# Coexistence of a Spin-Singlet Ground State with the 3D Magnetic Order in the CsC 60 Polymerized Fulleride

Barbara Simovic, Denis Jerome, F. Rachdi, G. Baumgartner, László Forró

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Barbara Simovic, Denis Jerome, F. Rachdi, G. Baumgartner, László Forró. Coexistence of a Spin-Singlet Ground State with the 3D Magnetic Order in the CsC 60 Polymerized Fulleride. Physical Review Letters, 1999, 10.1103/PhysRevLett.82.2298. [hal-04989001]

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Distributed under a Creative Commons Attribution 4.0 International License
Coexistence of a Spin-Singlet Ground State with the 3D Magnetic Order in the CsC₆₀ Polymerized Fulleride

Barbara Simovič,¹ Denis Jérome,¹ Férid Rachdi,² Gabriel Baumgartner,³ and László Forró³

¹Laboratoire de Physique des Solides (associé au CNRS), Université Paris-Sud, 91405 Orsay, France

²GDPC, Université Montpellier II, Place E. Bataillon, 34060 Montpellier, France

³Laboratoire de Physique des Solides Semicristallins, Département de Physique, Ecole Polytechnique Fédérale de Lausanne, Switzerland

(Received 3 August 1998)

The low temperature behavior of the CsC₆₀ polymer was investigated by NMR measurements on ¹³C and ¹³³Cs nuclei at ambient and under hydrostatic pressure up to 9 kbar. The existence of a second-order structural phase transition to a spin-singlet (nonmagnetic) ground state at Tₛ = 13.8 K is clearly established at ambient pressure. This state coexists with the magnetic order that develops at Tₙ = 30 K. The application of pressure first suppresses the magnetic order and a homogeneous nonmagnetic ground state is stabilized at 5 kbar. [S0031-9007(99)08654-8]

PACS numbers: 61.48.+c, 76.60.-k

The presence of parallel polymerized chains of C₆₀ molecules in orthorhombic alkali doped fullerides belonging to the AC₆₀ series (A = K, Rb, Cs) [1] may suggest the possibility of quasi-one-dimensional (1D) electronic properties. In this spirit, the onset of a metal-insulator transition near 40 K (50 K) in polymerized CsC₆₀ (RbC₆₀) was interpreted in terms of strong electron-electron correlations [2]. Magnetic fluctuations were evident [3] in nuclear magnetic resonance (NMR) experiments, dominating the relaxation rate of ¹³C up to 300 K. The temperature dependence of the ESR linewidth [2], which is narrow even in the presence of fluctuations at ambient temperature, was also ascribed to reduced dimensionality [4]. Magnetic fluctuations above the transition temperature and a metal-insulator transition of magnetic nature are consistent with the observed divergent relaxation rate and the concomitant strong broadening of the NMR spectra below 40 K (50 K) for the ¹³C and ¹³³Cs (⁸⁷Rb) nuclei [3] in CsC₆₀ (RbC₆₀). An antiferromagnetic resonance [5] below Tₙ ≈ 30 K in CsC₆₀ and 35 K in RbC₆₀ has corroborated the conclusions of the NMR studies. From this body of evidence a second-order metal-insulator transition to a magnetic ground state was inferred, in agreement with the suspected 1D spin and charge dynamics. Besides, x-ray diffraction [6] has shown a different chain orientation between KC₆₀ and RbC₆₀ but local density approximation calculations [7], performed in the RbC₆₀ structure [6], predict isotropic 3D energy bands. The corresponding metallic behavior was actually observed only in KC₆₀ [2]. Such a discrepancy between band calculations and experiments emphasizes that despite the polymerization, 1D features in RbC₆₀ and CsC₆₀ are not evident.

