Probing the interplay between lattice dynamics and short-range magnetic correlations in CuGeO3 with femtosecond RIXS

Investigations of magnetically ordered phases on the femtosecond timescale have provided significant insights into the influence of charge and lattice degrees of freedom on the magnetic sub-system. However, short-range magnetic correlations occurring in the absence of long-range order, for example in spin-frustrated systems, are inaccessible to many ultrafast techniques. Here, we show how time-resolved resonant inelastic X-ray scattering (trRIXS) is capable of probing such short-ranged magnetic dynamics in a charge-transfer insulator through the detection of a Zhang-Rice singlet exciton. Utilizing trRIXS measurements at the O K-edge, and in combination with model calculations, we probe the short-range spin-correlations in the frustrated spin chain material CuGeO3 following photo-excitation, revealing a strong coupling between the local lattice and spin sub-systems.


Introduction
Among the family of transition metal oxides, the charge-transfer materials are highly studied due to the realization of a number of exotic properties, from metal-insulator transition to high-Tc superconductivity. These phenomena often arise from the microscopic coupling between charge, spin, orbital and lattice degrees of freedom. In this regard, a significant advancement in understanding the origin of these exotic properties may be obtained by employing ultrafast time-resolved techniques to probe the dynamics of the relevant ordered phases. In the study of magnetism, the interplay between magnetic sub-lattices 1 and other degrees of freedom such as the crystal lattice 2-5 and charge [6][7][8][9][10] , have afforded numerous important insights. However, when materials crystallize in a purely one-dimensional (1D) crystal structure they cannot support long-range magnetic order 11 , even in the presence of strong short-range magnetic correlations. Such correlations are not easily accessible to many ultrafast techniques such as time-resolved photoemission, x-ray diffraction, or optical spectroscopies. In contrast, Resonant Inelastic Xray Scattering (RIXS) is able to probe both local magnetism and access elementary excitations rather than ordering phenomena [12][13][14] . Moreover, in contrast to most other local magnetic probes, the intrinsic timescale of the RIXS process (~1 fs) easily allows the extension of this technique to the ultrafast domain 15 . The main limitation for this class of experiments lies in the limited available time-integrated intensity. Indeed, only recently the progress of soft x-ray free-electron lasers (FELs) has allowed the very first few experiments of this kind [16][17][18][19][20] . The advent of the next-generation FELs worldwide is expected to overcome these limitations, enabling the study of a wide class of problems in condensed matter and beyond.
Therefore, using trRIXS holds great promise for widening our understanding of ultrafast magnetism in low-dimensional and frustrated magnetic systems, allowing insights into their rich physics that include spin glass phases, novel types of elementary excitations and the fractionalization of quasi-particles. In this class of materials, the complexity of the phase diagrams often results from the competition between nearly degenerate ground states, and a close competition between nearest neighbor (NN) and next-nearest neighbor (NNN) magnetic exchange coupling. A typical example of such physics is realized in the material CuGeO3, whose structure is shown schematically in Fig. 1(a). The basic building blocks of CuGeO3 are CuO4 plaquettes arranged in edge-shared chains running along the crystallographic c-axis 21 . The exchange interaction, J, between NN Cu ions depends on the interatomic distance and is antiferromagnetic (AFM), in large part due to a Cu-O-Cu bond angle of 99°2 2 . The system is unstable towards a lattice dimerization, opening a spin-Peierls (SP) gap in the magnetic spectrum below a temperature TSP = 14 K 23-26 . This process involves a magneto-elastic coupling between the 1D electronic system and the 3D phonon system. While the classical description of a SP transition holds only when the phonon energy is small compared to the other relevant energy scales, for CuGeO3 the phonon energy scale is of the same order as the NN exchange coupling J 27 . The resulting entanglement of spin and lattice degrees of freedom is further complicated by the magnetic frustration induced by the presence of a large NNN AF exchange. In further contrast to typical SP materials such as TiOCl where the lattice dimerization is associated with the softening of a particular phonon mode 28,29 no soft phonon was ever observed in CuGeO3. Even more remarkably, the two modes most strongly associated with the distortion are found to harden at low temperatures 30 . An additional quasi-elastic mode appears due to short-range fluctuations already well above the transition temperature 31 as evident in a number of experiments 32-34 . Therefore, due to the concomitant effect of low dimensionality and geometrical frustration, CuGeO3 does not order magnetically over a long-range, and the physics is instead dominated by short-range magnetic correlations.
