<figure><img src="image_1.png" /></figure>

HAL
open science

# 13C Knight shift of the doped Fullerene K3C60

Denis Jerome, R. Kerkoud, Pascale Auban-Senzier, J. M Lambert, A. Zahab,

Patrick Bernier

► To cite this version:

Denis Jerome, R. Kerkoud, Pascale Auban-Senzier, J. M Lambert, A. Zahab, et al. 13C Knight shift of the doped Fullerene K3C60. EPL - Europhysics Letters, 1994. hal-04994697

HAL Id: hal-04994697

https://hal.science/hal-04994697v1

Submitted on 17 Mar 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_2.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
¹³C Knight Shift of the Doped Fullerene K₃C₆₀.

R. KERKOUD(*), P. AUBAN-SENZIER(*), D. JÉROME(*), J. M. LAMBERT(**)

A. ZAHAB(**) and P. BERNIER(**)

(*) Laboratoire de Physique des Solides (associé au CNRS), Université Paris-Sud
91405 Orsay, France

(**) Groupe de Dynamique des Phases Condensées

Université des Sciences et Techniques du Languedoc - 34060 Montpellier, France

(received 16 September 1993; accepted in final form 16 December 1993)

PACS. 74.70Y - Other superconducting materials.

PACS. 76.60C - Chemical and Knight shifts.

**Abstract.** - We report the measurement of the ¹³C NMR frequency in K₃C₆₀ under pressure. Comparing pressure dependences of the hyperfine spin lattice relaxation rate and of the resonance frequency provides the first determination of the ¹³C Knight shift ((61 ± 4) p.p.m.) and of the chemical shift of the C₆₀³⁻ molecule (125 p.m.m./TMS). NMR data under pressure can be undestood with a weak-Coulomb-interaction model.

The discovery of superconductivity in alkali-doped fullerenes has considerably revamped the interest for molecular conductors. As in low-dimensional organic superconductors, electronic conduction in fullerenes proceeds through the overlap of partly filled conduction bands originating from π-orbitals of originally neutral molecules. However, they generate a three-dimensional isotropic lattice where electron-hole pairing instabilities are not favoured by a good nesting of the Fermi surface. Consequently, doped fullerenes (A₃C₆₀) retain the metallic character down to low temperature and are good candidates for superconductivity. Furthermore the weak π-π interball contact of the cubic structure should favour a narrow conduction band with large values of the density of states at the Fermi level (N(E_F)) and high superconducting transition temperatures (T_c). This point of view is supported by the experimental relation existing between T_c and the lattice constant obtained through the study of a series of isostructural compounds with composition A₃-xBₓC₆₀ (where A and B are Na, K, Rb, Cs) [1,2] and also through the variation of the lattice constant under pressure [3,4]. However, the validity of the rigid-band model for these half-filled band superconductors can be argued, since photoemission spectra of KₓC₆₀ present for x = 3 a pseudogap of about 0.5 eV at the Fermi level, which could result from the correlation effects among the C 2p-electrons [5]. Furthermore, it has been suggested that the phase x = 3 might be a Mott-Hubbard insulator and that superconductivity could be due to non-stoichiometry [6]. Models for superconductivity based on strong Coulombic interactions have also been proposed [7].

It is therefore important to correlate T_c with N(E_F) and to extract an estimate for the amplitude of the electron correlations. This goal can be achieved by investigating NMR properties (spin-lattice relaxation rate, T_1⁻¹ and Knight shift, K) of a compound while its
bandwidth is varied by the application of a high pressure. $T_1^{-1}$ in a conductor is usually related to $N(E_F)$ and probes the electron spin (charge) degrees of freedom. In molecular conductors, extrinsic relaxation channels may also be provided by molecular reorientations and $T_1$ data must be carefully analysed. Generally $K$ is also related to $N(E_F)$ but the small amplitude of its pressure dependence does not make the experimental investigation an easy task. Previous NMR studies have provided the pressure dependence of $T_1^{-1}$ in $K_3C_{60}$ [8]. However, these experiments performed at 2.62 T suffered from a limited sensitivity and field stability and failed to give reliable data for the pressure dependence of $K$.

