A setup for hard x-ray time-resolved resonant inelastic x-ray scattering at SwissFEL

The control of quantum phases is a focal point of modern condensed matter physics research. Through chemical doping, electric and magnetic fields, or external pressure, critical points can be surpassed, leading to the formation of new phases of matter. An especially noninvasive control parameter is provided by laser pulses, permitting the tailoring of quantum materials properties through strong electric-field effects and the generation of nonequilibrium quasiparticle densities.^1–3 Recent illustrative cases are ultrafast topology switching in Weyl semimetals,⁴ the electric-field enhancement of magnetic exchange interaction,⁵ metastable superconductivity,⁶ and the creation and control of light-induced magnetic vortex structures.^7,8

At the core of these complex phenomena is the interplay between nonequilibrium densities of the respective bosonic and fermionic quasiparticle densities belonging to the lattice, electronic, orbital, and spin degree of freedom of a material. In order to disentangle the dynamics of the various subsystems, a complete snapshot of the nonequilibrium quasiparticle dispersions and distributions in momentum space is wished for. Established ultrafast optical techniques such as time-resolved Raman scattering provide sensitivity to both fermionic and bosonic quasiparticles but are ill-suited to provide large momentum selectivity.^9–11 On the other hand, time- and angle-resolved photoemission spectroscopy (Tr-ARPES)^12–14 allows to capture fermionic quasiparticle dispersions and populations over a large momentum range (depending on the probe photon energy), but the bosonic degrees of freedom are indirectly accessed through coupling mechanisms.^15,16 The hiatus for large momentum selectivity probing of bosonic quasiparticles, i.e., phonons and magnons, as well as high-energy resolution for charge-transfer, Mott-Hubbard gap, and crystal-field excitations, was recently bridged by time-resolved resonant inelastic x-ray scattering (tr-RIXS). RIXS probing relies on a second-order photon-in/photon-out process involving photoelectron transitions from core levels to valence states. The energy loss between the incoming and outgoing photons and the corresponding momentum transfer permits the deduction of quasiparticle dispersion as in phonons,^16,17 magnons,^18,19 paramagnons,²⁰ and charge-density waves.²¹ 

With the advent of bright sources of ultrashort x-ray pulses, such as x-ray free-electron laser (XFELs), the possibility opened up to extend RIXS spectroscopy into time-domain studies, suggesting a new probe for nonequilibrium light-induced phases and bosonic quasiparticle dynamics. Tr-RIXS in the soft x-ray region has unveiled photoinduced changes of charge order in high-T_c cuprate superconductors,^22,23 the orbital dynamics in laser-induced insulator-to-metal transition,²⁴ the photoexcited kinetic process in the hematite photocatalyst,²⁵ and the short-range magnetic correlation in charge-transfer insulators.²⁶ 

In heavy 4f and 5d compounds, exotic states of matter emerge as multiple electron correlations reach comparable magnitudes and intertwine, such as superconductivity,^27–29 topological phases,³⁰ and quantum spin liquids.^31–34 Only very recently were the first tr-RIXS experiments in the hard x-ray region accomplished at the Linac Coherent Light Source XFEL (Sanford, USA), unveiling magnon and spin dynamics in Mott insulators Sr₂IrO₄³⁵ and antiferromagnet Sr₃Ir₂O_7.³⁶ These pioneering experiments highlighted the potential of hard x-ray tr-RIXS to explore laser-driven phenomena in quantum materials with 5d transition metals and 4f rare earth metals.³⁷ Despite the rising interest in tr-RIXS experiments and the rapid theoretical progress in understanding nonequilibrium inelastic photon scattering,^15,37–40 the number of available hard x-ray tr-RIXS apparata around the world remains limited.

