Early-stage dynamics of metallic droplets embedded in the nanotextured Mott insulating phase of ${\mathrm{V}}_2{\mathrm{O}}_3$

Unveiling the physics that governs the intertwining between the nanoscale self-organization and the dynamics of insulator-to-metal transitions (IMTs) is key for controlling on demand the ultrafast switching in strongly correlated materials and nanodevices. A paradigmatic case is the IMT in ${\mathrm{V}}_2{\mathrm{O}}_3$, for which the mechanism that leads to the nucleation and growth of metallic nanodroplets out of the supposedly homogeneous Mott insulating phase is still a mystery. Here, we combine x-ray photoemission electron microscopy and ultrafast nonequilibrium optical spectroscopy to investigate the early-stage dynamics of isolated metallic nanodroplets across the IMT in ${\mathrm{V}}_2{\mathrm{O}}_3$ thin films. Our experiments show that the low-temperature monoclinic antiferromagnetic insulating phase is characterized by the spontaneous formation of striped polydomains, with different lattice distortions. The insulating domain boundaries accommodate the birth of metallic nanodroplets, whose nonequilibrium expansion can be triggered by the photoinduced change of the $3d$-orbital occupation. We address the relation between the spontaneous nanotexture of the Mott insulating phase in ${\mathrm{V}}_2{\mathrm{O}}_3$ and the timescale of the metallic seeds growth. We speculate that the photoinduced metallic growth can proceed along a nonthermal pathway in which the monoclinic lattice symmetry of the insulating phase is partially retained.

Figure 1

Nanoscale insulating domains imaged by XLD-PEEM. (a) Left: x-ray absorption spectroscopy (XAS) spectrum showing the $L_{2,3}$ vanadium absorption lines. The light blue areas highlight the spectral regions where the maximum XLD signal is obtained. Middle: Sketch of the $L_{2,3}$ transitions from the V $2p$ levels to the doubly occupied V $t_{2g}$ levels further split into $a_{1g}$ and $e_g^{\pi }$ by the trigonal distortion of the lattice. Right: Trigonal distortion of the V atoms along the $c$-axis of the hexagonal unit cell. (b) Left: $a-c$ plane projection of the monoclinic lattice structure in the low-$T$ AFI phase. The $a_{\mathrm{m}}, b_{\mathrm{m}}$, and $c_{\mathrm{m}}$ axes of the monoclinic cell are indicated by the colored arrows. Right: $c-b$ plane projection of the corundum lattice structure in the high-$T$ PM phase. The $a_{\mathrm{h}}, b_{\mathrm{h}}$, and $c_{\mathrm{h}}$ axes of the hexagonal cell are indicated by the colored arrows. (c) Left top: XLD-PEEM image taken at 120 K (heating branch of the hysteresis) evidencing striped monoclinic domains. Left bottom: XLD intensity distribution (thick gray line) of the image. The analysis evidences a broad zero-centered distribution (green), corresponding to the resolution-broadened edges of the striped domains, and three distinct distributions with nonzero signal (red, blue, light blue), reflecting the different structural nanodomains within the AFI phase. Middle: Hysteresis cycle as obtained by resistivity measurements and by the metallic filling analysis of the temperature-dependent XLD-PEEM images (see Appendix pp4). The yellow (green) arrows indicate the heating (cooling) cycles. Right top: XLD-PEEM image taken at 200 K (heating branch of the hysteresis) showing a homogeneous background, typical of the PM phase. The residual red spots are due to defects used as reference to precisely align the XLD-PEEM images. Right bottom: XLD intensity distribution (thick gray line) of the image. The analysis evidences a zero-centered single-mode distribution.

Figure 2

Domain pinning and hysteresis. XLD-PEEM images at different temperatures during a heating and cooling cycle. After the complete melting of the AFI phase at $T=200\mathrm{K}$, the insulating striped domains form in the same spatial position when the system is cooled down to $T=120\mathrm{K}$.

Figure 3

Growth dynamics of metallic seeds. (a) Temperature-dependent XLD-PEEM images. The color scale is the same as that reported in Fig. 1. The black contours highlight the monoclinic domain on which the metallic filling analysis has been performed. The white contours indicate the metallic regions within the monoclinic domains as identified via the routine described in Appendix pp4. The arrow highlights the main processes leading to the complete insulator-to-metal phase transition. (b) Pump-induced filling-factor variation, $\delta F_M\left(\mathrm{\Delta }t\right)$, at different temperatures below (120 K), within (145–165 K), and above ($>180\mathrm{K}$) the $I-M$ coexistence region. The measurements have been performed using setup SU2, as described in Appendix pp3, with an incident pump fluence of $0.3\mathrm{mJ}/{\mathrm{cm}}^2$. (c) Absolute value of the long-time ($\mathrm{\Delta }t=25\mathrm{ps}$) reflectivity variation as a function of the temperature (blue line, left axis). The measurements have been performed using setups SU2 and SU3, as described in Appendix pp3. The maximum reflectivity variation, $\delta R/R$ (25 $\mathrm{ps})\simeq 2.2\times {10}^{-3}$ at 2.1 eV photon energy, is measured at $T\simeq 155\mathrm{K}$ and corresponds to a filling-factor variation $\delta F_M\simeq 3\%$. The dashed area between the solid and dashed blue lines indicates the uncertainty ($\sim 4\mathrm{K}$) in the actual sample temperature during the fast ramping up ($\sim 2\mathrm{K}$/min) of the temperature of the sample holder. For the sake of comparison, the black line represents the metallic filling in the heating cycle as extracted from the XLD-PEEM images [see Fig. 1]. The small mismatch between the temperatures at which $\delta R/R$ vanishes ($\sim 190\mathrm{K}$) and $F_M\simeq 1$ ($\sim 180\mathrm{K}$) is related to the finite resolution of the XLD-PEEM that is insensitive to insulating domains smaller than $\sim 30$ nm. The gray dashed area between the solid and dashed black lines corresponds to the estimated uncertainty of $F_M$ due to the finite PEEM resolution. See the supplementary information [46] for a detailed discussion of the role of PEEM resolution in retrieving the $F_M$ value from the pixel-segmentation analysis of the XLD-PEEM images. The colored dots indicate the temperatures of the XLD-PEEM images and time traces as reported in panel (b).

