Time-resolved X-Ray diffraction from coherent phonons during a laser-induced phase transition

Accelerating Quantum Materials Development with Advances in Transmission Electron Microscopy

Quantum materials are driving a technology revolution in sensing, communication, and computing, while simultaneously testing many core theories of the past century. Materials such as topological insulators, complex oxides, superconductors, quantum dots, color center-hosting semiconductors, and other types of strongly correlated materials can exhibit exotic properties such as edge conductivity, multiferroicity, magnetoresistance, superconductivity, single photon emission, and optical-spin locking. These emergent properties arise and depend strongly on the material's detailed atomic-scale structure, including atomic defects, dopants, and lattice stacking. In this review, we describe how progress in the field of electron microscopy (EM), including in situ and in operando EM, can accelerate advances in quantum materials and quantum excitations. We begin by describing fundamental EM principles and operation modes. We then discuss various EM methods such as (i) EM spectroscopies, including electron energy loss spectroscopy (EELS), cathodoluminescence (CL), and electron energy gain spectroscopy (EEGS); (ii) four-dimensional scanning transmission electron microscopy (4D-STEM); (iii) dynamic and ultrafast EM (UEM); (iv) complementary ultrafast spectroscopies (UED, XFEL); and (v) atomic electron tomography (AET). We describe how these methods could inform structure-function relations in quantum materials down to the picometer scale and femtosecond time resolution, and how they enable precision positioning of atomic defects and high-resolution manipulation of quantum materials. For each method, we also describe existing limitations to solve open quantum mechanical questions, and how they might be addressed to accelerate progress. Among numerous notable results, our review highlights how EM is enabling identification of the 3D structure of quantum defects; measuring reversible and metastable dynamics of quantum excitations; mapping exciton states and single photon emission; measuring nanoscale thermal transport and coupled excitation dynamics; and measuring the internal electric field and charge density distribution of quantum heterointerfaces- all at the quantum materials' intrinsic atomic and near atomic-length scale. We conclude by describing open challenges for the future, including achieving stable sample holders for ultralow temperature (below 10K) atomic-scale spatial resolution, stable spectrometers that enable meV energy resolution, and high-resolution, dynamic mapping of magnetic and spin fields. With atomic manipulation and ultrafast characterization enabled by EM, quantum materials will be poised to integrate into many of the sustainable and energy-efficient technologies needed for the 21st century.

Real-time imaging of acoustic waves in bulk materials with X-ray microscopy

The dynamics of lattice vibrations govern many material processes, such as acoustic wave propagation, displacive phase transitions, and ballistic thermal transport. The maximum velocity of these processes and their effects is determined by the speed of sound, which therefore defines the temporal resolution (picoseconds) needed to resolve these phenomena on their characteristic length scales (nanometers). Here, we present an X-ray microscope capable of imaging acoustic waves with subpicosecond resolution within mm-sized crystals. We directly visualize the generation, propagation, branching, and energy dissipation of longitudinal and transverse acoustic waves in diamond, demonstrating how mechanical energy thermalizes from picosecond to microsecond timescales. Bulk characterization techniques capable of resolving this level of structural detail have previously been available on millisecond time scales-orders of magnitude too slow to capture these fundamental phenomena in solid-state physics and geoscience. As such, the reported results provide broad insights into the interaction of acoustic waves with the structure of materials, and the availability of ultrafast time-resolved dark-field X-ray microscopy opens a vista of new opportunities for 3D imaging of materials dynamics on their intrinsic submicrosecond time scales.

Concepts and use cases for picosecond ultrasonics with x-rays

This review discusses picosecond ultrasonics experiments using ultrashort hard x-ray probe pulses to extract the transient strain response of laser-excited nanoscopic structures from Bragg-peak shifts. This method provides direct, layer-specific, and quantitative information on the picosecond strain response for structures down to few-nm thickness. We model the transient strain using the elastic wave equation and express the driving stress using Grüneisen parameters stating that the laser-induced stress is proportional to energy density changes in the microscopic subsystems of the solid, i.e., electrons, phonons and spins. The laser-driven strain response can thus serve as an ultrafast proxy for local energy-density and temperature changes, but we emphasize the importance of the nanoscale morphology for an accurate interpretation due to the Poisson effect. The presented experimental use cases encompass ultrathin and opaque metal-heterostructures, continuous and granular nanolayers as well as negative thermal expansion materials, that each pose a challenge to established all-optical techniques.

Nanoscale coherent phonon spectroscopy

Coherent phonon spectroscopy can provide microscopic insight into ultrafast lattice dynamics and its coupling to other degrees of freedom under nonequilibrium conditions. Ultrafast optical spectroscopy is a well-established method to study coherent phonons, but the diffraction limit has hampered observing their local dynamics directly. Here, we demonstrate nanoscale coherent phonon spectroscopy using ultrafast laser-induced scanning tunneling microscopy in a plasmonic junction. Coherent phonons are locally excited in ultrathin zinc oxide films by the tightly confined plasmonic field and are probed via the photoinduced tunneling current through an electronic resonance of the zinc oxide film. Concurrently performed tip-enhanced Raman spectroscopy allows us to identify the involved phonon modes. In contrast to the Raman spectra, the phonon dynamics observed in coherent phonon spectroscopy exhibit strong nanoscale spatial variations that are correlated with the distribution of the electronic local density of states resolved by scanning tunneling spectroscopy.

