality is independent of whether the first or subsequent pulses of the train were used for data collection. We also analyzed a mixture of microcrystals of jack bean proteins, from which the structure of native, magnesium-containing concanavalin A was determined.

Current-induced instability of domain walls in cylindrical nanowires.

We study the current-driven domain wall (DW) motion in cylindrical nanowires using micromagnetic simulations by implementing the Landau-Lifshitz-Gilbert equation with nonlocal spin-transfer torque in a finite difference micromagnetic package. We find that in the presence of DW, Gaussian wave packets (spin waves) will be generated when the charge current is suddenly applied to the system. This effect is excluded when using the local spin-transfer torque. The existence of spin waves emission indicates that transverse domain walls can not move arbitrarily fast in cylindrical nanowires although they are free from the Walker limit. We establish an upper velocity limit for DW motion by analyzing the stability of Gaussian wave packets using the local spin-transfer torque. Micromagnetic simulations show that the stable region obtained by using nonlocal spin-transfer torque is smaller than that by using its local counterpart. This limitation is essential for multiple DWs since the instability of Gaussian wave packets will break the structure of multiple DWs.

Thermal stability and topological protection of skyrmions in nanotracks.

Magnetic skyrmions are hailed as a potential technology for data storage and other data processing devices. However, their stability against thermal fluctuations is an open question that must be answered before skyrmion-based devices can be designed. In this work, we study paths in the energy landscape via which the transition between the skyrmion and the uniform state can occur in interfacial Dzyaloshinskii-Moriya finite-sized systems. We find three mechanisms the system can take in the process of skyrmion nucleation or destruction and identify that the transition facilitated by the boundary has a significantly lower energy barrier than the other energy paths. This clearly demonstrates the lack of the skyrmion topological protection in finite-sized magnetic systems. Overall, the energy barriers of the system under investigation are too small for storage applications at room temperature, but research into device materials, geometry and design may be able to address this.

Phase diagrams of vortex matter with multi-scale inter-vortex interactions in layered superconductors.

It was recently proposed to use the stray magnetic fields of superconducting vortex lattices to trap ultracold atoms for building quantum emulators. This calls for new methods for engineering and manipulating of the vortex states. One of the possible routes utilizes type-1.5 superconducting layered systems with multi-scale inter-vortex interactions. In order to explore the possible vortex states that can be engineered, we present two phase diagrams of phenomenological vortex matter models with multi-scale inter-vortex interactions featuring several attractive and repulsive length scales. The phase diagrams exhibit a plethora of phases, including conventional 2D lattice phases, five stripe phases, dimer, trimer, and tetramer phases, void phases, and stable low-temperature disordered phases. The transitions between these states can be controlled by the value of an applied external field.

Frequency-based nanoparticle sensing over large field ranges using the ferromagnetic resonances of a magnetic nanodisc.

Using finite element micromagnetic simulations, we study how resonant magnetisation dynamics in thin magnetic discs with perpendicular anisotropy are influenced by magnetostatic coupling to a magnetic nanoparticle. We identify resonant modes within the disc using direct magnetic eigenmode calculations and study how their frequencies and spatial profiles are changed by the nanoparticle's stray magnetic field. We demonstrate that particles can generate shifts in the resonant frequency of the disc's fundamental mode which exceed resonance linewidths in recently studied spin torque oscillator devices. Importantly, it is shown that the simulated shifts can be maintained over large field ranges (here up to 1 T). This is because the resonant dynamics (the basis of nanoparticle detection here) respond directly to the nanoparticle stray field, i.e. detection does not rely on nanoparticle-induced changes to the magnetic ground state of the disc. A consequence of this is that in the case of small disc-particle separations, sensitivities to the particle are highly mode- and particle-position-dependent, with frequency shifts being maximised when the intense stray field localised directly beneath the particle can act on a large proportion of the disc's spins that are undergoing high amplitude precession.