Raman study of the two-dimensional polymers ${\mathrm{Na}}_4{\mathrm{C}}_{60}$ and tetragonal ${\mathrm{C}}_{60}$

We present a Raman investigation of the monoclinic two-dimensionally polymerized phase ${\mathrm{Na}}_4{\mathrm{C}}_{60}$ and a comparison with the pure tetragonal ${\mathrm{C}}_{60}$ polymer and the doped ${\mathrm{K}}_3{\mathrm{C}}_{60}$ structure. The Raman spectrum of ${\mathrm{Na}}_4{\mathrm{C}}_{60}$ depends on the probing laser wavelength, and high wave-number modes are hard to observe with a low-energy laser excitation. The spectrum for ${\mathrm{Na}}_4{\mathrm{C}}_{60}$ is very rich with a pronounced splitting of the original $H_g$ modes and a large number of new modes. Several modes at low wave numbers support the presence of intermolecular bonds and the line broadening observed for low-frequency $H_g$ modes is typical for electron-phonon coupling in metallic fullerene systems. From the shift of the pentagonal pinch mode we deduce an unexpectedly low charge transfer of approximately three electrons per ${\mathrm{C}}_{60}$ molecule. The presence of a distinct mode around 980 ${\mathrm{cm}}^{\mathrm{-}1}$ throws doubts on earlier assumptions that modes in this range are connected to vibrations in the intermolecular cyclobutane rings found in ${\mathrm{C}}_{60}$ polymers. No superconductivity is observed in ${\mathrm{Na}}_4{\mathrm{C}}_{60},$ although the electron-phonon interaction derived from the Raman spectrum is similar to that in ${\mathrm{K}}_3{\mathrm{C}}_{60}.$