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# The Disorder-Free Non-BCS Superconductor Cs3C60 Emerges from an Antiferromagnetic Insulator Parent State

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Science  20 Mar 2009:
Vol. 323, Issue 5921, pp. 1585-1590
DOI: 10.1126/science.1169163

## Abstract

The body-centered cubic A15-structured cesium fulleride Cs3C60 is not superconducting at ambient pressure and is free from disorder, unlike the well-studied face-centered cubic A3C60 alkali metal fulleride superconductors. We found that in Cs3C60, where the molecular valences are precisely assigned, the superconducting state at 38 kelvin emerges directly from a localized electron antiferromagnetic insulating state with the application of pressure. This transition maintains the threefold degeneracy of the active orbitals in both competing electronic states; it is thus a purely electronic transition to a superconducting state, with a dependence of the transition temperature on pressure-induced changes of anion packing density that is not explicable by Bardeen-Cooper-Schrieffer (BCS) theory.

Superconductivity requires an attractive interaction between electrons to form Cooper pairs, which form a condensate that can move without electrical resistance. In simple metals and alloys, the Bardeen-Cooper-Schrieffer (BCS) theory explains how electron-phonon coupling overcomes the repulsion between negatively charged electrons (1). In high-temperature superconductors, such as the copper oxides and iron oxyarsenides, the origin of the attraction is less clear. Beyond the theoretical challenges, the experiments are complicated by imperfections within the materials, such as structural disorder, low symmetry and dimensionality, and variations in chemical valence at the electronically active sites. Here we show that in the cubic alkali metal fulleride Cs3C60, which is completely ordered and for which precise valences can be assigned, the 38 K superconducting state (2) emerges directly from a localized electron antiferromagnetic insulating (AFI) state with the application of pressure as the anion packing density increases. This transition maintains the threefold degeneracy of the active orbitals in both competing electronic states, and is thus a purely electronic transition to a superconducting state. The transition temperature Tc depends on the anion packing density in a way that is not explicable within a simple BCS approach.

In systems where the bands in which the electrons move are narrow, there are electron-electron correlation energies associated with interelectron repulsion, which are comparable to the electronic bandwidth. These electron correlation effects (3) need to be taken into account in understanding the mechanisms for formation of the Cooper pairs (4). These concepts have been developed primarily in d-electron–based systems such as the cuprates and iron oxyarsenides, where doping, with the associated structural disorder and distribution of metal charge states and d-electron counts within the material, is required to produce superconductivity by suppressing magnetically ordered states. In addition, recent theoretical work (5, 6) indicates that the competition between correlation and delocalization energies is critically controlled by the degeneracy of the orbitals (7) carrying the active electrons, but this cannot be investigated in d-electron–based superconductors because their low-symmetry crystal structures remove the degeneracy.

An ideal material for understanding the interactions producing superconductivity in such structurally and chemically complex correlated electron systems would allow the isolation of the influence of purely electronic factors without the complications of disorder, structural transitions, and low dimensionality, while maintaining the site symmetry required for orbital degeneracy in all the potentially competing electronic ground states. The threefold degeneracy of the t1u lowest unoccupied molecular orbital (LUMO) of the C60 molecule is maintained in the superconducting face-centered cubic (fcc) A3C60 alkali metal fullerides (8), which have electronic structures arising from weak overlap of the s/p-derived frontier orbitals of molecular anions. However, the properties of this family—in particular, the monotonic increase of the superconducting Tc to 33 K (9) with interfullerene separation—can be well explained by BCS-like theories where Tc is controlled by the increase in density of states at the Fermi level, N(EF), with expansion; an anomalous decrease of Tc at high interfullerene separations is only observed in heavily disordered fcc systems superconducting at ambient pressure (10). There is thus no definitive experimental evidence for a non-BCS origin for superconductivity, where correlation or orbital degeneracy would play a role, as no usefully comparable competing insulating state from which superconductivity emerges has been identified.

All of the fcc A3C60 fullerides are superconducting at ambient pressure, but the recently isolated (2) Cs3C60 (11, 12), which adopts the so-called A15 structure based on body-centered cubic (bcc) packing of the C603– anions (Fig. 1A), is not. Cs3C60 is the most expanded binary A3C60 system yet reported (2) and thus offers the opportunity to identify the electronic ground state that competes with superconductivity in the orbitally degenerate cubic fullerides. We used magnetization, optical reflectivity, muon spin relaxation (μSR), and 13C and 133Cs nuclear magnetic resonance (NMR) measurements, coupled with ultrahigh-resolution synchrotron x-ray diffraction under variable pressure and temperature, to identify the ambient-pressure nonsuperconducting electronic ground state of bcc-based Cs3C60 and investigate how it transforms into the superconducting state with the application of pressure.

