Time-resolved magnetic soft-X-ray spectroscopy
We investigate a typical nanometre-scale heterostructure consisting of an amorphous ferrimagnetic Gd25Co75 alloy with in-plane magnetic anisotropy, which exhibits deterministic picosecond AO-HIS induced by single laser pulses21. The thin Gd25Co75 layer (thickness 9.4 nm) is deposited on a Si substrate via magnetron sputtering, seeded at the bottom by a Ta layer (3.6 nm) and capped at the top with Cu (1.6 nm) and Pt (2.8 nm) to prevent oxidation of the ferrimagnetic film. For the studied Gd25Co75 alloy, the ferrimagnetic compensation point is above room temperature, where all measurements were carried out.
We enable an ultrafast and element-selective view on the dominant Gd sublattice magnetisation by femtosecond transverse magneto-optical Kerr effect (TMOKE) spectroscopy in the soft-X-ray spectral range. The experimental concept is illustrated in Fig. 1, combining a ϑ–2ϑ reflectometry and spectroscopy setup (see panel a) in a pump–probe scheme. The Gd sublattice magnetisation is probed around the Gd N5,4 resonance at ≈ 148 eV photon energy under an incidence angle of ϑ = 20°, using ≤ 27 fs (full width at half maximum; FWHM) short, broadband soft-X-ray pulses generated by a laboratory high-harmonic generation (HHG)-based light source22,23. The transient switching dynamics are excited by 27 fs (FWHM) short infrared (IR) pulses at 2.1 μm wavelength and probed by the magnetic asymmetry, i.e., the normalised difference of two spectra recorded for opposite directions of a saturating in-plane magnetic field applied to the sample (Fig. 1b).
Fig. 1: Experimental concept.
a Schematic of the employed pump–probe technique. The all-optical helicity-independent magnetisation switching (AO-HIS) of an in-plane magnetised Gd25Co75 sample is driven by 27 fs (FWHM) short infrared (IR) laser pulses of 2.1 μm wavelength. The dynamics are probed at the Gd N5,4 resonance by broadband transverse magneto-optical Kerr effect (TMOKE) spectroscopy, employing ≤ 27 fs (FWHM) short soft-X-ray pulses emitted by a high-harmonic generation (HHG) light source. Magnetic contrast is achieved by flipping a saturating in-plane magnetic field B↑,↓ applied to the sample perpendicular to the p-polarisation axis of the probing soft X-rays, recording two spectra I↑,↓ for opposite magnetisation directions (see inset). b The magnetic asymmetry, corresponding to (I↑ − I↓)/(I↑ + I↓), is recorded as a function of pump–probe delay. Due to wavelength-dependent probing depths in the vicinity of the atomic resonance, the spectra are sensitive to spatially inhomogeneous magnetisation dynamics along the depth of the Gd25Co75 layer, leading to peak shifts and non-uniform changes of the asymmetry. c Fitting the time-resolved spectra with magnetic scattering simulations enables the determination of the transient magnetisation distribution within the Gd25Co75 layer, linking ultrafast changes in the spectra to spatial changes of the depth profile.
Due to the distinct change of the complex refractive index along the Gd N5,4 resonance in conjunction with interlayer reflection and interference effects, the soft-X-ray reflectivity and attenuation length vary strongly as a function of photon energy. The resulting variation of the probing depth along the resonance leads to a strong sensitivity of the asymmetry spectra to both the structural properties of the individual layers, i.e., their thickness, density, and roughness, as well as to the magnetisation distribution within the Gd25Co75 layer20,24. Fitting the transient asymmetry spectra with calibrated magnetic scattering simulations25,26, therefore, allows determination of the transient magnetisation depth profiles (Fig. 1c). The broadband probing of the Gd N5,4 resonance at a fixed angle of incidence enables capturing highly correlated spectral changes in a single, short acquisition. Moreover, it ensures constant excitation conditions, as the angle at which the IR pulses impinge on the sample remains unchanged during the entire experiment.
The recorded evolution of the magnetic asymmetry at the Gd N5,4 resonance upon IR excitation is shown in Fig. 2, comparing the dynamics induced for different incident excitation fluences. The two depicted data sets for fluences of 5.0 and 6.0 mJ/cm2 are recorded slightly below and above the threshold fluence required for a full reversal of the Gd25Co75 layer magnetisation.