To obtain a better understanding of the intricate relation between spin and lattice degrees of freedom in this and other low-dimensional oxide materials, a direct measurement of the dynamics of short-range spin correlations is highly desirable. Here, we use time-resolved RIXS (trRIXS) to shed light on the interplay between lattice modulations, initiated by an ultrashort photoexcitation, and short-range magnetic correlations in a frustrated magnetic system. We employ 4.7 eV photons to excite the system across the charge-transfer gap, and O K-edge RIXS to track the photo-induced response of a Zhang-Rice singlet (ZRS) exciton, which is sensitive to the short-range spin correlations within the Cu-O chain of CuGeO3 35 . Following photoexcitation, we observe an exponential decrease of the ZRS intensity, with some deviation caused by a partial recovery within ~1 ps, followed by a gradual reduction on longer time scales (10 ps), which persists to long delays (500 ps). This long-time effect increases linearly with the pump fluence up to a saturation above a critical value of 5 mJ/cm 2 , which suggests the removal of a coupling channel between the magnetic and lattice sub-systems. Exact diagonalization calculations of the RIXS spectra at delays < 10 ps imply the influence of a damped phonon which modulates the on-site Cu energy, therefore affecting the spin-spin correlation function. The timescale involved is compatible with a magneto-elastic mode at ~1 THz. In this way, we explore the effect of lattice dynamics on the short-range spin correlations in a frustrated lowdimensional spin system, and set the stage for future investigations of these interactions exploiting next generation x-ray FEL sources.

Results
Zhang-Rice singlet detection with O K-edge RIXS. In our measurements, the energy of the FEL x-ray pulses is tuned to the O K-edge (~ 531 eV) and set to be resonant to an absorption peak sensitive to the upper Hubbard band (UHB) electrons 35 . The O K-edge XAS spectrum, collected with a synchrotron source, is presented in Fig. 1(b). Fig. 1(a) shows the schematics of the trRIXS experiment: the pump and probe pulses propagate collinearly and impinge with an angle of 45° on the sample surface. In the experimental geometry, the CuO4 plaquettes of copper-oxygen chains of CuGeO3 lie at an angle of 56° with respect to the cleavage plane. The sample is kept at a temperature of 20 K during the measurements. Fig. 1(c) displays a comparison between the O K-edge RIXS spectrum obtained in the trRIXS experiment (lower spectra) and a static high-resolution spectrum obtained under the same experimental conditions at a synchrotron source. Despite the lower statistics and energy resolution available in the FEL experiment, all of the main spectral components such as the quasi-elastic, d-d, and chargetransfer excitations are clearly visible. In particular, an excitation located at 3.8 eV 35 is well resolved and separated from the broad charge-transfer structure, located between 4 and 10 eV energy loss. Such excitation is due to the formation of a Zhang-Rice Singlet (ZRS) state.
In order to understand the relevance of the ZRS excitation for probing short-range spin correlations, we first clarify the mechanism of the ZRS formation in the RIXS experiment 35 . In the initial state (see Fig.1 (d)), the Cu ions in two neighboring CuO4 plaquettes have a (3d 9 , 3d 9 ) orbital configuration, with a single hole in a hybridized Cu 3dx 2 -y 2 /O 2p orbital per plaquette. We assume an initial configuration with antiparallel spins. When an x-ray photon is absorbed, it promotes an electron from the oxygen 1s core level to fill a hole in the valence band and the plaquettes assume a (d 9 , d 10 1s) configuration. From this excited state, a possible de-excitation channel involves the relaxation of one ligand electron from the neighboring plaquette to fill the core-hole, leaving the system in a (d 9 L, d 10 ) configuration (see Fig. 1(e)). This mechanism involves a nonlocal charge transfer process, which is detected by the RIXS measurement 35,36 . In the RIXS final state, the two holes residing on the same plaquette inherit the initial antiparallel spin configuration and adopt the ZRS wave function. As a result of this bound ZRS exciton, the process gives rise to a peak at an energy transfer smaller than the charge gap (Δ) and separated from the continuum of charge-transfer excitations. It has been shown that the probability for such a process depends on the tendency of the neighboring Cu spins to be AFM oriented 35,37,38 . For this reason, the strength of the short-range AFM correlations is encoded in the spectral weight of the ZRS excitations probed by RIXS. We excite the system across the charge transfer gap using a 4.7 eV ultraviolet laser pulse. By comparing the O K-edge RIXS spectrum collected before (-1 ps) and after (+6 ps) the photoexcitation, presented in Fig. 1(c), one can clearly identify a suppression in the intensity of the ZRS excitation as compared to the rest of the spectrum, which remains essentially unchanged.