In this work, we present the hard x-ray tr-RIXS setup at the beamline Bernina⁴¹ of the SwissFEL^42,43 at the Paul Scherrer Institute (PSI), Villigen, Switzerland. Under an incident x-ray bandwidth of ∼120 meV from a Si(333) monochromator at the Ir L₃-edge (11.214 keV), a Johann-type spectrometer with a Rowland radius of R = 0.5 m provides an energy resolution of around ∼180 meV and a spectroscopic resolving power approaching 10⁵. The commissioning experiment focuses on electronic dynamics in the honeycomb 5d iridate α-Li₂IrO₃. We show that photoexcitation via the ligand-to-metal charge-transfer (LMCT) state leads to a modulation in the RIXS-scattering efficiency of the Ir-to-Ir inter-site excitation of α-Li₂IrO₃, which we tentatively attribute to a transient screening of the on-site Coulomb repulsion.

Bernina is the condensed matter end station of the Aramis Hard x-ray arm at SwissFEL.³⁶ The hard x-ray flux reaches ∼5 × 10¹³ photons/s at 11 keV (3 × 10¹⁴ photons/s at 2 keV) with a pulse length of 40 fs (FWHM) at 100 Hz repetition rate in high charge mode. The self-amplified spontaneous emission (SASE) hard x-ray source can be operated at photon energies of ∼2 keV up to ∼12.7 keV, spanning a wide range of metal K and L edges. For RIXS experiments, the SASE spectrum (∼0.15% Bandwidth) is monochromatized using a Silicon double crystal monochromator (DCM) equipped with [311] and [111] oriented crystals. For experiments, which require higher-energy resolution, Si(333) and (555) reflections can be used to reduce the bandwidth to ∼120 meV and ∼26 meV at the Ir L₃-edge (11.214 keV), which reduces transmissions by 5 × 10⁻³ and 1 × 10⁻⁴, respectively. The monochromatized x-ray pulse is focused with a vertical spot size of 50 μm on the sample surface by a Kirkpatrick–Baez (KB) mirror, as shown in Fig. 1. A pulsed pump laser source tunable from UV to THz pulses may be used for sample excitation. The timing jitter between the optical pump and x-ray probe pulses is usually larger than the pulse duration, thus reducing the temporal resolution in time-resolved XFEL experiments. At the Bernina beamline, timing is measured and controlled by laser arrival monitors (LAM) and an XFEL bunch arrival monitor (BAM) synchronized to a master timing clock, yielding a temporal resolution of ∼50 fs. Additional laser-to-x-ray arrival time measurements by cross-correlation allow data re-sorting and pulse-length limited time-resolution. The x-ray pulse energy and position were monitored at four points along the beamline by measuring the backscattered intensity of Si₃N₄ targets on four diodes. While the knowledge of the incident x-ray pulse energy is vital for normalizing the measured signal in diffraction experiments, the dominant noise source of RIXS experiments is photon counting statistics. The spectrum of the SASE pulses was stabilized in time by keeping the central energy of the x-ray pulses constant, which was measured by a single shot spectrometer upstream the monochromator. The Si (333) monochromator defined the energy used for the experiment. The relative arrival time of the x-ray pulses was measured with respect to spectrally chirped white light generated by the same laser used to pump the sample in time-resolved measurements. The signals of this timing tool were not large enough to correct the arrival time on a single shot, but drifts of the arrival time could be monitored and corrected for by adjusting the global laser arrival time. Furthermore, details on the Bernina beamline at the SwissFEL can be found in Ref. 41.

The physical phenomena under investigation impose stringent criteria on the choice and design rationale of the spectrometer. Whereas for core-to-core level RIXS studies, the low energy and momentum resolving power of a von Hamos-type spectrometer would suffice, collective modes in solid-state materials are only probed by core-to-valence RIXS and therefore require a larger Johann-type spectrometer, though at the expense of throughput. A Johann-type spectrometer was therefore selected for the tr-RIXS setup at Bernina. In the Johann/Johansson type, scattered x rays are collected by a spherically curved crystal (termed “analyzer”) and focused on the detector in a point-to-point geometry. By scanning the incident Bragg angle on the analyzer while simultaneously positioning the detector on the Rowland circle, different emission energies fulfilling Bragg's law are recorded on the detector to obtain the energy loss spectrum. The radius of the Rowland circle, the analyzer radius and dicing, and the utilized Bragg reflection determine the final energy and momentum resolution.

