Cooperative Mercury Motion in the Ionic Conductor ${\mathrm{Cu}}_2{\mathrm{HgI}}_4$

We present the observation of glasslike dynamic correlations of mobile mercury ions in the ionic conductor ${\mathrm{Cu}}_2{\mathrm{HgI}}_4$, detected in both NMR and nonlinear conductivity experiments. The results show that dynamic cooperativity appears in systems seemingly unrelated to glassy and soft arrested materials. A simple kinetic two-component model is proposed, which seems to provide a good description of the cooperative ionic dynamics.

Figure 1

(a) NMR lines of copper and mercury, below and above $T_c$. Frequency is relative to Larmor frequencies, 145.6 MHz for ${}^{65}\mathrm{Cu}$ and 91.2 MHz for ${}^{199}\mathrm{Hg}$. Pulse excitation width is $\sim 150\mathrm{kHz}$. Copper lines are normalized to have the same integrals, while the low-temperature mercury line is multiplied by 10 after normalization. Significant motional narrowing is observed for mercury above $T_c$. (b) Spin-lattice relaxation measurements for ${}^{63}\mathrm{Cu}$. Left inset is frequency dependence at 280 K. Lines are fits obtained from a superposition of phonon and two defect diffusion processes (mercury and copper). Temperature ranges where each of the processes comes into play are indicated. Right inset is order parameter in dependence on reduced temperature.

Figure 2

(a) dc conductivity (circles) is smaller than conductivity predicted from mercury NMR (squares), indicating anomalous behavior. The discrepancy between conductivities closely follows the number of correlated ions (diamonds, estimated from nonlinear conductivity and NMR) (b) nonlinear conductivity in dependence on frequency. Peaks clearly show the existence of a cooperativity time scale. Nonlinear response below $T_c$ is negligible. Lines are guides to the eye.

Figure 3

Stimulated spin echo NMR measurements at 380 K, giving evidence of mercury ion trapping at the characteristic time scale ${\tau }_{\mathrm{corr}}$. Inset is raw measurement, the square denoting the zoomed-in segment where dynamic trapping effects are visible. Main graph is compensated for spin-lattice relaxation, showing only the correlation contribution. Full line is from simulation, and the dotted line a stretched exponential fit.

Figure 4

Some results of the two-dimensional simulation. Inserted frame at 2000 steps shows formed mercury islands ($D^{*}=0.0022$, simulation box $300\times 300$ cells). A correlation time scale is nicely visible in the time dependence of the four-point correlation ${\chi }_4$, for several $D^{*}$.