Fig. 2: Time-resolved magnetic soft-X-ray spectroscopy.
a Transient transverse magneto-optical Kerr effect (TMOKE) asymmetry (colour map) recorded at the Gd N5,4 resonance under an incidence angle of ϑ = 20° as a function of pump–probe delay, comparing excitation below (5.0 mJ/cm2) and above (6.0 mJ/cm2) the threshold fluence for all-optical helicity-independent magnetisation switching (AO-HIS). For long delay times, the return to the initial unswitched state is obvious from the asymmetry spectrum for 5.0 mJ/cm2 excitation, while switching to a state with reversed asymmetry occurs when the excitation fluence is raised to 6.0 mJ/cm2. b Normalised asymmetry time traces were obtained by integrating the time-resolved spectra over different regions of interest (ROIs) around the main resonance peak. The different colours correspond to the ROIs as indicated by the inset. The strong spectral dependence of the TMOKE observable causes transient differences of up to ≈ 80% normalised to the unpumped equilibrium state and even partial sign reversal of the spectrum (compare ROI 1 and 3 for 5.0 mJ/cm2 excitation). The error bars are calculated from the standard error of the mean.
For both excitation fluences, the time-resolved data show a non-uniform change of the magnetic asymmetry along the Gd N5,4 resonance. Irrespective of whether the final state is switched or not, the asymmetry starts to gradually reverse from higher to lower photon energies on time scales ≥ 1 ps after excitation, see Fig. 2a. In the case of full switching (6.0 mJ/cm2 excitation), the sign reversal of the entire spectrum is completed within a few picoseconds, whereas in the non-switching case (5.0 mJ/cm2 excitation), the reversed part of the spectrum begins to relax back to the initial direction at ≈ 4.5 ps.
Integrating the magnetic asymmetry over different spectral regions around the main resonance peak (ROIs 1–3 in Fig. 2b) reveals the high sensitivity of the TMOKE spectra to the probing soft-X-ray photon energy27,28. Due to the wavelength-dependent absorption length of the TMOKE observable, this is a clear indication of spatially inhomogeneous dynamics evolving along the depth of the magnetic layer20, pointing at either partial or propagating AOS.
Transient magnetisation depth profiles
In order to quantitatively relate the observed spectral changes of the asymmetry to spatial changes in the magnetisation depth profile of the Gd25Co75 layer, the time-resolved TMOKE data is analysed via magnetic scattering simulations25,26. The results of this analysis are presented in Fig. 3 for selected delays before and after excitation.
Fig. 3: Determination of the magnetisation depth profiles from the time-resolved transverse magneto-optical Kerr effect (TMOKE) data.
a Experimentally recorded (dots) and fitted (lines) asymmetry spectra for selected pump–probe delays. The data was fitted by varying the magnetisation distribution within the Gd25Co75 layer. b Resulting magnetisation depth profiles for the respective excitation fluence and pump–probe delay. The black dashed line corresponds to the unpumped profile (−1.0 ps) scaled to the same average magnetisation value as the profile recorded at 0.5 ps.
Already before the pump pulse excites the sample (−1.0 ps), the fit converges for a non-uniform distribution of magnetisation within the Gd25Co75 layer, slightly decreasing towards the neighbouring Cu and Ta layers. This observation can be attributed to effects like interlayer diffusion, reducing the magnetisation at the interfaces with other non-magnetic materials29,30. Furthermore, static heating induced by the repetitive absorption of the pump radiation also affects the magnetisation of the unpumped state, which is particularly apparent by the fluence-dependent decrease towards the Cu interface.
For both excitation fluences and within the experimental uncertainty, the data shows that up to 0.5 ps after excitation, the Gd25Co75 layer demagnetises mostly homogeneously along the depth-axis, leading to a uniform change of the magnetisation profile relative to the unpumped state at −1.0 ps, where essentially no new magnetisation gradients are introduced (see dashed line in Fig. 3b). This is reasonable, as the simulated absorption profile of the 2.1 μm pump radiation predicts only a slight optical excitation gradient within the Gd25Co75 layer itself (see inset of Supplementary Fig. 8b). At later times, however, the pump-induced change becomes strongly inhomogeneous, tilting the depth profile towards the top Cu interface. At this point in space, the magnetisation is completely quenched and subsequently reverses its sign.
