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Non-equilibrium phase precursors to the insulator-metal transition in V2O3

The discovery of novel phases of matter is at the core of modern physics. In quantum materials, subtle variations in atomic-scale interactions can induce dramatic changes in macroscopic properties and drive phase transitions. Despite their importance, the mesoscale processes underpinning phase transitions often remain elusive because of the vast differences in timescales between atomic and electronic changes and thermodynamic transformations. Here, we photoinduce and directly observe with x-ray scattering an ultrafast enhancement of the structural long-range order in the archetypal Mott system V2O3. Despite the ultrafast change in crystal symmetry, the change of unit cell volume occurs an order of magnitude slower and coincides with the insulator-to-metal transition. The decoupling between the two structural responses in the time domain highlights the existence of a transient photoinduced precursor phase, which is distinct from the two structural phases present in equilibrium. X-ray nanoscopy reveals that acoustic phonons trapped in nanoscale blocks govern the dynamics of the ultrafast transition into the precursor phase, while nucleation and growth of metallic domains dictate the duration of the slower transition into the metallic phase. The enhancement of the long-range order before completion of the electronic transition demonstrates the critical role the non-equilibrium structural phases play during electronic phase transitions in correlated electrons systems.

Vanadium sesquioxide (V 2 O 3 ) undergoes an insulator-to-metal transition upon heating at 160 K: the electric conductivity grows by five orders of magnitude (see Fig. S1) via percolation of the high-temperature (HT) paramagnetic, metallic domains within the lowtemperature (LT) antiferromagnetic, insulating domains [8][9][10] . The electronic phase transition is accompanied by a structural phase transition, where the crystal symmetry increases from monoclinic to rhombohedral, and the volume shrinks via reduction of the average hexagon edge from 2.91 Å to 2.87 Å (see Fig. 1a) [11][12][13] . While the symmetry and volume are coupled in equilibrium, here we show that ultrafast photoexcitation decouples these structural degrees of freedom, and the phase transformation occurs via a nonequilibrium transient pathway (see Fig. 1b).
We study a 100 nm thin V 2 O 3 film grown along the (024) Rh crystallographic direction (see Supplement). The difference in the hexagon edge lengths results in two well distinct X-ray Bragg peaks along the film normal, ! " : (024) Rh and (022) Mon (see inset in Fig. 1c).
The LT diffraction peak is broader than the HT peak in the direction parallel to the film, Fig. 1c). The excess broadening results from a reduction of the long-range order (coherence length) due to the breaking of the crystal symmetry at low temperatures: three monoclinic structures are possible, each distorted along a different hexagon edge 11,12 . When heated quasi-statically through the phase transition temperature, the height of the HT peak grows, while the height of the LT peak decreases monotonically.
The LT diffraction peak width is proportional to the LT peak height, while the width of the HT peak is static (see Fig. S2).
We use short, optical laser pulses (E=1.55 eV, 40 fs duration, 500 µm spot size) to induce an insulator-to-metal phase transition in V 2 O 3 . We probe the structural response to photoexcitation with short x-ray pulses (E=9 keV, 10 fs duration, 200 µm spot size) in stroboscopic mode at the Linac Coherent Light Source 14,15 . After photoexcitation, the height of the HT peak grows as expected (see Fig. 1c), as the optical laser pulse heats the film. Because the HT peak grows, one may expect a drop in the LT peak height.
Unexpectedly, the height of the LT peak grows for 2.5 ps before it declines for larger time delays (see Fig. 1d). From the 4D data set (3D reciprocal space and time, see Supplement and Fig. S3), we find that the LT peak height grows by narrowing the LT peak. Since the peak broadening in the ground state originates from the decrease in long range order, we conclude that photoexcitation induces higher symmetry in the LT phase after 2.5 ps. At these short timescales however, the photoexcited LT phase retains its unit cell volume, as revealed by the unmodified Bragg peak position (see Fig. 1b).
The photoinduced structural phase transition displays two processes with vastly different characteristic time scales. First, the structural coherence length in the photoexcited LT phase, x(t), grows rapidly within 2.5 ps (see Fig 2a, left axis) and remains high for more than 100 ps. Second, the HT phase fraction, P HT (t), grows gradually within 100 ps after photoexcitation. The unit cell volume of the photoexcited LT regions shrinks discontinuously and the HT phase emerges, evidenced by decrease of the LT and increase of the HT integral peak intensity (see right axis in Fig. 2a, and Fig. S4). Furthermore, the coherence length and the phase fraction depend differently on the pump fluence. The coherence length x(2.5ps) increases linearly with the pump fluence before it saturates at ~5 mJ/cm 2 (see Fig. 2b). The dynamic saturation value at 1.3 above the ground state agrees with the maximum coherence length of the LT phase measured in equilibrium (see Fig. S2). In contrast, the final HT phase fraction P HT (100 ps) displays a fluence threshold 7,16 around 1 mJ/cm 2 : the growth rate increases significantly when the pump energy overcomes the energy barrier due to the latent heat (see Fig. 2c). At fluences higher than 5 mJ/cm 2 the phase fraction P HT (100 ps) saturates at its maximum value of one, when the entire volume is in the HT phase. While the presence of the fluence threshold and the duration of the HT phase growth are both consistent with the photoinduced electronic transition 7 , the origin of the 2.5 ps time scale remains elusive. To understand the mechanism underpinning this ultrafast coherence length growth, we use X-ray nanoscopy.
