Magnons are quantized collective excitations of long-range ordered spins. At nanometre wavelengths, exchange interactions increasingly govern their dynamics, giving rise to a largely unexplored regime of couplings between magnons and other quasi-particles; however, detecting such short-wavelength spin waves has remained a key experimental challenge. Here we introduce magnon momentum microscopy-a quasi-elastic, resonant magnetic soft-X-ray scattering technique that directly images magnon populations across two-dimensional momentum space. Owing to its remarkable sensitivity, it can capture nonlinear magnon interactions over large regions of the dispersion plane. We apply magnon momentum microscopy to the prototypical magnonic material yttrium iron garnet and reveal a rich variety of previously unobserved nonlinear magnon interactions. With its element specificity and bulk sensitivity, as well as intrinsic access to nanometre-scale wavelengths without frequency limitation, this technique establishes a powerful and versatile platform for exploring short-wavelength and nonlinear magnonics.

When the dimensions of structures shrink to the order of the inelastic mean free path of the energy-carrying quasi-particles, the character of energy transport changes from diffusive to ballistic. However, the point of transition remains a matter of debate. Here, we leverage the fluence-dependent transport efficiency to distinguish ballistic and diffusive electron transport in an approach not relying on the transport velocity. We follow the energy that is rapidly transferred across Cu layers of different thicknesses via hot electrons from a photo-excited Pt layer into a buried Ni detection layer. In the Ni layer, the transported energy linearly relates to a rapid lattice expansion, which we probe via ultrafast x-ray diffraction. A nonlinear dependence of the Ni strain amplitude on the absorbed laser fluence indicates that the transport through Cu becomes more efficient with increasing fluence, which is inconsistent with a ballistic scenario but reproduced by a diffusive energy transport model. We already identify that for a Cu thickness of about 50 nm, i.e., about twice the electronic inelastic mean free path, diffusive electronic energy transport dominates the spatial energy distribution. Our experimental approach is generally applicable to distinguish diffusion from ballistic energy transport.

The nature of the melting transition in two-dimensional systems of particles has attracted considerable research attention since the development of Kosterlitz-Thouless-Halperin-Nelson-Young theory. The hexatic phase proposed by this theory has been recently identified experimentally in ensembles of magnetic skyrmions, quasiparticles formed in a magnetically ordered crystal. Here, we use quasiparticle dynamical simulations to study how the anisotropy of the skyrmion-skyrmion interactions induced by the atomic lattice influences the melting transition. For isotropic interactions, we find a transition from a solid phase through a hexatic phase stable in a narrow temperature range to an isotropic liquid phase. However, if the interactions between skyrmions are forced to be anisotropic by the atomic lattice, then a direct solid-liquid transition can be observed with orientational order persisting up to temperatures of 30 K in the liquid phase.

Ultrafast control of lattice motion in metals is a central challenge for high-frequency strain engineering and spintronic applications. Coherent strain control at terahertz (THz) frequencies in metals has remained elusive because free electrons are expected to delocalize energy beyond the optical penetration depth, preventing rapid and efficient stress generation. Here we show that robust and cost-effective metal-metal superlattices (SLs), where periodic repetitions of bilayers - each layer a few atoms thick - are deposited by sputtering, constitute thermoacoustic metamaterials that overcome this limitation. We combine femtosecond X-ray diffraction with mode-resolved density-functional theory and two-temperature modeling to show that electron pressure, rather than phonon stress, drives a large-amplitude coherent terahertz (1 THz) lattice oscillation in sputtered Pt/Cu superlattices. We establish electron pressure as an engineerable, dominant actuation mechanism in metallic metamaterials which can be tailored by the pitch and the constituent materials of the sputtered SL structure, enabling applications such as ultrafast strain-mediated antiferromagnetic spintronic devices.