High-resolution diffraction data (2) show that the cubic symmetry of A15 Cs3C60, and thus the point symmetry producing the t1u orbital degeneracy, is maintained to the lowest temperatures at ambient pressure, so we undertook magnetization measurements to reveal the electronic ground state in competition with superconductivity. The temperature dependence of the paramagnetic susceptibility χ [also measured via the high-field slope of field-dependent magnetization, M(H) isotherms] of a representative A15-rich Cs3C60 sample (13) [which also contains the body-centered orthorhombic (bco) Cs3+xC60 and the fcc Cs3C60 polymorphs (2)] is shown in Fig. 1C. These data reveal a well-defined cusp in χ(T) at 46 K; at higher temperatures, the susceptibility obeys the Curie-Weiss law with a negative Weiss temperature, consistent with antiferromagnetic correlations.

Field-cooled (FC) measurements in low applied fields (Fig. 1D) reveal a sharp increase in the magnetization M(T) at 46 K, exactly the same temperature at which the cusp in the susceptibility, χ(T), occurs. The spontaneous magnetic moment approaches a value of 5.5 emu Oe mol–1 at 2 K, corresponding to a very small moment per C60 of ∼0.001 Bohr magneton (μB). These data suggest a transition to an antiferromagnetically ordered state below the Néel temperature TN = 46 K, with a small spin canting between the two magnetic sublattices giving rise to weak ferromagnetism. Systematic FC magnetization measurements on a series of Cs3C60 samples further reveal that the spontaneous magnetic moment scales with the fraction of the A15 phase present in the measured samples (fig. S1) (13). In addition, pure bco Cs3+xC60 samples show no magnetic transitions (fig. S1), and both the cusp in χ(T) and the sharp increase in M(T) at 46 K are completely lost when the air-sensitive materials are exposed to air, ruling out adventitious contamination by metal oxide or metal particles as the origin of the magnetic transitions observed. Therefore, we attribute the antiferromagnetic response to the A15 Cs3C60 polymorph.

An even more definitive association of this magnetic behavior in the bulk sample with the A15 Cs3C60 phase that produces superconductivity upon application of pressure requires the use of a local probe to isolate the behavior of the A15 phase. The 13C and 133Cs nuclei in NMR studies are suitable probes because they allow direct identification of the component phases via their chemical shifts and site symmetries. In particular, the 133Cs NMR resonance, when recorded with the solid echo pulse sequence, is suppressed for the two high-symmetry (8c) (¼,¼,¼) and (4b) (½,½,½) Cs sites in the fcc structure, as they have no electric field gradient (14). This approach isolates the resonance from the Cs cations in the lower-symmetry (6c) (¼,½,0) sites within the A15 structure, which allow quadrupolar interactions to be present. [See (13) for details of the NMR measurements; a key point is that the cation sites in the bco phase also have lower than axial symmetry, which suppresses their signal amplitudes in these experiments by lineshape broadening.] The temperature dependence of the 133Cs NMR spectra of the A15 Cs3C60 polymorph reveals substantial line broadening below 46 K (Fig. 2A), which demonstrates that the M(T) and χ(T) features observed by magnetometry measurements indeed arise from antiferromagnetic ordering in this bcc-based phase. The lineshape broadening and the associated increase in the 133Cs NMR second moment M2 (Fig. 2B) arise from the onset of large dipolar fields of the C603– anions at the 133Cs sites in the antiferromagnetic phase. If we define $Math$—where $Math$ is the second moment associated with the nearly temperature-independent quadrupole interaction $Math$ and $Math$ is the electron-nuclear dipolar broadening—the dipolar coupling between the antiferromagnetically ordered moments of the C603– anions and the Cs cations $Math$ then allows an estimate of the ordered moment as ∼1 μB per anion (13). The lineshape change and broadening of the 13C spectra at the same temperature (fig. S2) (13) also confirm this interpretation. The 13C spin-lattice relaxation time T1 (Fig. 2C) is temperature-independent over the range 100 to 400 K, in contrast to the behavior of fcc A3C60 metallic fullerides, in which T1 follows the Korringa relation (15, 16).

