Introduction

When superconductivity in alkali fullerides was discovered1,2, it was mostly classified as BCS type3. Increasing experimental4,5,6 and theoretical7,8 evidence, however, is placing these materials into the family of strongly correlated superconductors9. A significant step in this direction is the study of expanded trivalent fullerides. These materials are so close to the Mott localization limit that a slight change in the lattice constant can induce a transition between a superconducting and an antiferromagnetic Mott insulating ground state10. Cs3C60 is an especially attractive member of this family because of its ordered and highly symmetric structure in both the insulating and superconducting phases4,5,6.

Cs3C60 exists in two polymorphs, one with a body-centered-based A15 structure4 and one with face-centered cubic (fcc) structure6 similar to K3C60 (ref. 11) and Rb3C60 (ref. 12). The A15 structure contains orientationally ordered fulleride ions, whereas in the fcc polymorph merohedral disorder is present. Experiments found both Cs3C60 polymorphs to be Mott insulators at ambient conditions5,6,13, with the ions in a low-spin (S=1/2) electronic state5,13,14. This low-spin state has been subject of intense discussion, where the possibility of a dynamic Jahn–Teller (JT) state was proposed5,14, putting these materials into the class of magnetic Mott–Jahn–Teller insulators. Below 46 K, A15 Cs3C60 becomes antiferromagnetic5. The fcc polymorph also develops antiferromagnetism below 2.2 K6, but as a result of the fcc structure this magnetic phase is frustrated6,13.

Moderate pressure turns both polymorphs into metals at high temperature15 (up to 280 K) and superconductors at low temperature4,6,16. The C60 t1u lowest unoccupied molecular orbital is triply degenerate, and this orbital degeneracy together with the lattice packing has a key role in stabilizing the metallic state against the Mott insulator17. The superconducting critical temperature (Tc) exhibits a dome-shaped curve as a function of pressure, with maximum Tc of 38 K for the A15 (ref. 4) and 35 K for the fcc polymorph6. Both the magnetic ground state and the appearance of a superconductivity dome on the phase diagram are signs of strong electron correlations, but there is no definitive understanding of the electronic and molecular structure of the resulting localized fulleride anionic species, which is key for the development of appropriate models for both the localized and nearby itinerant electronic states. The existence of the orientationally ordered and disordered polymorphs and the absence of structural transformations make this system a unique playground to study the electronic aspects of the insulator-to-superconductor transition. Approaching the problem from the molecular side, these expanded fullerides allow determination of the relative significance of the symmetry of the lattice and the molecular JT effect when a fulleride ion is placed in a solid18,19.

In this paper, we employ infrared (IR) spectroscopy to address the JT effect in fcc and A15 Cs3C60 as a function of temperature at ambient pressure. As in both cases the lattice possesses cubic symmetry higher than that of any possible JT distortion of the fulleride anions, the crystal field will have a secondary role to the inherent molecular interactions, which determine the distortion. We find a gradual change with temperature in the IR spectra, and explain it by the interplay of two effects: the presence of temperature-dependent solid-state conformers20, as observed in other JT systems21 and the decrease of the influence of crystal field with thermal expansion. As a result, at the highest temperature, a single type of distortion, subject to pseudorotation is observed in the A15 structure. The change in the population of the different conformers results in a continuous change of the spectrum with temperature, without a structural phase transition. These spectroscopic studies thus establish the underlying molecular electronic structure of the anion in cubic fullerides, which underpins the co-operative properties of both the superconducting and insulating members of this family.

Results

IR spectra

The IR spectra of both Cs3C60 polymorphs (Fig. 1) are markedly different from those of the metallic K3C60 and Rb3C60 compounds22. In the latter, the continuous absorption of the metallic electrons results in a strong background, which obscures the vibrational peaks. In Cs3C60, no such background is observed and the vibrational peaks are much sharper. In accordance with previous broadband spectra5 on A15 Cs3C60, these results confirm that both Cs3C60 polymorphs are insulators. This insulating state permits an analysis of the vibrational spectra, which has been impossible in other A3C60 superconductors because of metallic screening.

