Laser-driven resonant soft-X-ray scattering for probing picosecond dynamics of nanometre-scale order

TL;DR

The paper addresses the limited accessibility of time-resolved resonant soft-X-ray scattering for nanometre-scale order by developing a laboratory-based instrument powered by a laser-driven plasma source with a temporal resolution of $9\\mathrm{ps}$ and spectroscopic reach across transition-metal L-edges and rare-earth M-edges. It demonstrates the approach on a ferrimagnetic FeGd multilayer, delivering high-dynamic-range 2D SAXS data and extracting $M(t) \\propto \\sqrt{\\int I(q,t)\\,dq}$ alongside the peak position $q_{1st}$ to monitor domain dynamics under photoexcitation. The results reveal ultrafast demagnetisation followed by slower, thermally driven domain rearrangements and a complex, time-dependent peak shift that reflects lateral texture evolution and thermal gradients. This lab-scale platform enables flexible, multi-edge, multidimensional studies of emergent nanoscale order in complex materials under ultrafast stimuli, offering a practical alternative to beamline facilities and paving the way for higher flux and broader material classes in future investigations.

Abstract

X-ray scattering has been an indispensable tool in advancing our understanding of matter, from the first evidence of the crystal lattice to recent discoveries of nuclei's fastest dynamics. In addition to the lattice, ultrafast resonant elastic scattering of soft X-rays provides a sensitive probe of charge, spin, and orbital order with unparalleled nanometre spatial and femto- to picosecond temporal resolution. However, the full potential of this technique remains largely unexploited due to its high demand on the X-ray source. Only a selected number of instruments at large-scale facilities can deliver the required short-pulsed and wavelength-tunable radiation, rendering laboratory-scale experiments elusive so far. Here, we demonstrate time-resolved X-ray scattering with spectroscopic contrast at a laboratory-based instrument using the soft-X-ray radiation emitted from a laser-driven plasma source. Specifically, we investigate the photo-induced response of magnetic domains emerging in a ferrimagnetic heterostructure with 9$\,$ps temporal resolution. The achieved sensitivity allows for tracking the reorganisation of the domain network on pico- to nanosecond time scales in great detail. This instrumental development and experimental demonstration break new ground for studying material dynamics in a wide range of laterally ordered systems in a flexible laboratory environment.

Figures (4)

• Figure 1: Laboratory-based time-resolved SAXS experiment.a, Sketch of the laser-driven plasma source and the scattering setup. The SAXS pattern detected by a fast-readout area detector together with the direct beam is shown in panel d. b, Magnetic force microscopy image of the magnetic domain pattern in the FeGd multilayer. c,d, The time-resolved SAXS signal detected at the Gd M$_5$ absorption edge (1189 eV photon energy). The composite image in d shows the sum of detector frames taken before laser excitation ($t < \qty{0}{ps}$, left) and frames taken after laser excitation ($\qty{35}{ps} < t < \qty{685}{ps}$, right). For data analysis, the 2D detector frames are azimuthally integrated as shown in c. The 1st and 3rd order maxima of the scattering intensity are indicated in both panels.
• Figure 2: Results of the time-resolved resonant SAXS experiment following the laser-driven dynamics of magnetic domains in the FeGd multilayer.a, The $q$-dependent, transient SAXS intensity, $I(q, t)$, at the Fe L$_3$ absorption edge at an incident fluence of 25mJ cm. Data are averaged for three selected delay intervals A, B, and C as indicated by shaded areas in panel b and then fitted by a $\Gamma$-distribution (lines). The grey dashed line indicates the peak position before photoexcitation. b, Extracted magnetisation and relative peak shift in dependence of pump--probe delay. Data are fitted by the sum of three exponential functions to extract the relevant time scales (lines). c, Differences of the SAXS intensities, $I(q, t)$, for better visualisation of the peak shift. The data and fits from panel a are normalised by their respective peak intensities before subtracting the data before photoexcitation (A) from the data at positive peak shift (B, blue) and negative peak shift (C, red). Markers refer to differences of the experimental data, and lines refer to the differences of the fits. Data points were additionally smoothed by a running average. d,e, Delay scans of the transient magnetisation, $M(t)$, probed at the two absorption edges Fe L$_3$ (d) and Gd M$_5$ (e) for a series of excitation fluences. The data is fitted by a double-exponential function to extract the relevant time scales. All error bars correspond to the statistical standard error of the mean.
• Figure E1: One-dimensional heat diffusion simulation after laser excitation of the investigated FeGd heterostructure. Details of the simulations are described in the Method section. Values for the electronic and phononic thermal conductivities of FeGd are taken from Ref. Hopkins2012. a, Time-dependent temperature distribution within the entire sample (cap layer, magnetic multilayer, SiN substrate, Al heat sink). The vertical solid grey lines indicate the top and bottom of the actual magnetic multilayer, and the vertical dashed grey line its centre dividing the layer in a "top" and "bottom" part (see panel c). b, Line-outs of the spatial temperature distribution for different pump-probe delays $t$ as indicated. c, Average temperature of different regions of the sample heterostructure as function of the pump-probe delay $t$.
• Figure E2: Hysteresis scan of the investigated FeGd heterostructure. The black arrows indicate the scan direction of the applied magnetic field, $B$. a, Magneto-optical Kerr-effect (MOKE) measurement of the net out-of-plane magnetisation. In remanence, no net magnetisation is detectable as the contributions from oppositely magnetised domains cancel out. At larger fields ($B > \qty{75}{mT}$) all domains align parallel into ferromagnetic saturation. b, The SAXS peak intensity at the Fe L$_3$ absorption edge exhibits maximum contrast approximately in remanence. The scattering intensity vanishes at high fields when the domain structure disappears in ferromagnetic saturation.