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A central paradigm of non-equilibrium physics concerns the dynamics of heterogeneity and disorder, impacting processes ranging from the behavior of glasses to the emergent functionality of active matter. Understanding these complex mesoscopic systems requires probing the microscopic trajectories associated with irreversible processes, the role of fluctuations and entropy growth, and the timescales on which non-equilibrium responses are ultimately maintained. Approaches that illuminate these processes in model systems may enable a more general understanding of other heterogeneous non-equilibrium phenomena, and potentially define ultimate speed and energy cost limits for information processing technologies. Here, we apply ultrafast single shot x-ray photon correlation spectroscopy to resolve the non-equilibrium, heterogeneous, and irreversible mesoscale dynamics during a light-induced phase transition. This approach defines a new way of capturing the nucleation of the induced phase, the formation of transient mesoscale defects at the boundaries of the nuclei, and the eventual annihilation of these defects, even in systems with complex polarization topologies. A non-equilibrium response spanning >10 orders of magnitude in timescales is observed, with multistep behavior similar to the plateaus observed in supercooled liquids and glasses. We show how the observed time-dependent long-time correlations can be understood in terms of the stochastic dynamics of domain walls, encoded in effective waiting-time distributions with power-law tails. This work defines new possibilities for probing the non-equilibrium and correlated dynamics of disordered and heterogeneous media.

Ultrafast X-ray diffraction by the LCLS free-electron laser has been used to probe Charge Density Wave (CDW) systems under applied external currents. At sufficiently low currents, CDW wavefronts bend in the direction transverse to the 2k$_F$ wave vector. We show that this shear effect has the ability to focus or defocus hard X-ray beams, depending of the current direction, making it an electronic lens of a new kind, tunable at will from the Fraunhofer to the Fresnel regime. The effect is interpreted using the fractional Fourier transform showing how the macroscopic curvature of a nanometric modulation can be beneficially used to modify the propagation of X-ray beams., Comment: 3 pages, 3 figures

We use an x-ray free-electron laser to study the ultrafast lattice dynamics following above band-gap photoexcitation of the incipient ferroelectric potassium-tantalate, \kto. % We use ultrafast near-UV (central wavelength 266\,nm and 50 fs pulse duration) laser light to photoexcite charge carriers across the gap and probe the ultrafast lattice dynamics by recording the x-ray diffuse intensity throughout multiple Brillouin zones using pulses from the Linac Coherent Light Source (LCLS) (central wavelength 1.3\,\AA\, and $< 10$~fs pulse duration). We observe changes in the diffuse intensity that we conclude are associated with a hardening of the soft transverse optical and transverse acoustic phonon branches along $\Gamma$ to $X$ and $\Gamma$ to $M$. Using ground- and excited-state interatomic force constants from density functional theory (DFT) and assuming the phonon populations can be described by a time-dependent temperature, we fit the quasi-equilibrium thermal diffuse intensity to the experimental time-dependent intensity. We obtain the instantaneous lattice temperature and density of photoexcited charge carriers as a function of time delay. The DFT calculations demonstrate that photoexcitation transfers charge from oxygen $2p$ derived $\pi$-bonding orbitals to Ta $5d$ derived antibonding orbitals, further suppressing the ferroelectric instability and increasing the stability of the cubic, paraelectric structure., Comment: 8 pages, 4 figures

Superconductivity in the cuprates is found to be intertwined with charge and spin density waves. Determining the interactions between the different types of order is crucial for understanding these important materials. Here, we elucidate the role of the charge density wave (CDW) in the prototypical cuprate La$_{1.885}$Sr$_{0.115}$CuO$_4$, by studying the effects of large magnetic fields ($H$) up to 24 Tesla. At low temperatures ($T$), the observed CDW peaks reveal two distinct regions in the material: a majority phase with short-range CDW coexisting with superconductivity, and a minority phase with longer-range CDW coexisting with static spin density wave (SDW). With increasing magnetic field, the CDW first grows smoothly in a manner similar to the SDW. However, at high fields we discover a sudden increase in the CDW amplitude upon entering the vortex-liquid state. Our results signify strong coupling of the CDW to mobile superconducting vortices and link enhanced CDW amplitude with local superconducting pairing across the $H-T$ phase diagram., Comment: 7 pages, 3 figures

