(EDO-TTF) 2 PF 6 (where EDO-TTF is ethylenedioxytetrathiafulvalene) is a quasi-one-dimensional, 3/4-band-filled charge-transfer organic salt that undergoes a thermally induced insulator-to-metal phase transition at a critical temperature of T c ≈ 280 K (ref. 21) and also a highly efficient and ultrafast photo-induced phase transition22,23,24. Its electronic structure resembles that of Bechgaard salts, which provided the first organic superconductor, (TMTSF) 2 PF 6 (see ref. 25). The origin of its insulator-to-metal phase transition involves a variety of collective phenomena23: Peierls-and-Holstein-type electron–phonon26 and antiferromagnetic interactions27 , that coexist with order–disorder21,24 charge localization, and long-range Coulombic interactions have an important role in charge disproportionation28. In its metallic or high-temperature (HT) phase, electron donor EDO-TTF molecules (D) form columns of cations that are separated by sheets of acceptor PF 6 anions. The distribution of positive charges among EDO-TTF molecules along the stacking direction is represented by (D+0.5D+0.5D+0.5D+0.5) as shown in Fig. 1 (top right)21,22,23,24. The high positive charge mobility along the cation stacks confers metallic properties at room temperature. The holes localize below T c and endow the low-temperature (LT) phase with insulating properties. In the LT phase, the EDO-TTF molecules present a charge-ordered21,22,23,24 state (D+1D+0D+0D+1), in which a large bending of the neutral moieties promotes the doubling of the unit cell akin to a Peierls mechanism in a half-band-filled system, as shown in Fig. 1 (top left). Model calculations predict that vertical photo-excitation via the second charge-transfer band26 leads to a localized {D+2D+0D+0D+0} excited state. Time-resolved optical reflectivity measurements in combination with theoretical modelling indicate23 that this initial excited state evolves in less than 100 fs into a (D+1D+0D+1D+0) charge-disproportionate state, which has a lifetime of about 4 ps. Time-resolved optical studies in the near- and mid-infrared region identify large charge fluctuations as the driving process that finally leads to the complete randomization and melting of the charge order after about 100 ps (ref. 24).

Figure 1: Insulator-to-metal first-order phase transition in (EDO-TTF) 2 PF 6 . Top panels, illustration of the molecular and electronic changes associated with the thermal insulator-to-metal phase transition. Bottom panels, diffraction patterns for the LT and HT phases, obtained at 230 K and 295 K, respectively. The inset shows the assigned Miller indices (h, k, l). The symmetry breaking (cell doubling) corresponds to peaks indexed with k = 2n + 1 in the LT phase. For details about the definition of unit cell axes, see Supplementary Information section 6.1. Full size image Download PowerPoint slide

To probe the structural evolution in (EDO-TTF) 2 PF 6 directly during its photo-induced insulator-to-metal phase transition, we performed femtosecond electron diffraction (FED) studies employing a recently developed ultrabright femtosecond electron source7,8,9 that can deliver high-quality diffraction from low-atomic-number materials even at the very low repetition rate of only 10 Hz used to avoid the adverse effects caused by cumulative heating. FED experiments were performed in transmission mode, with the electron beam propagating nearly perpendicular to the stacking direction of the EDO-TTF moieties to ensure high sensitivity to the most relevant molecular motions, that is, those associated with the dynamics of the EDO-TTF moieties and PF 6 counter-ions. Samples were kept at 230 K (for the LT phase) and photo-excited by 60-fs, 800-nm light while being monitored by ultrabright femtosecond electron pulses, with 200 or more reflections enabling us to track time-dependent changes beyond the noise level. See the Supplementary Information for detailed information about methodology (sections 1–3), sample preparation (section 5), sample orientation (sections 6.1 and 6.4), and control experiments (section 4).

Figure 1 depicts the molecular arrangement of EDO-TTF moieties with their respective charge distributions for the LT and HT phases, along with the corresponding electron diffraction patterns. The appearance of a new family of peaks in the diffraction pattern of the LT phase is indicative of a cell-doubling effect, with the clear difference between the diffraction patterns of the LT and HT phases confirming that the crystal orientation allows the observation of the relevant structural changes.

