Resolving length-scale-dependent transient disorder through an ultrafast phase transition

Material functionality can be strongly determined by structure extending only over nanoscale distances. The pair distribution function presents an opportunity for structural studies beyond idealized crystal models and to investigate structure over varying length scales. Applying this method with ultrafast time resolution has the potential to similarly disrupt the study of structural dynamics and phase transitions. Here we demonstrate such a measurement of CuIr2S4 optically pumped from its low-temperature Ir-dimerized phase. Dimers are optically suppressed without spatial correlation, generating a structure whose level of disorder strongly depends on the length scale. The redevelopment of structural ordering over tens of picoseconds is directly tracked over both space and time as a transient state is approached. This measurement demonstrates the crucial role of local structure and disorder in non-equilibrium processes as well as the feasibility of accessing this information with state-of-the-art XFEL facilities.

The development of materials with specialized and highly efficient properties increasingly relies on complex local structures that stray from the ideal of a perfect crystal [1][2][3] .In particular, advancements in electronics technology drive a need for materials that switch between distinct states: either electrical (e.g., memristors 4 , ferroelectrics 5 ), magnetic (e.g., ferromagnets 6 , antiferromagnets 7 ) or structural (e.g., charge density wave states 8 ).A key example is the metalinsulator transition 9,10 .It is well established that local structure plays a central role in many equilibrium phase transitions driven by the competition of energy and entropy [11][12][13] .Some nonequilibrium phase transitions can be triggered on demand using ultrafast laser pulses.Local structure has also been implicated in these transitions 14,15 , but this is less understood due to a lack of appropriate means to quantify length scale dependent local disorder in these ultra-fast transient states.
In studies at equilibrium, the pair distribution function (PDF) plays an integral role in characterizing locally broken structural symmetry and structural disorder 16,17 .This function of interatomic distances in the scattering material, generated through a Fourier transform of an appropriately normalized scattering pattern, is a quantitative and easily interpretable probe for atomic structure on all length scales from local to bulk.X-ray free electron laser (XFEL) facilities offer a key opportunity to apply the PDF technique to picosecond structural dynamics, such as phase transitions, using high brilliance 100 fs X-ray pulses.This would represent a x10 9 increase in temporal resolving power compared to a typical synchrotron experiment that does not severely compromise brilliance with slicing or fast shutter methods 18 .In comparison to electrons, which can also be generated in ultra-short pulses, X-rays scatter kinematically and can generate quantitatively reliable PDFs.
Here, we demonstrate the feasibility of XFEL ultrafast-PDF (uf-PDF) to track an optically pumped phase transition in CuIr2S4 (CIS).This measurement shows that while the local atomic structure transitions in less than a picosecond, the average structure on length scales longer than a unit cell continues to strongly evolve for tens of picoseconds as long-range order between local regions is established.Although the pumping process produces a transition between two ordered phases, this measurement tracks the pivotal role of disorder through the transition itself.CIS is a spinel material exhibiting a metal-to-insulator phase transition (generally described as Peierls-like) upon cooling through 226 K 19 .Above this temperature, it consists of a cubic Fd3 !m unit cell with Ir atoms, the dominant X-ray scatterers, forming a pyrochlore substructure of regular tetrahedra with edge length ~3.5 Å (Fig. 1a).This generates a strong PDF peak at this interatomic distance.Below 226 K, the Ir undergo charge and orbital ordering as their effective 3.5+ charge disproportionates to a nominally 3+/4+ state.Simultaneously, spin dimerization (Fig. 1b,c) shortens (dimers) and lengthens some Ir-Ir distances with a separation in length of ~0.7 Å.The resulting 'M'-shaped signature in the difference of PDF profiles across the transition is significant enough to be well resolved with the limited resolution of an XFEL measurement (Fig. 1d).The dramatic loss in symmetry through this transition is reflected by a new triclinic P1 ! unit cell 19 .The Ir dimerization can be described by chains running along two distinct [110]-type cubic directions 20 (Fig. 1b, arrows) or, alternatively, by two topologically identical 8 atom bicapped hexamers (referred to from here as Ir octamers) 19 .These consist either of Ir 4+ (containing dimerized bonds) or Ir 3+ (containing non-dimerized bonds) ions and together tile 3D space (Fig. 1c, bold outlines).In 2019, high-resolution synchrotron PDF was used to investigate how the local structure of CIS harbingers the bulk phase transition 21 .While the metallic phase is cubic on average, each Ir-Ir bond dynamically fluctuates by <0.1 Å due to an orbital degeneracy lifting (ODL) precursor effect that reduces the local symmetry to tetragonal I41/amd (a subgroup of Fd3 !m).These ODL dimers, which are correlated over increasing distances as the phase transition is approached, cast doubt on the Peierls mechanism of the metal-to-insulator transition and suggest a greater complexity that is unlikely to be understood from equilibrium structural measurements.