We map the static nanoscale spatial distribution of the two structural phases (see Fig. 3a) and their coherence length (see Fig. S5) by scanning a 20 nm X-ray beam across the sample. The typical size of an LT domain (connected blue region in Fig. 3a) is 100 nm, consistent with near-field imaging of insulating and metallic pockets 10 . Surprisingly, the broadening of the LT diffraction peak is present in the diffraction collected during a single exposure by the 20nm nanobeam (see Fig. 3b). Thus, the monoclinic distortion reduces the long-range order on a length scale much smaller than the size of a LT domain. X-ray diffraction at higher angles (see  17 , where L=8 nm is the size of the crystallite and 1 = 2.5 nm/ps is the sound velocity in monoclinic V 2 O 3 (Ref. 18 ). The 8 nm large crystallites act as internal traps for acoustic phonons, which drive the symmetry enhancement by shear motion 19 . The degree of alignment grows linearly with pump fluence (see Fig. 2b), characteristic of a continuous phase transition as described by Landau theory extended to ultrafast transitions 20 . The photoinduced phase transition completes with a unit cell volume contraction within 100 ps, while the crystallites remain aligned with an enhanced coherence length. This longer process displays a fluence threshold: the hallmark of a first-order phase transition due to the latent heat 7,16 . The volume contraction is governed by the nucleation and ballistic growth through 100 nm large LT domains moving at the sound velocity 7 (see Fig. 3a).
Laser pulse energies well below the fluence threshold align the crystallites in the LT phase, yet avoid the transition into the HT phase (see Fig. S9). At these low fluences the enhanced long-range order prevails for more than 100 ps as measured in our experiment.
This duration represents the lower time scale for the spontaneous symmetry breaking into structurally equivalent monoclinic lattices, whose presence possibly stabilizes the transient higher symmetry phase. Above the fluence threshold, the coherence length enhancement and the HT phase fraction growth both saturate at 5 mJ/cm 2 , indicating that the transient non-equilibrium state is a precursor to the metallic state.
The size of the monoclinic crystallites ξ we determine from X-ray nanoscopy is in excellent agreement with the electronic correlation length ξ el found in bulk V 2 O 3 (Ref. 21 ).
We conclude a strong interdependence between the electronic correlations and structural twinning of the LT phase into different monoclinic crystallites in equilibrium. By assuming that the electronic correlation length and the crystallite size remain coupled after photoexcitation ξ el (t)=ξ(t), we estimate the behavior of the dynamic Mott gap via The photoexcited phase is structurally similar to the paramagnetic insulating phase, which in equilibrium occurs with chromium doping or equivalently with negative pressure [11][12][13] . Thus, the observation of the ultrafast quench of the monoclinic distortion indicates an ultrafast quench of the antiferromagnetic order. This is further supported by the negative thermal expansion in V 2 O 3 within the hexagon plane, which results in transient negative pressure after photoexcitation: in equilibrium, the negative pressure reduces the antiferromagnetic order and the monoclinic distortion 13 . The photoinduced insulator-to-metal transition in V 2 O 3 lasts for tens of picoseconds 7 , consistent with the duration of the structural unit cell volume change reported here. The long-range order enhancement through cooperative nanoscale alignment occurs before the electronic transition completes. Because long-range order is essential for electronic transport 8 , we anticipate that the presence of the photoinduced structural order impacts the dynamics of the electronic transition.

Experiment description
We deposit V 2 O 3 thin films on R-plane sapphire substrates by RF magnetron sputtering 1 .
The film thickness is 100 nm, determined by laboratory x-ray reflectivity measurements.
Transport measurement show a resistance change of 5 orders of magnitude (see Fig. S1).
The time-resolved x-ray experiment is conducted at the XPP instrument of the LCLS. To control the temperature, we use a cryo-jet and conduct the experiment at ambient conditions. An x-ray spot of 200 µm x 200 µm, a laser spot of 500 µm x 500 µm, and collinear x-ray and optical laser pulses are used. The nanodiffraction data is collected at the ID-26 instrument at the Argonne Photon Source; the temperature is controlled by a liquid nitrogen flow cryostat and the experiment is done in vacuum. All experiments presented in the main text and the supplement are conducted on a film grown on a single substrate piece, sliced into smaller pieces for further measurements.

