Nanoscale self-organization and metastable non-thermal metallicity in Mott insulators

Abstract

Mott transitions in real materials are first order and almost always associated with lattice distortions, both features promoting the emergence of nanotextured phases. This nanoscale self-organization creates spatially inhomogeneous regions, which can host and protect transient non-thermal electronic and lattice states triggered by light excitation. Here, we combine time-resolved X-ray microscopy with a Landau-Ginzburg functional approach for calculating the strain and electronic real-space configurations. We investigate V₂O₃, the archetypal Mott insulator in which nanoscale self-organization already exists in the low-temperature monoclinic phase and strongly affects the transition towards the high-temperature corundum metallic phase. Our joint experimental-theoretical approach uncovers a remarkable out-of-equilibrium phenomenon: the photo-induced stabilisation of the long sought monoclinic metal phase, which is absent at equilibrium and in homogeneous materials, but emerges as a metastable state solely when light excitation is combined with the underlying nanotexture of the monoclinic lattice.

Fig. 1. Phase diagram and corundum structure.

a Phase diagram of ${\left({\mathrm{V}}_{1-x}{M}_x\right)}_2{\mathrm{O}}_3$, with M = Cr, Ti, as a function of the doping concentration x and pressure, from ref. . AFM and PM stand for antiferromagnetic and paramagnetic, respectively. All transition lines (solid black lines) are first order, with the one separating PM metal from PM insulator that terminates into a second-order critical point (black dot). The paramagnetic metal and insulating phases of Cr-doped V₂O₃ are commonly referred to as α and β phases, respectively, and shown in the figure. b Non-primitive hexagonal unit cell of the high-temperature corundum phase. The V–V nearest neighbour distance within the a_H−b_H plane, ℓ₀, and along c_H, d₀, are also shown. Also shown is the reference frame we use throughout the work, with a_H∥x and c_H∥z. c Sketch of the electronic Mott transition in V₂O₃. In the atomic limit, the two conduction electrons of V³⁺ occupy the t_2g orbital of the cubic-field split 3d-shell. Because of the additional trigonal distortion, the t_2g is further split into a lower $e_g^{\pi }$ doublet and higher a_1g singlet. The two electrons thus sit into the $e_g^{\pi }$ orbital, in a spin triplet configuration because of Hund's rules. In the solid the atomic levels corresponding to removing or adding one electron broaden into lower and upper Hubbard bands, LHB and UHB, respectively. The LHB has prevailing $e_g^{\pi }$ character while the UHB has dominant a_1g character. Note that we do not show, for simplicity, the multiplet structure that the Hubbard bands must have because of Coulomb exchange splitting. In the metal phase, overlapping quasiparticle bands appear at the Fermi level.

Fig. 2. Magnetic and structural properties of the monoclinic phase.

Magnetic order in the hexagonal plane (a) and in the y–z plane, equivalent to the a_m–c_m one (b). In the hexagonal plane we also draw the nearest neighbour bond lengths: l_y, which is ferromagnetic, and l₁ and l₂, both antiferromagnetic. The dimers, with bond length d, lie in the y–z plane and are ferromagnetic, see (b), where we also show the monoclinic lattice vectors a_m and c_m. c The pseudo-hexagonal unit cell that we use throughout this work. d The dimer, in yellow, which in the rhombohedral phase lies along z∥c_H, rotates anticlockwise around x∥b_m = a_H and elongates, so that the vanadium atoms at the endpoints move towards the octahedral voids.

Fig. 3. X-ray microscopy.

