Electronic and ionic conductivities in superionic ${\mathrm{Li}}_4{\mathrm{C}}_{60}$

The 10 GHz microwave conductivity, $\sigma \left(T\right)$ and high field, 222 GHz electron spin resonance (HF-ESR) of ${\mathrm{Li}}_4{\mathrm{C}}_{60}$ fulleride is measured in a wide temperature range. We suggest that the majority of ESR active sites and at least some of the charge carriers for $\sigma \left(T\right)$ are electrons bound to a small concentration of surplus or vacancy ions in the polymer phase. Both $\sigma \left(T\right)$ and the ESR line shape depend on ionic motion. A change of the activation energy of $\sigma \left(T\right)$ at 125 K coincides with the onset of the ionic DC conductivity. The ESR line shape is determined mainly by Li ionic motion within octahedral voids below 150 K. At higher temperatures, fluctuations due to ionic diffusion change the environment of defects from axial to effectively isotropic on the ESR time scale. $\sigma \left(T\right)$ data up to 700 K through the depolymerization transition confirm that the monomeric phase of ${\mathrm{Li}}_4{\mathrm{C}}_{60}$ is a metal.

Figure 1

Room-temperature infrared spectrum of ${\mathrm{Li}}_4{\mathrm{C}}_{60}$ compared to that of ${\mathrm{Na}}_4{\mathrm{C}}_{60}, {\mathrm{K}}_4{\mathrm{C}}_{60}$, and ${\mathrm{K}}_3{\mathrm{C}}_{60}$ shifted and scaled for clarity. ${\mathrm{Li}}_4{\mathrm{C}}_{60}$ and ${\mathrm{Na}}_4{\mathrm{C}}_{60}$ have similar IR spectra with a mode around $800{\text{cm}}^{-1}$ signaling single bonds in the polymer, whereas the IR spectrum of monomeric ${\mathrm{K}}_4{\mathrm{C}}_{60}$ is markedly different. The spectrum of ${\mathrm{K}}_3{\mathrm{C}}_{60}$ (Ref. [28]) shows metallic character with high background absorption and Fano line shape of the ${\mathrm{T}}_{1\text{u}}\left(4\right)$ mode at 1360 ${\mathrm{cm}}^{-1}$.

Figure 2

Temperature dependence of the 10 GHz microwave conductivity of ${\mathrm{Li}}_4{\mathrm{C}}_{60}$ normalized at 295 K. Red triangles: heating (heating rate $0.2$ K/s), blue dotted squares: cooling. Unpaired electron concentration increases above 300 K, depolymerization is significant above 400 K.

Figure 3

Arrhenius plot of the 10 GHz (electronic) conductivity in ${\mathrm{Li}}_4{\mathrm{C}}_{60}$ (filled squares, this work) and the DC (ionic) conductivity (solid curve, Ref. [12]). The conductivities are normalized to their respective 295 K values. The electronic conductivity is larger than the ionic, however, its absolute value is not known. Straight lines are fits to the data. Note the marked upturn in both electronic and ionic conductivities at about 125 K (dotted vertical line), which is attributed to the onset of ${\mathrm{Li}}^{+}$ diffusion.

Figure 4

Schematics of the suggested ESR active defect. Large blue circles are polymeric fulleride ions. Dark and light molecules are in the front and back, respectively. Green (red) circles are ${\mathrm{Li}}^{+}$ ions in octahedral (tetrahedral) sites. In stoichiometric ${\mathrm{Li}}_4{\mathrm{C}}_{60}$, octahedral voids are occupied by $2{\mathrm{Li}}^{+}$ ions and have 2 unoccupied sites. The unpaired electron is bound to the void occupied by $3{\mathrm{Li}}^{+}$ ions marked by a dashed line contour.

Figure 5

Temperature evolution of the 222 GHz ESR spectrum of ${\mathrm{Li}}_4{\mathrm{C}}_{60}$. The measured experimental (exp.) and the fitted (fit) spectra are shown for each temperature. Below 290 K, the spectra consist of an isotropic (black) and a uniaxially anisotropic $g$-factor distribution (blue) component. Above 290 K, the anisotropic component is better described by a rhombic $g$-factor anisotropy (red).

Figure 6

(a) Temperature dependence of ESR intensity of the isotropic component divided by the total one, $I_{\text{(iso)}}/I_{\text{(tot)}}$. $T^{*}$ indicates the onset of ${\mathrm{Li}}^{+}$ ion motion [22]. (b) Temperature dependence of the $g$-factor anisotropy, $\mathrm{\Delta }B/B_{\text{0}}$, of the ESR line measured at the same frequency (222 GHz).

Figure 7

Depolymerization-polymerization cycles of ${\mathrm{Li}}_4{\mathrm{C}}_{60}$ measured by the 10 GHz microwave conductivity (normalized at 295 K). Full cycle: heating (blue dots) and cooling (blue triangles) rates $\approx 0.1$ K/s. Partial cycle (red squares): cooling and heating rates $\approx 0.07$ K/s.