The spectrometer design is inspired from those of the SuperXAS beamline of the Swiss Light Source (SLS, Villigen, Switzerland) and of beamline ID20 of the European Synchrotron Radiation Facility (ESRF, Grenoble, France).^44,45 The combination of the essential components from both designs is adapted to accommodate the beamline machinery at Bernina for hard x-ray tr-RIXS experiments. The schematic instrumental configuration is depicted in Fig. 1. The incident hard x-ray beam first passes through a DCM, and is focused onto the sample surface at a grazing angle through the Kirkpatrick–Baez (KB) mirror. The scattered light from the sample is collected at ∼90° with respect to the incidence beam direction to minimize elastic scattering. Inelastically scattered x rays are monochromatized by a diced spherical crystal analyzer (currently present: Si(533) and Si(884) with a dicing index of 1 mm × 1 mm) of 100 mm diameter and 1 m radius of curvature, which focuses the energy-dispersed x rays onto the detector in a Rowland geometry of a radius of 0.5 m. Efficient hard x-ray detection is achieved with a JUNGFRAU 512 × 512 pixel charge-integrating hybrid pixel photon detector developed at PSI⁴⁶ with a pixel size of 75 μm × 75 μm. This analyzer configuration alone resolves 35 meV at the Ir L₃-edge using the herefore optimal Si(844) analyzers. Using the DCM at the Si(333) reflection and the Si(844) analyzer crystal, we estimate an overall energy resolution of 130 meV at the Ir L₃-edge, limited by the bandwidth of the incoming x rays (see supplementary material S2⁷⁶). Consequently, the energy resolution can further be enhanced to an estimated 60 meV using the Si(555) reflection of the DCM at the expense of a fivefold reduction in the photon flux. The whole scattering beam path including analyzer and photon detector is enclosed inside a helium-filled chamber in order to minimize the absorption and scattering of x rays by air (Fig. 2).

In the Johann scanning configuration, accurate and simultaneous positioning of the analyzer and detector is critical. The analyzer manipulator in Bernina is composed of four motorized translational and rotational stages, enabling fine positioning along all relevant spatial degrees of freedom. Two additional crystal analyzers next to the central analyzer, as shown in Fig. 2, can be used to extend the effective collection solid angle for the most photon-hungry studies at the expense of momentum resolution and an increased alignment complexity.^39,41 Alternatively, the secondary analyzers can be used to simultaneously detect multiple Brillouin zones in crystalline samples.⁴⁷ The photon detector is mounted on a combination of two translational stages and one rotational stage to ensure accurate positioning of the photon-sensitive chip on the Rowland circle. The spectrometer design permits an easy mirroring of the detector arm configuration, by which the accessible momentum space is effectively doubled. The spectrometer is installed on a large theta/2-theta goniometer platform, which can carry an N-dimensional sample manipulator or a hexapod sample manipulator. Sample cooling can be realized by means of cryogenic blowers. A dedicated cryostat reaching a temperature of T = 4 K is planned in the future.