Dynamics of ultrafast phase transitions in MgF2 triggered by laser-induced THz coherent phonons

The advent of free-electron lasers opens new routes for experimental high-pressure physics, which allows studying dynamics of condensed matter with femtosecond resolution. A rapid compression, that can be caused by laser-induced shock impact, leads to the cascade of high-pressure phase transitions. Despite many decades of study, a complete understanding of the lattice response to such a compression remains elusive. Moreover, in the dynamical case (in contrast to quasi-static loading) the thresholds of phase transitions can change significantly. Using the third harmonic pump–probe technique combined with molecular dynamics to simulate the terahertz (THz) spectrum, we revealed the dynamics of ultrafast laser-induced phase transitions in MgF₂ in all-optical experiment. Tight focusing of femtosecond laser pulse into the transparent medium leads to the generation of sub-TPa shock waves and THz coherent phonons. The laser-induced shock wave propagation drastically displaces atoms in the lattice, which leads to phase transitions. We registered a cascade of ultrafast laser-induced phase transitions (P42/mnm ⇒ Pa-3  ⇒ Pnam) in magnesium fluoride as a change in the spectrum of coherent phonons. The phase transition has the characteristic time of 5–10 ps, and the lifetime of each phase is on the order of 40–60 ps. In addition, phonon density of states, simulated by molecular dynamics, together with third-harmonic time-resolved spectra prove that laser-excited phonons in a bulk of dielectrics are generated by displacive excitation (DECP) mechanism in plasma mediated conditions.

Direct Observation of Coherent Longitudinal and Shear Acoustic Phonons in TaAs Using Ultrafast X-Ray Diffraction

Using femtosecond time-resolved x-ray diffraction, we investigated optically excited coherent acoustic phonons in the Weyl semimetal TaAs. The low symmetry of the (112) surface probed in our experiment enables the simultaneous excitation of longitudinal and shear acoustic modes, whose dispersion closely matches our simulations. We observed an asymmetry in the spectral line shape of the longitudinal mode that is notably absent from the shear mode, suggesting a time-dependent frequency chirp that is likely driven by photoinduced carrier diffusion. We argue on the basis of symmetry that these acoustic deformations can transiently alter the electronic structure near the Weyl points and support this with model calculations. Our study underscores the benefit of using off-axis crystal orientations when optically exciting acoustic deformations in topological semimetals, allowing one to transiently change their crystal and electronic structures.

X-ray free-electron laser based dark-field X-ray microscopy: a simulation-based study

Dark-field X-ray microscopy (DFXM) is a nondestructive full-field imaging technique providing three-dimensional mapping of microstructure and local strain fields in deeply embedded crystalline elements. This is achieved by placing an objective lens in the diffracted beam, giving a magnified projection image. So far, the method has been applied with a time resolution of milliseconds to hours. In this work, the feasibility of DFXM at the picosecond time scale using an X-ray free-electron laser source and a pump–probe scheme is considered. Thermomechanical strain-wave simulations are combined with geometrical optics and wavefront propagation optics to simulate DFXM images of phonon dynamics in a diamond single crystal. Using the specifications of the XCS instrument at the Linac Coherent Light Source as an example results in simulated DFXM images clearly showing the propagation of a strain wave.

Evolution of laser-induced strain in a Ge crystal for the [111] and [100] directions probed by time-resolved X-ray diffraction

Ultra-short laser-pulse-induced strain propagation in a Ge crystal is studied in the [111] and [100] directions using time-resolved X-ray diffraction (TXRD). The strain propagation velocity is derived by analysis of the TXRD signal from the strained crystal planes. Numerical integration of the Takagi–Taupin equations is performed using open source code, which provides a very simple approach to estimate the strain propagation velocity. The present method will be particularly useful for relatively broad spectral bandwidths and weak X-ray sources, where temporal oscillations in the diffracted X-ray intensity at the relevant phonon frequencies would not be visible. The two Bragg reflections of the Ge sample, viz. 111 and 400, give information on the propagation of strain for two different depths, as the X-ray extinction depths are different for these two reflections. The strain induced by femtosecond laser excitation has a propagation velocity comparable to the longitudinal acoustic velocity. The strain propagation velocity increases with increasing laser excitation fluence. This fluence dependence of the strain propagation velocity can be attributed to crystal heating by ambipolar carrier diffusion. Ge is a promising candidate for silicon-based optoelectronics, and this study will enhance the understanding of heat transport by carrier diffusion in Ge induced by ultra-fast laser pulses, which will assist in the design of optoelectronic devices.

Efficient First-Principles Methodology for the Calculation of the All-Phonon Inelastic Scattering in Solids

Inelastic scattering experiments are key methods for mapping the full dispersion of fundamental excitations of solids in the ground as well as nonequilibrium states. A quantitative analysis of inelastic scattering in terms of phonon excitations requires identifying the role of multiphonon processes. Here, we develop an efficient first-principles methodology for calculating the all-phonon quantum mechanical structure factor of solids. We demonstrate our method by obtaining excellent agreement between measurements and calculations of the diffuse scattering patterns of black phosphorus, showing that multiphonon processes play a substantial role. The present approach constitutes a step towards the interpretation of static and time-resolved electron, x-ray, and neutron inelastic scattering data.