Figure 1: IR spectra of A15 and fcc Cs3C60 at 28 and 300 K.
figure 1

The energy range shown corresponds to the intramolecular vibrations. The spectra of insulating C60 and metallic K3C60 at 300 K are also shown for comparison. Curves have been shifted and scaled for clarity. Splitting of the T1u vibrational modes and activation of low-intensity peaks, which are silent in C60, indicate a distortion of the fulleride ion in both Cs3C60 polymorphs.

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The IR spectrum of neutral, undistorted (point group Ih) C60 consists of four bands, each corresponding to a threefold-degenerate T1u vibration. Among these, the highest frequency T1u(4) mode is the most sensitive to both charge and symmetry reduction23. This peak is observed in both Cs3C60 polymorphs around 1360 cm−1 and is split into several components. Weaker modes, which are silent in the icosahedral C60 molecule appear in the range 600–800 cm−1 (Table 1). The splitting and the activation of previously silent modes is caused by the symmetry reduction of the fulleride ion: splitting reflects the lifted degeneracy and activation of silent modes the change in selection rules. The new peaks and the splitting pattern of the T1u(4) peak depend on the temperature and are different in the two polymorphs.

Table 1 Assignment of the newly activated weak modes in fcc and A15 Cs3C60.
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Temperature dependence

To study the temperature dependence, we fitted the T1u(2) and the T1u(4) peaks (Fig. 2) with Lorentzian functions. The T1u(2) vibrational mode remains unsplit in the case of the fcc Cs3C60, but appears as a doublet below about 300 K in the A15 Cs3C60. In the spectral range of the T1u(4) vibration, five components can be resolved at low temperature for both polymorphs. As the threefold degenerate T1u peak cannot split into five peaks, the silent Gu(6) mode, which is found in the same frequency region24 should also be taken into account. This mode becomes IR active upon symmetry reduction, as also seen in solid C60 at low temperature25. With increasing temperature, the number of components needed for the fit gradually decreases but no distinct transition temperatures are apparent. The fits shown are for typical temperatures, where the T1u(4) peak can be fitted with five (Fig. 2a,d), four (Fig. 2b,e) and (in the case of A15 Cs3C60) three components (Fig. 2c), respectively. The parameters of the fitted Lorentzian peaks are shown in Supplementary Figs S1,S2. The low-intensity peaks from newly activated modes disappear at different temperatures for each mode (Supplementary Fig. S3).

Figure 2: Lorentzian peak fits in the spectral region of the T1u(2) and the T1u(4) vibrational modes at selected temperatures.
figure 2

Fits are shown for A15 Cs3C60 at (a) 28 K, (b) 180 K, (c) 400 K, for fcc Cs3C60 at (d) 28 K, (e) 320 K. The low-temperature splitting pattern changes gradually to the one at room temperature around 80 K. In A15 Cs3C60, a further gradual transition takes place around 300 K.

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Discussion

The simplest explanation for the observation of multiple peaks would have been that they reflect the multiphase character of the sample. This assumption is discarded after simulating the spectra of phase-pure fcc and A15 Cs3C60 using the measured spectra of the fcc-rich and A15-rich samples, those of bco Cs4C60 (ref. 26) and CsC60 (ref. 27) and the known compositions of the samples. None of the additional features in Fig. 2 consistent with symmetry lowering disappears after subtracting the spectra of the known phases with the appropriate scaling factors (Supplementary Fig. S4). Thus, the splitting and the activated modes are indeed signs of symmetry reduction. A prerequisite for the observation of symmetry reduction is that the molecules are not rotating. Therefore, the rotation of the fulleride ions can be considered as static on the 10−11 s timescale of the IR measurement in both Cs3C60 polymorphs, in accordance with structural data5,6.

Reduction of symmetry can occur via two mechanisms and it has been ambiguous which is the dominant one in the fullerides: the crystal field shaping the molecule to its own symmetry or the molecular JT effect resulting in a symmetry reduction independent of the environment. The most important interaction in fulleride solids with large cations is the cation-fulleride ion repulsion28. In the A4C60 salts (A=K, Rb, Cs)26 at low temperature, steric crowding and symmetry effects cause the molecular symmetry to conform to the crystalline environment imposed by the space group (orthorhombic for Cs4C60, tetragonal for the other two) and to adopt a static D2h distortion, which is the largest common subgroup of the Ih point group and the space groups. In the present case, however, the cation distribution has higher symmetry than the molecular symmetry indicated by the spectra.