The complete data set, evaluating the depth-resolved dynamics over the full range of pump–probe delays scanned in the experiment, is shown in Fig. 4. For a quantitative comparison of the dynamics occurring at the top, centre, and bottom of the Gd25Co75 layer, the magnetisation was spatially integrated over 1 nm-sized slices as indicated in Fig. 4a and normalised to the unpumped state before excitation, leading to the magnetisation time traces shown in Fig. 4b. On time scales > 0.5 ps, the depth-dependent dynamics lead to the formation of a highly inhomogeneous magnetisation profile, transiently dividing the 9.4 nm thin Gd25Co75 layer into domain-like regions magnetised in opposite directions at the top and the bottom of the thin film (red and blue colours in Fig. 4a). This bipolar state lasts for in total ≈ 4.5 ps (grey-shaded area in Fig. 4b), during which the region with opposite magnetisation direction starts to grow, corresponding to the propagation of the domain wall-like boundary between the two regions from the top towards the bottom of the magnetic layer. Depending on the excitation fluence, it either expands over the entire Gd25Co75 depth or relaxes back towards the initial unpumped direction (see Supplementary Movie 1 for an animation of the depth dynamics for the two fluences).
Fig. 4: Depth-resolved magnetisation dynamics.
a Transient magnetisation distribution (colour map) within the Gd25Co75 layer as a function of pump–probe delay. The white area corresponds to zero magnetisation, i.e., a transient boundary between the two regions with opposite magnetisation directions. b Spatially integrated and normalised magnetisation time traces, comparing the dynamics within 1 nm thin regions at the top, centre, and bottom of the Gd25Co75 layer as indicated in (a). The grey-shaded area corresponds to the time interval during which the layer is transiently split into oppositely magnetised domain-like regions at the top and the bottom of the magnetic film.
Intriguingly, the switching dynamics of the top 1 nm region appear to be identical for both excitation fluences within the first 3 ps after excitation, irrespective of the final outcome of the entire film being switched or not switched. This observation indicates that already for 5.0 mJ/cm2 excitation, which does not lead to a complete reversal of the Gd25Co75 layer, the switching threshold is nevertheless initially overcome within this confined surface-near region, resulting in early AOS dynamics that do not gain further amplitude and speed by increasing the excitation strength.
In contrast, the dynamics observed at the centre and bottom of the layer show a clear fluence-dependence on the same time scale (≤ 3 ps), with the demagnetisation scaling with the fluence, i.e., depending on the energy deposited into the magnetic layer. This suggests that after the initial ultrafast demagnetisation and partial reversal at the top, the thermal state as well as the remanent magnetisation in the not yet reversed part of the Gd25Co75 layer are crucial for whether the switched domain can further grow into the depth or is quenched again. Accordingly, the dynamics in the bottom slice shows a clear two-step behaviour in the case of 6.0 mJ/cm2 excitation, allowing the determination of the time needed for the reversed domain to expand over the entire depth (9.4 nm) of the layer, which according to Fig. 4b is of the order of ≈ 4.5 ps, indicating an average velocity of the domain boundary of ≈ 2000 m/s.
Tracing the origin of magnetisation switching
To further disentangle the fluence- and depth-dependence of the AO-HIS, the magnetisation depth profiling was carried out for a wide range of excitation fluences while keeping the pump–probe delay fixed at different times after excitation (Fig. 5a and Supplementary Fig. 4). The depth profiles recorded at late times (20 ps) exhibit simply a homogeneous transition from below to above the threshold fluence for AO-HIS (Fsw). In stark contrast, the data recorded at an earlier delay of 3 ps shows a strongly fluence-dependent formation of spatially inhomogeneous switching dynamics, starting already at 4 mJ/cm2, for which the surface-near region starts to transiently reverse. Again, a closer inspection of the magnetisation amplitudes at the early delay reveals that after the switching threshold is locally overcome at a certain depth within the top, surface-near region, the switching amplitude at this point in time gets saturated at ≈ −15% and does not further increase as a function of excitation fluence. Instead, increasing the fluence only leads to the initially switched region (≈ −15% amplitude at 3 ps) reaching further into the depth of the Gd25Co75 layer. By increasing the excitation fluence, more volume of the Gd25Co75 layer is driven into the direct laser-driven regime of AO-HIS, where the switching dynamics occur homogeneously within this region due to the local inter-sublattice angular momentum transfer as proposed by established theoretical models.
Fig. 5: Fluence-dependence and phenomenological picture of the propagating all-optical helicity-independent magnetisation switching (AO-HIS).
a Fluence-dependence of the transient magnetisation distribution (colour map) within the Gd25Co75 layer, comparing different times after excitation. The magnetisation depth profiles are obtained by fitting transient transverse magneto-optical Kerr effect (TMOKE) spectroscopy data recorded at fixed pump–probe delays (3 and 20 ps) as a function of excitation fluence (2.0 to 7.0 mJ/cm2). The dashed green line indicates the threshold fluence Fsw = 5.5 mJ/cm2, which is required for a full reversal of the Gd25Co75 layer magnetisation. b Schematic of the growth of a domain-like directly-switched region (left, blue) into the depth of the sample (right, red). The sublattice magnetisation of Co and Gd atoms is sketched by the green and orange curves. Exchange between Co and Gd, as well as between Gd–Gd and Co–Co at the propagating boundary between switched and unswitched regions, is indicated by arrows. The coloured wedge symbolises the quasi-static temperature gradient from hot (white/yellow) to cold (red/black) as calculated from the diffusive two-temperature model (2TM).