New insights into correlated materials in the time domain-combining far-infrared excitation with x-ray probes at cryogenic temperatures

Modern techniques for the investigation of correlated materials in the time domain combine selective excitation in the THz frequency range with selective probing of coupled structural, electronic and magnetic degrees of freedom using x-ray scattering techniques. Cryogenic sample temperatures are commonly required to prevent thermal occupation of the low energy modes and to access relevant material ground states. Here, we present a chamber optimized for high-field THz excitation and (resonant) x-ray diffraction at sample temperatures between 5 and 500 K. Directly connected to the beamline vacuum and featuring both a Beryllium window and an in-vacuum detector, the chamber covers the full (2-12.7) keV energy range of the femtosecond x-ray pulses available at the Bernina endstation of the SwissFEL free electron laser. Successful commissioning experiments made use of the energy tunability to selectively track the dynamics of the structural, magnetic and orbital order of Ca₂RuO₄and Tb₂Ti₂O₇at the Ru (2.96 keV) and Tb (7.55 keV)L-edges, respectively. THz field amplitudes up to 1.12 MV cm^-1peak field were demonstrated and used to excite the samples at temperatures as low as 5 K.

Visualization of dynamic polaronic strain fields in hybrid lead halide perovskites

Excitation localization involving dynamic nanoscale distortions is a central aspect of photocatalysis¹, quantum materials² and molecular optoelectronics³. Experimental characterization of such distortions requires techniques sensitive to the formation of point-defect-like local structural rearrangements in real time. Here, we visualize excitation-induced strain fields in a prototypical member of the lead halide perovskites⁴ via femtosecond resolution diffuse X-ray scattering measurements. This enables momentum-resolved phonon spectroscopy of the locally distorted structure and reveals radially expanding nanometre-scale strain fields associated with the formation and relaxation of polarons in photoexcited perovskites. Quantitative estimates of the magnitude and shape of this polaronic distortion are obtained, providing direct insights into the dynamic structural distortions that occur in these materials^5-9. Optical pump-probe reflection spectroscopy corroborates these results and shows how these large polaronic distortions transiently modify the carrier effective mass, providing a unified picture of the coupled structural and electronic dynamics that underlie the optoelectronic functionality of the hybrid perovskites.

The topology of electronic band structures

The study of topology as it relates to physical systems has rapidly accelerated during the past decade. Critical to the realization of new topological phases is an understanding of the materials that exhibit them and precise control of the materials chemistry. The convergence of new theoretical methods using symmetry indicators to identify topological material candidates and the synthesis of high-quality single crystals plays a key role, warranting discussion and context at an accessible level. This Perspective provides a broad introduction to topological phases, their known properties, and material realizations. We focus on recent work in topological Weyl and Dirac semimetals, with a particular emphasis on magnetic Weyl semimetals and emergent fermions in chiral crystals and their extreme responses to excitations, and we highlight areas where the field can continue to make remarkable discoveries. We further examine open questions and directions for the topological materials science community to pursue, including exploration of non-equilibrium properties of Weyl semimetals and cavity-dressed topological materials.

Imaging phonon dynamics with ultrafast electron microscopy: Kinematical and dynamical simulations

Ultrafast x-ray and electron scattering techniques have proven to be useful for probing the transient elastic lattice deformations associated with photoexcited coherent acoustic phonons. Indeed, femtosecond electron imaging using an ultrafast electron microscope (UEM) has been used to directly image the influence of nanoscale structural and morphological discontinuities on the emergence, propagation, dispersion, and decay behaviors in a variety of materials. Here, we describe our progress toward the development of methods ultimately aimed at quantifying acoustic-phonon properties from real-space UEM images via conventional image simulation methods extended to the associated strain-wave lattice deformation symmetries and extents. Using a model system consisting of pristine single-crystal Ge and a single, symmetric Lamb-type guided-wave mode, we calculate the transient strain profiles excited in a wedge specimen and then apply both kinematical- and dynamical-scattering methods to simulate the resulting UEM bright-field images. While measurable contrast strengths arising from the phonon wavetrains are found for optimally oriented specimens using both approaches, incorporation of dynamical scattering effects via a multi-slice method returns better qualitative agreement with experimental observations. Contrast strengths arising solely from phonon-induced local lattice deformations are increased by nearly an order of magnitude when incorporating multiple electron scattering effects. We also explicitly demonstrate the effects of changes in global specimen orientation on the observed contrast strength, and we discuss the implications for increasing the sophistication of the model with respect to quantification of phonon properties from UEM images.

Probing Electronic Strain Generation by Separated Electron-Hole Pairs Using Time-Resolved X-ray Scattering

Photogeneration of excess charge carriers in semiconductors produces electronic strain. Under transient conditions, electron-hole pairs may be separated across a potential barrier. Using time-resolved X-ray diffraction measurements across an intrinsic AlGaAs/n-doped GaAs interface, we find that the electronic strain is only produced by holes, and that electrons are not directly observable by strain measurements. The presence of photoinduced charge carriers in the n-doped GaAs is indirectly confirmed by delayed heat generation via recombination.