Ultrafast reflectivity studies 26,27 have shown that dimerized CIS responds to optical pumping with reflectivity decreasing and recovering over sub-picosecond and tens of picosecond timescales respectively.Using multi-pulse techniques, it has been argued that the (so far unidentified) pumped phase represents a new transient structure and not a return to the high temperature Fd3 !m state 26 .The pumped phase is weakly conducting, suggesting removal of strong dimerization, and could therefore be speculatively related to an ordered variant of the ODL state.As the removal of strong dimerization in CIS would generate a large enough PDF signal to be clearly resolvable in an XFEL measurement (Fig. 1d), this pumped transition is ideal for appraising the uf-PDF technique while simultaneously examining how CIS transitions between insulating and conducting states.Note that dimerized CIS is also known to be sensitive to continuous irradiation by UV or X-ray photons over hundreds of milliseconds [22][23][24][25] .In this markedly distinct regime of photon energies and peak fluences, the X-ray Bragg scattering signature of dimers is removed.However, PDF has shown that only long-range dimer order is destroyed while the dimers themselves persist locally 23 .
To investigate this optically driven transition, a layer of powdered CIS was pumped at 150 K using an 800 nm laser pulse.The pumped sample was stroboscopically probed using X-ray pulses using a transmission scattering geometry at the MFX beamline of the LCLS XFEL facility (Fig. 1e, see Methods).A scattering momentum transfer range from 1.6 Å -1 to 12.6 Å -1 was achieved using 23.1 keV photons.This can be compared to other current XFEL scattering and PDF (without time resolution) measurements achieving only maximum momentum transfers of 5 -8 Å -1 that severely limit real space resolution and degrade the information needed for quantitative analysis 14,28,29 .A reference (unpumped) measurement of the sample was also taken at the same temperature at the Advanced Photon Source synchrotron with a larger maximum momentum transfer of 23 Å -1 .

Results
Initial observations regarding the structural response to the pump laser can be made in reciprocal space.The reduced structure factors (), where  is the scattering momentum transfer, and the difference curves Δ(), where an averaged unpumped reference is subtracted to amplify more subtle changes, are shown as a function of pump-probe delay in Figure 2a,b.There is a clear abrupt change in the patten upon crossing 0 ps pump-probe delay, indicating a structural response.These changes then evolve smoothly in time over the measured  range and do not begin to reverse in the 100 ps measurement time, indicating a lifetime at least this long for the pumped structural phase.These observations suggest that the pumping process can be described in terms of three structures: the Dimerized structure before pumping (which is well characterized), the Prompt structure immediately upon pumping (characterized in this work) and the Transient structure that the material relaxes to over tens of picoseconds (also characterized here).Importantly, no significant response -including heating induced lattice expansion -was observed when pumping the high temperature phase (Supplementary Figure 1, 2).PDFs (), where  is interatomic distance, are generated from sine Fourier transforms of the reduced structure factor (Fig. 2c,d), where the finite range of measured  applies a well understood convolution that broadens peaks and introduces termination ripples.Despite these termination artefacts, analyzing the data in real space has several key advantages.First, subtle and/or broadband changes to diffuse scattering are converted to changes in the positions and shapes of peaks that are easier to identify, interpret and model.Second, focusing on different regions of a PDF reveals how the average atomic structure varies over different length scales.This provides information on structural ordering.Here, the difference curves Δ() display the 'W' signature that some strong Ir-Ir dimers are removed by the laser pump (Fig. 2e [arrows] opposite to the 'M' feature in Fig. 1d [arrows]).The central positive peak of this 'W' along with the two adjacent negative valleys represents a reduction in the spread of Ir-Ir distances as they shift towards a central value.As this signature is fully formed at 1 ps pump-probe delay, this strong dimer suppression must occur on femtosecond timescales and is not probed temporally here.This is consistent with optical dimer removal in VO2, for example, which occurs over 100 fs 14 .The shape of the sub-nanometer response bears a strong qualitative agreement to a simple calculation of multiple unit cells in which either a single or all Ir-Ir dimers are lengthened by 0.4 Å (see Supplementary Note 1 for details).