To determine the splitting in the T1u(4) spectral region for the case when the fulleride ion is distorted only by the crystal field, the standard correlation method has been used29, leading to the splitting pattern listed in Table 2 after taking into account the fulleride ion site symmetry Th in A15 and Oh in fcc Cs3C60 and the fact that A15 Cs3C60 contains two molecules per primitive unit cell, thereby allowing for in- and out-of-phase collective modes (Davydov splitting). The last column of Table 2 gives the number of IR bands originating from the C60 T1u and Gu modes, respectively after considering the selection rules for dipole transitions (allowed transitions are marked (IR) in the table). As the intensity of the previously silent Gu-derived modes is expected to be lower than that of the T1u modes, the data in Table 2 predict one strong and one weak vibrational band in both cases, in contradiction with the experiment.

Table 2 Splitting of the T1u and Gu representations of the ion in the crystal field of A15 and fcc-structured Cs3C60.
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Having excluded the multiphase character of the sample and the crystal field as the origin of the complexity of the IR spectra, the only remaining candidate is a JT distortion of the molecular units. Fulleride ions are subject to the JT effect because the extra electrons in the threefold degenerate t1u orbitals couple to the eight Hg vibrations of the C60 molecule. Thus the ion is a JT system30. According to theory31, the distortion is bimodal. The most symmetric model for such a distortion is the point group D2h, with the three C2 twofold axes acting as principal axes. As the D2h point group does not contain degenerate irreducible representations, the t1u orbitals are split threefold, leading to the observed S=1/2 spin state (Fig. 3).

Figure 3: Molecular orbitals of molecular ions indicating the T1u(4) vibrations.
figure 3

(a) Ih symmetry with an unsplit t1u molecular orbital, (b) D2h Jahn–Teller distorted molecule with threefold splitting (b1u, b2u and b3u orbitals). 'Inverted Hund's rule coupling' leads to a low-spin (S=1/2) state and the splitting of vibrational bands. Arrows represent the largest atomic displacements of the T1u(4) modes. The magnitude of the distortion in the molecular model is exaggerated.

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As the fulleride ions contain 15 twofold axes, 30 distortions are possible with the same shape but the principal axis in different directions. The molecule can be statically frozen into a single distortion or move between the differently directed distortions20 by tunnelling or pseudorotation, leading to a dynamic JT effect. In a molecular solid built from such dynamic JT units, several scenarios are possible: free, hindered or frozen pseudorotation and in the latter case, order or disorder of the static distortion. The detection of the JT effect is complicated by the possibility of these scenarios and by the fact that the largest atomic displacement produced by the distortion is on the order of 0.04 Å (refs 32,33). In a distorted molecule, not only the electronic orbitals split but also the vibrational levels do so as well, leading to an increased number of lines in the IR spectrum. As IR spectroscopy detects the distortions through intramolecular vibrations, the contributions from molecules distorted (and oriented) in different directions add up, instead of averaging in space. To avoid time averaging, that is to detect dynamic distortions, the timescale of one spectroscopic excitation event has to be shorter than the timescale of interconversion between differently directed distortions34. In many cases, vibrational spectroscopy is such a method35, as its timescale is about 10−11 s.

Vibrational spectroscopy has identified the nature of the distortions in localized electron fullerides, which do not have the key charge. For instance, the A4C60 (A=K,Rb,Cs) compounds were found to be nonmagnetic Mott–Jahn–Teller insulators26,36,37,38. The physical properties of these systems are mainly determined by the simultaneous presence of electron correlations and the JT effect, although the picture is complicated by the symmetry of the lattice. Neutron diffraction32 in Cs4C60 proved an orthorhombic lattice distortion. This distortion can in principle be explained as a cooperative JT state (D2h molecules ordered by translational symmetry), but as it coincides with the symmetry of the cations, it has to be regarded as a crystal field effect. NMR measurements38 indicated a transition across a spin gap, which is evidence for JT splitting of energy levels but not diagnostic of the resulting symmetry (that is, if the splitting is two- or threefold). In this respect, vibrational spectroscopy is unique: the T1u vibrations have the same symmetry as the t1u frontier orbitals, therefore they split in an analogous fashion to the electronic orbitals. In addition, as vibrational spectroscopy detects transitions from the ground state to the vibrationally excited levels, the splitting will be seen directly if selection rules permit. This way, the static D2h to dynamic D3d or D5d transition was detected in the A4C60 phases with the transition temperature determined by the lattice constant26.