Tracking picosecond strain pulses in heterostructures that exhibit giant magnetostriction

We combine ultrafast X-ray diffraction (UXRD) and time-resolved Magneto-Optical Kerr Effect (MOKE) measurements to monitor the strain pulses in laser-excited TbFe₂/Nb heterostructures. Spatial separation of the Nb detection layer from the laser excitation region allows for a background-free characterization of the laser-generated strain pulses. We clearly observe symmetric bipolar strain pulses if the excited TbFe₂ surface terminates the sample and a decomposition of the strain wavepacket into an asymmetric bipolar and a unipolar pulse, if a SiO₂ glass capping layer covers the excited TbFe₂ layer. The inverse magnetostriction of the temporally separated unipolar strain pulses in this sample leads to a MOKE signal that linearly depends on the strain pulse amplitude measured through UXRD. Linear chain model simulations accurately predict the timing and shape of UXRD and MOKE signals that are caused by the strain reflections from multiple interfaces in the heterostructure.

Mapping spin-correlations with hard X-ray free-electron laser

Time-resolved X-ray diffraction from Ga091Mn0 09As was recorded with a hard X-ray free-electron-laser. The influence of spin-orders on phonons was investigated; our result suggests a new method for mapping the spin-correlations in low doped magnetic systems, especially the short-range spin-correlation.

Revealing Electron-Phonon Interactions and Lattice Dynamics in Nanocrystal Films by Combining in Situ Thermal Heating and Femtosecond Laser Excitations in 4D Transmission Electron Microscopy

We present a comparative investigation on static equilibrium and transient structural dynamics of nanocrystalline gold films on silicon nitride supports performed at various in situ temperatures and by ultrafast laser excitations in a four-dimensional ultrafast transmission electron microscope (4D-UTEM). The change of relative diffraction intensity and lattice spacing with rising temperatures was systematically measured for {220} Debye-Scherrer rings via the in situ heating technique, which leads to a precise determination of the actual Debye temperature and a finding of significant depression of lattice expansions in the films. The diffraction intensity/lattice spacing-temperature relationship calibrated by the static, thermally equilibrium observations was then employed for investigating ultrafast transient dynamics on the same specimen region. The electron-phonon coupling constant g was determined to be 7.2 × 10¹⁵ W/m³ K in combination with simple two-temperature model analysis. We found a marked variation of temperature rise maximum (at quasi-equilibrium states) in between the temporal evolutions of lattice spacing and diffraction intensity, a phenomenon which may only be explained by the effect of nonthermal equilibrium relaxation dynamics following femtosecond laser excitations. The method demonstrated here can thus be applied to quantitative evaluations of nonthermal equilibrium contributions during the electron-lattice thermalization.

Hot phonon and carrier relaxation in Si(100) determined by transient extreme ultraviolet spectroscopy

The thermalization of hot carriers and phonons gives direct insight into the scattering processes that mediate electrical and thermal transport. Obtaining the scattering rates for both hot carriers and phonons currently requires multiple measurements with incommensurate timescales. Here, transient extreme-ultraviolet (XUV) spectroscopy on the silicon 2p core level at 100 eV is used to measure hot carrier and phonon thermalization in Si(100) from tens of femtoseconds to 200 ps, following photoexcitation of the indirect transition to the Δ valley at 800 nm. The ground state XUV spectrum is first theoretically predicted using a combination of a single plasmon pole model and the Bethe-Salpeter equation with density functional theory. The excited state spectrum is predicted by incorporating the electronic effects of photo-induced state-filling, broadening, and band-gap renormalization into the ground state XUV spectrum. A time-dependent lattice deformation and expansion is also required to describe the excited state spectrum. The kinetics of these structural components match the kinetics of phonons excited from the electron-phonon and phonon-phonon scattering processes following photoexcitation. Separating the contributions of electronic and structural effects on the transient XUV spectra allows the carrier population, the population of phonons involved in inter- and intra-valley electron-phonon scattering, and the population of phonons involved in phonon-phonon scattering to be quantified as a function of delay time.

Tuning and Tracking of Coherent Shear Waves in Molecular Films

We have determined the time-dependent displacement fields in molecular sub-micrometer thin films as response to femtosecond and picosecond laser pulse heating by time-resolved X-ray diffraction. This method allows a direct absolute determination of the molecular displacements induced by electron-phonon interactions, which are crucial for, for example, charge transport in organic electronic devices. We demonstrate that two different modes of coherent shear motion can be photoexcited in a thin film of organic molecules by careful tuning of the laser penetration depth relative to the thickness of the film. The measured response of the organic film to impulse heating is explained by a thermoelastic model and reveals the spatially resolved displacement in the film. Thereby, information about the profile of the energy deposition in the film as well as about the mechanical interaction with the substrate material is obtained.

Spatial Distortion of Vibration Modes via Magnetic Correlation of Impurities

Long wavelength vibrational modes in the ferromagnetic semiconductor Ga_{0.91}Mn_{0.09}As are investigated using time resolved x-ray diffraction. At room temperature, we measure oscillations in the x-ray diffraction intensity corresponding to coherent vibrational modes with well-defined wavelengths. When the correlation of magnetic impurities sets in, we observe the transition of the lattice into a disordered state that does not support coherent modes at large wavelengths. Our measurements point toward a magnetically induced broadening of long wavelength vibrational modes in momentum space and their quasilocalization in the real space. More specifically, long wavelength vibrational modes cannot be assigned to a single wavelength but rather should be represented as a superposition of plane waves with different wavelengths. Our findings have strong implications for the phonon-related processes, especially carrier-phonon and phonon-phonon scattering, which govern the electrical conductivity and thermal management of semiconductor-based devices.