The >1 ps time-evolution of the pumped PDFs strongly depends on length scale .Following the laser pump, the features in the difference curve ∆() are initially similar in scale at all  (Fig. 2d).With continuing delay, these scales evolve differently above and below ~9 Å -the length scale of one unit cell / octamer (Supplementary Figure 3).While the PDF below 9 Å, and therefore the distribution of nearest neighbor atomic distances, could be tentatively argued to continue to subtly evolve with delay just above the noise level (Fig. 2e insets), any changes are dwarfed by the initial abrupt response.This is clear from the constant Root Mean Square (RMS) of Δ() from 2 -9 Å, reducing the information in Δ() to a simple magnitude of the PDF change (Fig. 2f).In contrast, this same metric at longer length scales (18 -25 Å and 34 -41 Å) features a similar initial step change followed by strong growth incomplete within 100 ps.This implies that the pumped Prompt and Transient phases are the same on local length scales but distinct over length scales averaging over multiple unit cells.Both differ from the starting Dimerized phase at all length scales.The longer timescale increase in the RMS metric over 34 -41 Å follows an exponential time constant of (38 ± 6) ps.
A picture emerges from these real-space observations.The structural changes instigated by the optical removal of Ir-dimers (a stochastic process) are initially uncorrelated between local regions of the sample.That is, in the Prompt phase, the spatial arrangement of bond lengths differs from one local region to the next.Internal strain imposed by this disorder likely drives the redevelopment of a non-equilibrium long-range order over time.This alters the PDF over longer length scales as the Transient phase is approached while leaving the local PDF over sub-unit cell length scales largely unchanged.A minor evolution of the local PDF with delay could be permitted as external strain on each unit cell reduces with decreasing disorder.Note that the observation of the removal of strong dimers precludes the pumped state from being the same as that reached under continuous UV or X-ray irradiation in which local dimerization is preserved 23 .The average W signature centered at 3.5 Å in ∆() can be compared to the same signature generated by the equilibrium (thermally driven) transition in which all strong dimers are removed.While qualitatively very similar, the thermally driven signature must be scaled by ~0.29x to match the pumped signature intensity.This indicates that ~29% of probed dimers in the pumped sample are suppressed.As the pump laser is expected to penetrate 40 nm into each ~0.7 μm powder grain 26 , we would expect only a maximum of ~4% of probed dimers to be suppressed depending on the fraction of dimer suppression within the pumped volume.This suggests that either a) the characterization of the powder was inaccurate and the average grain size is smaller than determined by confocal microscopy (Supplementary Figure 4) or b) the transition occurs within a greater depth with energy carried by, for example, non-thermal photoexcited electrons 30,31 .Although the pumped phase fraction cannot be unambiguously determined, there is a lower bound of ~29% on the proportion of dimers suppressed within the pumped volume.