We report the observation of photo-induced plasmon-phonon coupled modes in the group IV-VI semiconductor PbTe using Fourier-transform inelastic X-ray scattering at the Linac Coherent Light Source (LCLS). We measure the near-zone-center dispersion of the heavily screened longitudinal optical (LO) phonon branch as extracted from differential changes in x-ray diffuse scattering intensity following above band gap photoexcitation., Comment: 5 pages, 2 figures

We study ultrafast x-ray diffraction on the charge density wave (CDW) of SmTe$_3$ using an x-ray free electron laser. The CDW peaks show that photoexcitation with near-infrared pump centered at 800 nm generates domain walls of the order parameter propagating perpendicular to the sample surface. These domain walls break the CDW long range order and suppress the diffraction intensity of the CDW for times much longer than the $\sim 1$~ps recovery of the local electronic gap. We reconstruct the spatial and temporal dependence of the order parameter using a simple Ginzburg-Landau model and find good agreement between the experimental and model fluence dependences. Based on the model we find that at long times, depending on the pump fluence, multiple domain walls remain at distances of few nm from the surface.

X-ray Absorption Spectroscopy (XAS) is a widely used X-ray diagnostic method. While synchrotrons have large communities of XAS users, its use on X-Ray Free Electron Lasers (XFEL) facilities has been rather limited. At a first glance, the relatively narrow bandwidth and the highly fluctuating spectral structure of XFEL sources seem to prevent high-quality XAS measurements without accumulating over many shots. Here, we demonstrate for the first time the collection of single-shot XAS spectra on an XFEL, with error bars of only a few percent, over tens of eV. We show how this technique can be extended over wider spectral ranges towards Extended X-ray Absorption Fine Structure (EXAFS) measurements, by concatenating a few tens of single-shot measurements. Such results open indisputable perspectives for future femtosecond time resolved XAS studies, especially for transient processes that can be initiated at low repetition rate., Comment: 11 pages, 5 figures

We present a combined ultrafast optical pump-probe and ultrafast x-ray diffraction measurement of the CDW dynamics in SmTe$_3$ at 300 K. The ultrafast x-ray diffraction measurements, taken at the Linac Coherent Light Source reveal a $\sim 1.55$ THz mode that becomes overdamped with increasing fluence. We identify this oscillation with the lattice component of the amplitude mode. Furthermore, these data allow for a more clear identification of the frequencies present in the optical pump-probe data. In both, reflectivity and diffraction, we observe a crossover of the response from linear (for small displacements) to quadratic in the amplitude of the order parameter displacement. Finally, a time-dependent Ginzburg-Landau model captures the essential features of the experimental observations., Comment: 7 pages, 5 figures

We report on the ultrafast dynamics of charge order and structural response during the photoinduced suppression of charge and orbital order in a mixed-valence manganite. Employing femtosecond time-resolved resonant x-ray diffraction below and at the Mn K absorption edge, we present a method to disentangle the transient charge order and structural dynamics in thin films of Pr0.5Ca0.5MnO3. Based on the static resonant scattering spectra, we extract the dispersion correction of charge ordered Mn3+ and Mn4+ ions, allowing us to separate the transient contributions of purely charge order from structural contributions to the scattering amplitude after optical excitation. Our finding of a coherent structural mode at around 2.3 THz, which primarily modulates the lattice, but does not strongly affect the charge order, confirms the picture of the charge order being the driving force of the combined charge, orbital and structural transition.