We present the measurement of the ¹³C NMR line position of $C_{60}^{3-}$ in $K_3C_{60}$ referenced to the neutral molecule $C_{60}^0$ line position vs. pressure up to 8 kbar, in a magnetic field of 9.4 T (100 MHz). As chemical shifts of organic molecules such as $C_{60}$ depend on the charge provided by the cation, this frequency shift cannot be taken as a Knight shift. To reach the actual value of $K$ in such a conductor, one ought to have access to the position of the NMR line of the molecule with a similar charge in the insulating state taken as a reference; this situation is met in some organic conductors [9]. The diamagnetism of $K_3C_{60}$ in the superconducting state induces a decrease of the average internal induction from the applied field which is large enough to prevent any determination of $K$ [10]. Alternatively, when $T_1^{-1}$ and the line position depend significantly on pressure (or temperature), following a well-established relation, one can extrapolate the line position corresponding to zero relaxation rate. This is the method which has been used in the present work for the determination of the ¹³C chemical shift of $C_{60}^{3-}$ and of the ¹³C Knight shift in $K_3C_{60}$.

All NMR data presented here have been obtained using isotopically ¹³C-enriched samples up to 10 at.%, whose preparation has been described previously [8]. The dimensions of the pressure cell enabled us to use about 10 mg of $K_3C_{60}$ powder.

For the Knight-shift determination, the presence of neutral $C_{60}$ molecules was necessary as a magnetic-field marker. The composition of this sample, as checked by magic-angle spinning (MAS) NMR technique, was around 60 mol% of $C_{60}$ in $K_3C_{60}$. Previously published $T_1$ measurements under pressure [8], also reported in this work, were performed on a $K_3C_{60}$ sample containing only ≈ 5% of unreacted $C_{60}$.

Although it is not likely that the modest pressures used in this work will significantly affect the chemical shift of $C_{60}$ molecules, we have checked that the ¹³C NMR resonance of $C_{60}$ remains under pressure at the same position relative to the ¹³C resonance of the pressure medium.

At ambient pressure, the $K_3C_{60}$ spectrum shows the $C_{60}^{3-}$ resonance peak at the usual position, i.e. shifted 43.5 p.p.m. downfield from the unreacted $C_{60}$ peak. Typical spectra for different pressures at room temperature are presented in fig. 1. As the repetition rate ($\tau = 1$ s) has been kept constant at different pressures, one may notice several features:

i) At low pressure the $^{13}$C-$C_{60}^{3-}$ spectrum is narrow (FWHH = 14 p.p.m.) in agreement with previously published data [11, 12] and the $^{13}$C-$C_{60}^{0}$ line has a small intensity.

ii) In the pressure regime 3–5 kbar, the $C_{60}^{3-}$ line contains a narrow peak (FWHH = 14 p.p.m.) superimposed over a broad spectrum (FWHH ≈ 50 p.p.m.) and the intensity of the $C_{60}^{0}$ line grows relative to the $C_{60}^{3-}$ signal. This superposition of NMR signals is better seen in another sample under pressure containing a smaller proportion of $C_{60}$ (inset of fig. 1).

iii) Above 7 kbar, the $C_{60}^{3-}$ spectrum contains only the broad component which is strongly overlapping with the $C_{60}^{0}$ spectrum.

iv) Finally, the $C_{60}^{3-}$ line remains symmetric at all pressures, as also observed for the temperature dependence, down to ≈ 200 K [11, 12].
<figure><img src="image_3.png" /></figure>

Fig. 1. – Room temperature ¹³C spectra of the C₆₀-enriched K₃C₆₀ sample, at different pressures (for a constant repetition rate τ = 1 s). The inset shows the broadening of the line at P = 5 kbar for a second sample containing a smaller proportion of unreacted C₆₀.

This last point allowed us to measure the shift $\delta$ of the C$_{60}^{3-}$ line relative to the C$_{60}^{0}$ one from the relative position of the maxima of the two peaks as a function of pressure, within an accuracy of $\pm$ 0.5 p.p.m. (fig. 2 (left)). A linear pressure dependence is observed with a slope $d\delta/dP \approx -0.73$ p.p.m./kbar.