FemtoMAX - an X-ray beamline for structural dynamics at the short-pulse facility of MAX IV

The FemtoMAX beamline facilitates studies of the structural dynamics of materials. Such studies are of fundamental importance for key scientific problems related to programming materials using light, enabling new storage media and new manufacturing techniques, obtaining sustainable energy by mimicking photosynthesis, and gleaning insights into chemical and biological functional dynamics. The FemtoMAX beamline utilizes the MAX IV linear accelerator as an electron source. The photon bursts have a pulse length of 100 fs, which is on the timescale of molecular vibrations, and have wavelengths matching interatomic distances (Å). The uniqueness of the beamline has called for special beamline components. This paper presents the beamline design including ultrasensitive X-ray beam-position monitors based on thin Ce:YAG screens, efficient harmonic separators and novel timing tools.

Nanoscale diffractive probing of strain dynamics in ultrafast transmission electron microscopy

The control of optically driven high-frequency strain waves in nanostructured systems is an essential ingredient for the further development of nanophononics. However, broadly applicable experimental means to quantitatively map such structural distortion on their intrinsic ultrafast time and nanometer length scales are still lacking. Here, we introduce ultrafast convergent beam electron diffraction with a nanoscale probe beam for the quantitative retrieval of the time-dependent local deformation gradient tensor. We demonstrate its capabilities by investigating the ultrafast acoustic deformations close to the edge of a single-crystalline graphite membrane. Tracking the structural distortion with a 28-nm/700-fs spatio-temporal resolution, we observe an acoustic membrane breathing mode with spatially modulated amplitude, governed by the optical near field structure at the membrane edge. Furthermore, an in-plane polarized acoustic shock wave is launched at the membrane edge, which triggers secondary acoustic shear waves with a pronounced spatio-temporal dependency. The experimental findings are compared to numerical acoustic wave simulations in the continuous medium limit, highlighting the importance of microscopic dissipation mechanisms and ballistic transport channels.

Communication: Demonstration of a 20 ps X-ray switch based on a photoacoustic transducer

We have studied an X-ray switch based on a gold coated indium antimonide crystal using time-resolved X-ray diffraction and demonstrated that the switch could reduce the pulse duration of a 100 ps X-ray pulse down to 20 ps with a peak reflectivity of 8%. We have used a dynamical diffraction code to predict the performance of the switch, which was then confirmed experimentally. The experiment was carried out at the FemtoMAX beamline at the short-pulse facility of the MAX IV laboratory. The performance and limitation of the switch are discussed in terms of acoustic transport properties between the two materials and the electron transport properties of gold.

Heterodyne x-ray diffuse scattering from coherent phonons

Here, we report Fourier-transform inelastic x-ray scattering measurements of photoexcited GaAs with embedded ErAs nanoparticles. We observe temporal oscillations in the x-ray scattering intensity, which we attribute to inelastic scattering from coherent acoustic phonons. Unlike in thermal equilibrium, where inelastic x-ray scattering is proportional to the phonon occupation, we show that the scattering is proportional to the phonon amplitude for coherent states. The wavevectors of the observed phonons extend beyond the excitation wavevector. The nanoparticles break the discrete translational symmetry of the lattice, enabling the generation of large wavevector coherent phonons. Elastic scattering of x-ray photons from the nanoparticles provides a reference for heterodyne mixing, yielding signals proportional to the phonon amplitude.

Robust reconstruction of time-resolved diffraction from ultrafast streak cameras

In conjunction with ultrafast diffraction, streak cameras offer an unprecedented opportunity for recording an entire molecular movie with a single probe pulse. This is an attractive alternative to conventional pump-probe experiments and opens the door to studying irreversible dynamics. However, due to the "smearing" of the diffraction pattern across the detector, the streaking technique has thus far been limited to simple mono-crystalline samples and extreme care has been taken to avoid overlapping diffraction spots. In this article, this limitation is addressed by developing a general theory of streaking of time-dependent diffraction patterns. Understanding the underlying physics of this process leads to the development of an algorithm based on Bayesian analysis to reconstruct the time evolution of the two-dimensional diffraction pattern from a single streaked image. It is demonstrated that this approach works on diffraction peaks that overlap when streaked, which not only removes the necessity of carefully choosing the streaking direction but also extends the streaking technique to be able to study polycrystalline samples and materials with complex crystalline structures. Furthermore, it is shown that the conventional analysis of streaked diffraction can lead to erroneous interpretations of the data.

Bragg Coherent Diffractive Imaging of Zinc Oxide Acoustic Phonons at Picosecond Timescales

Mesoscale thermal transport is of fundamental interest and practical importance in materials such as thermoelectrics. Coherent lattice vibrations (acoustic phonons) govern thermal transport in crystalline solids and are affected by the shape, size, and defect density in nanoscale materials. The advent of hard x-ray free electron lasers (XFELs) capable of producing ultrafast x-ray pulses has significantly impacted the understanding of acoustic phonons by enabling their direct study with x-rays. However, previous studies have reported ensemble-averaged results that cannot distinguish the impact of mesoscale heterogeneity on the phonon dynamics. Here we use Bragg coherent diffractive imaging (BCDI) to resolve the 4D evolution of the acoustic phonons in a single zinc oxide rod with a spatial resolution of 50 nm and a temporal resolution of 25 picoseconds. We observe homogeneous (lattice breathing/rotation) and inhomogeneous (shear) acoustic phonon modes, which are compared to finite element simulations. We investigate the possibility of changing phonon dynamics by altering the crystal through acid etching. We find that the acid heterogeneously dissolves the crystal volume, which will significantly impact the phonon dynamics. In general, our results represent the first step towards understanding the effect of structural properties at the individual crystal level on phonon dynamics.

