Narrowing of phonon spectrum induced by ultrafast charge fluctuations in an organic dimer Mott insulator

We have observed the characteristic temperature dependence of the intermolecular phonon spectrum in the organic dimer Mott insulator \ensuremath{\kappa}-(ET)${}_{2}$Cu${}_{2}$(CN)${}_{3}$ exhibiting a dielectric anomaly at \ensuremath{\sim}30 K. The anomalous spectral narrowing of the 55 cm${}^{\ensuremath{-}1}$ phonon peak at \ensuremath{\sim}30 K was analyzed in terms of motional narrowing within the framework of a stationary Gaussian process, i.e., the phonon frequency is modulated by the ultrafast charge fluctuation. The spectral narrowing occurs because the time constant of the correlation time ${\ensuremath{\tau}}_{c}$ and the amplitude $\ensuremath{\Delta}$ of the frequency modulation satisfy the relation ${\ensuremath{\tau}}_{c}<1/\ensuremath{\Delta}$ at 30 K. At temperatures below 30 K, the motional narrowing is disturbed by the increase of ${\ensuremath{\tau}}_{c}$, near the charge-glass or the short-range order at 6 K. On the other hand, for temperatures above 30 K, the motional narrowing is disturbed by the increase of $\ensuremath{\Delta}$ with increasing temperature.