¹³C spin-lattice relaxation time measurements have been performed at room temperature using a saturation recovery technique, integrating a narrow window of the FT spectrum centred on the peak, in order to isolate the K₃C₆₀ signal from that of C₆₀. Recovery curves were fitted by an exponential relaxation although some small deviations from this law (increasing with pressure) have been observed above 3 kbar. T₁⁻¹ data for the C₆₀-enriched K₃C₆₀ sample are displayed in fig. 2 (right) together with previously published values obtained on a C₆₀-poor sample at ambient pressure and between 5 and 12 kbar [8].

Below 5 kbar, T₁⁻¹, remains higher than the extrapolation from the high-pressure region. This behaviour can be understood in terms of a contribution to the relaxation coming from molecular reorientations. This is equivalent to the contribution to T₁⁻¹ giving rise to the maximum at T = 230 K in a mangetic field H₀ = 7 T [12] which should shift up to ≈ 240 K at 9.4 T with a slightly larger intensity. This maximum is also expected to move up to room temperature under a pressure of few kbar. This extrinsic contribution cannot be studied with much accuracy, since the present pressure equipment is not adapted to a good pressure control in the low-pressure domain. However, our relaxation data suggest that it is suppressed above 5 kbar.

The disagreement between T₁'s of the two samples in the high-pressure region is obvious
and remains beyond the experimental uncertainty. However, the $T_1$ of the C$_{60}$-enriched K$_3$C$_{60}$ sample can be understood when the coupling, via spin diffusion, between the two $^{13}$C baths is taken into account. At ambient pressure, the separation between the two lines is larger than the small dipolar interaction and prevents the spin diffusion. Hence, both samples have the same $T_1$. Then, the difference of $T_1$'s increases under pressure as the progressive increase of the overlap between $C_{60}^-$ and $C_{60}^0$ spectra allows spin diffusion between the two spin species. The effective $T_1$ of K$_3$C$_{60}$ is longer than in the C$_{60}$-poor sample as $T_1$ of pure C$_{60}$ increases rapidly with pressure ($T_1 \approx 2-10$ s) above the phase transition at 3 kbar [13, 14], according to a pressure investigation we have performed on neutral C$_{60}$, and remains always longer than that of the K$_3$C$_{60}$ phase. Moreover, the estimate of $T_1$ for the $C_{60}^0$ part of the spectrum gives lower values than in pure C$_{60}$ confirming the presence of spin diffusion.

Considering the known small proportion of C$_{60}$ in the C$_{60}$-poor sample, we have assumed that $T_1$ data obtained previously [8] are representative of the intrinsic $C_{60}^-$ electron-induced relaxation between 5 and 12 kbar.

It may be stressed out that the Korringa relation is meaningless for a comparison between the electron-induced relaxation and the Knight shift not only because the dominant part of the hyperfine relaxation is coming from a dipolar coupling of electrons from $p\pi$ orbitals [15], but also because the exact value of K is not known. The dipolar relaxation remains proportional to the square of the density of states at the Fermi level. We shall use this proportionality relation and the experimental pressure dependence of both $T_1$ and $N(E_F)$ to extract the actual Knight shift.

We have plotted in fig. 3 $(1/T_1)^{1/2}$ (measured in the C$_{60}$-poor K$_3$C$_{60}$ sample [8]) vs. the frequency shift $\delta$ (in p.p.m.) relative to the $C_{60}^0$ resonance, using the linear pressure dependence determined up to 8 kbar and extrapolated up to 12 kbar with the same pressure coefficient. Data between 5 and 12 kbar follow very accurately the law $(1/T_1)^{1/2} \propto (\delta - \delta_0)$, where $\delta_0 \approx -18 \pm 4$ p.p.m. The point extrapolated from this law back to ambient pressure leads to the hyperfine relaxation rate of $(T_1^{-1})_e = (2.44 \pm 0.25) \text{ s}^{-1}$. The comparison with experimental value (also plotted in fig. 2 (right) and 3) indicates that about 20% of the relaxation under ambient conditions should be attributed to molecular motion, which is in fair agreement with the maximum of the extrinsic relaxation at 7 T [12].