The initial formation of the switched region at the top of the layer can thus be understood by the material- and layer-dependence of the optical excitation within the heterostructure, with the largest amount of energy deposited in the Pt capping layer (see inset of Supplementary Fig. 8b). The strongly excited Pt layer acts as an effective source of heat and hot electrons, causing an additional indirect excitation reaching the Gd25Co75 layer from the top due to heat diffusion and ballistic electron transport across the highly conductive Cu layer31. Such hot electron pulses are known to induce ultrafast switching in GdFeCo-based heterostructures, even when the highly conductive spacer layer is thick enough to prevent direct optical excitation of the magnetic film32,33. Note that this observation is also in line with earlier depth-resolved studies on the ultrafast demagnetisation of a GdFe-based system, which have revealed that the strong absorption in Pt can even lead to an enhanced demagnetisation at the bottom of the magnetic film, when the Pt is used as a seed instead of a capping layer20. It further demonstrates how strongly the dynamics of the magnetic layer can be influenced by the heterostructure design, in particular, the choice of the surrounding layers, which also opens a potential route for tuning, e.g., directionality and energy efficiency of the switching.
In theory, the excitation fluence could be increased until the entire depth of the layer is directly driven into the AO-HIS regime. In reality, the slight gradient in optical excitation of the Gd25Co75 layer itself, in combination with the highly absorbing Pt layer, leads to an excessive heat load at the surface of the magnetic layer, degrading the sample when it is exposed to fluences above 6.0 mJ/cm2 for a prolonged period of time. Hence, the full, persistent switching of the entire film, observed above the clearly visible threshold fluence of 5.5 mJ/cm2 (Fsw), can only be achieved via a second, non-local process, which drives the boundary between the two magnetic regions towards the bottom of the magnetic layer.
To better understand the nature of this non-local switching mechanism, we will now discuss the role of different phenomena that can potentially lead to the propagation of the AO-HIS switching boundary into the depth of the magnetic layer.
Diffusive two-temperature model (2TM) simulations25 predict the electronic and phononic heat baths to be almost fully equilibrated already after ≈ 2 ps (see Supplementary Fig. 8). Furthermore, at the time when the bottom of the Gd25Co75 layer starts to reverse its magnetisation (> 3 ps in Fig. 4b), the temperatures are already decreasing within this region due to efficient heat dissipation into the Si substrate. Hence, the simulations suggest that picosecond heat transport along the depth of the heterostructure is not able to drive the lower regions of the Gd25Co75 layer into the AO-HIS regime via thermal demagnetisation and, therefore, cannot explain the delayed onset of the switching observed within this region.
Instead, the continuous heat dissipation into the Si substrate leads to the formation of a long-lived thermal gradient of 10–30 K between the hotter surface-near region and the colder bottom of the Gd25Co75 layer (determined at the boundaries of the grey-shaded area in Supplementary Fig. 8), persisting throughout the time interval in which the switched region expands. Such temperature gradients are known to cause a thermally-driven domain wall motion, either due to spin or magnon currents generated by the spin Seebeck effect34,35 or to maximise the domain wall entropy36,37, playing a crucial role in multiple-pulse induced AOS observed in ferromagnetic thin films and multilayers38,39. In case of ferrimagnets, the direction of the domain wall motion has been predicted to depend on whether the temperature of the material is below or above the angular momentum compensation point (Tcomp) of the two magnetic sublattices, driving the domain wall either towards the colder or hotter regions, respectively40. Although this mechanism could possibly explain the fluence-dependent propagation of the observed boundary, where direction and velocity depend on the depth-dependent temperatures transiently reached after electron-phonon thermalisation, its role in view of the highly non-equilibrium energy and heat distribution on femto- to picosecond time scales needs to be further investigated.