Coherent acoustic phonons, whose damping sets the upper bound of quality factors in acoustic resonators, play a critical role in advanced telecommunication and quantum information technologies. Yet, probing their decay in the GHz regime remains challenging using conventional surface-based techniques. Dark-field X-ray microscopy (DFXM) offers a solution by enabling through-depth, non-destructive and full-field imaging of strain fields and dislocations inside bulk materials with high spatial and angular resolution. We previously used kinematic diffraction theory to describe DFXM signals based on how the Bragg peak shifts due to the strain wave, allowing us to reconstruct the frequency spectrum of coherent phonons as a function of depth through the sample. The approach of tracking the Bragg peak shifts to study phonon dynamics, however, places an upper-bound to the highest phonon frequency that can be studied, determined by the spatial resolution of the measurement. In this work, we discuss how coherent phonon dynamics can be studied with DFXM from time-dependent intensity oscillation sidebands. This approach simultaneously allows studying coherent phonon dynamics in real and reciprocal space, overcoming frequency resolution limits imposed by the real-space resolution of Bragg-peak tracking. Using Takagi-Taupin dynamical diffraction formalism, we establish the spatial and reciprocal space resolution achievable for studying the coherent phonon dynamics and evaluate conditions for observing long-lived intensity oscillations. We close by proposing experimental strategies to optimize excitation bandwidths and reciprocal-space selectivity. The formalism in the paper enables the design of DFXM experiments for quantitative, frequency-resolved measurements of acoustic phonon decay and phonon-defect interactions in bulk crystalline materials.

We performed time-resolved x-ray resonant magnetic reflectivity measurements on a laser-excited ferromagnetic Fe thin film to simultaneously probe the transient structural and magnetic depth profiles with nanometer spatial and femtosecond temporal resolution. Our results show that during the first picoseconds after optical excitation, the magnetization of the Fe layer is strongly inhomogeneous, especially in the vicinity of the buried interface. By comparing our experimental results to predictions based on the microscopic three-temperature model and simulations of laser-induced spin-currents, we demonstrate that local and non-local angular momentum transfer phenomena take place simultaneously. After a few picoseconds, the magnetization relaxes back to equilibrium while the total thin film thickness starts oscillating periodically, with a maximum dilation of approximately 1.3

Light-induced magnetisation switching is one of the most intriguing and promising areas where an ultrafast phenomenon can be utilised in technological applications. So far, experiment and theory have considered the origin of all-optical helicity-independent magnetisation switching (AO-HIS) in individual magnetic films only as a microscopically local, thermally-driven process of angular momentum transfer between different subsystems. Here, we demonstrate that this local picture is insufficient and that AO-HIS must also be regarded as a spatially inhomogeneous process along the depth within a few-nanometre thin magnetic layer. Two regions of opposite magnetisation directions are observed, separated by a highly mobile boundary, which propagates along the depth of a 9.4 nm thin Gd25Co75 alloy. The dynamics of this transient boundary determines the final magnetisation state as well as the speed of AO-HIS throughout the entire magnetic layer. The ability to understand the influence of nanoscale and transient inhomogeneities on ultrafast switching phenomena and more generally on phase transitions will open new routes for material design and excitation scenarios in future devices for transferring and storing information.

Magnons represent quantised collective motions of long-range ordered spins. For wavelength below 100 nm, exchange interactions dominate their physics, which gives rise to a so far unexplored regime of nonlinearities and couplings between magnons and other quasiparticles. Besides their selective excitation, also the detection of such short-wavelength spin waves remains a challenge of current research and technology. Here, we probe the intensity and wave vector of magnons by means of quasi-elastic, resonant soft-X-ray scattering. This Magnon Momentum Microscopy (MMM) can access magnons directly in momentum space with remarkable sensitivity and high photon efficiency up to THz frequencies and down to few-nanometre wavelengths. The two-dimensional information obtained by this light-scattering-based technique is especially valuable for studying the nonlinear interactions of exchange-dominated magnons within technologically relevant thin-film samples. In doing so, we uncover a rich variety of deeply nonlinear magnon interactions, highlighting their potential for applications in novel computing schemes. With its intrinsic element-selectivity and ability to probe also buried layers, soft-X-ray MMM has the potential to establish itself as an advanced tool for ultrabroadband studies of short-wavelength magnonics.