a Experimental setup. X-rays bunches with tunable energy resonant with the vanadium L_2,3 edge impinge on the sample at ~75^∘ incidence. The X-ray linear polarization can be rotated from in-plane (Horizontal) to out-of-plane (Vertical). The electrons emitted from the sample are collected and imaged through electrostatic lenses. In the time-resolved configuration, the signal originated by isolated X-rays pulses with linear horizontal (LH) polarization is collected by suitable synchronized gating of the detection apparatus. The pump infrared laser is synchronized to the synchrotron pulses. b XLD-PEEM images taken at 100 K evidencing striped monoclinic domains characterized by different XLD intensity. The three panels show images taken for different polarization angles of the impinging X-ray pulses. The indicated angle refers to the initial (left panel) polarization, which is taken as reference. The colour scale indicates the amplitude (arb. units) of the PEEM signal. We note the existence of the three distinct domains (red, blue, yellow), namely the three monoclinic twins. The XLD signal, as demonstrated in Supplementary Note 3 (See the Supplementary Material), is minimum (blue scale in the panels) when the electric field (grey arrows on top of the images) is parallel to the monoclinic b_m axis, which can be any of the primitive hexagonal vectors, a_H, b_H or −a_H–b_H, and maximum when E ⋅ b_m = 0. Comparing the theoretical prediction with the data, we infer the three primitive hexagonal vectors shown in the figure, and further conclude that that the interface between two twins is perpendicular to the b_m axis of the third domain. c XLD signal as a function of the angle between the X-ray polarization and the sample axis. The pink square, green circle and yellow triangle refer to the positions indicated in (a). Within each domain, the XLD signal displays the expected 180^∘ periodicity. When comparing the three distinct domains, the XLD signal shows the predicted 60^∘ phase shift.

Fig. 4. Phase diagram of uniform phases.

a Phase diagram from the energy functional (12) as a function of τ at K = κ = 0. E_rM, E_mM and E_mI are, respectively, the energies of the rhombohedral metal, red line, monoclinic metal, green line, and monoclinic insulator, blue line, namely, the depths of the corresponding local minima. The energy crossing between E_rM and E_mI signals the actual first-order transition. The vertical dashed lines at τ = τ_m and τ = τ_r are, respectively, the monoclinic and rhombohedral spinodal points. For τ ∈ [τ_r, τ_m] there is phase coexistence. We note the existence of a metastable monoclinic metal, with energy E_mM. b The energy landscape at τ = 10 as a function of η and ϵ₂ ≥ 0. We note the existence of three minima: a global monoclinic insulating one (mI), and two local minima: a lower monoclinic metal (mM), at ϵ₂ > 0 and η < 0, and an upper rhombohedral metal (rM), at ϵ₂ = 0 and η < 0.

Fig. 5. Calculated nanotexture of the monoclinic insulating phase.

Calculated real space distribution of the shear strain ϵ₂(r) deep inside the monoclinic insulating phase. The colours correspond to the three equivalent shear-strain vectors ${\mathit{ϵ}}_{2,1}=\left(+\sqrt{3}/2,+1/2\right)$, ${\mathit{ϵ}}_{2,2}=\left(-\sqrt{3}/2,+1/2\right)$ and ϵ_2,3 = (0, − 1), shown on the left, which characterize the three equivalent monoclinic twins, see Eq. (5). The figure is a superposition of three different ones. The first is obtained plotting the y-component of ϵ₂(r) on a colour scale from −1 (plum) to 0 (white); the second plotting the x-component from $+\sqrt{3}/2$ (blue) to 0 (white), and the third plotting still the x-component but now from $-\sqrt{3}/2$ (orange gold) to 0 (white). Evidently, when the lighter regions of all three plots overlap that implies both x and y components are nearly zero, thus a small strain. We note that the interfaces between different domains evidently satisfy the curl-free condition (9).

Fig. 6. Simulated dynamics of monoclinic domains across the transition.

Calculated domain pattern across the first-order transition upon rising temperature. Top panel: colour map of the shear strain ϵ₂(r), specifically, the monoclinic domains are indicated by the same colour scale as that used in Fig. 5, in which the colours indicate the three equivalent shear-strain vectors. The rhombohedral domains are indicated in green. To enhance the contrast, we use, unlike Fig. 5, a colour scale that does not distinguish between small and zero strain. Bottom panel: colour map of the square modulus of the shear strain ϵ₂(r)². Blue keys indicate the monoclinic insulating domains, ${ϵ}_2{\left(\mathbf{r}\right)}^2>{ϵ}_{\mathrm{IMT}}^2$, while red keys the metallic ones, ${ϵ}_2{\left(\mathbf{r}\right)}^2<{ϵ}_{\mathrm{IMT}}^2$.

Fig. 7. Metastable monoclinic metal.