The pumped signature can also be compared to a simple 'small box' model, a numerically generated PDF of a perfect crystal (with experimental effects such as termination artefacts reproduced) that is typically compared to an experimental PDF over a certain interatomic distance range.These models parameterize, with symmetry constraints, the atomic positions within a unit cell and the Atomic Displacement Parameters (ADPs) that smear these positions both due to thermal motion (temporal variance) and any disorder between local regions (spatial variance).For describing this narrow -range, we assume a simple model where the Ir substructure linearly transitions between the dimerized and un-dimerized configurations (Supplementary Note 3).Using this model, we find that the resolution and signal-to-noise ratio is not high enough to distinguish between Ir dimers being significantly weakened or entirely removed (Supplementary Note 3).This model, implicitly assuming that all strong dimers in the pumped volume are suppressed by the pump, suggests a pumped phase fraction of ~20%.The small shift between the W signatures of the pumped and equilibrium transition (Figure 3a) could indicate an inflated Ir ADP due to the pumping (Supplementary Note 3) or simply represent a small (~3%) inaccuracy in the intensity normalization of the PDFs.The small box methodology is also applied to non-local length scales (8.8 -40 Å).In this case, the larger  range allows meaningful 3D structural information to be extracted.The experimental PDFs are modelled as a sum of a calculated pumped phase and an assumed static unpumped phase that is here defined as proportional to the measurement at -20 ps pump-probe delay.Including experimental data as a model component will artificially reduce fit residuals  (see Methods for definition) as this component will, by definition, capture any systematic errors/artefacts present in the data.Accordingly, more focus must be applied to relative differences between pump-probe delays and between different structural models.In the high temperature equilibrium phase, weak fluctuating dimers exist locally but are uncorrelated over multiple unit cells to average out to a cubic structure in space group Fd3 !m at non-local length scales.Applying the Fd3 !m unit cell here leads to a larger  over the first 25 ps delay, indicating underfitting of short delay data and a lack of model complexity (Fig. 4b).Therefore, the averaged pumped structure is not Fd3 !m but a new phase in agreement with a previous reflectivity study 26 .These higher residuals are reduced by using a tetragonal structure in space group I41/amd (a sub-group of Fd3 !m).This is the unit cell used to describe the high temperature local ODL structure.At low delays, residuals can be further improved by reducing the symmetry again to an orthorhombic structure in Fddd (a sub-group of I41/amd).The orthorhombic and tetragonal residuals converge at higher delays.Note that both I41/amd and Fddd descriptions are simple, high symmetry models with Ir atom positions fixed within the unit cell and any change in Ir-Ir distances are dependent on the lattice parameters.Further increasing the complexity of the model, for example by using a tetragonal F4 !2m unit cell that allows some limited changes to Ir atom positions independent of the unit cell parameters, offers no further improvement in  and begins to enter the regime of overfitting.While higher resolution data, taken with a future higher energy XFEL or novel detector geometry, may be able to successfully resolve a lower symmetry model in the future, this data is therefore best described non-locally by an orthorhombic unit cell at lower delay times (the Prompt phase) and a tetragonal unit cell at longer delay times (the Transient phase).The apparent increase in symmetry with delay at non-local length scales reflects an evolution in the longer-range order between the local, strong dimer removed, regions and is consistent with the model-independent analysis.Note that these models provide pumped phase fractions of 20-25 % (Supplementary Figure 13), consistent with the above analysis of the local PDF.
Modelling provides access to information that is not obvious from the raw data alone.For example, both I41/amd and Fddd unit cells involve a new well defined exponential timescale of (12 ± 1) ps governing the lattice parameters (Fig. 4c, interpreted below).With the knowledge to carefully search for it, this timescale can be identified in the raw data where it tracks the subtle shifting of some peak positions in Δ() (Supplementary Figure 14).Modelling also provides access to ADPs.For the I41/amd unit cell, the Ir ADPs decrease over tens of ps (Fig. 4d) indicating a reduction in spatial disorder and/or thermal motion as expected.By re-refining this model over a narrower sliding window of , ADPs can capture how disorder varies as a function of length scale.The model is re-refined using a sliding window of width 8.2 Å -a window size that did not risk overfitting.While unit cell structure does not significantly depend on the refinement range (Supplementary Figure 15), the resulting Ir ADPs show a strong dependence (Fig. 4e).This dependence does not correlate with other model parameters and is therefore not a result of overfitting (Supplementary Figure 15).As a similar strong dependence is also observed for the more complex tetragonal F4 !2m model, this is also not a consequence of model underfitting.Below ~25 Å (i.e., 2-3 unit cells), the Ir ADPs are easily attributed to thermal effects (~0.006Å 2 ) and show no significant delay dependence indicating insignificant laser heating.At larger length scales, the ADPs initially increase by over 350% (to ~0.022 Å 2 ) before decreasing with delay with a characteristic time of (39 ± 9) ps (Fig. 4f).This tracks the ~40 ps time scale of the PDF RMS metric (Fig. 2f).At short delays (Prompt phase), the pumping of regions separated above a critical distance (seemingly 2-3 unit cells) can be considered independent and their spatial arrangement of bond lengths uncorrelated.This inflates ADPs forced to capture this disorder.The resulting strain between local regions drives lattice relaxation and a (39 ± 9) ps fall in the disorder-related ADP component as the Transient phase is approached.

