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Free-electron lasers provide bright, ultrashort, and monochromatic x-ray pulses, enabling novel spectroscopic measurements not only with femtosecond temporal resolution: The high fluence of their x-ray pulses can also easily enter the regime of the non-linear x-ray–matter interaction. Entering this regime necessitates a rigorous analysis and reliable prediction of the relevant non-linear processes for future experiment designs. Here, we show non-linear changes in the L 3-edge absorption of metallic nickel thin films, measured with fluences up to 60 J/cm2. We present a simple but predictive rate model that quantitatively describes spectral changes based on the evolution of electronic populations within the pulse duration. Despite its simplicity, the model reaches good agreement with experimental results over more than three orders of magnitude in fluence, while providing a straightforward understanding of the interplay of physical processes driving the non-linear changes. Our findings provide important insights for the design and evaluation of future high-fluence free-electron laser experiments and contribute to the understanding of non-linear electron dynamics in x-ray absorption processes in solids at the femtosecond timescale.

A fundamental understanding of the interplay between lattice structure, polarization and electrons is pivotal to the optical control of ferroelectrics. The interaction between light and matter enables the remote and wireless control of the ferroelectric polarization on the picosecond timescale, while inducing strain, i.e., lattice deformation. At equilibrium, the ferroelectric polarization is proportional to the strain, and is typically assumed to be so also out of equilibrium. Decoupling the polarization from the strain would remove the constraint of sample design and provide an effective knob to manipulate the polarization by light. Here, upon above-bandgap laser excitation of the prototypical ferroelectric BaTiO 3 , we induce and measure an ultrafast decoupling between polarization and strain that begins within 350 fs, by softening Ti-O bonds via charge transfer, and lasts for several tens of picoseconds. We show that the ferroelectric polarization out of equilibrium is mainly determined by photoexcited electrons, instead of the strain. At equilibrium, the ferroelectric polarization is proportional to the strain. At ultrafast timescales, an above-bandgap laser excitation decouples strain and polarization, which, out of equilibrium, is mainly determined by the photoexcited electrons.

A bright, ultrashort X-ray pulse is used to transiently create and characterize warm dense copper. As the pulse intensity is increased, the opacity of copper is strongly altered. The recorded X-ray absorption spectra, substantiated by a theoretical electronic structure model, provide insight into the non-equilibrium electron dynamics during the formation of warm dense matter.

Resonant inelastic X-ray scattering (RIXS) is an ideal X-ray spectroscopy method to push the combination of energy and time resolutions to the Fourier transform ultimate limit, because it is unaffected by the core-hole lifetime energy broadening. Also, in pump–probe experiments the interaction time is made very short by the same core-hole lifetime. RIXS is very photon hungry so it takes great advantage from high-repetition-rate pulsed X-ray sources like the European XFEL. The Heisenberg RIXS instrument is designed for RIXS experiments in the soft X-ray range with energy resolution approaching the Fourier and the Heisenberg limits. It is based on a spherical grating with variable line spacing and a position-sensitive 2D detector. Initially, two gratings were installed to adequately cover the whole photon energy range. With optimized spot size on the sample and small pixel detector the energy resolution can be better than 40 meV (90 meV) at any photon energy below 1000 eV with the high-resolution (high-transmission) grating. At the SCS instrument of the European XFEL the spectrometer can be easily positioned thanks to air pads on a high-quality floor, allowing the scattering angle to be continuously adjusted over the 65–145° range. It can be coupled to two different sample interaction chambers, one for liquid jets and one for solids, each state-of-the-art equipped and compatible for optical laser pumping in collinear geometry. The measured performances, in terms of energy resolution and count rate on the detector, closely match design expectations. The Heisenberg RIXS instrument has been open to public users since the summer of 2022.

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. A beam‐splitting off‐axis zone plate setup to measure transient X‐ray absorption spectroscopy is presented, as implemented at the Spectroscopy and Coherent Scattering instrument at the European X‐ray Free‐Electron Laser.