<figure><img src="image_4.png" /></figure>

Fig. 2. – Left: room temperature pressure dependence of the resonance frequency shift $\delta$ of the $^{13}$C-$C_{60}^-$ line relative to the $C_{60}^0$ one in the C$_{60}$-enriched K$_3$C$_{60}$ sample. A typical error bar ($\pm$ 0.5 p.p.m.) is shown. The regression line gives the slope $d\delta/dP \approx -0.73$ p.p.m./kbar. Right: room temperature pressure dependence of the $^{13}$C spin-lattice relaxation rate $1/T_1$ for the C$_{60}$-enriched K$_3$C$_{60}$ sample (●) and the C$_{60}$-poor one (▽) [8]. The continuous line for the second sample is the fit deduced from the plot of fig. 3 and the pressure dependence of $\delta$. T = 295 K for both diagrams.
<figure><img src="image_5.png" /><figcaption>Fig. 3.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Fig. 4.</figcaption></figure>

Fig. 3. – Relation between the C₆₀⁻ electronic relaxation rate and the resonance frequency shift δ relative to C₆₀, measured at different pressures, plotted as (1/T₁)¹/² vs. δ, yielding the actual Knight shift K. T = 295 K, (1/T₁)¹/² ~ (δ + 18) p.p.m.

Fig. 4. – Natural logarithm of the superconducting transition T_c(P) [20, 21] plotted against the inverse of the Knight shift K(P) in K₃C₆₀. The continuous line is a linear regression of the data giving Ω-ph and λ in the BCS formula. ln T_c = 6.38 – 209(1/K).

The absolute Knight shift under ambient pressure as deduced from fig. 3 becomes then K = (δ - δ₀) ≈ 61 ± 4 p.p.m. instead of the 43.5 p.p.m. positive shift measured from the neutral C₆₀ molecule NMR signal. The Knight shift has several contributions, one which is scalar (isotropic) due to the density of s-electrons at nuclear sites and another dominant one which has a dipolar origin (anisotropic), related to the p-atomic wave functions. What we measure is a site and powder average.

Furthermore, our findings mean that the three extra charges which are transferred to the C₆₀ orbital modify the chemical shift of the molecule which becomes 18 p.p.m. more diamagnetic as compared to the neutral molecule. This result agrees as least in sign if not in amplitude with the usual relation for aromatic compounds which predicts a diamagnetic shift of 8 p.p.m. (160 p.p.m./π electron/carbon) [16] with respect to the C₆₀ line position. The discrepancy could be attributed to ring currents contributions as was suggested in the case of C₆₀⁻ [17].

The pressure dependence of the resonance frequency (fig. 2 (left)) shows that K decreases by ≈ 7 p.p.m., i.e. (1.1 ± 1.5)% under 10 kbar. At the same time, the electronic contribution to T⁻¹ drops by (21.5 ± 3)% under 10 kbar. These results compare very well with the extended Hückel band structure calculation [1, 18], leading to an 11% reduction of N(E<sub>F</sub>) taking a lattice parameter reduction of 1.2% [4]. Therefore the enhancement of the spin susceptibility cannot be large, which disagrees with the ESR susceptibility [19], enhanced by a factor of almost three as compared to band calculation.

From this experimental pressure dependence of K, or N(E<sub>F</sub>), although at room temperature, and the published variation of the superconducting transition T<sub>c</sub>(P) [20, 21], we can estimate the phonon frequency Ω<sub>ph</sub> and the electron-phonon coupling constant λ = N(E<sub>F</sub>)V in the BCS formula T<sub>c</sub> = Ω<sub>ph</sub> exp[-1/λ], if V is assumed to be unaffected by pressure. In fig. 4, ln (T<sub>c</sub>(P)) is plotted against 1/K(P) and a linear regression of the data gives Ω<sub>ph</sub> = (600 ± 60) K and λ ≈ 0.3. The evaluation of K at low temperature assuming a reduction of 6.6% during cooling (equivalent to an applied pressure of 6 kbar at room temperature) yields about the same value for Ω<sub>ph</sub>. This kind of extrapolation must be taken
with care, considering the large error bars on both K and $T_c$ which are measured on the same sample. However, fig. 4 suggests that the electronic states responsible for the superconductivity in these compounds are rather strongly coupled to intramolecular vibrational modes in agreement with Raman and neutron diffraction results [22, 23].