In this Letter, we report a detailed study of ¹³C and ¹³³Cs-NMR in the CsC₆₀ polymerized fulleride at ambient and under hydrostatic pressure. The analysis of the ¹³³Cs quadrupolar spin echo enables us to measure the effects of lattice distortions with a great sensitivity. We find

a second-order structural transition to a nonmagnetic singlet state at Tₛ = 13.8 K (±0.2) which coexists with the magnetic phase developed at Tₙ = 30 K. The applied pressure suppresses the magnetic fluctuations and stabilizes the homogeneous spin-singlet ground state for which Ts increases up to 20 K at 5 kbar. The measurements were made on two samples, one of them ¹³C isotopically enriched, with entirely consistent results.

The ¹³³Cs-NMR measurements in the CsC₆₀ polymeric phase were performed at ambient pressure and temperatures below 20 K. The quadrupole moment Q of ¹³³Cs (I = 7/2) interacts with the local electric field gradient (EFG). In the present case Q is small and its coupling with the EFG can be treated in first-order perturbation theory. When the magnetic broadening and the nuclear spin-spin dipolar interaction are negligible compared to the first-order quadrupolar interaction, a two pulse sequence can be applied [8,9] to create purely quadrupolar spin echoes. In our system, time dependence due to the dipolar interaction between ¹³³Cs spins is negligible during the echo delay (τ) [10]. However, in the magnetic phase the inhomogeneous magnetic broadening causes a strong dephasing; i.e., the quantum coherence of the state created by the first pulse is rapidly damped, and the quadrupolar spin echoes are suppressed. Yet we observed the expected quadrupolar spin echoes for the *I* = 7/2 ¹³³Cs spin at temperatures far below the magnetic transition, down to 4.2 K, proving that at least some of the ¹³³Cs sites are not involved in the magnetic order. For these sites the quadrupolar frequency νQ (proportional to the electric field gradient) and the isotropic Knight shift (proportional to the local susceptibility) can be evaluated from the Fourier transformation of the purely quadrupolar spin echo refocused at 3τ (Fig. 1 inset) [11].

Figure 1a shows the temperature dependence of νQ below 16 K. The 13% enhancement of the quadrupolar frequency at 4.2 K reveals a significant structural change
<figure><img src="image_2.png" /><figcaption>FIG. 1. (a) Temperature dependence of the quadrupolar frequency of <sup>133</sup>Cs at ambient pressure. Only the sites not coupled to the magnetic ordering contribute to the signal. The solid line represents a fit with a mean field power law expression used for the order parameter below T<sub>S</sub>. The dashed line indicates the critical temperature. The inset shows the quadrupolar spectrum at 11 K obtained from the quadrupolar echo at 3τ. The frequency scale for the <sup>133</sup>Cs spectrum is in terms of fractional shifts Δν/ν<sub>0</sub> relative to 1 M CsCl(aq) at 9.4 T (ν<sub>0</sub> = 52 MHz). (b) Temperature dependence of the Knight shift of <sup>133</sup>Cs at 1 bar. The data are normalized to the Knight shift value at T<sub>S</sub>. The solid line is a fit to an activated temperature dependence.</figcaption></figure>

in the environment of the <sup>133</sup>Cs site. The continuous variation of ν<sub>Q</sub> around T<sub>S</sub> = 13.8 K is consistent with the temperature dependence of the order parameter for a second-order transition. The critical exponent deduced from ν<sub>Q</sub>(T) is 0.44 (±0.07), not far from the mean field value of 0.5.

The drop of the <sup>133</sup>Cs Knight shift below T<sub>S</sub>, illustrated in Fig. 1b, indicates the nonmagnetic character of the transition. We attribute the minimum shift (−57.5 ppm), at base temperature, to the intrinsic chemical shift of <sup>133</sup>Cs in this phase. Below T<sub>S</sub> the shift was fit to an activated temperature dependence [12], (K/K<sub>S</sub>)α(1/√T)e<sup>−2Δ(T)/T</sup>, where 2Δ(T) = 2Δ(0)√[1 − (T/T<sub>S</sub>)]. We obtained 2Δ(0) = 61.4K (±4K), corresponding to the dimensionless ratio 2Δ(0)/k<sub>B</sub>T<sub>S</sub> = 4.45.