Recording and analyzing the 4D dataset
We acquire the 3D reciprocal space representation by rocking the crystal from -1 to +1 degrees in 21 steps and by transforming the data into a Cartesian grid in reciprocal space, similar to the work in Bragg Coherent Diffractive Imaging 2 . A representation of the 4D dataset is shown in Supplementary Figure S3. The inset in Figure 1c of the main text shows a projection along the normal to patterns shown in Figure S3 (a, e, i). Figures 1c,d show the results by directly analyzing the height both peaks in these images, which were measure for time delays from -2 to 10 ps. For longer time delays shown in Figures 2a we first measure a single slice through the reciprocal space (the geometrical direction of this slice is indicated in Figures S3 b, c), and second, calculated the peak width from the peak height in this slice assuming the total intensity of the whole 3D reciprocal space remains constant during the dynamic structural phase transition. The latter analysis is in agreement with the direct calculation of the width and height of the peaks for time delays from -2 to 10 ps.

Diffraction at higher q values
The width of the low temperature peak shown in the inset of Figure 1c can be well approximated with three Gaussian functions: two symmetric side Gaussians and a Gaussian in the center. To understand the nature of these three contributions, we collect x-ray diffraction data at high momentum transfer q along q ⟂ , i.e. (022) Mon (data in the main text), (033) Mon , (044) Mon (see Fig. S6). The peak in the center significantly broadens at high q, indicating high tilt distribution in the structure corresponding to this peak, while the side peaks retain their widts. This observation is similar to the Williamson-Hall analysis 3 .
However, here we look perpendicular to the Bragg peak and the strain in the Williamson-Hall analysis is consistent with the 'tilt' of the Bragg planes 4 .

Statistical analysis of the nanodiffraction data
To estimate the number of mosaic blocks in the volume exposed to the x-ray beam, we assume each block is either in orientation A or B. (The peak corresponding to the third monoclinic distortion is significantly suppressed in diffraction and is only noticeable at lowest measured temperatures of 130 K.) Assuming we illuminate N blocks with the nanobeam the total x-ray intensity is calculated via I=P·y A +N/2·y S +(N-P) ·y B , where y A and y B are the intensities of a single block in orientation A and B, and y S is a strain term which does not depend on orientation (see diffraction at higher q in Fig. S6). P is the number of blocks in orientation A calculated assuming a binomial distribution with a total number of blocks N and the probability of 0.5. A total of 20000 intensity profiles I j are calculated for a number of mosaic blocks N, j=1…N. Subsequently, the ratio of the width of the average intensity (width of I avg =SI j ) to the average of the widths of single intensities is determined. This ratio in the data is 1.0035, which according to our analysis corresponds to N=200 of mosaic blocks in the beam volume. Given the volume of the beam 20 nm·20 nm ·100 nm /sin(23°)=102000 nm 3 yields an average volume of around 500 nm 3 per cube.
Assuming cubic blocks we conclude that each block is (8 nm) 3 in size.  (also the surface normal). The 3D reciprocal space is projected onto the plane defined by q ⟂ , q || , and the widths are determined as root mean squares. The LT peak width in the time resolved experiment is shown for the ground state, and the maximum correlation length enhancement at t=2.5 ps and a fluence of 5 mJ/cm 2 . The smallest peak width in the time resolved experiments (highest correlation length) is close to the minimum peak width measured in equilibrium at 190 K. Figure S3: Analysis of the 4D dataset. 3D reciprocal space measured in the ground state (a-d), and at time delays of 2 ps (e-g) and 10 ps (i-l). The data was measured at a base temperature of 157 K and images represent different views on the 3D reciprocal space. The vertically arranged dots visible best in (b, f, j) are due to the substrate scattering. Note the reduction of the width of the monoclinic peak (lower peak) in (a, e, i) and the growth of the rhombohedra peak in j. The intersection with the Ewald sphere is shown in b, c. The separation between peaks is 0.04 Å -1 and the angular width of the LT peak (broader peak) is 1° in (a, e, i) (compare with Fig. S6).   Fig. 3b). The LT peak is wider than the HT peak, however, the difference in widths is slightly smaller than in the time resolved measurements, because the angular divergence of the nanobeam widens both peaks. No correlations between the LT peak intensity and LT peak width (inverse coherence length) is observed. For example, point 1 (indicated by crosses in a, b, c) has high peak intensity and a large width, point 2 (indicated by crosses in a, b, c) has a low peak intensity and a large width, point 3 (indicated in a, b, c) has a large peak intensity and a is in between regions with large and small width.  In our x-ray data at 100 K, we observe a splitting in the same direction by 1°, which supports our microscopic twinning model and indicates a strain region between the twins. The splitting angle is lower at higher temperatures (see Fig. S2).  The ultrafast increase of the HT diffraction peak is associated with the increase of the LT peak, whose tail has a non-vanishing intensity at the position of the HT peak.