Discussion
The evolution of non-local (8.8 -40 Å) pumped CIS from the Prompt to the Transient structures contains distinct ~12 ps and ~40 ps timescales governing lattice parameters and Ir ADPs respectively.The existence of two seemingly independent timescales can be tentatively explained.The average unit cell averages over the local structure at every point in the pumped material.Upon initial pumping, there will likely be different local arrangements of atoms that give near-equivalent distributions of nearest-neighbor bond lengths.Our data is not sensitive to these different configurations.These different local structures average to the non-local unit cell, with the proportions of each configuration changing over the ~12 ps timescale.The proportions of local structural configurations gives little information on how spatially ordered they are with respect to one another, which is instead tracked by the ~ 40 ps timescale.
In summary, this uf-PDF investigation has shown that optical pumping suppresses strong Ir-Ir dimers in low temperature CIS.Despite transitioning between phases with long-and intermediate-range order respectively, this optically driven transition is fundamentally characterized by a period of high structural disorder.Above a critical distance (approximately 2 unit cells), the sub-picosecond suppression of Ir-dimers is uncoordinated with local regions taking on different spatial arrangements of bond lengths.We propose that internal strain drives a recovery of order over ~40 ps and an evolution in the average crystallographic structure.This timescale matches the recovery of reflectivity in previous studies 26,27 .The key power of PDF to explicitly isolate ranges of length scales for structural modelling has here allowed disorder, measured through ADPs, to be mapped over both length-and time-scales.This disorder mapping could be widely applied to other non-equilibrium systems.
In agreement with reflectivity studies 26 , we find that pumped CIS is not driven back to the equilibrium room temperature phase.Instead, the non-local structure at longer delay times is best described using the I41/amd crystal space group that also describes the local ODL structure at room temperature.It is possible that this new phase is related to the ODL state with the fluctuating weak dimers now ordered over long length scales.In similar spinel structures, such as LiRh2O4 32 , the metal-to-insulator transition involves first the ordering of fluctuating dimers and then spin dimerization at two distinct temperatures.In CIS, these processes are simultaneous.Speculatively, the non-equilibrium pumped phase may be this otherwise inaccessible (hidden) intermediate orbitally ordered state lacking spin singlet dimerization.Notably, this phase is distinct from the disordered dimer state achieved by UV, electron, and X-ray irradiation which preserves the dimers locally [22][23][24][25] .We caveat these conclusions by noting that the data, although currently the best available, is limited by a higher minimum , lower maximum  and broader -resolution than desirable.In a future experiment, it might be possible to distinguish between the symmetries of structural models more robustly and describe the pumped structure with a lower symmetry unit cell.These current resolution limitations prevent an in-depth structural analysis of the local (sub-unit cell) structure beyond the key observation that strong Ir dimers are optically suppressed.
Methodologically, this work has successfully demonstrated uf-PDF as a practical and powerful technique given a favorable sample with structural changes significant enough to be resolvable at current XFEL facilities.Despite the reduced PDF resolution and shot-to-shot consistency of an XFEL measurement compared to a synchrotron, these are not significant enough to obscure critical length-scale dependent structural information.Proven feasible, uf-PDF could be applied to better understand systems, such as VO2 14,33 and 1T-TaS2 34 , that also display transient disorder.This technique will only improve as experimental and data handling protocols are optimized and higher XFEL energies, possibly in the pipeline for the next decade, increase spatial resolution.As the picosecond time resolution of this experiment was set by precision expectations for the laser pump delay line, there is no reason why this now-demonstrated technique couldn't be pushed far into the femtosecond regime.As a complement to studies of diffuse scattering that remain in reciprocal space 14 , uf-PDF is highly quantitative through straightforward comparison to structural models.

Sample Synthesis
CuIr2S4 was prepared by solid state reaction in evacuated quartz ampoules.Stoichiometric quantities of the metals and elemental sulfur were thoroughly mixed, pelletized, and sealed under vacuum.The ampoules were slowly heated to 650-750 o C and soaked for several weeks with intermediate regrinding and pelletizing.The reaction was deemed complete when no further changes in x-ray powder diffraction scans were observed.The product was found to be a single spinel phase.