At low temperature and ambient pressure the <sup>13</sup>C spec-
trum consists of two contributions [13]: a broad compo-
nent with a very short relaxation time, which arises only
below 25 K, and a slowly relaxing component which re-
mains narrow down to 4.2 K. Similar results were reported
in Ref. [3], where the strongly nonexponential behavior of
the magnetization recovery of <sup>13</sup>C and <sup>133</sup>Cs below 30 K
was linked to the onset of the magnetic order [3]. In the
magnetic phase, the <sup>133</sup>Cs nuclei exhibit a single broad
spectrum in spite of a nonexponential relaxation similar
to the <sup>13</sup>C nuclei. Nevertheless, at temperatures slightly
above T<sub>N</sub>, the slow relaxing component of <sup>133</sup>Cs NMR

[14] does not reveal the expected increase due to criti-
cal magnetic fluctuations and, therefore, could be related
to <sup>133</sup>Cs sites which contribute to the low-T quadrupolar
echoes (see Fig. 1 inset). For these reasons, we suspect
that the narrow component of the <sup>13</sup>C spectrum and these
<sup>133</sup>Cs sites are related to the same nonmagnetic phase. To
establish such a correlation we performed spin-spin relax-
ation time <sup>13</sup>T<sub>2</sub> measurements in the <sup>13</sup>C enriched sample.
The main result is shown in Fig. 2. A sharp peak is ob-
served in 1/<sup>13</sup>T<sub>2</sub> at 13.8 K, coinciding with the feature in
the <sup>133</sup>Cs quadrupole frequency (Fig. 1). We attribute this
behavior to a critical slowing down of lattice fluctuations,
due to a soft local distortion mode, typical of a second-
order structural phase transition. A similar peak was ob-
served earlier in RbC<sub>60</sub> at 10 K [15].

These ambient pressure measurements unambiguously establish the existence of a spin-singlet state below 13.8 K in two different samples of polymeric CsC<sub>60</sub>. This state is most likely related to a structural distortion, and it coexists with the magnetic order. A rough estimate of the two phases ratio can be obtained by comparing the relative intensities of the two components in the <sup>13</sup>C spectrum: about 40% of the <sup>13</sup>C sites are involved in the nonmagnetic ground state.

<sup>13</sup>C and <sup>133</sup>Cs NMR studies have been also performed
under hydrostatic pressure, in a homemade double-stage
copper-beryllium cell using fluor-inert as the pressure
<figure><img src="image_3.png" /><figcaption>FIG. 2. Temperature dependence of $(T_2)^{-1}$ for the central part of the $^{13}$C spectrum at 1 bar.</figcaption></figure>

medium. This high pressure apparatus enabled us to keep the pressure constant while cooling to low temperature. The relaxation rates and spectra of the two samples in our study did not show any irreversible pressure effect for pressures up to a maximum of 9 kbar. The 5 kbar data are shown in Figs. 3a and 3b. Hydrostatic pressure suppresses the magnetic order, in agreement with previous $^{13}$C NMR data in RbC$_{60}$ under pressure [15]. Below 20 K the T dependences of the spin-lattice relaxation rate (1/T$_{1}$) of both $^{13}$C and $^{133}$Cs are activated, suggesting the opening of a spin gap. The absence of any divergence of 1/T$_{1}$ and of any line broadening (see Fig. 3a inset) shows that the magnetic phase has been completely suppressed in favor of the homogeneous spin-singlet state. At 5 kbar the nonmagnetic phase is present up to about 20 K. Finally, above 5 kbar a metallic phase gradually gives way to the spin-singlet state [16].

