Random Field Driven Spatial Complexity at the Mott Transition in ${\mathrm{VO}}_2$

We report the first application of critical cluster techniques to the Mott metal-insulator transition in vanadium dioxide. We show that the geometric universal properties of the metallic and insulating puddles observed by scanning near-field infrared microscopy are consistent with the system passing near criticality of the random field Ising model as temperature is varied. The resulting large barriers to equilibrium may be the source of the unusually robust hysteresis phenomena associated with the metal-insulator transition in this system.

Figure 1

Scanning near-field infrared microscopy on ${\mathrm{VO}}_2$ as temperature is increased through the Mott metal-insulator transition regime, over the same $4\mu \mathrm{m}\times 4\mu \mathrm{m}$ sample area. These figures are Ising mapped from the original SNIM images in Ref. [6] with threshold scattering amplitude $a_{\text{th}}=2.5$. The metallic regions, colored green, give higher near-field scattering amplitude, $a>a_{\text{th}}$, compared with the insulating regions with $a\le a_{\text{th}}$, colored blue.

Figure 2

(a) Metal-insulator coexistence region terminating in disorder-induced critical end point, inferred from Nishikawa et al. [9], Fig. 3. Schematic theoretical phase diagrams showing coexistence region (in green) (b) in the experimental temperature versus disorder strength plane, (c) with respect to model temperature ${\mathrm{T}}_{\text{model}}$, effective field ${\mathrm{h}}_{\text{model}}$, and disorder strength.

Figure 3

Power law fits of internal clusters from the ${\mathrm{VO}}_2$ SNIM image data sets with threshold scattering amplitude $a_{\text{th}}=2.5$ for (a) $D(s)\propto s^{-\tau }$, (b) $R_s\propto s^{1/d_v}$, and (c) $R_h\propto h^{1/d_h}$, at three intermediate temperatures $T=342.6\mathrm{K}$, $T=342.8\mathrm{K}$, and $T=343\mathrm{K}$. The insets show the extracted $\tau$, $1/d_v$, and $1/d_h$ (with error bars) as a function of $a_{\text{th}}$ at $T=342.8\mathrm{K}$.

Figure 4

Exponent comparison charts. (a) Critical exponent $\tau$. (b) Critical exponents $d_v$ (blue) and $d_h$ (green). The horizontal lines are our extracted exponents from the SNIM images, with the shaded regions being their error bars. The circles represent theoretical values [8, 14] for the fixed points of Eq. (1). When comparing with 3D models, we have to use the effective values of $d_v$ and $d_h$ corresponding to taking 2D cross sections of the clusters embedded in 3D, i.e., $d_v^{*}=2d_v/3$ and $d_h^{*}=d_h/2$ [8]. These effective values are represented by the open circles.

Figure 5

Power law fits of internal avalanches from the ${\mathrm{VO}}_2$ SNIM image data sets with threshold scattering amplitude $a_{\text{th}}=2.5$ for (a) $D(s)\propto s^{-{\tau }^{\prime }}$, (b) $R_s\propto s^{1/d_v^{\prime }}$, and (c) $R_h\propto h^{1/d_h^{\prime }}$, at three intermediate intervals with $\mathrm{\Delta }T=0.2\mathrm{K}$ through the Mott transition.