Critical Slowing Down at the Abrupt Mott Transition: When the First-Order Phase Transition Becomes Zeroth Order and Looks Like Second Order

We report that the thermally induced Mott transition in vanadium sesquioxide shows critical slowing down and enhanced variance (“critical opalescence”) of the order parameter fluctuations measured through low-frequency resistance-noise spectroscopy. Coupled with the observed increase of the phase-ordering time, these features suggest that the strong abrupt transition is controlled by a critical-like singularity in the hysteretic metastable phase. The singularity is identified with the spinodal point and is a likely consequence of the strain-induced long-range interaction.

Figure 1

(a) Temperature dependence of resistance of ${{\mathrm{V}}_2\mathrm{O}}_3$ shows a sharp and hysteretic transition around 153 K while cooling and 162 K while heating. (Inset) A large latent heat is also measured in a differential thermal analysis [23]. (b) Return-point memory [15, 52, 53]: Although multivalued in the hysteretic region, after any excursion out of a given hysteresis loop in the form of a minor loop, the same value of the resistance is recovered on return. Thus, the memory of the excursion is wiped out. (c) Mean-field free energy as a function of the spatially averaged order parameter $\varphi$ for the compressible Ising model (essentially, the ${\varphi }^6$ theory) [23] can be used to capture transition semiquantitatively. The points corresponding to curves (i)-(v) are also roughly marked on the resistance curve in Fig. 1. Curve (iii) represents the binodal where the two minima are equal, and curves (ii) and (iv) are the two spinodals where one minimum becomes an inflection point. ${\tau }_2$ is the relaxation time of fluctuations measured through the autocorrelation of the resistance noise, and ${\tau }_1$ is the time associated with phase ordering. (d) Location of extrema of the above free energy as a function of temperature with the same points (i)-(v) marked. In the temperature window of $\sim 153–162\mathrm{K}$ where hysteresis is seen, the order parameter $\varphi$ has globally stable, metastable, and unstable extrema.

Figure 2

Time series of the resistance fluctuations at different temperatures. The left column depicts the measurements done under cooling, and the right panel shows them under heating. (a),(b) Normalized resistance fluctuations after the time series were detrended by imposing a low-frequency cutoff of about $10^{-3}\mathrm{Hz}$ [54]. (c),(d) The probability distribution of fluctuations. Solid lines represent the Gaussian distribution with zero mean, and the given variance and the error bars roughly represent 99.7% confidence for this distribution. (e),(f) Variance of the order parameter fluctuations $⟨\delta {\varphi }^2(0)⟩$ roughly inferred from the resistivity time series. The fluctuations are expected to follow the divergence of ${\chi }_T$ around the spinodals [Eq. (5)].

Figure 3

Critical slowing down of fluctuations around the spinodals. (a),(b) Normalized noise power spectral density (PSD) $S_R/R^2$ at some representative temperatures. (c),(d) Temperature dependence of exponent $\mu$, where $S_f\sim f^{-\mu }$. (e),(f) A surface plot of $f\times S_R/R^2$ to visualize the non-$1/f$ behavior when the spectral weight shifts to lower frequencies.

Figure 4

(a) The temperature dependence of the relaxation time ${\tau }_2$ for the autocorrelation of the detrended resistance fluctuations, and (b) the phase ordering time ${\tau }_1$ during heating and cooling. See Supplemental Material [54] for the details of the phase-ordering experiments. Solid lines are to guide the eye. The region between $\sim 153-162\text{K}$ is the metastable phase. Critical slowing down reflected in both ${\tau }_1$ and ${\tau }_2$. In the linear approximation, they are equal to ${\tau }_{k=0}$ and diverge with the susceptibility exponent.