Static and dynamic Jahn-Teller effect in the alkali metal fulleride salts $A_4{\mathrm{C}}_{60}$ $(A=\mathrm{K},\mathrm{Rb},\mathrm{Cs})$

We report the temperature dependent mid- and near-infrared spectra of ${\mathrm{K}}_4{\mathrm{C}}_{60}$, ${\mathrm{Rb}}_4{\mathrm{C}}_{60}$, and ${\mathrm{Cs}}_4{\mathrm{C}}_{60}$. The splitting of the vibrational and electronic transitions indicates a molecular symmetry change of ${\mathrm{C}}_{60}^{4-}$ which brings the fulleride anion from $D_{2h}$ to either a $D_{3d}$ or a $D_{5d}$ distortion. In contrast to ${\mathrm{Cs}}_4{\mathrm{C}}_{60}$, low temperature neutron diffraction measurements did not reveal a structural phase transition in either ${\mathrm{K}}_4{\mathrm{C}}_{60}$ and ${\mathrm{Rb}}_4{\mathrm{C}}_{60}$. This proves that the molecular transition is driven by the molecular Jahn-Teller effect, which overrides the distorting potential field of the surrounding cations at high temperature. In ${\mathrm{K}}_4{\mathrm{C}}_{60}$ and ${\mathrm{Rb}}_4{\mathrm{C}}_{60}$ we suggest a transition from a static to a dynamic Jahn-Teller state without changing the average structure. We studied the librations of these two fullerides by temperature dependent inelastic neutron scattering and conclude that both pseudorotation and jump reorientation are present in the dynamic Jahn-Teller state.

Figure 1

(a) Possible Jahn-Teller distortions in fulleride ions. The axis along which the distortion occurs is perpendicular to the plane of the paper through the center of the molecule. The atoms above the plane of the paper are black while those under it are gray. (b) The two standard orientations in fullerene/fulleride solids. The $z$ crystal axis coincides with the $C_2$ molecular axis shown.

Figure 2

Top: Some possible arrangements of fulleride ions in the crystal structures in $A_4{\mathrm{C}}_{60}$ systems and their molecular distortions. Ellipses with horizontal and vertical bars, respectively, represent the standard orientations in Fig. 1b. O stands for orthorthombic, T for tetragonal crystal structure. Bottom: splitting of the HOMO $\left(t_{1u}\right)$ and the LUMO $\left(t_{1g}\right)$ molecular orbitals of ${\mathrm{C}}_{60}^{4-}$ in a $D_{2h}$ (cooperative static, static) and $D_{3d}$ or $D_{5d}$ (staggered static, dynamic) distorted molecule, respectively. Infrared-active vibrations of $T_{1u}$ symmetry show similar splitting. Arrows denote dipole allowed transitions between split states.

Figure 3

(Color online) Neutron diffraction profiles of (a) ${\mathrm{K}}_4{\mathrm{C}}_{60}$ and (b) ${\mathrm{Rb}}_4{\mathrm{C}}_{60}$ at two temperatures, showing only a small thermal contraction of the lattice but no change in symmetry or unit cell. LeBail fits for lattice parameter determination for (c) ${\mathrm{K}}_4{\mathrm{C}}_{60}$ at $6\mathrm{K}$ and (d) ${\mathrm{Rb}}_4{\mathrm{C}}_{60}$ at $4\mathrm{K}$. The measured data on these latter two graphs are shown by blue dots, the fits by blue lines, and the difference plots by black lines.

Figure 4

Temperature-dependent lattice parameters normalized to the $300\mathrm{K}$ values of ${\mathrm{K}}_4{\mathrm{C}}_{60}$ and ${\mathrm{Rb}}_4{\mathrm{C}}_{60}$. The lowest and highest temperature values are given in Table . The solid lines are guides to the eye.

Figure 5

(Color online) MIR spectrum of (a) ${\mathrm{K}}_4{\mathrm{C}}_{60}$, (b) ${\mathrm{Rb}}_4{\mathrm{C}}_{60}$, and (c) ${\mathrm{Cs}}_4{\mathrm{C}}_{60}$ at selected temperatures above and below the change in symmetry (colored lines). The highest-frequency mode can be fitted with three Lorentzians at low temperature and two Lorentzians at high temperature (black lines). These splittings indicate a molecular symmetry change with temperature.

Figure 6

Temperature dependence of the peak heights of selected MIR lines in ${\mathrm{K}}_4{\mathrm{C}}_{60}$, ${\mathrm{Rb}}_4{\mathrm{C}}_{60}$, and ${\mathrm{Cs}}_4{\mathrm{C}}_{60}$. Changes are apparent around 270, 330, and $400\mathrm{K}$, respectively.

Figure 7

Combined MIR-NIR spectra of ${\mathrm{K}}_4{\mathrm{C}}_{60}$, ${\mathrm{Rb}}_4{\mathrm{C}}_{60}$, ${\mathrm{Cs}}_4{\mathrm{C}}_{60}$, and ${\mathrm{C}}_{60}$ without background correction. The intermolecular transition at around $4000{\mathrm{cm}}^{-1}$ (broad background) gets weaker with increasing cation size. (The sharp peaks around $3700{\mathrm{cm}}^{-1}$, denoted by asterisks, arise from atmospheric water absorption.)

Figure 8

(Color online) Baseline-corrected NIR spectrum of (a) ${\mathrm{K}}_4{\mathrm{C}}_{60}$, (b) ${\mathrm{Rb}}_4{\mathrm{C}}_{60}$, and (c) ${\mathrm{Cs}}_4{\mathrm{C}}_{60}$ at selected temperatures (colored lines). The spectra were fitted with Gaussians, with the exception of the lowest frequency peak of ${\mathrm{Cs}}_4{\mathrm{C}}_{60}$ at 151 and $298\mathrm{K}$ where a Lorentzian produced a better fit. These fits are shown with black lines.

Figure 9

(Color online) (a) Fixed momentum transfer scans of ${\mathrm{K}}_4{\mathrm{C}}_{60}$ at 100, 200, and $300\mathrm{K}$ at $Q=5.5{\mathrm{\AA }}^{-1}$. (b) Fixed momentum transfer scans of ${\mathrm{Rb}}_4{\mathrm{C}}_{60}$ at 100 and $300\mathrm{K}$ at $Q=5.5{\mathrm{\AA }}^{-1}$. Symbols are the measured data, lines are fits as described in the text. (c) Fixed energy transfer scans at $E=2.4$ and $5\mathrm{meV}$ of ${\mathrm{K}}_4{\mathrm{C}}_{60}$ along with the neutron diffraction pattern scaled to emphasize the diffuse background.

Figure 10

(Color online) Possible structural models of Jahn-Teller distorted fulleride ions (light blue) in a crystal field. The dark background symbolizes the volume in which the molecule is confined by the crystal field. The figures within each column depict fulleride ions on different lattice points. The magnitude of the distortion of the fulleride ions is overemphasized for clarity. (1) Static $D_{2h}$ distortion, following the shape of the crystal field. (2) Static $D_{3d}∕D_{5d}$ distortion. The direction of the distortions can be ordered (staggered static Jahn-Teller state) or disordered. (3) Dynamic distortion in preferred directions appearing in an anisotropic crystal field. Both pancake-shaped $D_{2h}$ and $D_{3d}∕D_{5d}$ distortions are realized with time. (4) Free pseudorotation of the $D_{3d}∕D_{5d}$ distortion in a weak isotropic crystal field. The deeper blue of the molecules in models (3) and (4) represents a temporal average. This picture illustrates only the distortion of the anions; for their orientation see Fig. 2.