Phase transition in bulk single crystals and thin films of $\mathrm{V}{\mathrm{O}}_2$ by nanoscale infrared spectroscopy and imaging

We have systematically studied a variety of vanadium dioxide $\left(\mathrm{V}{\mathrm{O}}_2\right)$ crystalline forms, including bulk single crystals and oriented thin films, using infrared (IR) near-field spectroscopic imaging techniques. By measuring the IR spectroscopic responses of electrons and phonons in $\mathrm{V}{\mathrm{O}}_2$ with sub-grain-size spatial resolution $(\sim 20\mathrm{nm})$, we show that epitaxial strain in $\mathrm{V}{\mathrm{O}}_2$ thin films not only triggers spontaneous local phase separations, but also leads to intermediate electronic and lattice states that are intrinsically different from those found in bulk. Generalized rules of strain- and symmetry-dependent mesoscopic phase inhomogeneity are also discussed. These results set the stage for a comprehensive understanding of complex energy landscapes that may not be readily determined by macroscopic approaches.

Figure 1

(a) Temperature-dependent dc magnetization susceptibility of bulk single-crystal $\mathrm{V}{\mathrm{O}}_2$. $T_{\mathrm{MIT}}\approx 341\pm 2\mathrm{K}$. (Inset) Top: microscopic image of selected $\mathrm{V}{\mathrm{O}}_2$ single crystals; bottom: magnetization curve expanded in the vicinity of the phase transition.

Figure 2

Temperature-dependent resistivity (black) and corresponding derivative (blue) curves for $30\text{-nm}\mathrm{V}{\mathrm{O}}_2/\mathrm{Ti}{\mathrm{O}}_2{\left[001\right]}_{\mathrm{R}}$ film. $T_{\mathrm{MIT}}\approx 290\pm 10\mathrm{K}$. Inset, x-ray diffraction intensity (arbitrary units). The solid and open circles represent temperature ramping up and down, respectively.

Figure 3

(a) Schematic of real-space lattice structures of monoclinic M1, M2, and rutile R phases. Blue (green) filled circles: vanadium atoms in M1 (M2) phase; red filled circles: vanadium atoms in R phase. Blue (green) solid line: unit cell of M1 (M2) phase. Blue (green) dashed line: V-V pairing in M1 (M2) phase. Red solid line: unit cell of R phase. The arrows indicate the corresponding lattice axes. (b) Matrix equation of M1-R, M2-R lattice relationship.

Figure 4

(a)–(f) IR scattering amplitude $S_3$ of $\mathrm{V}{\mathrm{O}}_2$ bulk single crystals acquired at different temperatures. Note that the temperature difference from (d) to (f) is only $\sim 0.14\mathrm{K}(\pm 0.03\mathrm{K})$. The stripes in the M2 phase are depicted by the white dashed lines. For enhanced contrast of (a)–(f) see Fig. S2 in Supplemental Materials [50]. (g),(h) simultaneously acquired scattering $S_3$ and AFM images of $30\text{−}\mathrm{nm}\mathrm{V}{\mathrm{O}}_2/\mathrm{Ti}{\mathrm{O}}_2{\left[001\right]}_{\mathrm{R}}$ film. The dashed squares in (g) and (h) indicate the area whose expanded view is shown in (i)–(l): (i) near-field $S_4$ amplitude; (j) near-field $S_4$ phase; (k) AFM amplitude; and (l) AFM phase. The IR probing frequency (from a QCL laser) is $1000\mathrm{c}{\mathrm{m}}^{-1}$. The measurements for panels (g)–(l) are taken at $295\mathrm{K}$.

Figure 5

Near-field amplitude $S_3$ (a) and AFM (b) images of $\mathrm{V}{\mathrm{O}}_2$ bulk crystals at $340\mathrm{K}$. (c) Line profiles of near-field amplitude $S_3$ (blue) and topography (red) taken along the dashed lines in (a) and (b), respectively. (d),(e) Near-field amplitude $S_3$ and AFM topography of $100\text{−}\mathrm{nm}\mathrm{V}{\mathrm{O}}_2/\mathrm{Ti}{\mathrm{O}}_2{\left[001\right]}_{\mathrm{R}}$ film. The substrate induces a strain-dependent $\mathrm{V}{\mathrm{O}}_2$ metallicity. (f) Line profiles of the near-field amplitude $S_3$ (blue) and topography (red) taken along the dashed line in (d) and (e), respectively.

Figure 6

IR scattering amplitude $\left(S_3\right)$ of $\mathrm{V}{\mathrm{O}}_2$ single crystals at (a) less-evolved and (b) more-evolved MIT regions at $340\mathrm{K}$. (c) Histograms of (a) and (b) show a bimodal insulator–to-metal phase transition. In contrast, $100\text{−}\mathrm{nm}\mathrm{V}{\mathrm{O}}_2/\mathrm{Ti}{\mathrm{O}}_2{\left[001\right]}_{\mathrm{R}}$ film at (d) less-strained and (e) more-strained regions of the film at $295\mathrm{K}$ exhibit a rather gradual and continuous MIT transition. The strain-relieved buckled edge is close to the left edge of Fig. 6 (not shown). (f) Histograms show gradual phase transitions spanning almost uniformly across the images, indicating a continuous evolution of the intermediate insulator-metallic states. All figures have the same scale. Scale bar: $500\mathrm{nm}$.