Dynamics of the short-range antiferromagnetic correlations. Changing the pump-probe delay allows us to follow the development of the O K-edge trRIXS spectrum in the time domain. Although all the different excitations in the RIXS spectrum show some evolution following the arrival of the pump pulse, only the changes in the ZRS are clearly visible above the noise level. Therefore, in the following we focus our analysis on the evolution of the ZRS intensity as a function of the pump-probe delay. Figure 2(a) shows the O K-edge RIXS spectra between the elastic line and the charge transfer structure measured as a function of the time delay for a laser fluence F = 37.4 mJ/cm 2 . Such a high incident fluence is used due to the large penetration depth of photons at the pump wavelength 39,40 and corresponds to an excitation of ~ 0.023 electrons per unit cell (see the Supplementary Materials, section S1, for the derivation of this value). The RIXS spectra in the region of the ZRS excitation are presented in Fig. 2(d) for selected time delays. After 0.5 ps from the arrival of the pump pulse, we observe a rapid suppression of the ZRS intensity and a partial recovery, as evidenced by a plateau in the dynamics (≈ 1 ps). This is followed by a further suppression which does not recover to the original intensity even after >100 ps (see Fig. 3(d)). By employing a multi-component Gaussian fitting (as exemplified in Fig. 2(b)), we extract the dependence of the ZRS integrated intensity as a function of the time delay, as shown in Fig. 2(c), which confirms the dynamics already ascertained from the raw data. Directly after the laser excitation, we detect the fast suppression of the ZRS intensity with the additional plateau (~1 ps) followed by a longer reduction of intensity, saturating after ~10 ps. We note that the short time behavior depends strongly on the fitting model: in supplementary Fig. S6c this plateau instead appears as a distinct peak, which we discuss further below. While the dynamics on the longer timescale are probably dominated by the quasi-thermal heating of the lattice, the short timescale plateau may have a non-thermal origin. In the following, we will address first the slow dynamics and then return to the origin of the rapid non-thermal behavior.
The time-dependent behavior up to long time-delays is presented in Fig. 3 (d) for two different values of the laser fluence. The magnitude of the suppression of the ZRS peak intensity shows a large fluence-dependence, being prominent at F = 37.4 mJ/cm 2 and almost negligible at F = 2.5 mJ/cm 2 . By fixing the time delay at 100 ps, we have investigated the ZRS intensity for various pump excitation fluences, as presented in Fig. 3(a). Using the fit procedure described before to extract the reduction of the ZRS reveals the onset of an abrupt saturation of the suppression for F > 5 mJ/cm 2 (see Fig. 3(b)). Since these data are acquired at long delays, we initially assume that they predominantly reflect the reduction of the ZRS intensity caused by the increase in the thermal energy of the lattice at quasi-equilibrium with the spin and electronic systems. In the 1D crystal structure, the neighboring chains are decoupled, which results in inefficient heat transfer away from the probed volume into the crystal and may explain the observation that, even at very long delays, the ZRS intensity remains strongly depleted for high incident fluences. The long time value of the ZRS intensity can be converted into an effective temperature by assuming a one-to-one correspondence with temperature-dependent static RIXS data (see Section S3 of the Supplementary Materials). The effective temperature, reported as a function of the fluence in Fig. 3(c), saturates at a value of ≈ 230 K. In contrast, the static temperature-dependent data only present a saturation behavior above room temperature. Such a deviation from the equilibrium behavior is surprising as heat transport is likely to dominate on such long time-scales, and at higher fluences more thermal energy is pumped into the system. The same fitting analysis and comparison with static data can be applied to the transient ZRS behavior to extract the quasi-thermal evolution of the magnetic sub-system during the ultrafast measurements. The transient reduction of the ZRS peak as a function of time, again for F = 37.4 mJ/cm 2 [ Fig. 2(c)], is fitted with an exponential decay (see Section S3 of the Supplementary Materials). In order to gain further insight into these dynamics we perform a commonly applied two-temperature model analysis. The model assumes that the electronic and lattice sub-systems are coupled heat baths that exchange energy following a pulsed excitation, which is captured by a system of two coupled differential equations (see Section S3 of the Supplementary Materials for full details). The evolution of the electronic (Telectronic) and lattice temperature (Tlattice) can therefore be estimated from the electronic and lattice specific heats, and the amount of energy deposited by the laser pulse. The temporal evolution of the effective magnetic temperature can be quantitatively reproduced by this simple model, as shown in Fig.  3(e), but only by assuming an absorbed heat content substantially lower than the amount estimated in the experiment. Indeed, by considering the mismatch in the penetration depth between the pump and the probe beams, for an incident laser fluence of 37.4 mJ/cm 2 at the sample surface, we estimate an absorbed fluence of 140 mJ/cm 3 within the volume probed by the x-rays (see Supplementary text S1). However, using the estimated 140 mJ/cm 3 as the input to the two-temperature model results in a dramatic overestimation of the rise in temperature when compared with that obtained from the ZRS intensity reduction. In fact, our model requires an input fluence of only 83 mJ/cm 3 to describe correctly the experimental data. Thus, the magnetic system is cooler than expected as compared with a simple two-temperature analysis of the electronic and lattice systems. This discrepancy further implies that the ZRS selectively probes the dynamics of the magnetic sub-system, and that this becomes decoupled from the lattice and electronic systems in accordance with the fluence dependent results discussed above.