Strong spin–orbit coupled honeycomb materials have been suggested as a solid-state platform for the realization of a Kitaev spin liquid phase.^48,49 The edge-sharing geometry between the metal-ligand octahedra and the resulting dominant bond-directional exchange is prerequisites for the realization of this fractionalized spin state.³² However, the parasitic presence of isotropic interactions, stemming from small structural distortions away from the ideal honeycomb structure, prohibits the formation of a pure spin liquid phase at low temperatures.⁵⁰ In addition to conventional tailoring of the magnetic state by chemical doping,^51,52 pressure,^53–55 or magnetic fields,⁵⁶ various suggestions have been made to use light–matter interactions, more specifically, Floquet-engineering and photodoping,^57–59 to drive materials toward a spin liquid phase. However, difficulties in probing the microscopic nature of the nonequilibrium magnetic state arise due to the apparent absence of long-range order. A suggestion is therefore to probe the transient electronic excitation spectrum in order to resolve electronic and exchange interactions in the photoinduced state.^60,61 The second-order nature of the RIXS process relaxes the selection rules while enabling larger energy transfer, covering a high momentum space, making it a preferred choice over optical probe techniques for this purpose.

In this experiment, we intend to evaluate the possibility of probing transient exchange interactions through time-resolved RIXS (tr-RIXS) spectroscopy in the honeycomb iridate α-Li₂IrO₃. In iridates, the large crystal-field splitting leads over Hund's rule and results in all 5d valence electrons occupying the lower t_2g levels, leaving an empty e_g level. The strong spin–orbit coupling further splits the t_2g levels into a fully filled J = 3/2 level and a half-filled J = ½ level. α-Li₂IrO₃ shows a monoclinic distortion away from the ideal honeycomb structure. This results in a slight mixing of the J = ½ level with higher-lying orbitals. In addition, the monoclinic distortion leads to isotropic exchange interactions, resulting in spiral antiferromagnetic spin order at low temperatures.⁵⁰ 

We first discuss the RIXS spectrometer performance under equilibrium conditions. For our study, a ∼1 × 1 mm² single crystal α-Li₂IrO₃, grown by chemical transport reaction growth,⁶² was mounted on the goniometer stage. The experiment was performed at ambient conditions. The incident x-ray energy was tuned to the iridium L₃-edge at 11.214 eV. A 90-degree configuration suppresses the detection of elastically scattered x-ray photons. The Si(844) plane in a Si(533) diced analyzer was used to disperse the inelastically scattered light onto the JUNGFRAU detector. Figure 3 shows the recorded steady-state RIXS energy loss spectrum at k=[0 –9 3] and compares it to the measurement of the powder sample recorded by Gretarsson et al. at the MERIX spectrometer in 30 ID beamline of Advanced Photon Source (USA).^63,64 The elastic peak has a FWHM of 177 ± 5 meV (supplementary Fig. S2⁷⁶), which provides us with an upper limit of the instrumental energy resolution for experiments at the iridium L₃-edge. We note that this value is not far from the estimated resolution (128 meV) bearing in mind the fact that it is affected by the phonon broadening at room temperature and the skewed Bragg reflection from the Si(844) plane of the Si(533) diced analyzer (supplementary material S2⁷⁶).

Compared to Gretarsson et al.’s, despite our lower-energy resolution primarily due to a smaller Rowland circle, the measured RIXS spectrum captures all the features observed in the synchrotron study. The various exchange interactions and non-trivial crystallographic structure of α-Li₂IrO₃ lead to a rather intricate RIXS spectrum composed of various on-site and inter-site electronic excitations. In Fig. 3(a), on-site spin–orbit (SO) excitations (J_3/2 -> J_1/2) are found around 0.7–1.0 eV. The experimental resolution does not permit further resolving this localized excitation manifold.^17,63 The broad energy loss peak around 3–4 eV consists of t_2g-e_g orbital d-d excitations, which are also localized. More important to our study are the delocalized excitations around energy losses of 0.4, 1.3, and 1.6 eV, as depicted in Fig. 3(b), which result from the hopping nature of 5d electrons in the honeycomb lattice. This assignment is based on theoretical and experimental studies. Kim et al.⁶⁵ showed that these two features are absent in the single-site simulation but emerge in a four-site cluster simulation, which points to their itinerant origin. Furthermore, experimental evidence from high-resolution oxygen (O) K-edge RIXS¹⁷ revealed that the feature near 0.4 eV is a dispersive spin–orbit exciton, whereas the features of 1.3 and 1.6 eV are inter-site excitations between the spin–orbit coupled t_2g levels of two neighboring Ir sites in the honeycomb, which also aligns with optical conductivity studies.^54,66 The energy of 0.4 eV lies right across the Mott gap of honeycomb iridates,⁶⁶ and we believe it represents the low-energy excitation of “bound” holon–doublon pairs, i.e., Hubbard excitons,^67,68 with a dressed mixing of local spin–orbit excitons, whereas 1.3 eV provides more energy to create “unbound” holons and doublons. Since the L-edge RIXS predominately probes the local environment, the appearance of these two itinerant features hints to a clear degree of mixing between inter-site and on-site excitation. The data presented in Fig. 3(a) were collected over 1.2 h with a x-ray flux of 10¹¹ photons/s. Taking into account the difference in x-ray flux and detector diameter, we have comparable collection efficiency as in Refs. 63 and 64.