As mentioned above, the JT effect distorts the molecular ion into the D2h point group and the line splitting can be handled in a straightforward way based on simple molecular symmetry reduction34. The results are given in Table 3 and include three T1u- and three Gu-derived modes. As the Gu vibration is IR inactive in the neutral C60 molecule, the peaks originating from this vibration are expected to have lower intensity, if detectable at all. These predictions agree clearly much better with the measured spectra than those in Table 2, thus providing a clear indication of the JT character of the distortion.

Table 3 Splitting of the T1u and Gu representations of the ion on symmetry reduction from the Ih to the D2h point group.
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Although the crystal field distorts the fulleride ion only slightly (from point group Ih to Th, Table 2), it can alter the energy of the differently directed JT distortions. Distortions having principal axes parallel to the edge of the unit cell will not be equivalent to those oriented in other directions (Fig. 4a). The crystal field can also change the exact shape of the molecular distortion, which then influences the IR spectrum. The shape of the crystal field depends on the position of the Cs+ ions surrounding the fulleride ions. This is different in the two Cs3C60 polymorphs, thus accounting for the crystal structure dependence of the spectra, although the details of the exact distortions are far beyond our capacities to predict.

Figure 4: Temperature evolution in the population of the two sets of differently directed JT distortions.
figure 4

(a) The hexagon–hexagon C-C 'double bonds' that the twofold axes intersect in the two kinds of distortions are labelled with blue and red on the C60 molecule. The crystallographic principal axes are indicated. (b), (c) and (d) Temperature dependence of the energy relations of the potential energy minima (potential energy versus deformation coordinate Q) of the two sets of distortions. The arrow at the bottom represents increasing temperature. The filling of the energy levels is also shown. In (d) the energy minima are equivalent, thus coloured purple. The graphs are only for illustrating trends; choosing the red distortion as being lower in energy is arbitrary.

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The two different possible distortions also determine the temperature evolution of the IR spectra. We use the molecular model of temperature-dependent solid-state conformers21, discussed thoroughly in ref. 20. We start from two sets of distortions inequivalent in energy and follow their evolution with temperature (Fig. 4b). It may be possible that at low temperature, only the lower energy distortions will be realized. On heating, two effects should be taken into account. First, thermal expansion gradually reduces the strength of the crystal field (the potential energy difference between the two sets of distortions will become smaller). Second, higher energy levels become increasingly occupied (Fig. 4c), thus enhancing the proportion of molecules JT distorted in the direction less favoured by the crystal field. This gradual change is facilitated by the hindered pseudorotation between all possible distortions. The potential barrier decreases with temperature until there is no difference between the two sets of distortions and the molecule performs fast pseudorotation, although still somewhat hindered (Fig. 4d).

Let us now consider the splitting found in the IR spectra. The low-temperature case with one set of distortions (Fig. 4b) would result in one set of peaks (3+3). The intermediate temperature with two sets of distortions (Fig. 4c) causes two sets of peaks. This is in contrast to the observation that the number of peaks decreases on heating. Thus above 28 K both sets of distortions are present with a continuous change in their ratio (Fig. 4c), giving an upper limit of 28 K≈20 cm−1 of the energy difference δ between the conformers. The fact that the population is changing smoothly with temperature proves the dynamic nature of the JT effect; it means that the barrier between conformations is low enough for continuous change of the deformation. The high-temperature case where all distortions are equivalent (δ=0, Fig. 4d) corresponds to one set of peaks in the IR spectrum, and thus observing fewer peaks than at intermediate temperatures. This is what is found in the measurements. There is no exact match with the predicted number of peaks (12 at low temperature to 6 at high temperature), but the number of potentially allowed peaks is such that the spectra cannot be fitted unambiguously; also the peaks assigned to the Gu mode, which was silent in Ih C60, are expected to have lower intensity.