Figure 7

(a) Top: AFM topography of an M1-M2 interface in $\mathrm{V}{\mathrm{O}}_2$ single crystal at $337\mathrm{K}$; bottom: AFM line scan of the striped M2 phase (along the white dashed line in the top panel). (b) Normalized nano-IR spectra $S_2$ at different locations corresponding to the spots indicated by the short white arrows in Fig. 7. Since the $c_{\mathrm{R}}$ axis is in plane [white horizontal arrow in Fig. 7], the major contribution of the signal is from $A_{\mathrm{u}}$ phonon modes $(E//a_{\mathrm{R}})$. (c) Top: AFM topography of the $100\text{-nm}\mathrm{V}{\mathrm{O}}_2/\mathrm{Ti}{\mathrm{O}}_2{\left[001\right]}_{\mathrm{R}}$ film at room temperature. Bottom: AFM line scans of the buckles and the microbeams (along white dashed line in the top panel). (d) Normalized nano-IR spectra $S_2$ taken at the center of the microbeams with different beam widths. Three out of the five representative spectra are taken at the probe spots indicated by the short white arrows in (c). Since the $c_{\mathrm{R}}$ axis is out of plane, the major contribution of the signal is from $B_{\mathrm{u}}$ phonon modes. For clarity, the curves in (d) are shifted vertically. The original positions of each curve are indicated at the high-frequency end of the same panel. We note that since the tip-scattered IR wave vector and its polarization is not well defined, the assignments of $A_{\mathrm{u}}$ and $B_{\mathrm{u}}$ modes in (b) and (d) are qualitative. We also note that all the $S_2$ spectra shown in Figs. 7 and 7 have a $\sim 20\text{-nm}$ spatial resolution.

Figure 8

(a) $\mathrm{V}{\mathrm{O}}_2$ temperature-strain phase diagram. The vertical position of the arrows indicates the global $T_{\mathrm{MIT}}$ of corresponding $\mathrm{V}{\mathrm{O}}_2$ samples. The horizontal span of the arrows indicates the extent of the strain environment in the samples. The phonon resonance blueshifts in single crystals and redshifts in films with out-of-plane $c_{\mathrm{R}}$ axis, with increasing tensile and compressive strain along $c_{\mathrm{R}}$, respectively, as indicated at the top of Fig. 8. The films are referring to $\mathrm{V}{\mathrm{O}}_2$ films on $\mathrm{Ti}{\mathrm{O}}_2$ substrates. (b) Generalized strain-symmetry-inhomogeneity trends of $\mathrm{V}{\mathrm{O}}_2$ crystals and films. With increasing global in-plane symmetry (see text), the mesoscopic patterns probed by nanoimaging become more homogeneous $(\mathrm{heterogeneous}\to \mathrm{anisotropic}\to \mathrm{homogeneous})$. With increasing local strain, the periodicity of the stripelike pattern (in the case of $\mathrm{V}{\mathrm{O}}_2/\mathrm{Ti}{\mathrm{O}}_2{\left[110\right]}_{\mathrm{R}}$ [36, 55]) or strain-induced metallicity (in the case of $\mathrm{V}{\mathrm{O}}_2/\mathrm{Ti}{\mathrm{O}}_2{\left[001\right]}_{\mathrm{R}}$) changes accordingly. The phonon resonance shift probed by broadband nano-IR is a good indicator of the local strain which modifies the lattice structure. Bottom left panel: $100\text{−}\mathrm{nm}\mathrm{V}{\mathrm{O}}_2/\mathrm{r}$ sapphire at $343\mathrm{K}$; top middle: $50\text{−}\mathrm{nm}\mathrm{V}{\mathrm{O}}_2/\mathrm{Ti}{\mathrm{O}}_2{\left[110\right]}_{\mathrm{R}}$ at $340\mathrm{K}$ (higher local strain); middle: $100\text{−}\mathrm{nm}\mathrm{V}{\mathrm{O}}_2/\mathrm{Ti}{\mathrm{O}}_2{\left[110\right]}_{\mathrm{R}}$ at $332\mathrm{K}$ (lower local strain); bottom middle: $\mathrm{V}{\mathrm{O}}_2$ single crystal at $340\mathrm{K}$; top right: $100\text{−}\mathrm{nm}\mathrm{V}{\mathrm{O}}_2/\mathrm{Ti}{\mathrm{O}}_2{\left[001\right]}_{\mathrm{R}}$ at $300\mathrm{K}$ (selected scan window far away from buckles, higher local strain); middle right: $100\text{−}\mathrm{nm}\mathrm{V}{\mathrm{O}}_2/\mathrm{Ti}{\mathrm{O}}_2{\left[001\right]}_{\mathrm{R}}$ at $300\mathrm{K}$ (selected scan window closer to buckles, lower local strain). All images in (b) are $3\times 3\mathrm{mm}$ taken with near-field amplitude $S_3$, except for $\mathrm{V}{\mathrm{O}}_2$ on sapphire $\left(S_2\right)$.