Non-thermal behavior at short timescales. A possible scenario resulting in the plateau in the otherwise exponential decrease of the ZRS spectral weight dynamics is a partial recovery caused by a damped coherent phonon oscillation, modulating the local magnetic correlations. Indeed, a large involvement of the lattice degrees of freedom was found in the transient response of CuGeO3 following photoexcitation using optical techniques 41,42 . Even at equilibrium, the magnetic and lattice degrees of freedom are known to be strongly coupled in CuGeO3. In particular, the bond angle between the Cu-O-Cu atoms of the plaquettes sensitively affects the AFM coupling strength. Even before the transition to the SP-phase, the lattice undergoes structural changes by compressing the plaquettes along the a-axis and extending them along the c-axis 22 . This compression further increases the Cu-O-Cu bond angle and, therefore, enhances the AFM correlations. Below TSP an additional motion of the Ge side group is known to occur during the formation of the SP order 22,27,30 , which also affects the AFM coupling.
In order to address whether a coherent phonon oscillation can lead to a modulation of the shortrange magnetic order, we have utilized a cluster model of the plaquettes (Ref. 35 and Section S4 of the Supplementary Materials). To capture the short-time dynamics of CuGeO3, we introduced a coherent oscillation in our cluster, coupling linearly and uniformly to the charge transfer energy Δ = − . We also introduced an effective temperature in our model, to capture the long-time dynamics. The RIXS spectra are then calculated at each time delay using exact diagonalization and the Kramers-Heisenberg formalism (see further details in Section S4 of the Supplementary Materials). The results of this calculation in the region of the ZRS are presented in Fig. 4(a) with cuts at selected time delays shown in Fig. 4(b). Modulating the charge-transfer energy of the chains in the manner of a damped phonon oscillation, shown in Fig. 4(c) provides us with a possible explanation for the plateau at 1 ps in the observed fast dynamics of the ZRS intensity [ Fig. 4(d)], namely the reduction and recovery after laser excitation. The slow reduction is also well reproduced by the effective temperature based on the experiment, as described above.

Discussion
Our results reveal that the evolution of the magnetic degrees of freedom in CuGeO3 decouple from the other degrees of freedom on a 100 ps time scale and possibly follow a non-thermal behavior on the 1 ps time scale.
The observation of a saturation of the ZRS intensity as a function of fluence at Δt = 100 ps ( Fig.  3(b)) points towards the loss of an efficient coupling channel between the spin and phonon systems out-of-equilibrium. We note that while it is conceivable that this saturation could be caused by the suppression of the ZRS intensity due to the thermally heated lattice, such a scenario does not explain why the saturation occurs already at an equivalent temperature of ≈ 230 K, and not 300 K as observed in static RIXS (see Supplementary Materials, Fig. S7). This suggests a non-thermal behavior of the magnetic sub-system on a 100 ps timescale. Furthermore, it strongly implies the ZRS intensity is not a good measure of the quasiequilibrium lattice temperature at all times, and can only reliably be used to probe the effective magnetic sub-system temperature. This conclusion is additionally supported by our two temperature model, which requires a significantly lower input energy density than in the experiment to reproduce the observed magnetic temperature.