We monitor the structural evolution of the system by collecting diffraction patterns at different time delays after photoexcitation and using the pattern of the initial LT phase as a reference, with the resulting difference patterns shown in Fig. 2a. For comparison, Fig. 2b shows the difference between the diffraction patterns of the HT and LT phases (shown in Fig. 1). Figure 2c gives the temporal evolution of normalized intensity changes for some selected Bragg reflections, which allow separation of the observed photo-induced structural dynamics into a ‘fast’ component in the subpicosecond-to-picosecond range and a ‘slow’ structural change proceeding on the 100-ps timescale. The fast dynamics can be explained as femtosecond optical excitation altering the charge distribution, modifying the inter- and intramolecular forces and driving coherent molecular motions. The slow dynamics are attributed to uncorrelated motions that provide an ensemble-averaged picture of the structural evolution, that is, a thermal relaxation process that brings the system to a metallic HT-type state24. The transfer of heat to the lattice manifests itself as slow oscillations of diffracted intensities (see right panel in Fig. 2c) which are probably introduced through the generation of strain waves29. The most noteworthy feature is the plateau behaviour observed for time delays from about 3 ps to 10 ps (left panel of Fig. 2c), which reflects a transient intermediate structure (TIS). Given that optical studies indicate large charge fluctuations23 prevailing in this time span24, it seems plausible that the effective intermolecular forces are screened and the structure therefore transiently locked.

Figure 2: Photo-induced time-dependent structural changes monitored by ultrabright FED. a, Differences between the diffraction patterns of the photo-induced and the initial LT phases as a function of the time delay between the optical excitation and electron probe pulses. b, Difference between the diffraction patterns of the HT and LT phases (shown in Fig. 1). c, Relative intensity changes for a few selected reflections. On the left side of the vertical green line, fast dynamical processes are shown; on the right side, slow dynamical processes are shown. The excitation fluence was 0.55 mJ cm−2. The sample was photo-excited by 60-fs, 800-nm optical pulses at a repetition rate of 10 Hz. Error bars represent the standard deviation of measured values within the set of ten identical trials. Full size image Download PowerPoint slide

To obtain a time-dependent map of the relevant molecular motions driving the insulator-to-metal phase transition and the formation of the TIS, we developed a structural refinement algorithm based on a parameterized molecular model (see equations (4), (6), (7) and (8) in Supplementary Information section 7). The model makes use of the LT and HT structures as previously determined by X-ray diffraction21 and considers about 40 Bragg reflections in the refinement calculations. The selection of reflections was based on their proximity to the Ewald sphere (Bragg condition) and the necessity of removing overlapped peaks.

The entire data set of diffraction images was reduced to the square root of intensities, that is, structure factor amplitudes (besides a k-dependent constant), where k denotes the scattering vector (or Miller indices) and t is a given time delay. Given that optical excitation causes only a small fraction of unit cells (η exc ) to undergo structural changes (see Supplementary Figs 9, 12 and 15), the observed experimental structure factor amplitudes can be written30 as , where is the relevant part showing time-dependent changes and F LT (k) are the structure factor amplitudes of the initial LT phase. The structure factor amplitudes are weighted by the fraction of unit cells being altered, and remaining in the LT phase, respectively. Our model refinement calculations compare with simulated amplitudes and maximize the Pearson correlation coefficient, . This figure of merit γ varies between 0 (no correlation) and 1 (full correlation) and was found to provide well-behaved maxima across the full time series (see Supplementary Figs 14 and 15).