In-house time-resolved photocrystallography on the millisecond timescale using a gated X-ray hybrid pixel area detector

With the remarkable progress of accelerator-based X-ray sources in terms of intensity and brightness, the investigation of structural dynamics from time-resolved X-ray diffraction methods is becoming widespread in chemistry, biochemistry and materials science applications. Diffraction patterns can now be measured down to the femtosecond time-scale using X-ray free electron lasers or table-top laser plasma X-ray sources. On the other hand, the recent developments in photon counting X-ray area detectors offer new opportunities for time-resolved crystallography. Taking advantage of the fast read-out, the internal stacking of recorded images, and the gating possibilities (electronic shutter) of the XPAD hybrid pixel detector, we implemented a laboratory X-ray diffractometer for time-resolved single-crystal X-ray diffraction after pulsed laser excitation, combined with transient optical absorption measurement. The experimental method and instrumental setup are described in detail, and validated using the photoinduced nitrosyl linkage isomerism of sodium nitroprusside, Na₂[Fe(CN)₅NO]·2H₂O, as proof of principle. Light-induced Bragg intensity relative variations ΔI(hkl)/I(hkl) of the order of 1%, due to the photoswitching of the NO ligand, could be detected with a 6 ms acquisition window. The capabilities of such a laboratory time-resolved experiment are critically evaluated.

A multi-MHz single-shot data acquisition scheme with high dynamic range: pump-probe X-ray experiments at synchrotrons

The technical implementation of a multi-MHz data acquisition scheme for laser-X-ray pump-probe experiments with pulse limited temporal resolution (100 ps) is presented. Such techniques are very attractive to benefit from the high-repetition rates of X-ray pulses delivered from advanced synchrotron radiation sources. Exploiting a synchronized 3.9 MHz laser excitation source, experiments in 60-bunch mode (7.8 MHz) at beamline P01 of the PETRA III storage ring are performed. Hereby molecular systems in liquid solutions are excited by the pulsed laser source and the total X-ray fluorescence yield (TFY) from the sample is recorded using silicon avalanche photodiode detectors (APDs). The subsequent digitizer card samples the APD signal traces in 0.5 ns steps with 12-bit resolution. These traces are then processed to deliver an integrated value for each recorded single X-ray pulse intensity and sorted into bins according to whether the laser excited the sample or not. For each subgroup the recorded single-shot values are averaged over ∼10⁷ pulses to deliver a mean TFY value with its standard error for each data point, e.g. at a given X-ray probe energy. The sensitivity reaches down to the shot-noise limit, and signal-to-noise ratios approaching 1000 are achievable in only a few seconds collection time per data point. The dynamic range covers 100 photons pulse^-1 and is only technically limited by the utilized APD.

Identifying and Visualizing Macromolecular Flexibility in Structural Biology

Structural biology comprises a variety of tools to obtain atomic resolution data for the investigation of macromolecules. Conventional structural methodologies including crystallography, NMR and electron microscopy often do not provide sufficient details concerning flexibility and dynamics, even though these aspects are critical for the physiological functions of the systems under investigation. However, the increasing complexity of the molecules studied by structural biology (including large macromolecular assemblies, integral membrane proteins, intrinsically disordered systems, and folding intermediates) continuously demands in-depth analyses of the roles of flexibility and conformational specificity involved in interactions with ligands and inhibitors. The intrinsic difficulties in capturing often subtle but critical molecular motions in biological systems have restrained the investigation of flexible molecules into a small niche of structural biology. Introduction of massive technological developments over the recent years, which include time-resolved studies, solution X-ray scattering, and new detectors for cryo-electron microscopy, have pushed the limits of structural investigation of flexible systems far beyond traditional approaches of NMR analysis. By integrating these modern methods with powerful biophysical and computational approaches such as generation of ensembles of molecular models and selective particle picking in electron microscopy, more feasible investigations of dynamic systems are now possible. Using some prominent examples from recent literature, we review how current structural biology methods can contribute useful data to accurately visualize flexibility in macromolecular structures and understand its important roles in regulation of biological processes.

Communication: The formation of rarefaction waves in semiconductors after ultrashort excitation probed by grazing incidence ultrafast time-resolved x-ray diffraction

We explore the InSb-semiconductor lattice dynamics after excitation of high density electron-hole plasma with an ultrashort and intense laser pulse. By using time resolved x-ray diffraction, a sub-mÅ and sub-ps resolution was achieved. Thus, a strain of 4% was measured in a 3 nm thin surface layer 2 ps after excitation. The lattice strain was observed for the first 5 ps as exponentially decaying, changing rapidly by time and by depth. The observed phenomena can only be understood assuming nonlinear time dependent laser absorption where the absorption depth decreases by a factor of twenty compared to linear absorption.

Pump-probe spectrometer for measuring x-ray induced strain

A hard x-ray pump-probe spectrometer using a multi-crystal Bragg reflector is demonstrated at a third generation synchrotron source. This device derives both broadband pump and monochromatic probe pulses directly from a single intense, broadband x-ray pulse centered at 8.767 keV. We present a proof-of-concept experiment which directly measures x-ray induced crystalline lattice strain.