Map of the space-dependent calculated shear-strain amplitude (grey colour-scale) and metastable monoclinic metallic regions (purple solid areas). The different filling fractions (ff) of the metastable phase correspond to different values of ϵ_IMT(f). Darker grey indicates smaller strain amplitude. The purple areas highlight the spatial regions in which the electronic metallic solution with monoclinic strain is the stable one (absolute minimum in the free-energy), i.e. when the condition ϵ₂(r) ≤ ϵ_IMT(f) is fulfilled. We stress that in all panels the same equilibrium space-dependent monoclinic shear strain, ϵ₂(r), of the top-left panel (colours correspond to the three equivalent shear-strain vectors, as in Fig. 5) is considered. The filling fraction of the photo-induced non-thermal metallic phase is indicated for each panel.

Fig. 8. Insulator-to-metal transition.

a Reflectivity change of the V₂O₃ crystal across the temperature-driven insulator-to-metal phase transition. The sample reflectivity is measured at 2.4 eV photon energy as a function of the sample temperature during the heating (red curve) and cooling (blue curve) processes. The graph displays the relative reflectivity variation with respect to the reflectivity measured at T = 100 K. b PEEM image taken at 100 K evidencing stripe-like domains corresponding to the different monoclinic distortions. Note that the experimental configuration of the image shown (polarization parallel to one of the hexagon edges) is such that only two domains are visible. c PEEM image taken at 180 K evidencing a homogeneous background, typical of the metallic corundum phase. The colour scale indicates the amplitude of the PEEM signal. d The asymptotic value of the relative reflectivity variation (yellow trace), i.e. δR/R(100 ps) = [R(Δt = 100 ps)-R(Δt = 0 ps)]/R(Δt = 0 ps) where Δt is the pump–probe delay, is measured at 2.4 eV probe photon energy and T = 100 K as a function of the incident pump fluence. The black solid line is a guide to the eye.

Fig. 9. Time-resolved microscopy.

a Time-resolved PEEM image taken at T = 100 K and at negative delay (−150 ps) between the infrared pump and the X-ray probe pulses. b Time-resolved PEEM image taken at T = 100 K and at positive delay (+30 ps) between the infrared pump and the X-ray probe pulses. The colour scale for both panels (a) and (b) is the same than that used in Fig. 8. c XLD contrast profile along the segments 1 → 2 and 3 → 4, as indicated in panel (b). The blue profiles are taken at negative delay (−150 ps), whereas the yellow profiles correspond to positive delay (+30 ps). d Relative contrast (see the Supplementary Information) between different domains as a function of the delay between the infrared pump and the X-ray probe pulses. The error bar accounts for the average fluctuation of the signal within the domains considered for the calculation of the relative contrast. The grey solid line is the cross-correlation between the infrared pump and the X-ray probe pulses measured by exploiting the non-linear photoemission from surface impurities on the sample (see Supplementary Note 1 (See the Supplementary Material).

Fig. 10. Strain engineering of the metastable monoclinic metallic phase.

a Metallic filling fraction, retrieved from the asymptotic value of the relative reflectivity variation, i.e. δR/R(100 ps), as a function of the pump incident fluence for a 50 nm V₂O₃ film directly grown on the sapphire substrate (green circles) and for a 55 nm V₂O₃ film grown on a 60 nm Cr₂O₃ buffer layer (blue squares). The grey solid lines represent the numerical filling fractions, calculated as the ratio between non-thermal metallic areas (purple areas in Fig. 7) and the total area. b Values of the estimated critical strain variation δϵ_IMT, calculated with respect to the reference sample V₂O₃/Cr₂O₃/Al₂O₃ (55 nm/60 nm/substrate). δϵ_IMT is plotted as a function of the room temperature a-axis lattice parameter, as measured by X-ray diffraction, for samples with (blue points) and without (green points) the Cr₂O₃ buffer layer. The symbols refer to the following samples: blue square V₂O₃/Cr₂O₃/Al₂O₃ (55 nm/60 nm/substrate); blue triangle V₂O₃/Cr₂O₃/Al₂O₃ (67 nm/40 nm/substrate); green diamond V₂O₃/Al₂O₃ (40 nm/substrate); green circle V₂O₃/Al₂O₃ (50 nm/substrate). The error bars account for the uncertainty in the measurement of the lattice parameter and in the determination of δϵ_IMT.