Advances in Free-Electron-Laser based scattering techniques and spectroscopic methods

Abstract

In 2005, the FLASH soft X-ray free-electron laser (FEL) in Hamburg, Germany, achieved its first lasing, marking the beginning of an intensive phase of global FEL construction. Subsequently, the United States, Japan, South Korea, China, Italy, and Switzerland have all commenced building this type of photon facility. Recently, the new generation of FEL has started to utilize superconducting acceleration technology to achieve high-repetition-rate pulse output, thereby improving experimental efficiency. Currently completed facilities include the European XFEL, with ongoing constructions of the LCLS-II in the United States and the SHINE facility in Shanghai. The Shenzhen Superconducting soft X-ray Free-electron Laser (S³FEL) is also in preparation.<br>These FEL facilities generate coherent and tunable ultrashort pulses across the extreme ultraviolet to hard X-ray spectrum, advancing FEL-based scattering techniques such as ultrafast X-ray scattering, spectroscopy, and X-ray nonlinear optics, thereby transforming the way we study correlated quantum materials at ultrafast timescales.<br>The Self-Amplified Spontaneous Emission (SASE) process in FEL leads to timing jitter between FEL pulses and the synchronized pump laser, impacting the accuracy of ultrafast time-resolved measurements. To address this issue, timing tools have been developed to measure these jitters and reindex each pump-probe signal after measurement. This success enables ultrafast X-ray diffraction (UXRD) to be first realized, a systematic study of Peierls distorted materials is demonstrated. Furthermore, the high flux of FEL pulses enable Fourier Transform Inelastic X-ray Scattering (FT-IXS) method, which allows the extraction the phonon dispersion curves throughout the entire Brillouin zone by applying the Fourier transform to the measured momentum dependent coherent phonon scattering signals, even when the system is in a non-equilibrium state.<br>UXRD is typically employed to study ultrafast lattice dynamics, which requires hard X-ray wavelengths. In contrast, time resolved resonant elastic X-ray scattering (tr-REXS) in the soft X-ray regime has become a standard method for investigating nano-sized charge and spin orders in correlated quantum materials at ultrafast time scales.<br>In correlated quantum materials, the interplay between electron and lattice dynamics represents another important research direction. In addition to Zhi-Xun Shen's successful demonstration of the combined tr-ARPES and UXRD method at SLAC, this paper also reports attempts to integrate UXRD with Resonant X-ray Emission Spectroscopy (RXES) for the simultaneous measurement of electronic and lattice dynamics.<br>Resonant Inelastic X-ray Scattering (RIXS) is a powerful tool for studying elementary and collective excitations in correlated quantum materials. However, in FEL-based soft X-ray spectroscopy, the wavefront tilt introduced by the widely used grating monochromators inevitably stretches the FEL pulses, which degrades the time resolution. Therefore, the new design at FEL beamlines employs low line density gratings with long exit arms to reduce pulse stretch and achieve relatively high energy resolution. For example, the Heisenberg-RIXS instrument at the European XFEL achieves an energy resolution of 92 meV at the Cu L₃ edge and approximately 150 fs time resolution.<br>In recent years, scientists at SwissFEL's Furka station have drawn inspiration from femtosecond optical covariance spectroscopy to propose a new method for generating two-dimensional time-resolved Resonant Inelastic X-ray Scattering (2D tr-RIXS) spectra. This method involves real-time detection of single-shot FEL incident and scattered spectra, followed by deconvolution calculation to avoid photon waste and wavefront tilt caused by monochromator slits. The SQS experimental station at European XFEL, in 2023, features a 1D-XUV spectrometer that utilizes subtle variations in photon energy absorption across the sample to induce spatial energy dispersion. Using Wolter mirrors, it directly images spatially resolved fluorescence emission from the sample onto the detector to generate 2D tr-RIXS spectra without the need for deconvolution. However, this design is limited to specific samples. Currently, the S3FEL is designing a novel 2D tr-RIXS instrument that uses an upstream low line density grating monochromator to generate spatial dispersion of the beam spot, allowing the full bandwidth of SASE to project spatially dispersed photon energy onto the sample. Subsequently, a similar optical design to the 1D-XUV spectrometer will be employed to achieve two-dimensional tr-RIXS spectra, thereby expanding the applicability beyond specific liquid samples. These new instruments are designed to minimize pulse elongation by fully utilizing SASE's full bandwidth, approaching Fourier-transform-limited RIXS spectra in both time and energy resolution.<br>Nonlinear X-ray optics techniques such as sum-frequency generation (SFG) and second-harmonic generation are being adapted for X-ray wavelengths, opening new avenues for probing elementary excitations. X-ray transient grating spectroscopy extends capabilities to study charge transport and spin dynamics on ultrafast timescales. The future developing of these scattering methods offer unique opportunities for probing dynamical events in a wide variety of systems, including surface and interface processes, chirality, nanoscale transport and the termed as multidimensional core-level spectroscopy.