We demonstrate experimentally Hanbury Brown and Twiss (HBT) interferometry at a hard X-ray Free Electron Laser (XFEL) on a sample diffraction patterns. This is different from the traditional approach when HBT interferometry requires direct beam measurements in absence of the sample. HBT analysis was carried out on the Bragg peaks from the colloidal crystals measured at Linac Coherent Light Source (LCLS). We observed high degree (80%) spatial coherence of the full beam and the pulse duration of the monochromatized beam on the order of 11 fs that is significantly shorter than expected from the electron bunch measurements., Comment: 32 pages, 10 figures, 2 tables

Silicon drift detectors (SDDs) revolutionized spectroscopy in fields as diverse as geology and dentistry. For a subset of experiments at ultra-fast, x-ray free-electron lasers (FELs), SDDs can make substantial contributions. Often the unknown spectrum is interesting, carrying science data, or the background measurement is useful to identify unexpected signals. Many measurements involve only several discrete photon energies known a priori, allowing single event decomposition of pile-up and spectroscopic photon counting. We designed a pulse function and demonstrated that the signal amplitude and rise time are obtained for each pulse by fitting, thus removing the need for pulse shaping. By avoiding pulse shaping, rise times of tens of nanoseconds resulted in reduced pulse pile-up and allowed decomposition of remaining pulse pile-up at photon separation times down to hundreds of nanoseconds while yielding time-of-arrival information with precision of 10 nanoseconds. Waveform fitting yields simultaneously high energy resolution and high counting rates (2 orders of magnitude higher than current digital pulse processors). We showed that pile-up spectrum fitting is relatively simple and preferable to pile-up spectrum deconvolution. We developed a photon pile-up statistical model for constant intensity sources, extended it to variable intensity sources (typical for FELs) and used it to fit a complex pile-up spectrum. We subsequently developed a Bayesian pile-up decomposition method that allows decomposing pile-up of single events with up to 6 photons from 6 monochromatic lines with 99% accuracy. The usefulness of SDDs will continue into the x-ray FEL era of science. Their successors, the ePixS hybrid pixel detectors, already offer hundreds of pixels, each with similar performance to an SDD, in a compact, robust and affordable package, Comment: 16 pages, 11 figures, 4 tables

We use ultrafast x-ray pulses to characterize the lattice response of SrTiO3 when driven by strong terahertz (THz) fields. We observe transient changes in the diffraction intensity with a delayed onset with respect to the driving field. Fourier analysis reveals two frequency components corresponding to the two lowest energy zone-center optical modes in SrTiO3. The lower frequency mode exhibits clear softening as the temperature is decreased while the higher frequency mode shows slight temperature dependence., Comment: 15 pages, 5 figures

We employ time-resolved resonant x-ray diffraction to study the melting of charge order and the associated insulator-metal transition in the doped manganite Pr$_{0.5}$Ca$_{0.5}$MnO$_3$ after resonant excitation of a high-frequency infrared-active lattice mode. We find that the charge order reduces promptly and highly nonlinearly as function of excitation fluence. Density functional theory calculations suggest that direct anharmonic coupling between the excited lattice mode and the electronic structure drive these dynamics, highlighting a new avenue of nonlinear phonon control.

Selective optical excitation of a substrate lattice can drive phase changes across hetero-interfaces. This phenomenon is a non-equilibrium analogue of static strain control in heterostructures and may lead to new applications in optically controlled phase change devices. Here, we make use of time-resolved non-resonant and resonant x-ray diffraction to clarify the underlying physics, and to separate different microscopic degrees of freedom in space and time. We measure the dynamics of the lattice and that of the charge disproportionation in NdNiO3, when an insulator-metal transition is driven by coherent lattice distortions in the LaAlO3 substrate. We find that charge redistribution propagates at supersonic speeds from the interface into the NdNiO3 film, followed by a sonic lattice wave. When combined with measurements of magnetic disordering and of the metal-insulator transition, these results establish a hierarchy of events for ultrafast control at complex oxide hetero-interfaces., Comment: 20 pages, 4 figures

The study of photoexcited strongly correlated materials is attracting growing interest since their rich phase diagram often translates into an equally rich out-of-equilibrium behavior, including non-thermal phases and photoinduced phase transitions. With femtosecond optical pulses, electronic and lattice degrees of freedom can be transiently decoupled, giving the opportunity of stabilizing new states of matter inaccessible by quasi-adiabatic pathways. Here we present a study of the ultrafast non-equilibrium evolution of the prototype Mott-Hubbard material V2O3, which presents a transient non-thermal phase developing immediately after photoexcitation and lasting few picoseconds. For both the insulating and the metallic phase, the formation of the transient configuration is triggered by the excitation of electrons into the bonding a1g orbital, and is then stabilized by a lattice distortion characterized by a marked hardening of the A1g coherent phonon. This configuration is in stark contrast with the thermally accessible ones - the A1g phonon frequency actually softens when heating the material. Our results show the importance of selective electron-lattice interplay for the ultrafast control of material parameters, and are of particular relevance for the optical manipulation of strongly correlated systems, whose electronic and structural properties are often strongly intertwinned., Comment: 6 pages, 4 figures