Measurements
A 2-3 µm layer of powdered CIS (grain size ~ 1 µm), spread onto Kapton tape, was measured using a transmission pump-probe geometry at the MFX beamline of the LCLS XFEL source.Full Debye-Scherrer rings of scattered X-rays were collected using a Rayonix MX340 CCD positioned ~70 mm downstream of the sample (i.e. a Rapid Acquisition PDF setup 35 ) at an acquisition rate of 30 shots/second.An 800 nm ~100 fs laser pulse from a Coherent Vittara was used to pump the sample with 41 µJ of energy over a 400 µm Full Width at Half Maximum Gaussian spot.A 23.1 KeV X-ray beam probed the sample in ~100 fs pulses.The probed area, a 300 µm top-hat spot, was smaller than the pumped region to minimize any effects from the spatial distribution of pump energy.The sample was cooled using a N2 cryostream at a nozzle temperature of 150 K.Each delay time was measured stroboscopically and averaged over hundreds of pump-probe cycles.The pump-probe delays were measured in a pseudo-random order to ensure no accruing permanent structural changes (i.e.damage) from repeated pumping.Background measurements were acquired of both bare Kapton tape and air scatter, and dark measurements were taken without application of the Xray probe pulse.

PDF Generation
The 2D diffraction image associated with each pump-probe delay time was the average of hundreds of individual stroboscopic measurements.The number of averaged images was not constant with delay due to the varying number of 'bad shots' filtered out (where the measurement fails due to a mechanical or electrical fault).Background measurements of air scatter and bare Kapton tape were removed.The images were normalized for the polarization dependance of the detector's detection efficiency and for any variation in detection efficiency across the detector (the 'flat field').An unexpected intensity was noted that was broadband in  and did not vary in intensity around the Debye-Scherrer rings (as expected from the polarization dependance).This was likely the result of multiple-scattering events due to the sample thickness.As this did not vary in intensity around the rings like the single-scatter data, it could be removed post-hoc.The 2D images were converted to 1D diffraction patterns using the pyFAI software 36 .
Reference unpumped measurements from the APS synchrotron with higher maximum momentum transfer magnitude Q ~ 23 Å -1 were used to guide and confirm detector-sample position calibrations.Typically, diffraction patterns () are converted to reduced structure factors () and PDFs using the software PDFgetX3 37 .This conversion requires material-and measurement-dependent corrections () = () () + () for unknown broadband functions , .PDFgetX3 estimates these functions ad hoc based partially on asymptotic behavior of () at high and low .Due to the limited measured  range, these estimates were found to be incorrect for the XFEL data by comparison to the unpumped PDFs generated from the synchrotron reference (accounting for different detector properties etc.).Functions  and  were instead found by comparison to the reference unpumped measurements and fixed for all delay times.A comparison of synchrotron and XFEL PDFs is shown in Supplementary Figure 16.
To normalize the diffraction patterns by the average probe X-ray fluence, it is assumed that the total scattering intensity measured is constant with pump-probe delay.This accounts for both X-ray probe intensity and any change in sample volume due to the possibility of some sample ablation.This self-normalization procedure was verified by comparing the lowest physical PDF peak (Cu-S / Ir-S Fig. 1d) with pump-probe delay which did not meaningfully evolve (as expected, Supplementary Figure 17).

PDF Fitting
PDF structure fitting was carried out using the diffpy.cmiPython package wrapping the PDFFIT2 engine 38 .Structural models were optimized to minimize the root-square-difference between experimental  !"# () and numerical  $%&$ () PDFs, as quantified by residual (%) = 100 × 3∫[ !"# () −  $%&$ ()] '  ∫[ !"# ()] '  9 .Local and average PDF length scales are separated at 8.8 Å as this threshold does not cut through any PDF peaks.The unpumped reference PDF was defined as the PDF measured with -20 ps pump-probe delay, which could be scaled in magnitude during the fitting to account for the fraction of unpumped material.For fits of the average structure, no parameter constraints were applied beyond those required by the crystal symmetry.Atomic displacement parameters presented represent variance in atomic positions, typically denoted as  ()* , and not the alternative  value given by 8 '  ()* also presented in literature.