Ultrafast structural dynamics of the orthorhombic distortion in the Fe-pnictide parent compound BaFe2As2

Using femtosecond time-resolved hard x-ray diffraction, we investigate the structural dynamics of the orthorhombic distortion in the Fe-pnictide parent compound BaFe2As2. The orthorhombic distortion analyzed by the transient splitting of the (1 0 3) Bragg reflection is suppressed on an initial timescale of 35 ps, which is much slower than the suppression of magnetic and nematic order. This observation demonstrates a transient state with persistent structural distortion and suppressed magnetic/nematic order which are strongly linked in thermal equilibrium. We suggest a way of quantifying the coupling between structural and nematic degrees of freedom based on the dynamics of the respective order parameters.

Strong Amplification of Coherent Acoustic Phonons by Intraminiband Currents in a Semiconductor Superlattice

Sound amplification in an electrically biased superlattice (SL) is studied in optical experiments with 100 fs time resolution. Coherent SL phonons with frequencies of 40, 375, and 410 GHz give rise to oscillatory reflectivity changes. With currents from 0.5 to 1.3 A, the Fourier amplitude of the 410 GHz phonon increases by more than a factor of 2 over a 200 ps period. This amplification is due to stimulated Čerenkov phonon emission by electrons undergoing intraminiband transport. The gain coefficient of 8×10^{3}  cm^{-1} is reproduced by theoretical calculations and holds potential for novel sub-THz phonon emitters.

Picosecond x-ray strain rosette reveals direct laser excitation of coherent transverse acoustic phonons

Using a strain-rosette, we demonstrate the existence of transverse strain using time-resolved x-ray diffraction from multiple Bragg reflections in laser-excited bulk gallium arsenide. We find that anisotropic strain is responsible for a considerable fraction of the total lattice motion at early times before thermal equilibrium is achieved. Our measurements are described by a new model where the Poisson ratio drives transverse motion, resulting in the creation of shear waves without the need for an indirect process such as mode conversion at an interface. Using the same excitation geometry with the narrow-gap semiconductor indium antimonide, we detected coherent transverse acoustic oscillations at frequencies of several GHz.

Time-resolved crystallography using the Hadamard transform

We describe a method for performing time-resolved X-ray crystallographic experiments based on the Hadamard transform, in which time resolution is defined by the underlying periodicity of the probe pulse sequence, and signal/noise is greatly improved over that for the fastest pump-probe experiments depending on a single pulse. This approach should be applicable on standard synchrotron beamlines and will enable high-resolution measurements of protein and small-molecule structural dynamics. It is also applicable to other time-resolved measurements where a probe can be encoded, such as pump-probe spectroscopy.

Exploring Mbar shock conditions and isochorically heated aluminum at the Matter in Extreme Conditions end station of the Linac Coherent Light Source (invited)

Recent experiments performed at the Matter in Extreme Conditions end station of the Linac Coherent Light Source (LCLS) have demonstrated the first spectrally resolved measurements of plasmons from isochorically heated aluminum. The experiments have been performed using a seeded 8-keV x-ray laser beam as a pump and probe to both volumetrically heat and scatter x-rays from aluminum. Collective x-ray Thomson scattering spectra show a well-resolved plasmon feature that is down-shifted in energy by 19 eV. In addition, Mbar shock pressures from laser-compressed aluminum foils using velocity interferometer system for any reflector have been measured. The combination of experiments fully demonstrates the possibility to perform warm dense matter studies at the LCLS with unprecedented accuracy and precision.

Perspective: structural dynamics in condensed matter mapped by femtosecond x-ray diffraction

Ultrashort soft and hard x-ray pulses are sensitive probes of structural dynamics on the picometer length and femtosecond time scales of electronic and atomic motions. Recent progress in generating such pulses has initiated new directions of condensed matter research, exploiting a variety of x-ray absorption, scattering, and diffraction methods to probe photoinduced structural dynamics. Atomic motion, changes of local structure and long-range order, as well as correlated electron motion and charge transfer have been resolved in space and time, providing a most direct access to the physical mechanisms and interactions driving reversible and irreversible changes of structure. This perspective combines an overview of recent advances in femtosecond x-ray diffraction with a discussion on ongoing and future developments.

Bent crystal spectrometer for both frequency and wavenumber resolved x-ray scattering at a seeded free-electron laser

We present a cylindrically curved GaAs x-ray spectrometer with energy resolution ΔE/E = 1.1 × 10(-4) and wave-number resolution of Δk/k = 3 × 10(-3), allowing plasmon scattering at the resolution limits of the Linac Coherent Light Source (LCLS) x-ray free-electron laser. It spans scattering wavenumbers of 3.6 to 5.2/Å in 100 separate bins, with only 0.34% wavenumber blurring. The dispersion of 0.418 eV/13.5 μm agrees with predictions within 1.3%. The reflection homogeneity over the entire wavenumber range was measured and used to normalize the amplitude of scattering spectra. The proposed spectrometer is superior to a mosaic highly annealed pyrolytic graphite spectrometer when the energy resolution needs to be comparable to the LCLS seeded bandwidth of 1 eV and a significant range of wavenumbers must be covered in one exposure.