Figure 4

Energy-resolved differential reflectivity variation. (a) Illustration of the photoexcitation across the Mott gap. The change in the occupation of the $a_{1g}$ and $e_g^{\pi }$ orbitals gives rise to the orbital polarization change $\delta p=\delta (n_{e_g^{\pi }}-n_{a_{1g}}$), which triggers the growth of metallic seeds. (b) Equilibrium infrared/visible reflectivity change, $[R(T,\omega )-R_M\left(\omega \right)]/R(T,\omega$), as a function of the sample temperature during a heating cycle. $R_M\left(\omega \right)$ is taken as the average of $R(T,\omega$) between 190 and 250 K. The arrow and the dashed lines graphically show the procedure to obtain the value $[R_M\left(\omega \right)-R$(145 K, $\omega \left)\right]/R$(145 K, $\omega$), reported in panel (c), for 2 eV (600 nm) photon energy. The measurements have been performed using setup SU3, as described in Appendix pp3. (c) Frequency dependence of the equilibrium reflectivity change, $[R_M\left(\omega \right)-R$(145 K, $\omega \left)\right]/R$(145 K, $\omega$) (colored dots, left axis), and of the time-resolved $\delta R/R(\omega$) signal (gray line, right axis) measured at $\mathrm{\Delta }t=25\mathrm{ps}$ and $T=145\mathrm{K}$. The measurements have been performed using setup SU1, as described in Appendix pp3. As a reference, we remind the reader that the amplitude of the reflectivity variation measured at $T=155\mathrm{K}$ and $\hslash \omega \simeq 2.1$ eV is $\delta R/R$(25 $\mathrm{ps})\simeq 2.2\times {10}^{-3}$.

Figure 5

Avrami model for the metallic growth. (a) Avrami plot of the dynamics of $\delta F_{\text{rel}}\left(\mathrm{\Delta }t\right)=[\delta R/R\left(\mathrm{\Delta }t\right)]/[\delta R/R\left(\infty \right)]$ at different temperatures. The value of $\delta R/R(\infty$) is given by the asymptotic value of the exponential fitting to the data in the 0–20 ps time window. The gray traces represent the curves obtained assuming $\delta R/R\left(\infty \right)\pm 10\%$. The slope does not significantly depend on the value of $\delta R/R(\infty$). The black lines indicate the expected curves for $N=2$ and $3/4$. Inset: Avrami coefficient $N$ of the long-lived dynamics ($\mathrm{\Delta }t>1$ ps) as a function of the temperature. The red line indicates the asymptotic value $N=3/4$. (b) Avrami plot of $\delta F_{\text{rel}}\left(\mathrm{\Delta }t\right)$ at 145 K for different values of $E_{\text{abs}}$. The solid black line indicates the expected curve for $N=3/4$. The dashed line indicates the time at which the growth dynamics saturates. (c) The asymptotic value of the relative reflectivity variation, i.e., $\delta R/R$(25 ps), measured at 600 nm wavelength and $T=145\mathrm{K}$, is reported as a function of the absorbed energy density. The black thin line is the linear fit to the data. The dashed line indicates the energy threshold $E_{\text{th}}$ above which THz mesoscopic conductivity has been observed [11]. The measurements reported in panels (a), (b), and (c) have been performed using setup SU2, as described in Appendix pp3.

Figure 6

Illustration of the nonequilibrium metallic growth dynamics. (a) Sketch of the stacked honeycomb planes in the low-temperature monoclinic and high-temperature corundum phases. In the corundum metal, the hexagonal symmetry preserves the equivalence of the V (blue) and ${\mathrm{V}}^{*}$ (red) sites and, therefore, of the two degenerate $e_g^{\pi }$ and $e_g^{\pi *}$ orbitals. In the monoclinic insulating phase, the distortion of the hexagons (red arrows) lifts the $e_g^{\pi }$ degeneracy, whereas the out-of-plane motion of the vanadium atoms (black arrows), associated with the tilting of the hexagons, controls the $a_{1g}-e_g^{\pi }$ energy distance. (b) Sketch of the possible transient metal-like monoclinic state. The photoinduced change of $\delta (n_{e_g^{\pi }}-n_{a_{1g}})$ triggers the restoring of the ${\mathrm{V}}_1-{\mathrm{V}}_2$ distance (tilting back of the hexagons), whereas it does not affect the in-plane hexagonal distortion. Photoexcitation thus triggers the growth of already formed metallic droplets via the propagation of a transient nonequilibrium lattice rearrangement (monoclinic metal). The black, red, and green borders of the hexagons indicate the monoclinic insulator, the corundum metal, and the monoclinic metal, respectively. The red arrows indicate the in-plane distortion of the hexagons, whereas the dots (crosses) indicate the out-of-plane inward (outward) motion of the vanadium atoms associated with the hexagons tilting.