A potential origin for this loss of coupling between the two sub-systems is the removal of a low energy magneto-elastic mode at 0.9 THz observed in the SP-phase 43-49 . It has been suggested that this mode is a bound pair of magnons held together by the spin-phonon interaction 50,51 giving it a strong phononic component. Since this mode is gradually removed by temperature at thermal equilibrium, it may also be quenched by the increased quasi-equilibrium temperature on the 10's of ps timescale.
Our model calculation reveals that a damped oscillation could be responsible for the observed non-thermal ultrafast dynamics of the ZRS. We emphasize that the plateau feature in our data depends strongly on the model used to fit the trRIXS spectra, and in particular whether the width of the ZRS is held constant or is left as a free fit parameter. In supplementary Fig. S6 (c), we show that, in the latter case, the plateau is replaced by a clear peak in the time dynamics, with the ZRS width also changing rapidly after excitation. This gives further weight to the hypothesis that the plateau obtained in the more conservative analysis is indeed the result of a damped oscillation. However, there remains the possibility that a non-equilibrium state occurs where the ZRS is broadened non-thermally. Given the currently limited statistics we leave this question open for future investigations. From the data in Fig. 2(c), we can estimate an energy scale of ~ 4 meV (1 ps) from the frequency of this mode. There remains the question of exactly which atomic motion causes the change of the magnetic coupling. For the NN exchange in CuGeO3, there are two significant factors that lead to an overall AFM nature of the coupling. The first is the fact that the Cu-O-Cu bond angle differs significantly from 90°, which removes the symmetry restriction on superexchange imposed by a 90° bond. The second is that the degeneracy of the O px and py orbitals is removed by the presence of a Ge side-group out of the plane of the CuO4 plaquettes 22,52 , allowing additional AFM coupling. Both the Cu-O and the Ge-O bonds change at the SP-distortion, and both may contribute to the modulation of the charge transfer energy (), which equivalently modulates J. However, the frequencies of phonon modes most strongly associated to the motion of the Cu-O-Cu bond (3.3 and 6.8 THz) 30 and Ge bond (5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18) are too large to account for the period of ≈ 1 ps (1 THz) that our data suggest. It is possible that the low energy mode at 0.9 THz discussed above may account for this behavior. To fully validate such a scenario will require further in-depth studies using next generation x-ray FEL sources.
Based on our current findings we postulate the following speculative picture of the dynamics following excitation, as outlined in Fig. 5. Our measurements are performed at a temperature of 20 K. Although this temperature is higher than TSP, short range order fluctuations towards the spin-Peierls dimerization and concomitant singlet spin pairing are strong 32,33,53 . Within this environment, the intense ultraviolet pulse of 37.4 mJ/cm 2 excites the electronic sub-system and creates a charge transfer from the O to the Cu ions. This leads to a spatial redistribution of the electronic density in the CuO2 chains of CuGeO3 at 0 ps and acts as a trigger for launching a coherent oscillation with a period of < 2 ps, as observed in the spin response detected by RIXS via the ZRS excitation. We speculate here that this oscillation corresponds to the excitation of fluctuating magneto-elastic quasiparticles at very low energy. By modulating the bound magnon pairs via the spin-phonon coupling, this therefore results in a temporal modulation of the short-range AFM order, which is reflected in the ZRS intensity. Since the order is shortranged, the coherent oscillation is strongly damped. At the same time, energy is efficiently transferred from the electronic into the lattice sub-system, raising the quasi-temperature of the lattice. As the quasi-temperature of the lattice increases, the magneto-elastic coupling gradually disappears. The rising lattice temperature has likely two consequences: (i) it contributes further to the damping of the coherent oscillation and (ii) the energy transfer into the magnetic subsystem becomes less efficient, because the suppression of the magneto-elastic quasiparticles closes a coupling channel between the two sub-systems.
Our time-resolved RIXS study uncovers intriguing physics in the non-equilibrium dynamics of a quasi-one-dimensional cuprate, CuGeO3, allowing us to elaborate a possible scenario for their ultrafast evolution on the ps time scale. It calls for further experiments, with a more systematic approach regarding fluence and temperature dependences in particular. This will be made possible with next generation x-ray free electron facilities, allowing for higher statistics and for the acquisition of extensive data sets within a few days. In parallel, it would be important to reveal the ultrafast dynamics of the lattice degrees of freedom of CuGeO3 directly. For instance, a future experiment using time-resolved x-ray diffraction to monitor the structural distortion related to the spin-Peierls phase would be highly beneficial.
