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The recent extension of transient grating (TG) spectroscopy to the X-ray regime at X-ray free electron lasers (XFEL) facilities has opened new possibilities for studying ultrafast dynamics and nanoscale transport. Recent experiments have employed the Talbot effect to generate excitation gratings in the hard X-rays, e.g., at 7 keV, using X-ray phase masks, enabling simplified, collinear TG setups with only two beams. Despite promising experimental progress, a comprehensive theoretical framework for understanding far-field diffraction patterns in Talbot-based X-ray TG is still lacking. In this work, we present a detailed theoretical study of stationary far-field diffraction patterns in TG spectroscopy using the Talbot effect, providing essential insights for interpreting and optimizing recent XFEL experiments. We systematically investigate: (1) the influence of the sample material properties such as, index of refraction and thickness, and beam intensity, included in the phase effectivity parameter causing broadening of the spatial spectrum; (2) the role of wavefront curvature in modulating diffraction regimes; (3) the effect of sample position on far-field patterns; (4) the emergence of heterodyne effects due to phase shifts across diffraction orders; and (5) the impact of using two different wavelengths for pump and probe beams and analyzing the effect of their relative intensities. Our analysis focuses on static spatial properties rather than dynamical transients, offering a foundation for precise material characterization and nonlinear spectroscopy. Simulations are performed using parameter values representative of XFEL conditions, including hard X-ray wavelengths and sub-micrometer grating periods. The results highlight how phase effectivity, beam parameters, and sample placement govern the formation of non-trivial diffraction patterns, providing critical guidance for future X-ray TG experiments. The model focuses on nonlinear phase effects at hard X-ray energies, which are generally very weak and become relevant only at high intensities. This study delivers the first systematic theoretical framework for Talbot-based TG spectroscopy, bridging a vital gap in understanding far-field diffraction effects in cutting-edge XFEL applications.

Surface acoustic waves (SAWs) are excited by femtosecond extreme ultraviolet (EUV) transient gratings (TGs) in a room-temperature ferrimagnetic DyCo5 alloy. TGs are generated by crossing a pair of EUV pulses from a free electron laser with the wavelength of 20.8 nm matching the Co M-edge, resulting in a SAW wavelength of Λ = 44 nm. Using the pump-probe transient grating scheme in reflection geometry, the excited SAWs could be followed in the time range of −10 to 100 ps in the thin film. Coherent generation of TGs by ultrafast EUV pulses allows to excite SAW in any material and to investigate their couplings to other dynamics, such as spin waves and orbital dynamics. In contrast, we encountered challenges in detecting electronic and magnetic signals, potentially due to the dominance of the larger SAW signal and the weakened reflection signal from underlying layers. A potential solution for the latter challenge involves employing soft x-ray probes, albeit introducing additional complexities associated with the required grazing incidence geometry.

Quantifying the dynamics of normal modes and how they interact with other excitations is of central importance in condensed matter. Spin-lattice coupling is relevant to several sub-fields of condensed matter physics; examples include spintronics, high- T c superconductivity, and topological materials. However, experimental approaches that can directly measure it are rare and incomplete. Here we use time-resolved X-ray diffraction to directly access the ultrafast motion of atoms and spins following the coherent excitation of an electromagnon in a multiferroic hexaferrite. One striking outcome is the different phase shifts relative to the driving field of the two different components. This phase shift provides insight into the excitation process of such a coupled mode. This direct observation of combined lattice and magnetization dynamics paves the way to access the mode-selective spin-lattice coupling strength, which remains a missing fundamental parameter for ultrafast control of magnetism and is relevant to a wide variety of materials. Experimental approaches that can directly measure spin-lattice coupling are rare. Here, authors report direct observation of the coupling of the phonon and magnon dynamics of a coherently driven electromagnon in a multiferroic hexaferrite using time-resolved X-ray diffraction. (277 characters in total).

The advent of free-electron laser (FEL) sources delivering two synchronized pulses of different wavelengths (or colours) has made available a whole range of novel pump–probe experiments. This communication describes a major step forward using a new configuration of the FERMI FEL-seeded source to deliver two pulses with different wavelengths, each tunable independently over a broad spectral range with adjustable time delay. The FEL scheme makes use of two seed laser beams of different wavelengths and of a split radiator section to generate two extreme ultraviolet pulses from distinct portions of the same electron bunch. The tunability range of this new two-colour source meets the requirements of double-resonant FEL pump/FEL probe time-resolved studies. We demonstrate its performance in a proof-of-principle magnetic scattering experiment in Fe–Ni compounds, by tuning the FEL wavelengths to the Fe and Ni 3 p resonances. Two-colour X-ray free electron laser is a powerful tool for pump–probe measurements, but currently constrained by limited tunability. Here, Ferrari et al . develop a configuration that allows tuning both the pump and the probe to specific electronic excitations, providing element selectivity.

Chirped pulse amplification in optical lasers is a revolutionary technique, which allows the generation of extremely powerful femtosecond pulses in the infrared and visible spectral ranges. Such pulses are nowadays an indispensable tool for a myriad of applications, both in fundamental and applied research. In recent years, a strong need emerged for light sources producing ultra-short and intense laser-like X-ray pulses, to be used for experiments in a variety of disciplines, ranging from physics and chemistry to biology and material sciences. This demand was satisfied by the advent of short-wavelength free-electron lasers. However, for any given free-electron laser setup, a limit presently exists in the generation of ultra-short pulses carrying substantial energy. Here we present the experimental implementation of chirped pulse amplification on a seeded free-electron laser in the extreme-ultraviolet, paving the way to the generation of fully coherent sub-femtosecond gigawatt pulses in the water window (2.3–4.4 nm). Short laser pulses of femtosecond time scales are in high demand in order to explore the fast electron dynamics in light-matter interactions. Here, the authors demonstrated the compression of free electron laser pulses in the extreme ultraviolet range by using a chirped pulse amplification technique.