Spatially inhomogeneous AO-HIS dynamics have also been theoretically predicted in synthetic ferrimagnets, namely, Co/Gd bilayers41. Here, the proposed mechanism is based on exchange scattering across neighbouring atomic layers. This would lead to the nucleation of a front of reversed Co magnetisation at a Co/Gd interface, which can subsequently propagate away from the interface through the Co layer in a few picoseconds and over several nanometres. The exchange scattering with nearest neighbours enables AO-HIS far away from the compensation point of the total bilayer at a comparable speed (≈ 1000 m/s, obtained from Fig. 3 of ref. 41 assuming a Co monolayer thickness of 0.2 nm) as observed in our experiment (≈ 2000 m/s). The proposed mechanism, however, does involve an initial complete demagnetisation of the entire Co layer induced by the direct optical excitation. In contrast, our experimental results reveal a sizeable magnetisation of the Gd sublattice in the lower, not directly-switched region of the Gd25Co75 layer, see Fig. 5b, requiring the switching mechanism to overcome a large magnitude of remanent magnetisation.
The propagation speed of the observed boundary (≈ 2000 m/s) thereby lies within the top range of the fastest velocities of domain wall motion that have so far been realised experimentally in ferrimagnetic GdCo and GdFeCo wires, driven by current-induced SOT when the RE and TM sublattices are close to angular momentum compensation (≈ 1300–2000 m/s)42,43. This suggests that the reduced net magnetisation and increased domain wall velocity in the vicinity of the ferrimagnetic compensation point might play a decisive role in the second, non-local switching mechanism, facilitating an efficient growth of the switched region over the entire depth of the layer.
Our results show that even in sub-10 nm thin alloy films embedded into a typical nanolayered heterostructure, the combination of local and non-local processes is essential for achieving complete AO-HIS. We find that asymmetric excitation conditions can drive parts of the ferrimagnetic layer into direct switching, but in other regions, the laser-driven demagnetisation is not sufficient to enter the narrow transient regime for AO-HIS. Instead, a switching front travelling into the depth of the material is crucial to achieve complete AO-HIS under suitable conditions. While thermal gradients are present, we rule out simple heat transport into the depth of the film as the essence of the switching mechanism, based on the observed time scale of the switching front propagation. Nevertheless, the thermal gradients and additional channels for exchange at the boundary between switched and unswitched regions, see Fig. 5b, provide a key ingredient for alternative, propagation-based microscopic mechanisms. While they are present on the relevant picosecond time and nanometre length scales, their actual influence on the switching process needs to be clarified in future studies, including a theoretical treatment. To this end, the variation of the stacking sequence, the capping and seed layer materials, as well as the composition and thickness of the magnetic film, will enable direct control over the layer-dependent absorption and, accordingly, the formation, size, and direction of excitation gradients and related transport phenomena. Hence, a systematic investigation of AO-HIS for well-considered heterostructure designs will shed light on the conditions under which non-local, propagation-based switching can be observed, as well as on the actual mechanism driving the propagation of the transient boundary. Disentangling longitudinal and transverse spin dynamics might provide further insights into the nature and shape of the observed boundary, as well as the microscopic processes occurring on the different time scales of direct and propagation-based switching. Furthermore, modelling the observed inhomogeneous dynamics, e.g., employing atomistic spin dynamics simulations, could help to identify the key ingredients for the occurrence of either local or non-local switching processes and also to transfer the obtained insights to switching phenomena in other types of magnetic materials.
In summary, our findings add a new dimension to the parameter space for achieving AO-HIS as an ultrafast and efficient route to deterministic magnetisation switching without external magnetic fields. In particular, the fluence-dependence of the speed of AO-HIS averaged over the full thickness of a ferrimagnetic layer can be well explained by our findings as a transition between local, direct switching and the non-local effect of a propagating switching front. Accordingly, tailoring the excitation conditions across the magnetic heterostructure can significantly improve the overall speed and energy efficiency of AO-HIS. In perspective, impulsively triggered switching processes such as AO-HIS must generally be considered as inhomogeneous on ultrafast time scales and over distances as short as a few nanometres along the depth of typical thin-film samples. This becomes particularly relevant when the active layer is embedded in a heterostructure, as the surrounding layers can easily cause an inherent inhomogeneity along the depth, leading to asymmetric excitation conditions that facilitate the formation of inhomogeneous dynamics or even determine their direction. We expect these findings to be relevant for phase transitions driven via non-equilibrium conditions in general. In this context, we would like to conclude by noting that our method for obtaining depth resolution is merely based on a spectroscopic observable and thus not limited to the investigation of magnetic effects. Therefore, we anticipate its application also for a wider range of non-magnetic phenomena. The ability to resolve such dynamics in time and space, in particular with element-specificity, can resolve puzzling observations of distinctively different dynamics for the same material systems, but, e.g., for different sample geometries.