The delayed demagnetization in Ni relative to Fe in the ultrafast demagnetization studies in FeNi alloy has led to two competing theoretical explanations: The Inhomogeneous Magnon Generation (IMG) and the Optically Induced Spin Transfer (OISTR) model. The IMG attributes the delay to the preferential magnon generation at the Fe sites and its subsequent propagation to Ni, while OISTR proposes direct spin transfer from Ni to Fe. In this study, we employ element-resolved extreme ultraviolet spectroscopy to investigate the effect of excitation strength on this delay, aiming to resolve the controversy. The data indicate a significant reduction in the delay with increasing fluence, which is inconsistent with the theoretical predictions of OISTR. These findings, in conjunction with the observation of a saturation of Fe demagnetization at the onset of Ni demagnetization, indicate that a spin-wave instability within the IMG framework may provide a potential explanation for the experimental results.

Using time-resolved X-ray magnetic linear dichroism in reflection, we provide a direct probe of the Néel vector dynamics in TmFeO_3 on a ultrafast timescale. Our measurements reveal that, following optical excitation, the Néel vector undergoes a spin reorientation transition primarily within the a-c plane, completing a full 90 rotation within approximately 20 ps. This study highlights the ability to probe dynamics of antiferromagnets at its intrinsic timescale in reflection geometry, paving the way for investigations of a wide range of antiferromagnets grown on application relevant substrates.

Phase transitions are governed by both intrinsic and extrinsic heterogeneities, yet capturing their spatio-temporal dynamics remains a challenge. While ultrafast techniques track phase changes on femtosecond timescales, the spatial complexity and stochastic nature of the processes often remain hidden. Here, we present an experimental approach that combines well-established ultrafast hard-X-ray diffraction with a propagating strain pulse as a universal and non-invasive probe. This ultrafast X-ray sonography can capture the spatio-temporal phase heterogeneity in great detail by resolving the phase-specific strain response. We apply this approach to the antiferromagnetic-to-ferromagnetic magneto-structural phase transition in FeRh and identify the ferromagnetic phase to nucleate at the surface as narrow columnar domains of approximately 30 nm diameter. Besides reconciling the diverse experimental results in the literature on FeRh, X-ray sonography offers a versatile platform for investigating a wide range of phase transitions accompanied by structural changes.

The delayed demagnetization in Ni relative to Fe in the ultrafast demagnetization studies in FeNi alloy has led to two competing theoretical explanations: The Inhomogeneous Magnon Generation (IMG) and the Optically Induced Spin Transfer (OISTR) model. The IMG attributes the delay to the preferential magnon generation at the Fe sites and its subsequent propagation to Ni, while OISTR proposes direct spin transfer from Ni to Fe. In this study, we employ element-resolved extreme ultraviolet spectroscopy to investigate the effect of excitation strength on this delay, aiming to resolve the controversy. The data indicate a significant reduction in the delay with increasing fluence, which is inconsistent with the theoretical predictions of OISTR. These findings, in conjunction with the observation of a saturation of Fe demagnetization at the onset of Ni demagnetization, indicate that a spin-wave instability within the IMG framework may provide a potential explanation for the experimental results.

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 FeGd 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.

The development of spectroscopic techniques in the extreme ultraviolet (XUV) spectral range has significantly advanced the understanding of ultrafast interactions in magnetic systems triggered by optical excitation. In this work, we introduce a previously missing geometry that facilitates the observation of the ultrafast magnetization dynamics of magnetic systems with an out-of-plane magnetization grown on XUV opaque substrates. This approach to probing ultrafast magnetization dynamics combines the magneto-optical Kerr effect with the strong dependence of a sample's reflectance near its Brewster angle. It therefore works with linearly polarized light and does not require any additional polarizing optics. We provide a comprehensive analysis of the technique by presenting both simulations and experimental data as a function of the energy and the polarization of the XUV probe radiation as well as of the delay time after optical excitation.