The term ξ is an atomic structural parameter composed of the three time-dependent generalized reaction coordinates (ξ F , ξ B, ξ P ) assigned to the motion of three independent dynamic groups: flat EDO-TTF molecules, bent EDO-TTF moieties and PF 6 anions, respectively. The configuration space was created from a linear interpolation (for each dynamic group) between the initial {ξ = (0, 0, 0)} LT and the final {ξ = (1, 1, 1)} HT-type structures (see Supplementary Table 2). We believe that the reduction of the problem to such reaction coordinates (see Fig. 3a) should capture most of the physics and, at the same time, avoid unphysical results as a consequence of over-fitting. A value of η exc ≈ 0.1 was obtained by maximizing γ(η exc ) in the time interval of 0–10 ps (see Supplementary Fig. 15) and found to be in very good agreement with the estimated number of converted unit cells into the HT-type state obtained from equation (5) of the Supplementary Information and from the decrease at t = 1 ns in the structure factor amplitude averaged over (h, k = 2n + 1, l)-reflections (where n is an integer) shown in Supplementary Fig. 9. Such reflections disappear in the HT phase owing to its higher symmetry (see Supplementary Information section 6.2).

Figure 3: Reaction coordinates and their temporal evolution in the formation of TIS. a, Three unit cells illustrating the arrangement of EDO-TTF molecules and PF 6 counter-ions in the LT phase. Selected dynamical groups are illustrated using different background colours in the central unit cell: flat EDO-TTF moieties have a green background, bent EDO-TTF moieties have a pink background, and PF 6 anions have a cyan background. Green sticks denote the atomic displacements from the initial LT structure to the TIS (unit cell on the left) and the HT-type structure (unit cell on the right); displacements were magnified 10 and 5 times, respectively, for clarity. The root-mean-square displacement between the LT structure and the TIS is 0.18 Å and between the LT and HT-type structures is 0.44 Å. The atomic coordinates of the TIS are listed in Supplementary Table 2. b, Temporal evolution of ξ in a (ξ F , ξ B, ξ P )-Cartesian configuration space. Circles indicate optimized structures. The red trace is a multi-exponential fit of the optimum correlation trajectory. The green trajectories are two-dimensional projections. c, Temporal evolution of each reaction coordinate and its contribution in the formation of the TIS. Error bars represent the full-width at half-maximum (FWHM) of the global maximum peaks of the Pearson correlation coefficient in reaction coordinate space. Solid traces are multi-exponential fits; see equation (9) in the Supplementary Information and Supplementary Table 1. See Supplementary Videos for full molecular movies highlighting the key molecular motions leading to the formation of the TIS state. Full size image Download PowerPoint slide

These last two estimations of η exc rely on the fact that by t = 1 ns the system has fully thermalized in a HT-type state and little residual thermal stress is left. These are fair assumptions considering that for t > 500 ps, the oscillations are damped, the estimated temperature increase is less than 50 K and the effect of residual stress is minimized for reflections satisfying Bragg’s law29. From optical reflectivity and in situ transmission measurements we estimated that, for the excitation level used in the experiments, about 8% of the LT unit cells are initially photo-excited (see Supplementary Information section 2). The above observations indicate that the initial excitonic correlation length only extends over about one LT unit cell, promoting local structural changes.

Figure 3a depicts the selected dynamical groups (central unit cell) and the atomic displacements connecting the LT structure with the TIS (on the left) and the HT-type structures (on the right), respectively. The root-mean-square displacement between the LT structure and the TIS is 0.18 Å and between the LT and HT structures is 0.44 Å. Figure 3b summarizes the time-dependent changes of ξ, illustrated in a (ξ F , ξ B, ξ P )-Cartesian configuration space. As can be seen from the two-dimensional projections, the motions of flat EDO-TTF moieties and of PF 6 counter-ions are correlated. The temporal evolution of each reaction coordinate is also shown in Fig. 3c, for clearness. The relative values among reaction coordinates suggest that optical excitation mostly drives the formation of the TIS through the sliding of flat EDO-TTF moieties and the correlated motion of PF 6 counter-ions. This observation is also supported by their respective overshoot values, Δ ≡ ξ(1 ps) − ξ(5 ps), which are indicative of an over-damped half-cycle motion. The close proximity of PF 6 anions to EDO-TTF molecules and the observed correlation suggest that steric effects—that is, short-range repulsive interactions— are also important in the crystalline order and positioning of the anions.