Microscopic dynamics of $A{\mathrm{C}}_{60}$ compounds in the plastic, polymer, and dimer phases investigated by inelastic neutron scattering

We present inelastic neutron-scattering results for $A$C${}_{60}$ $(A$=K,Rb,Cs) compounds. The spectra of the high-temperature fcc phases strongly resemble the ones of pristine C${}_{60}$ in the plastic phase. At equal temperatures we find identical rotational diffusion constants for pristine C${}_{60}$ and Rb${}_1{\mathrm{C}}_{60}$ ${(D}_r$=2.4 10${}^{10}$ s${}^{-1}$ at 400 K). The changes taking place in the inelastic part of the spectra on cooling $A$C${}_{60}$ indicate the formation of strong intermolecular bonds. The buildup of intensities in the gap region separating internal and external vibrations in pure C${}_{60}$ is the most prominent signature of this transition. The spectra of the low-temperature phases depend on their thermal history. The differences can be explained by the formation of a polymer phase (upon slow cooling from the fcc phase) and a dimer phase (upon fast cooling), respectively. The experimental data are analyzed on the basis of lattice dynamical calculations. The density-of-states are well modeled assuming a [2+2] bond for the polymer and a single intercage bond for the dimer. Indications for different intercage bonding are also found in the internal mode spectra, which, on the other hand, react only weakly to the charge transfer. The dimer phase is metastable and converts into the polymer phase with a strongly temperature-dependent time constant. The transition from the polymer to the fcc phase is accompanied by inelastic precursor effects which are interpreted as the signature of inhomogeneities arising from plastic monomer regions embedded in the polymer phase. In the polymer phase $A$C${}_{60}$ compounds show strong anharmonic behavior in the low-temperature region. The possible connection with the metal-to-insulator transition is discussed.