The dynamical processes associated with electric field manipulation of the polarization in a ferroelectric remain largely unknown but fundamentally determine the speed and functionality of ferroelectric materials and devices. Here we apply sub-picosecond duration, single-cycle terahertz pulses as an ultrafast electric field bias to prototypical BaTiO$_3$ ferroelectric thin films with the atomic-scale response probed by femtosecond x-ray scattering techniques. We show that electric fields applied perpendicular to the ferroelectric polarization drive large amplitude displacements of the titanium atoms along the ferroelectric polarization axis, comparable to that of the built-in displacements associated with the intrinsic polarization and incoherent across unit cells. This effect is associated with a dynamic rotation of the ferroelectric polarization switching on and then off on picosecond timescales. These transient polarization modulations are followed by long-lived vibrational heating effects driven by resonant excitation of the ferroelectric soft mode, as reflected in changes in the c-axis tetragonality. The ultrafast structural characterization described here enables direct comparison with first-principles-based molecular dynamics simulations, with good agreement obtained.

Vanadium dioxide, an archetypal correlated-electron material, undergoes an insulator-metal transition near room temperature that exhibits electron-correlation-driven and structurally-driven physics. Using ultrafast optical spectroscopy and x-ray scattering we show that these processes can be disentangled in the time domain. Specifically, following intense sub-picosecond electric-field excitation, a partial collapse of the insulating gap occurs within the first ps. Subsequently, this electronic reconfiguration initiates a change in lattice symmetry taking place on a slower timescale. We identify the kinetic energy increase of electrons tunneling in the strong electric field as the driving force, illustrating a novel method to control electronic interactions in correlated materials on an ultrafast timescale.

Using femtosecond time-resolved resonant magnetic x-ray diffraction at the Ho L3 absorption edge, we investigate the demagnetization dynamics in antiferromagnetically ordered metallic Ho after femtosecond optical excitation. Tuning the x-ray energy to the electric dipole (E1, 2p -> 5d) or quadrupole (E2, 2p -> 4f) transition allows us to selectively and independently study the spin dynamics of the itinerant 5d and localized 4f electronic subsystems via the suppression of the magnetic (2 1 3-tau ) satellite peak. We find demagnetization timescales very similar to ferromagnetic 4f systems, suggesting that the loss of magnetic order occurs via a similar spin-flip process in both cases. The simultaneous demagnetization of both subsystems demonstrates strong intra-atomic 4f-5d exchange coupling. In addition, an ultrafast lattice contraction due to the release of magnetostriction leads to a transient shift of the magnetic satellite peak.

The interactions between electrons and phonons drive a large array of technologically relevant material properties including ferroelectricity, thermoelectricity, and phase-change behaviour. In the case of many group IV-VI, V, and related materials, these interactions are strong and the materials exist near electronic and structural phase transitions. Their close proximity to phase instability produces a fragile balance among the various properties. The prototypical example is PbTe whose incipient ferroelectric behaviour has been associated with large phonon anharmonicity and thermoelectricity. Experimental measurements on PbTe reveal anomalous lattice dynamics, especially in the soft transverse optical phonon branch. This has been interpreted in terms of both giant anharmonicity and local symmetry breaking due to off-centering of the Pb ions. The observed anomalies have prompted renewed theoretical and computational interest, which has in turn revived focus on the extent that electron-phonon interactions drive lattice instabilities in PbTe and related materials. Here, we use Fourier-transform inelastic x-ray scattering (FT-IXS) to show that photo-injection of free carriers stabilizes the paraelectric state. With support from constrained density functional theory (CDFT) calculations, we find that photoexcitation weakens the long-range forces along the cubic direction tied to resonant bonding and incipient ferroelectricity. This demonstrates the importance of electronic states near the band edges in determining the equilibrium structure., Comment: 9 page, 3 figures