For the time-resolved experiment, we photoexcite the α-Li₂IrO₃ sample with 400 nm (3.1 eV) optical pulses at a fluence of ∼45 mJ/cm². In terms of photons/cm², this fluence at 3.1 eV is comparable with the fluence at 0.62 eV used by Dean et al. on Sr₂IrO_4.³⁵ Calculation of the pump fluence and excitation fraction (i.e., number of electron–hole pair per unit cell) are described in § S3. The pumped and unpumped RIXS spectra over 0 to 2 eV energy loss range were recorded by continuously alternating the time delay between +1 ps and −28 ns, respectively. Therefore, any long-term drift will not discriminate either pumped or unpumped spectra. All raw pumped (unpumped) spectra were summed up as measured without imposing any normalization procedure. Based on the electronic structure calculation⁶⁹ and the photoemission experiment,⁶⁶ a pump energy of 3.1 eV corresponds to an ligand-to-metal charge-transfer dipole excitation from the oxygen 2p orbital to the Ir atoms. Figure 4(a) shows the unpumped (static) RIXS spectrum (black solid circle) vs the spectrum at 1 ps after photoexcitation (purple circle) in the 0 to 2 eV energy loss region, while the lower panel shows the transient RIXS spectrum calculated by $( RIXS pumped− RIXS unpumped)/ RIXS unpumped$⁠. Zooms to two specific energy loss regions are given in Figs. 4(b) and 4(c). These results were collected over 8 h of data acquisition at a repetition rate of 100 Hz and a photon flux of around 10¹¹ photons/s of the monochromatic x-ray beam. Compared with the pioneering hard x-ray tr-RIXS by Dean et al., the bottleneck of our energy resolution is the larger incident x-ray bandwidth (116 meV vs 50 meV). As indicated in Sec. II, we can adopt a Si(555) monochromator to achieve better resolution, however, at the expense of a reduced flux and hence much longer data acquisition time for a similar signal-to-noise ratio (SNR).

Although the transient RIXS spectrum is quite noisy, we note the following: (I) two features that overshoot the variation of the elastic peak (gray-shaded area) appear at ∼0.4 and 1.3–1.6 eV, corresponding to the itinerant behavior of the honeycomb 5d electrons, and are zoomed into in Figs. 4(b) and 4(c), respectively; (II) although the 0.7 eV feature is the most intense in the steady-state RIXS spectrum as a localized excitation, there is no clear hint of a response there; (III) the signal observed at ∼0.4 eV is relatively small compared to the signal in the 1.3–1.6 eV region. Five Lorentzian peaks were fitted to both the pumped and unpumped RIXS spectra separately (supplementary material S4⁷⁶), which include: (i) the elastic scattering line; (ii) the spin–orbit exciton ∼0.4 eV; (iii) the on-site J_3/2 to J_1/2 transition 0.7 eV; (iv) the inter-site J_1/2 to J_1/2 transition ∼1.3 eV, and; (v) the inter-site J_3/2 to J_1/2 transition ∼1.6 eV. The fit results are shown in supplementary Fig. S3.⁷⁶ The orange trace in Fig. 4(a) compares the transient tr-RIXS spectrum with the transient one calculated from the fitted spectra in Figs. S3(a) and S3(b). They clearly show a much weaker 0.4 eV feature in the difference spectrum compared to the 1.3 and 1.6 eV features. Regarding the latter two, the fitted 1.3 eV peak undergoes an intensity decrease, while minimal change occurs to the fitted peak in the 1.6 eV region.