In summary, by allowing access to the short-range magnetic correlations in CuGeO3, trRIXS provides us with a powerful tool to probe the ultrafast dynamics of the local spin arrangement. Our current study outlines the complex interplay between the electronic, lattice and magnetic degrees of freedom in CuGeO3. This establishes trRIXS as a technique capable of resolving the femtosecond dynamics of short-range magnetic correlations in low-dimensional and frustrated materials.

Methods
Sample preparation and RIXS characterization. CuGeO3 single crystals were cleaved at room pressure and temperature, producing mirror-like surfaces, and quickly transferred into the vacuum chamber (base pressure 10 -9 mbar). The surface is oriented perpendicular to the [100] axis, so that the CuO4 plaquettes are tilted 56° away from the surface. RIXS experiments were performed at the ADRESS beamline 54 of the Swiss Light Source, Paul Scherrer Institut, using the SAXES spectrometer 55 . A scattering angle of 90° was used and all the spectra were measured at the specular position, meaning that no light momentum is transferred to the system along the chain direction. The combined energy resolution was 60 meV at the oxygen K edge (~ 530 eV). Further details on the static RIXS measurements can be found in Section S3 of the Supplementary Materials.

Time-resolved RIXS (trRIXS).
Measurements were carried out at the SXR beamline of the Linac Coherent Light Source operating at 120 Hz 56 . The system is excited using a 4.7 eV ultraviolet laser pulse of 50 fs duration generated by frequency addition in non-linear optical crystals. The energy of the 70-fs FEL x-ray pulses was tuned to the O K-edge (531 eV). The radiation scattered from the sample is collected by a compact spectrometer placed at a 90° scattering angle. The pump and probe pulses propagated collinearly and impinge with an angle of 45° on the sample surface. Both the laser pump pulse and the FEL probe pulse are horizontally polarized, i.e. the polarization vector lies in the scattering plane. In the experimental geometry, the CuO4 plaquettes of copper-oxygen chains of CuGeO3 lie at an angle of 56° with respect to the cleavage plane. The sample is kept at a temperature of 20 K during all the measurements. Further details on the trRIXS measurements can be found in Section S1 of the Supplementary Materials. All the data used in the present manuscript are available on request.     Due to the heat transfer to the lattice, this mode is gradually removed and therefore the lattice and magnetic temperatures separate.

Figure Captions
The pump and probe beams propagate collinearly to the sample with 45° incidence angle from the sample surface and the scattered photons are detected using a soft x-ray spectrometer placed at a scattering angle of 90°. Both the laser pump pulse and the FEL probe pulse are horizontally polarized such that the polarization vector lies in the scattering plane. We estimate the combined energy resolution to be 365 meV FWHM, obtained with the spectrometer grating set to the 1 st diffraction order. The spectrometer disperses the scattered x-rays vertically through a variable line-spacing grating, allowing it to collect a larger solid angle in the horizontal plane. This allows using an extended horizontal line focus that reduces the sample damage by the x-rays without increasing the time required to collect the signal. The spectrometer was equipped with an ANDOR Newton DO940P CCD camera operated at 120 Hz readout rate in 1D binning mode along the non-dispersive direction. The single-crystal CuGeO3 sample, synthesized as discussed elsewhere 5 , was placed on a manipulator equipped with a continuousflow Helium cryostat to maintain the sample at a constant temperature of 20 K during all measurements.
Most of the data have been collected using an incident laser fluence of 37.4 mJ/cm 2 . The use of such a large fluence is due to the mismatch between the penetration depth of soft x-rays and UV light. Indeed, assuming an exponential absorption profile in the sample, within the x-ray probing depth of 100 nm only ~5% of the total pump fluence is absorbed. This results in a total absorbed fluence of ~140 J/cm 3 in the volume probed by the x-rays. Assuming that every pump photon is absorbed by the electronic system, this leads to the excitation of ~0.023 electrons per unit cell. The inset of Fig. S1 shows a histogram of the intensity on the CCD camera in 15 minutes acquisition of the RIXS spectrum. The RIXS signal is partially separated from the dominant noise contribution, appearing as a large Gaussian peak. A single photon counting scheme, based on a 1D centroiding algorithm is then applied to the raw data, allowing a better separation of the 1-photon signal from the noise. Due to the limitations in photon statistics, we set the number of points in the centroid algorithm to be the same as the number of physical pixels in the CCD camera.