Antiferromagnetic ordering should be accompanied by ferrodistortive orbital ordering5 and this would mean a decrease in the number of peaks in the antiferromagnetic phases39,40. In the notation of Fig. 4, the single minimum in Fig. 4b would correspond to such a collective JT state. For the A15 polymorph, our measured temperature range reaches into the antiferromagnetic phase, but we do not observe any such effect. As the transition temperatures of orbital and spin ordering do not necessarily coincide20, we conclude that the static component of orbital ordering is still small at 28 K.

In conclusion, we have proven the principal role of the JT effect in the parent insulating state of the expanded superconductor Cs3C60. A direct implication of our findings is that the Coulomb exchange energy, JH, which favours highest total spin and orbital angular momentum (Hund's rule) should be smaller than the Jahn–Teller interaction JJT, caused by coupling of the electrons to symmetry-lowering molecular vibrations. Their calculated magnitudes from various sources (JH~0.03–0.1 eV and JJT~0.06–0.12 eV) are summarized in the review by Capone et al.7 Although both J values are in essence independent of the lattice constant, the quantity U/W (where U is the on-site Hubbard repulsion and W the bandwidth) strongly depends on it. As under our experimental conditions both polymorphs of Cs3C60 are on the localized side of the Mott transition, U/W exceeds the Mott localization limit and electron correlations are large. The localization requires U>W, so is a demonstration of the relative, rather than absolute, size of U, as W itself is also small. JH is smaller than U, but our measurements only address the competition between JH and JJT and prove the 'inverted Hund's rule coupling', that is, a low-spin state according to the JT effect (Fig. 3). As the theoretical estimates of these values, quoted above, are similar in size, the present experiments are decisive in establishing the relative magnitude of these key quantities.

The present results reveal that the JT effect is dynamic at all measured temperatures, but the distortion is observed as static on the timescale of the IR measurement, that is, the interconversion rate is less than 1011 s−1 up to 400 K, the highest measured temperature. The observed distortion is dominated by the JT effect and perturbed by the crystal field to cause both a crystal structure and a temperature dependence. The crystal field results in two sets of inequivalent distortions, which become equivalent on heating as the crystal field strength decreases with lattice expansion. These features are all typical of JT systems and therefore unequivocally prove the insulating state of these correlated superconductors to be that of a magnetic Mott–Jahn–Teller insulator. The high crystal symmetry of the Cs3C60 polymorphs is important in determining their highly correlated behaviour. The cubic structure does not lift the degeneracy of the t1u-based conduction band, and this triple degeneracy is crucial in allowing the metallic state to survive to very large values of the ratio U/W17. Our IR results show that the transition to the electron-correlation-driven localized state is accompanied by a loss of the degeneracy via the dynamic JT effect. As for the metallic state, we expect the degeneracy to be restored, and consequently the symmetry of the C60 units to conform to the crystal field35. Such symmetry was seen in IR spectroscopy22 and tunneling microscopy41 experiments and further spectroscopic investigations on metallic systems are underway to test these assumptions.

Methods

Sample preparation and characterization

The Cs3C60 samples used in this study were prepared by solution chemistry routes as described elsewhere4,6. The fcc-rich sample contained 86% fcc Cs3C60, 3% A15 Cs3C60, 7% body-centered orthorhombic (bco) Cs4C60 and 4% CsC60, whereas the A15-rich sample contained 14% fcc Cs3C60, 71% A15 Cs3C60 and 15% bco Cs4C60 according to Rietveld refinements of synchrotron X-ray diffraction profiles.

IR spectroscopy

IR measurements were performed on a Bruker IFS 66v FTIR instrument in a flowthrough He cryostat. We measured in the temperature range 28–480 K and frequency range 500–2,000 cm−1, with 0.25 cm−1 resolution. We found that heating promotes oxidation above 440 K for the A15, and above 350 K for the fcc polymorph even under dynamical vacuum, limiting the accessible temperature ranges for the measurements.

Additional information

How to cite this article: Klupp, G. et al. Dynamic Jahn–Teller effect in the parent insulating state of the molecular superconductor Cs3C60. Nat. Commun. 3:912 doi: 10.1038/ncomms1910 (2012).