This result is also compatible with a recent investigation of the $^{13}$C-$C_{60}^{3-}$ resonance in $Rb_3C_{60}$ at 196 p.p.m./TMS, obtained by MAS-NMR technique at 5 T [24] with a better accuracy than a previous result [25]. The difference of 10 p.p.m. between the two compounds may be ascribed only to an increase of the Knight shift as the chemical shift is fixed by the charge density on the $C_{60}$ molecule and gives $T_c = 31$ K for $Rb_3C_{60}$, using the same V and $\Omega_{ph}$ obtained in fig. 4.

In conclusion, we have determined the absolute value of the $^{13}$C Knight shift in $K_3C_{60}$ via combined $T_1$ and resonance frequency shift studies performed under pressure at room temperature. We have found that the chemical shift of the isolated $C_{60}^{3-}$ molecule (125 p.p.m.) lies in the typical range for aromatic molecules. The paramagnetic shift between $C_{60}^0$ and $C_{60}^{3-}$ confirms the importance of an anomalous component in the chemical shift of the neutral $C_{60}$ molecule due to paramagnetic ring currents flowing along the pentagons. The behaviour of $T_1$ under temperature and pressure together with the pressure coefficient of K do not allow to explain the large enhancement of the electron susceptibility inferred from the comparison between $\chi_{ESR}$ and the band calculation of $N(E_F)$. NMR experiments do not reveal significant effects of Coulomb correlations in $K_3C_{60}$.

***

We would like to thank P. WZIETEK for his helpful cooperation and advice. This research has been supported in parts by the Groupe de Recherche $C_{60}$ at CNRS.

REFERENCES

[1] FLEMING R. et al., *Nature*, **352** (1991) 787.

[2] TANIGAKI K. et al., *Nature*, **356** (1992) 419.

[3] SPARN G. et al., *Phys. Rev. Lett.*, **68** (1992) 1228.

[4] ZHOU O. et al., *Science*, **255** (1992) 833.

[5] TAKAHASHI T. et al., *Phys. Rev. Lett.*, **68** (1992) 1232.

[6] LOF R. W. et al., *Int. J. Mod. Phys. B*, **6** (1992) 331.

[7] CHAKRAVARTY S., GELFAND M. P. and KIVELSON S., *Science*, **254** (1991) 970.

[8] QUIRION G. et al., *Europhys. Lett.*, **21** (1993) 233.

[9] GOTSCHY B. et al., *J. Phys. I*, **2** (1992) 677.

[10] TYCKO R. et al., *Phys. Rev. Lett.*, **68** (1992) 1912.

[11] BARRETT S. E. and TYCKO R., *Phys. Rev. Lett.*, **69** (1992) 3754.

[12] YOSHINARI Y. et al., *Phys. Rev. Lett.*, **71** (1993) 2413.

[13] KRIZA G. et al., *J. Phys. I*, **1** (1991) 1361.

[14] SAMARA G. A. et al., *Phys. Rev. Lett.*, **67** (1991) 3136.

[15] ANTROPOV V. P. et al., *Phys. Rev. B*, **47** (1993) 12373.

[16] SPIESECKE H. and SCHNEIDER W. G., *Tetrahedron Lett.*, **14** (1961) 468.

[17] PASQUARELLO A., SCHLÜTER M. and HADDON R. C., *Phys. Rev. A*, **47** (1993) 1783.

[18] SAITO S. and OSHIYAMA A., *Phys. Rev. Lett.*, **66** (1991) 2637.

[19] JANOSSY A. et al., *Phys. Rev. Lett.*, **71** (1993) 1091.

[20] SPARN G. et al., *Science*, **252** (1992) 1829.

[21] SCHIRBER J. E. et al., *Physica C*, **178** (1991) 137.

[22] DUCLOS S. et al., *Science*, **254** (1991) 1625.

[23] PRASSIDES K. et al., *Nature*, **354** (1991) 462.

[24] ZIMMER G. et al., *Europhys. Lett.*, **24** (1993) 59.

[25] YANNONI C. S. et al., *Synth. Met.*, **59** (1993) 279.