The structural distortion at $T_S$ accompanying the formation of the spin-singlet ground state at ambient pressure suggests the existence of a strong electron-phonon coupling in CsC$_{60}$ polymers. Intramolecular vibrational modes of C$_{60}$ are strongly coupled to electrons in A$_4$C$_{60}$ [17] and they may mediate electron pairing in the A$_3$C$_{60}$ superconductors [18]. An intramolecular mechanism, such as a Jahn-Teller distortion could be the source of the spin pairing we have observed in polymeric CsC$_{60}$. Because the Jahn-Teller mechanism depends only on local molecular properties, it is expected to be much less sensitive to pressure than the magnetic order. However, unlike cubic A$_n$C$_{60}$ compounds, calculations indicate that the degeneracy of the molecular $t_{1u}$ orbital triplet of C$_{60}$ is already

<figure><img src="image_4.png" /><figcaption>FIG. 3. (a) Temperature dependence of the spin-lattice relaxation rate of $^{133}$Cs at 5 kbar. The inset shows the temperature dependence of the $^{133}$Cs linewidth at 1 bar from Ref. [3] (empty diamonds) and at 5 kbar (present study, black circles). (b) Temperature dependence of the $^{13}$C spin-lattice relaxation rate at 5 kbar.</figcaption></figure>

lifted in the polymerized C$_{60}$ phase, with an energy splitting in the range of 0.5 eV [7]. It is not at all obvious that, in the polymer, the energy gain due to charge redistribution is sufficiently large to drive a sharp phase transition. For this reason, we suspect that the spin-singlet instability, like the magnetic transition, is related to the existence of a 1D structure in CsC$_{60}$ polymers. Indeed, at 5 kbar, as shown on Fig. 3b, the $^{13}$C relaxation rate is temperature independent above 60 K. Such a feature is consistent with 1D Heisenberg chains [19], and, consequently, the onset of a spin singlet ground state below 20 K can be related to a 1D lattice instability, i.e., a spin-Peierls transition. The slight decrease of the $1/^{13}T_1$ between 20 and 60 K is the result of a three-dimensional $2k_F$ lattice fluctuations precursor to the spin-Peierls transition as found in $^{13}$C NMR in the organic conductor (TMTTF)$_2$PF$_6$ [20]. As for the $^{133}$Cs nucleus, the absence of any pressure dependence of $1/^{133}T_1$ up to 9 kbar between 100 and 300 K [16] implies that the relaxation of $^{133}$Cs is not governed by a hyperfine mechanism, and, consequently, the $^{133}$Cs site does not "see" the magnetic fluctuations. Taking into account the
form factor of the <sup>133</sup>Cs site in the orthorhombic structure, this observation can be easily anticipated for 1D antiferromagnetic fluctuations persisting in this temperature range [3]. Nevertheless, the processes involved in the relaxation of <sup>133</sup>Cs nuclei above 100 K are still to be clarified.

In conclusion, we have shown that a second-order structural transition at $T_S = 13.8$ K to a spin-singlet state takes place in the polymeric $CsC_{60}$ at ambient pressure. NMR experiments performed at 5 kbar have revealed that the magnetic order disappears in favor of the long range spin-singlet order for which $T_S$ increases up to 20 K. Such an interplay between the magnetic and the spin-singlet phases raises intriguing questions about the true nature of the ground state of the polymeric $CsC_{60}$ which is certainly not a 3D metal. As the <sup>13</sup>C NMR data at 5 kbar strongly suggest the existence of disordered spin chains at this pressure, the nonmagnetic transition may be a spin-Peierls instability. However, the spin-Peierls ground state unlike 3D magnetic order survives only in “purely” 1D nonmetallic compounds and, consequently, requires a Mott-Hubbard localization well above $T_S$. The persistence of developed 1D features under pressure, despite the disappearance of the magnetic phase, sharply contrasts with the deep decrease of the uniform spin susceptibility (ESR) at 300 K within the first 5 kbar [21]. This latter experiment proves indeed that the on-site Coulomb repulsion U enhancing the ESR susceptibility at ambient pressure is strongly reduced at 5 kbar and cannot be the main driving force for the spin localization.

We thank P. Auban-Senzier, S. Brazovskii, V. Brouet, M. Héritier, P. Launois, W. A. MacFarlane, H. Mayaffre, L. Mihaly, R. Moret, P. Sotta, and P. Wzietek for stimulating discussions. We are also very grateful to J. P. Cromières and M. Nardone for technical assistance.

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