Tailoring the exchange interaction in iridate honeycomb materials, more specifically through the modulation of the Ir-site covalency, has been demonstrated by metal intercalation.⁶⁰ A similar mechanism may lie at the origin of the change in the inter-site excitation scattering rate in α-Li₂IrO₃. Let us first consider the possible inter-site excitation picture in the RIXS process without optical photoexcitation. Since it involves two sites, the initial state can be written as 5d_i⁵5d_j⁵, where i and j denote two neighboring Ir sites. X-ray L-edge absorption creates an intermediate state: 2p5d_i⁶5d_j⁵, where 2p denotes the Ir 2p core hole. Finally, via recombination of core hole with the electron from the neighboring site, the system reaches a final state: 5d_i⁶5d_j⁴, leaving an inter-site excitation from site j to site i compared to the initial state. When the system is pumped, the strong CT photoexcitation induces a significant disequilibrated density of holes on the oxygen site and doubly occupied Ir sites (doublons, as 5d⁶). The initial state for the RIXS process has changed due to ligand holes and doublon population, which can be expressed as α|5d_i⁵;5d_j⁶L > + β|5d_i⁶L;5d_j⁵ > + γ|5d_i⁶L;5d_j⁶L>, where L denotes the O 2p ligand hole and α² + β² + γ² = 1. The induced screening of the on-site Coulomb repulsion U alters the Ir-O-Ir superexchange pathway strength set by ∼t²/U, with t being the pathway's hopping parameter.⁷⁰ The far-from-equilibrium electronic distribution leads to a change in the energy necessary for the Ir–Ir inter-site hopping, suggesting a modulation of the RIXS matrix element. Any pump-induced effect on the quasiparticle population is only expected for the lowest energy transfer region <0.1 eV, i.e., the asymmetric Stokes and anti-Stokes wings,^9,10,34 which is below the resolution limit of our experiment. Similar modulation of the exchange interaction with ultrafast laser pulses has also been reported in other systems, such as iron oxides⁷¹ and ferromagnetic insulator CrSiTe_3.⁷² A more detailed discussion of our results will be presented in a separate publication.

In summary, we presented the tr-RIXS setup at the hard x-ray Bernina beamline at SwissFEL (Paul Scherrer Institut, Villigen, Switzerland). The compact R = 0.5 m Johann-type spectrometer, which can be equipped with up to three crystal analyzers, permits efficient collection of RIXS spectra with a resolution of ∼150 meV. Pumping can be realized with a broad span of optical wavelengths. We demonstrated the functioning of the setup by photoexciting the honeycomb iridate α-Li₂IrO₃ in the charge-transfer manifold. Modulation of the Ir-to-Ir inter-site transition scattering efficiency is hinted to, which we ascribe to a transient screening of the on-site Coulomb interaction.