Section S2: Fitting of the RIXS spectra
In what follows, we present the fitting procedure used to extract the evolution of the Zhang-Rice singlet as a function of the time delay and the pump fluence. In our experiment, we typically acquire several runs of 15 minutes each at a given time delay. We then average them to obtain the final RIXS spectrum. In the following, the error bars associated to every experimental point are obtained by evaluating the variability between different 15-minutes accumulations under the same experimental conditions. The data were then normalized with respect to the total area under the RIXS spectrum to minimize possible artefacts resulting from intensity fluctuations due to experimental instabilities during the acquisition. Therefore, we assume that the total integrated emission from the sample presents only negligible changes as a function of the pump-probe delay. After normalization, we fit the RIXS spectra as shown in Figs. S2, S3, and S4. To reproduce the elastic line, we use a Gaussian function with the width fixed at the instrumental resolution. The asymmetry due to the quasi-elastic scattering is modelled using an additional Gaussian function with fixed position and width. Gaussian functions are used to describe the d-d excitations and the Zhang-Rice singlet (ZRS) excitation. The charge-transfer (CT) contribution, appearing as a complex structure extending from 4 eV to 15 eV energy loss, is modelled as a combination of six Gaussian functions with fixed widths. The relative energy position of each component of the CT, as well as its relative amplitude is fixed. Therefore, only a global shift and a global intensity variation is allowed for the CT, which accounts for fluctuations in the background while preserving the overall shape of the CT. Due to the low visibility of the elastic line, a fine calibration of the energy scale has been performed using the position of the d-d excitations as a reference, under the assumption that the energy associated to the d-d excitations does not change due to the laser pump within our energy resolution. To ensure the fit stability, we choose to fix the width of the ZRS peak to its equilibrium value. The RIXS data, along with the best-fit curves, are shown at different time delay for F = 37.4 mJ/cm 2 (Fig. S2) and for F = 2.5 mJ/cm 2 (Fig. S3), and as a function of the fluence at 100 ps time delay (Fig. S4).

Section S2.1: Sampling of the time delays
The timing tool available at the LCLS allows us to obtain a measurement of the actual time delay for each single FEL shot. As the low throughput of the present experiment does not allow obtaining a full RIXS spectrum at each shot, we accumulate ≥ 10 5 shots for each given time delay and laser pump fluence and choose a certain bin size in the time delay within which perform the summation. This choice affects the overall time resolution of the measurement. The data presented in the main manuscript and in the section above is obtained using a 400-fs grid that we judge appropriate to achieve significant statistics. In Fig. S5, we show the evolution of the ZRS intensity as a function of the time delay obtained by averaging the data on the 400-fs grid (blue symbols) and the data points obtained with a 200-fs grid (red symbols). The latter has twice as much time resolution, but nearly half the statistics. As compared to the 400-fs binning, the 200 fs binning shows a deeper suppression of the intensity at short time delays and might suggest that the actual oscillation frequency is higher than that obtained with the 400-fs grid data. However, the large fluctuations of the result, even in the region of negative time delays, suggests that the data points obtained with such sampling are limited by the low statistics.

Section S2.2 Alternative fitting model
In section S2, we have presented the fitting strategy to extract the evolution of the ZRS excitation as a function of the pump-probe time delay and fluence. In such fitting approach (Model #1), we have kept the width of the ZRS peak fixed to the equilibrium value in order to avoid fit instabilities. In this section, we report the fit results obtained by letting the width of the ZRS free to adjust to find the best agreement with the experimental data (Model #2). The best fit curves for the two models are compared to the experimental data in Fig. S6 (a-b) while the result of the two fitting approaches is compared in Fig. S6 (c-d). The two fit models return nearly the same optimal values except for Δt = 1 ps and 1.5 ps, in which the width of the ZRS increases in Model #2 and so does the total integrated intensity. For instance, at Δt = 1.5 ps, the FWHM of the ZRS obtained with Model #2 is more than 300 meV larger than the one obtained with Model #1. As a result, the damped oscillation observed is strongly amplified. This result confirms the presence of a non-thermal state below 2 ps, however, further experiments with a finer energy sampling and better statistics are needed to characterize such non-thermal state in greater detail.