Optical-domain transient grating (TG) spectroscopy is the ideal tool to investigate transport phenomena in gases, liquids and solids, but it is limited to typically micron-size grating periods. Extreme-Ultraviolet TG has represented a major leap forward to access the mesoscopic scales. Hard X-ray TGs open access in principle to the nanoscale. Hard X-ray TGs were recently generated using the Talbot effect and probed by optical pulses, but these hinder exploiting the advantages of the nanoscale gratings. Here, we present an all-X-ray TG study, in which few-femtosecond hard X-ray pulses are used both for excitation and probing. Our experiment was performed on an amorphous film of an FeGd alloy and on a thin silicon single crystal. The results show a manifestation of the TG induced by the X-ray pump and probe pulses in the form of Talbot carpets, as well as temporal evolution of the grating in crystalline silicon showing coherent optical phonons. Ultrafast all-X-ray TG spectroscopy has the potential to study fundamental excitations with femtosecond time resolution and nanometer spatial sensitivity. Using hard X-rays for transient grating (TG) spectroscopy, fundamental excitations can be followed with femtosecond temporal and nanometer spatial resolution, selecting momenta, chemical elements and their chemical environment. The authors demonstrate the first experiment of all X-ray TG on an amorphous film of FeGd and on a silicon single crystal.

Free-electron lasers and high-harmonic-generation table-top systems are new sources of extreme-ultraviolet to hard X-ray photons, providing ultrashort pulses that are intense, coherent and tunable. They are enabling a broad range of nonlinear optical and spectroscopic methods at short wavelengths, similar to those developed in the terahertz to ultraviolet regimes over the past 60 years. The extreme-ultraviolet to X-ray wavelengths access core transitions that can provide element and orbital selectivity, structural resolution down to the sub-nanometre scale and, for some methods, high momentum transfers across typical Brillouin zones; the possibilities for polarization control and sub-femtosecond time resolution are opening up new frontiers in research. In this Roadmap, we review the emergence of this field over the past 10 years or so, covering methods such as sum or difference frequency generation and second-harmonic generation, two-photon absorption, stimulated emission or Raman spectroscopy and transient grating spectroscopy. We then discuss the unique opportunities provided by these techniques for probing elementary dynamics in a wide variety of systems.Key pointsX-ray free-electron lasers and high-harmonic-generation sources of extreme-ultraviolet (EUV) to hard X-ray photons deliver intense ultrashort pulses and enable the extension of nonlinear methods to much shorter wavelengths.EUV to X-ray wavelengths access core transitions that can provide element and orbital selectivity. These wavelengths also achieve sub-nanometre structural resolution and high momentum transfer, with femtosecond and attosecond time resolution.Nonlinear EUV/X-ray methods that have emerged include sum or difference frequency generation, parametric down-conversion, second-harmonic generation, two-photon absorption, stimulated emission or Raman spectroscopy and transient grating spectroscopy.Nonlinear EUV/X-ray science is developing hand-in-hand with instrumentation, to improve pulse features and enhance accessibility with the use of table-top systems or compact accelerators.These techniques offer unique opportunities for probing dynamical events in a wide variety of systems, including surface and interface processes, chirality, nanoscale transport and multidimensional core-level spectroscopy.

The control of polarization state in soft and hard X-ray light is of crucial interest to probe structural and symmetry properties of matter. Thanks to their Apple-II type undulators, the FERMI-Free Electron Lasers are able to provide elliptical, circular or linearly polarized light within the extreme ultraviolet and soft X-ray range. In this paper, we report the characterization of the polarization state of FERMI FEL-2 down to 5 nm. The results show a high degree of polarization of the FEL pulses, typically above 95%. The campaign of measurements was performed at the Low Density Matter beamline using an electron Time-Of-Flight based polarimeter.

The potential of the two-color mode implemented at the FERMI free-electron laser (FEL) source for pumping and probing selectively different atomic species has been demonstrated by time-resolved scattering experiments with permalloy (FeNi alloy) and NiFe2O4 samples. We monitored the ultra-fast demagnetization of Ni induced by the pump FEL pulse, by tuning the linearly-polarized FEL probe pulse to the Ni-3p resonance and measuring the scattered intensity in the transverse magneto-optical Kerr effect geometry. The measurements were performed by varying the intensity of the FEL pump pulse, tuning its wavelength to and off of the Fe-3p resonance, and by spanning the FEL probe pulse delays across the 300–900 fs range. The obtained results have evidenced that for the case of NiFe2O4, there is a sensible difference in the magnetic response at the Ni site when the pump pulse causes electronic excitations at the Fe site.

The two single-pass, externally seeded free-electron lasers (FELs) of the FERMI user facility are designed around Apple-II-type undulators that can operate at arbitrary polarization in the vacuum ultraviolet-to-soft x-ray spectral range. Furthermore, within each FEL tuning range, any output wavelength and polarization can be set in less than a minute of routine operations. We report the first demonstration of the full output polarization capabilities of FERMI FEL-1 in a campaign of experiments where the wavelength and nominal polarization are set to a series of representative values, and the polarization of the emitted intense pulses is thoroughly characterized by three independent instruments and methods, expressly developed for the task. The measured radiation polarization is consistently >90% and is not significantly spoiled by the transport optics; differing, relative transport losses for horizontal and vertical polarization become more prominent at longer wavelengths and lead to a non-negligible ellipticity for an originally circularly polarized state. The results from the different polarimeter setups validate each other, allow a cross-calibration of the instruments, and constitute a benchmark for user experiments.