For future improvement on the setup performance, seeding would be highly beneficial for experiments requiring a small bandwidth, and upgrades of the SwissFEL Aramis branch have been an ongoing discussion. An alternative approach currently being explored at FELs is spectroscopy using the pink beam by measuring the incoming and outgoing spectrum of the x-ray pulses. Finally, the use of high-repetition rate XFELs will also help in improving the signal-to-noise ration. We note that magnetism and spin dynamics research could benefit from higher-energy resolution (∼50 meV) of the analyzer and the monochromator to resolve low-energy modes. Nevertheless, the hard x-ray tr-RIXS setup described here is readily capable of dynamical studies in the fields of chemistry, biology, and catalysis. An energy resolution of ∼150 meV is sufficient to resolve plasmons and element-specific charge-transfer excitations within the local chemical environment,⁷³ in addition to a threefold-extended solid angle to collect scattering in liquid/gas phase environment. Using hard x-ray tr-RIXS, real-time tracking of oxygen evolution reaction in iridium oxide,⁷⁴ and CO adsorption dynamics in Pt nanoparticles (Pt L₃-edg∼11.5 keV) could be performed.⁷⁵ We believe the newly commissioned hard x-ray tr-RIXS setup at Bernina, SwissFEL, will enable unique research in laser-driven quantum materials and ultrafast x-ray spectroscopy.

This project was funded by the ERC Advanced Grant DYNAMOX (ID 695197). We thank Marco Moretti Sala and colleagues for discussions on the design of the Johann-type RIXS spectrometer. We thank Markus Grüninger and Alessandro Revelli for exchanging information on RIXS spectroscopy and the sample. We thank Markus Grüninger and Bo Yuan for the insightful discussions on the results. We acknowledge the Paul Scherrer Institut, Villigen, Switzerland, for provision of free-electron laser beamtime at the Bernina instrument of the SwissFEL ARAMIS branch. H.-Y.C. acknowledges support from Taiwan-EPFL Ph.D. Scholarship. M.C. acknowledges support from the ERC Advanced Grant CHIRAX (ID 101095012). G.F.M. acknowledges support from ERC Starting Grant ULTRAIMAGE (851154), ERC PoC HYPER (101123123), Fondazione Cariplo 2020-2544 (NANOFAST), MUR PiXiE (R207A8MNNJ), and PRIN2022 DynaMAT (2022PR7CCY).

The authors have no conflicts to disclose.

Hui-Yuan Chen: Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Writing – original draft (equal); Writing – review & editing (equal). Rolf B. Versteeg: Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Validation (equal); Writing – review & editing (equal). Roman Mankowsky: Formal analysis (equal); Investigation (equal); Methodology (equal); Validation (equal); Writing – review & editing (equal). Michele Puppin: Formal analysis (equal); Validation (equal); Writing – review & editing (equal). Ludmila Leroy: Formal analysis (equal); Investigation (equal). Mathias Sander: Formal analysis (equal); Investigation (equal); Validation (equal); Writing – review & editing (equal). Yunpei Deng: Formal analysis (equal); Investigation (equal); Validation (equal); Writing – review & editing (equal). Roland Alexander Oggenfuss: Investigation (equal); Validation (equal); Writing – review & editing (equal). Thierry Zamofing: Investigation (equal); Validation (equal); Writing – review & editing (equal). Pirmin Böhler: Investigation (equal); Methodology (equal); Writing – review & editing (equal). Claude Pradervand: Investigation (equal); Methodology (equal); Validation (equal); Writing – review & editing (equal). Aldo Mozzanica: Investigation (equal); Methodology (equal); Validation (equal); Writing – review & editing (equal). Seraphin Vetter: Investigation (equal); Validation (equal); Writing – review & editing (equal). Grigory Smolentsev: Formal analysis (equal); Investigation (equal); Methodology (equal); Validation (equal); Writing – review & editing (equal). Linda Kerkhoff: Methodology (equal); Validation (equal); Writing – review & editing (equal). Henrik T. Lemke: Investigation (equal); Methodology (equal); Supervision (equal); Validation (equal); Writing – review & editing (equal). Majed Chergui: Conceptualization (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Supervision (equal); Writing – original draft (equal); Writing – review & editing (equal). Giulia F. Mancini: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Project administration (equal); Supervision (equal); Validation (equal); Writing – original draft (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding authors upon reasonable request.