Figure 1 |
Figure 1 | CuIr2S4 Ir Dimerization.a) Portion of the undistorted pyrochlore Ir substructure in the 300 K CIS structure described in space group symmetry Fd3 ! m.Structure refined from experimental data.b) Portion of the CIS Ir substructure at 150 K as described in triclinic space group P1 ! .Charge/orbital ordering and spin dimerization separates Ir-Ir bonds into significantly shortened (blue) and lengthened (red), or largely unaltered (grey) groups.Dimerized bonds run along two distinct [110]-type cubic directions (examples marked by arrows).Structure refined from experimental data.c) Different portion and view of the same 150 K CIS Ir substructure, emphasizing topologically equivalent bi-capped hexamers containing either Ir 3+ or Ir 4+ ions (bold outlines).d) Ir dimerization creates an 'M'-shaped differential PDF signature at the length scale of an Ir-Ir bond

Figure 2 |
Figure 2 | Structural Response to Laser Pump.a) Reduced structure factor (), a linear function of the diffraction pattern that magnifies high  features, with varying pump-probe delay.All negative delay signals (unpumped measurements) are colored grey.v) Δ() subtracting the average of {-20,-15,-10} ps to emphasize differences due to laser pump.Y-axis magnified x3.4 relative to ().c) PDF () with varying pump-probe delay.d) Δ() subtracting the average of {-20,-15,-10} ps to emphasize differences due to laser pump.Y-axis magnified x3.4 relative to ().e) Δ(r) over sub-nanometer length scales showing a sub-ps abrupt change.The signature of Ir-Ir dimer suppression, the inverse of the 'M' in Figure 1d, is marked with black arrows.Insets: Smaller changes to the PDF continue with increasing delay.f) Root-mean square (RMS) of ∆() calculated over equally sized ranges of interatomic distance, showing the same initial prompt response at 0 ps but a difference in further structural evolution at local and non-local length scales.∆() RMS over 34 -41 Å range follows exponential behavior with (38 ± 6) ps characteristic time (black dashed line).RMS of ∆() is also shown (grey) representing all accessible length scales.∆() normalised to match negative delay values for ∆() (representing the noise level).Error bars indicate uncertainty due to photon shot noise only.

Figure 3 |
Figure 3 | Dimer Suppression Signature.a) Experimental Δ() for both the pumped (black) and thermally driven equilibrium (red) transitions, showing the dimerized PDF subtracted from the un-dimerized PDF, over the low  range containing the W-signature centered at 3.5 Å of strong dimer removal.The pumped data averages over all positive pump-probe delay times with line thickness indicating uncertainty (Supplementary Note 2).The equilibrium data is scaled by x0.29 so that the signatures approximately match in scale.b) Uncertainty on PDF normalization is propagated to a Probability Density Function representing the scaling between the pumped and equilibrium dimer suppression signatures (Supplementary Note 2).Dashed line indicates the median probable value of 29.4%.Shaded areas indicate the central 68% and 95% probability intervals.

Figure 4 |
Figure 4 | Models of Non-Local Structure a) Crystal space groups used to model the average (8.8 -40 Å) length scale of the pumped PDFs.Arrows denote a group-subgroup relation.Each subgroup exposes more refinable structural parameters (denoted #Params).Each model fit also includes four parameters capturing properties of the experimental set-up.b) Residual  versus pump-probe delay.Dashed lines indicate reference  for unpumped models at 300 K (Fd3 !m) and 150 K (P1 ! ).c) Lattice parameters versus delay.Dashed line indicates reference lattice parameter for 300 K equilibrium measurement.d) Ir isotropic ADPs versus delay.Dashed lines indicate reference ADPs for unpumped 300 K and 150 K measurements.All error bars indicate uncertainty due to photon shot noise only.See Supplementary Fig. 11, 12 for example fit.e) I41/amd isotropic Ir ADPs refined over a sliding window of width 8.2 Å to generate a spatial-temporal disorder map.Refinement Length Scale indicates the center of the refinement windows.f) ADPs with delay for windows at three representative length scales.Longer length scale ADPs decrease over time with a time constant of ~ 40 ps while shorter length scale ADPs remain constant.Delay times are marked by dashed lines in e).