Measurement of transient atomic displacements in thin films with picosecond and femtometer resolution

We report measurements of the transient structural response of weakly photo-excited thin films of BiFeO3, Pb(Zr,Ti)O3, and Bi and time-scales for interfacial thermal transport. Utilizing picosecond x-ray diffraction at a 1.28 MHz repetition rate with time resolution extending down to 15 ps, transient changes in the diffraction angle are recorded. These changes are associated with photo-induced lattice strains within nanolayer thin films, resolved at the part-per-million level, corresponding to a shift in the scattering angle three orders of magnitude smaller than the rocking curve width and changes in the interlayer lattice spacing of fractions of a femtometer. The combination of high brightness, repetition rate, and stability of the synchrotron, in conjunction with high time resolution, represents a novel means to probe atomic-scale, near-equilibrium dynamics.

Transient crystalline superlattice generated by a photoacoustic transducer

Designing an efficient and simple method for modulating the intensity of x-ray radiation on a picosecond time-scale has the potential to produce ultrafast pulses of hard x-rays. In this work, we generate a tunable transient superlattice, in an otherwise perfect crystal, by photoexciting a metal film on a crystalline substrate. The resulting transient strain has amplitudes approaching 1%, wavevectors greater than [Formula: see text], and lifetimes approaching 1 ns. This method has the potential to generate isolated picosecond x-ray bursts with scattering efficiencies in excess of 10%.

Time-resolved X-ray diffraction investigation of the modified phonon dispersion in InSb nanowires

The modified phonon dispersion is of importance for understanding the origin of the reduced heat conductivity in nanowires. We have measured the phonon dispersion for 50 nm diameter InSb (111) nanowires using time-resolved X-ray diffraction. By comparing the sound speed of the bulk (3880 m/s) and that of a classical thin rod (3600 m/s) to our measurement (2880 m/s), we conclude that the origin of the reduced sound speed and thereby to the reduced heat conductivity is that the C44 elastic constant is reduced by 35% compared to the bulk material.

Measurements of light absorption efficiency in InSb nanowires

We report on measurements of the light absorption efficiency of InSb nanowires. The absorbed 70 fs light pulse generates carriers, which equilibrate with the lattice via electron-phonon coupling. The increase in lattice temperature is manifested as a strain that can be measured with X-ray diffraction. The diffracted X-ray signal from the excited sample was measured using a streak camera. The amount of absorbed light was deduced by comparing X-ray diffraction measurements with simulations. It was found that 3.0(6)% of the radiation incident on the sample was absorbed by the nanowires, which cover 2.5% of the sample.

Brillouin scattering of visible and hard X-ray photons from optically synthesized phonon wavepackets

We monitor how destructive interference of undesired phonon frequency components shapes a quasi-monochromatic hypersound wavepacket spectrum during its local real-time preparation by a nanometric transducer and follow the subsequent decay by nonlinear coupling. We prove each frequency component of an optical supercontinuum probe to be sensitive to one particular phonon wavevector in bulk material and cross-check this by ultrafast x-ray diffraction experiments with direct access to the lattice dynamics. Establishing reliable experimental techniques with direct access to the transient spectrum of the excitation is crucial for the interpretation in strongly nonlinear regimes, such as soliton formation.

Synchrotron ultrafast techniques for photoactive transition metal complexes

In the last decade, the use of time-resolved X-ray techniques has revealed the structure of light-generated transient species for a wide range of samples, from small organic molecules to proteins. Time resolutions of the order of 100 ps are typically reached, allowing one to monitor thermally equilibrated excited states and capture their structure as a function of time. This review aims at providing a general overview of the application of time-resolved X-ray solution scattering (TR-XSS) and time-resolved X-ray absorption spectroscopy (TR-XAS), the two techniques prevalently employed in the investigation of light-triggered structural changes of transition metal complexes. In particular, we herein describe the fundamental physical principles for static XSS and XAS and illustrate the theory of time-resolved XSS and XAS together with data acquisition and analysis strategies. Selected pioneering examples of photoactive transition metal complexes studied by TR-XSS and TR-XAS are discussed in depth.

Domain dynamics in thin solid films following ultrashort pulse excitation

MnAs epilayers grown on GaAs are used as a model system to study the effects of strain and epitaxial constraints on the dynamics of structural domains following 150 fs pulse pumping. Optical diffraction over 7 orders of magnitude of time is used to probe the evolution of the domains that are spatially periodic between 10 and 42 °C because of misfit strain and substrate mediated periodic elastic strain. Following excitation of 150 and 190 nm thick films, the domain fractions and the elastic strain oscillate with an ~400 ps period while the average low temperature phase fraction decreases monotonically for ~2 ns reflecting MnAs heat diffusion. Equilibrium structures are restored in 100 ns-2 μs via substrate heat diffusion. Excitation of transient periodic domains from the homogeneous low temperature phase can occur for temperatures as low as 4 °C but only after ~20 ns during film cooling.

Ultrafast three-dimensional imaging of lattice dynamics in individual gold nanocrystals

Key insights into the behavior of materials can be gained by observing their structure as they undergo lattice distortion. Laser pulses on the femtosecond time scale can be used to induce disorder in a "pump-probe" experiment with the ensuing transients being probed stroboscopically with femtosecond pulses of visible light, x-rays, or electrons. Here we report three-dimensional imaging of the generation and subsequent evolution of coherent acoustic phonons on the picosecond time scale within a single gold nanocrystal by means of an x-ray free-electron laser, providing insights into the physics of this phenomenon. Our results allow comparison and confirmation of predictive models based on continuum elasticity theory and molecular dynamics simulations.