Impulsive optical excitation can generate both coherent and squeezed phonons. The expectation value of the phonon displacement $$ oscillates at the mode frequency for the coherent state but remains zero for a pure squeezed state. In contrast, both show oscillations in $<|u_q|^2>$ at twice the mode frequency. Therefore it can be difficult to distinguish them in a second-order measurement of the displacements, such as in first-order x-ray diffuse scattering. Here we demonstrate a simple method to distinguish squeezed from coherent atomic motion by measurement of the diffuse scattering following double impulsive excitation. We find that femtosecond optical excitation generates squeezed phonons spanning the Brillouin zone in Ge, GaAs and InSb. Our results confirm the mechanism suggested in [Nature Physics 9, 790 (2013)]., Comment: 5 pages, 3 figures

We use femtosecond time-resolved hard x-ray scattering to detect coherent acoustic phonons excited during ultrafast laser demagnetization of bcc Fe films. We determine the lattice strain propagating through the film through analysis of the oscillations in the x-ray scattering signal as a function of momentum transfer. The width of the strain wavefront is ~100 fs, similar to demagnetization timescales. First-principles calculations show that the high-frequency Fourier components of the strain, which give rise to the sharp wavefront, could in part originate from non-thermal dynamics of the lattice not considered in the two-temperature model., Comment: 5 pages, 3 figures

Ultrafast light pulses can modify the electronic properties of quantum materials by perturbing the underlying, intertwined degrees of freedom. In particular, iron-based superconductors exhibit a strong coupling among electronic nematic fluctuations, spins, and the lattice, serving as a playground for ultrafast manipulation. Here we use time-resolved x-ray scattering to measure the lattice dynamics of photo-excited BaFe2As2. Upon optical excitation, no signature of an ultrafast change of the crystal symmetry is observed, but the lattice oscillates rapidly in time due to the coherent excitation of an A1g mode that modulates the Fe-As-Fe bond angle. We directly quantify the coherent lattice dynamics and show that even a small photo-induced lattice distortion can induce notable changes in the electronic and magnetic properties. Our analysis implies that transient structural modification can generally be an effective tool for manipulating the electronic properties of multi-orbital systems, where electronic instabilities are sensitive to the orbital character of bands near the Fermi level.

THz-frequency optical pulses can resonantly drive selected vibrational modes in solids and deform their crystal structure. In complex oxides, this method has been used to melt electronic orders, drive insulator to metal transitions or induce superconductivity. Strikingly, coherent interlayer transport strongly reminiscent of superconductivity can be transiently induced up to room temperature in YBa2Cu3O6+x. By combining femtosecond X-ray diffraction and ab initio density functional theory calculations, we determine here the crystal structure of this exotic non-equilibrium state. We find that nonlinear lattice excitation in normal-state YBa2Cu3O6+x at 100 K causes a staggered dilation/contraction of the Cu-O2 intra/inter- bilayer distances, accompanied by anisotropic changes in the in-plane O-Cu-O bond buckling. Density functional theory calculations indicate that these motions cause dramatic changes in the electronic structure. Amongst these, the enhancement in the dx2-y2 character of the in-plane electronic structure is likely to favor superconductivity., Comment: 28 pages, including Supplement

A double-crystal diamond (111) monochromator recently implemented at the Linac Coherent Light Source (LCLS) enables splitting of the primary X-ray beam into a pink (transmitted) and a monochromatic (reflected) branch. The first monochromator crystal with a thickness of 100 um provides sufficient X-ray transmittance to enable simultaneous operation of two beamlines. Here we report on the design, fabrication, and X-ray characterization of the first and second (300-um-thick) crystals utilized in the monochromator and the optical assemblies holding these crystals. Each crystal plate has a region of about 5 X 2 mm2 with low defect concentration, sufficient for use in X-ray optics at the LCLS. The optical assemblies holding the crystals were designed to provide mounting on a rigid substrate and to minimize mounting-induced crystal strain. The induced strain was evaluated using double-crystal X-ray topography and was found to be small over the 5 X 2 mm2 working regions of the crystals.