Section S3: Synchrotron RIXS measurements and two-temperature model analysis
The static O K-edge Resonant Inelastic X-ray Scattering (RIXS) measurements were carried out at the ADRESS beamline of the Swiss Light Source at the Paul Scherrer Institut, Switzerland. The x-ray beam was monochromatized using a plane grating and focused down to a spot size of ≤ 4x55 µm 2 at the sample position using an elliptical refocusing mirror. The incoming radiation was linearly polarized in the horizontal direction, i.e. with the polarization in the scattering plane. The scattering angle was set to 2θ = 90° while all measurements were performed at the specular condition, i.e. with the incoming beam forming an angle of 45° with respect to the sample surface. The combined energy resolution was 55 meV FWHM, determined by collecting the elastic scattering from a carbon tape reference. The sample temperature was varied using a sample manipulator equipped with a continuous flow Helium cryostat. RIXS spectra of CuGeO3 were obtained as a function of temperature between 20 K and 300 K, as show in Fig. S7 (a-b). This allowed the intensity evolution of the ZRS as a function of temperature to be systematically tracked (Fig. S7 (b-c)) under the same scattering geometry as utilized in our time-resolved measurements. Previously published results were obtained using a different geometry 6 . Due to the higher energy resolution available at the static experiment, the ZRS is well separated from the CT peak and its intensity vs temperature was extracted using a fitting procedure as described in the main text.
As outlined in the main text, a comparison is made between the static reduction of ZRS intensity caused by temperature and the temporal changes of the ZRS caused by the pump pulse in the time-resolved experiment. In this way, we obtain an estimate of the transient magnetic quasi-temperature. The transient ZRS intensity trace (normalized to 1 at -1 ps) is fitted with a single exponential decay (shown in Fig.  S8, left panel), which is assumed to result from transient heating. This exponential reduction is then compared with the purely thermal reduction from the static measurements. The comparison is made by fitting the ZRS intensity as a function of temperature with a third order polynomial in order to produce a relation between ZRS reduction and temperature (Fig. S8, right panel). We then map the reduction of the ZRS intensity as a function of delay onto the static temperature evolution, and from this extract an effective temperature. The saturation of ZRS reduction at long time delays is clearly seen to be below the thermal saturation in the static high temperature measurements.

Figure S 8: Extraction of thermal ZRS dynamics and comparison with static RIXS measurements as a function of temperature.
The reduction in the ZRS intensity as a function of delay is converted into an effective temperature by assuming a one-to-one correspondence with the temperature-dependent reduction obtained from the static RIXS data. Furthermore, we model this temperature evolution as described below, in order to compare the extracted temperature with that expected, given the heat input from the pump pulse. Using a simple twotemperature model ( These two equations describe the evolution of the electronic (Te) and lattice (Tl) temperatures. The first term in the electronic temperature equation is the source (pump laser pulse), modeled by a normalized Gaussian, which deposits heat into the electronic system leading to an increase of Te. The second term the coupling termis proportional to the difference between the electron and lattice temperatures and therefore transports heat from the electronic into the phononic system, which equilibrate after some time depending on the strength of the electron-phonon coupling.
A number of parameters are used in the two equations. Ce = γTe and Cl are the electron and lattice specific heat capacities (γ is the electronic contribution to the specific heat). The electron-phonon coupling is proportional to g. The laser parameters are: P, the absorbed energy density within the probed region; σ, the full-width at half maximum (in time) of the laser pulse; and t0, the time zero. The values of these parameters used in the calculations are given in Table S1 along with the relevant references from literature. P and σ are determined experimentally, however as discussed in the main text the value of P estimated from the experiment does not well reproduce the observed temperature dynamics. For this reason in the final two-temperature model P is adjusted to match the experimental temperature dynamics. This difference between the measured and modelled P implies a breakdown of the simple two-temperature model and a non-equilibrium thermal distribution between the lattice and magnetic sub-systems. The temperature dependence of Cl is approximated by a polynomial interpolation from the data in Ref. 7 until the Debye temperature of 360 K (Ref. 8 ), above which the tabulated value is used. The equations were solved numerically and the results presented in Fig. 3 Table S1. Input parameters for the two-temperature model.

Section S4: Model Calculations
We calculated the RIXS spectra using small cluster exact diagonalization and the Kramers-Heisenberg formalism. In this case, the Cu chains of CuGeO3 were modeled using a Cu3O8 cluster with open boundary conditions, as shown in Fig. S9. The orbital basis for this cluster included three Cu 3 orbitals ( = , 2 − 2 , and 3 2 − 2 ) at each copper site and two oxygen 2 orbitals ( = , ) at each oxygen site (twenty-five orbitals in total). The model is similar to the one used in Ref. 10