The delayed demagnetization in Ni relative to Fe in the ultrafast demagnetization studies in FeNi alloy has led to two competing theoretical explanations: The Inhomogeneous Magnon Generation (IMG) and the Optically Induced Spin Transfer (OISTR) model. The IMG attributes the delay to the preferential magnon generation at the Fe sites and its subsequent propagation to Ni, while OISTR proposes direct spin transfer from Ni to Fe. In this study, we employ element-resolved extreme ultraviolet spectroscopy to investigate the effect of excitation strength on this delay, aiming to resolve the controversy. The data indicate a significant reduction in the delay with increasing fluence, which is inconsistent with the theoretical predictions of OISTR. These findings, in conjunction with the observation of a saturation of Fe demagnetization at the onset of Ni demagnetization, indicate that a spin-wave instability within the IMG framework may provide a potential explanation for the experimental results.

Time-resolved soft-x-ray-diffraction experiments give access to microscopic processes in a broad range of solid-state materials by probing ultrafast dynamics of ordering phenomena. While laboratory-based high-harmonic generation (HHG) light sources provide the required photon energies, their limited photon flux is distributed over a wide spectral range, rendering typical monochromatic diffraction schemes challenging. Here, we present a scheme for energy-dispersive soft-x-ray diffraction with femtosecond temporal resolution and photon energies across the water window from 200 to 600 eV. The experiment utilizes the broadband nature of the HHG emission to efficiently probe large slices in reciprocal space. As a proof-of-concept, we study the laser-induced structural dynamics of a Mo/Si superlattice in an ultrafast, non-resonant soft-x-ray diffraction experiment. We extract the underlying strain dynamics from the measured shift of its first order superlattice Bragg peak in reciprocal space at photon energies around 500 eV via soft-x-ray scattering simulations.

The advent of free electron lasers has opened the opportunity to explore interactions between extreme ultraviolet (EUV) photons and collective excitations in solids. While EUV transient grating spectroscopy, a noncollinear four-wave mixing technique, has already been applied to probe coherent phonons, the potential of EUV radiation for studying nanoscale spin waves has not been harnessed. Here we report EUV transient grating experiments with coherent magnons in Fe/Gd ferrimagnetic multilayers. Magnons with tens of nanometers wavelengths are excited by a pair of femtosecond EUV pulses and detected via diffraction of a probe pulse tuned to an absorption edge of Gd. The results unlock the potential of nonlinear EUV spectroscopy for studying magnons and provide a tool for exploring spin waves in a wave vector range not accessible by established inelastic scattering techniques.

Skyrmions are localized, topological spin structures that can be described as quasiparticles. Skyrmions in thin films are an ideal model system to study Brownian motion and lattice formation in two dimensions. They follow an equation of motion, the Thiele equation, which includes a topology-dependent chiral term, linear in velocity, causing a skyrmion Hall effect and a drastic reduction of the diffusion coefficient for individual skyrmions, as compared to normal Brownian particles. Using Brownian dynamics simulations, we show that this topological suppression of the diffusion can be partially lifted in two-dimensional lattices of skyrmions. Counterintuitively, this causes enhanced diffusive properties with increasing particle density, similar to odd-diffusive Brownian particles. We show how the topological charge of the skyrmions influences the dynamics of topological lattice defects, which also affects the dynamics of the phase formation.

Ultrafast transverse magneto -optical Kerr effect (T-MOKE) spectroscopy in the extreme ultraviolet spectral range provides element -specific information about the magnetization dynamics of complex magnetic structures. However, the relationship between the T-MOKE observable, denoted magnetic asymmetry , and the magnetization of a sample can exhibit significant nonlinearities, even in the case of magnetization changes that are homogeneous along the depth of the sample and without considering any nonequilibrium spin dynamics. Here, we combine static and time -resolved experimental data with simulations based on a wave propagation algorithm for a prototypical magnetic heterostructure that exhibits pronounced deviations from a linear relationship between magnetic asymmetry and magnetization, including increasing values of asymmetry in spite of a reducing magnetization. As an outlook, we describe sample structures and experimental geometries for which a linear response of the T-MOKE observable remains a valid approximation.