Resonant absorption of a photon by bound electrons in a solid can promote an electron to another orbital state or transfer it to a neighboring atomic site. Such a transition in a magnetically ordered material could affect the magnetic order. While this process is an obvious road map for optical control of magnetization, experimental demonstration of such a process remains challenging. Exciting a significant fraction of magnetic ions requires a very intense incoming light beam, as orbital resonances are often weak compared to above‐band‐gap excitations. In the latter case, a sizeable reduction of the magnetization occurs as the absorbed energy increases the spin temperature, masking the non‐thermal optical effects. Here, using ultrafast X‐ray spectroscopy, this work is able to resolve changes in the magnetization state induced by resonant absorption of infrared photons in Co‐doped yttrium iron garnet, with negligible thermal effects. This work finds that the optical excitation of the Co ions affects the two distinct magnetic Fe sublattices differently, resulting in a transient non‐collinear magnetic state. The present results indicate that the all‐optical magnetization switching (AOS) most likely occurs due to the creation of a transient, non‐collinear magnetic state followed by coherent spin rotations of the Fe moments. This work demonstrates a fundamentally new scenario for dynamics of transient non‐collinear magnetic state in Fe‐sublattices by resonant pumping optically photoactive Co‐ions in garnets with a weak net magnetization. The time‐resolved X‐ray spectroscopy using EuXFEL facilities, which allowed us to reveal the underlying mechanism of magnetization reorientation through a spin‐polaronic cascade triggered by an anisotropy change of the Co ions.

Topological states of matter exhibit fascinating physics combined with an intrinsic stability. A key challenge is the fast creation of topological phases, which requires massive reorientation of charge or spin degrees of freedom. Here we report the picosecond emergence of an extended topological phase that comprises many magnetic skyrmions. The nucleation of this phase, followed in real time via single-shot soft X-ray scattering after infrared laser excitation, is mediated by a transient topological fluctuation state. This state is enabled by the presence of a time-reversal symmetry-breaking perpendicular magnetic field and exists for less than 300 ps. Atomistic simulations indicate that the fluctuation state largely reduces the topological energy barrier and thereby enables the observed rapid and homogeneous nucleation of the skyrmion phase. These observations provide fundamental insights into the nature of topological phase transitions, and suggest a path towards ultrafast topological switching in a wide variety of materials through intermediate fluctuating states. Time-resolved X-ray scattering is utilized to demonstrate an ultrafast 300 ps topological phase transition to a skyrmionic phase. This transition is enabled by the formation of a transient topological fluctuation state.

Warm dense matter is at the boundary between a plasma and a condensed phase and plays a role in astrophysics, planetary science and inertial confinement fusion research. However, its electronic structure and ionic structure upon irradiation with strong laser pulses remain poorly understood. Here, we use an intense and ultrafast X-ray free-electron laser pulse to simultaneously create and characterize warm dense copper using L -edge X-ray absorption spectroscopy over a large irradiation intensity range. Below a pulse intensity of 10 15  W cm −2 , an absorption peak below the L edge appears, originating from transient depletion of the 3 d band. This peak shifts to lower energy with increasing intensity, indicating the movement of the 3 d band upon strong X-ray excitation. At higher intensities, substantial ionization and collisions lead to the transition from reverse saturable absorption to saturable absorption of the X-ray free-electron laser pulse, two nonlinear effects that hold promise for X-ray pulse-shaping. We employ theoretical calculations that combine a model based on kinetic Boltzmann equations with finite-temperature real-space density-functional theory to interpret these observations. The results can be used to benchmark non-equilibrium models of electronic structure in warm dense matter. Warm dense copper, created by an X-ray free-electron laser, features a transition from reverse saturable absorption to saturable absorption. The results can be used to benchmark non-equilibrium models of electronic structure in warm dense matter.

The complex electronic structure of metallic ferromagnets is determined by a balance between exchange interaction, electron hopping leading to band formation, and local Coulomb repulsion. By combining high energy and temporal resolution in femtosecond time-resolved X-ray absorption spectroscopy with ab initio time-dependent density functional theory we analyze the electronic structure in fcc Ni on the time scale of these interactions in a pump-probe experiment. We distinguish transient broadening and energy shifts in the absorption spectra, which we demonstrate to be captured by electron repopulation respectively correlation-induced modifications of the electronic structure, requiring to take the local Coulomb interaction into account.

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