We conclude that the A15 Cs3C60 phase is an insulator at ambient pressure, as also confirmed by infrared reflectivity data (Fig. 2D). Below ∼100 K, 1/T1 suddenly begins to decrease and shows nearly activated behavior, implying the opening of a spin gap at temperatures well above TN. The onset of antiferromagnetic long-range order is also confirmed by complementary zero-field muon spin relaxation (ZF-μ+SR) measurements. A heavily damped spontaneous muon precession present below 46 K (Fig. 2E) demonstrates coherent ordering of the C603– electronic moments. The quasi-static nature of the local magnetic field is confirmed by the complete recovery of the asymmetry in a longitudinal field of 250 Oe (fig. S3) (13). The μ+ Larmor frequency νμ is 0.624 ± 0.002 MHz at 5 K and corresponds to a static internal field at the muon site, 〈Bμ〉 = 46.0 ± 0.2 G (Fig. 2F); νμ is comparable to the value of 0.64 ± 0.01 MHz observed for the (NH3)K3C60 antiferromagnet (17), which has a magnetic moment of ∼1 μB/C60. Thus, all of these experimental results indicate the presence of S = ½ moments localized on the fulleride anions in the insulating A15 Cs3C60 phase at ambient pressure and ordering to form the AFI phase at 46 K, thereby demonstrating the key role played by electron correlation in the fulleride superconductor systems.

High-resolution synchrotron x-ray powder diffraction at 14.6 K shows that the application of hydrostatic pressure to the cubic-localized electron S = ½ C603– AFI with the bcc-derived A15 structure (space group $Math$) produces no structural change over the range 1 bar to 25 kbar (fig. S4) (13). The effect of increased pressure is thus solely to decrease the interfullerene contact distances isotropically (Fig. 3A), thereby increasing the overlap between t1u orbitals on neighboring C603– anions and thus the bandwidth W, which favors electron delocalization. Initially, at pressures P ≤ 3.6 kbar, the AFI state is retained with TN (signaled by the onset of weak ferromagnetism measured in the FC magnetization), increasing with pressure to a maximum of 49.5 K (Fig. 3B). This is consistent with the t1u electrons remaining localized with enhanced exchange coupling caused by the closer intermolecular contacts.

However, in the pressure range 2.6 to 4 kbar, concurrent zero field–cooled (ZFC) magnetization measurements reveal that the antiferromagnetic state coexists in the sample with superconductivity, consistent with a first-order transition from the AFI state to superconductivity without intervening electronic states (Fig. 3B, inset). Superconductivity (with a broad diamagnetic response at the trace level of ∼ 0.1%) is initially observed to coexist with the AFI state at 29 K at 2.6 kbar; Tc increases rapidly to 35 K at 3.6 kbar with an associated increase in shielding fraction (to ∼1%). The fraction of the AFI phase decreases in this coexistence regime, as evidenced by the decrease in the FC spontaneous magnetization with increasing P (Fig. 3B). At 4.2 kbar, the signal of the AFI state in the magnetization is suppressed. However, the superconducting Tc continues to increase with P to a broad maximum of 38 K near ∼7 kbar (2). Upon further pressure increase, the trend is reversed (Fig. 3C) and Tc now decreases monotonically with increasing P to the highest pressure of the present experiments, 24.3 kbar (Fig. 4A). Tc is insensitive to cooling rate, consistent with the absence of orientational disorder in the A15 Cs3C60 superconductor that was apparent from the structural analysis.

These experimental data demonstrate the localized electron AFI state that is the decisive signature of the importance of correlation in the superconducting A3C60 fullerides. Observation of this state is essential in understanding the non-BCS behavior of the superconducting state that emerges directly from the AFI state with application of pressure. The observation of localized electron magnetism indicates that in cubic A15 Cs3C60 at ambient pressure, the electrons occupying the degenerate t1u orbitals lie on the insulating side of the Mott-Hubbard transition, because the electron correlations quantified by the Hubbard U (the on-site interelectron repulsion) overcome the kinetic energy favoring electron delocalization quantified by the bandwidth W. Density functional theory (DFT) calculations show that despite the reduced anion packing density, the value of W in A15 Cs3C60 is comparable to that in metallic fcc K3C60 because of the more favorable intermolecular contact geometry (Fig. 1B) (18). The value of U is greater than that of W in all the fcc A3C60 phases, but the metallic state is stabilized over the insulator by two key factors. One of these, the threefold frontier orbital degeneracy of the high-symmetry C603– anion [which enhances intermolecular hopping relative to the singly degenerate case (19)], is retained in the case of AFI A15 Cs3C60 because cubic symmetry is observed under all conditions corresponding to the measurements reported here. The absence of the second key feature of the fcc materials, geometrical lattice frustration (19), in the bcc-based A15 Cs3C60 results in the observation of the localized electron AFI state, an electronic ground state not accessible in the fcc A3C60 family; A15 Cs3C60 has the point and lattice symmetry to allow the electronic state directly competing with superconductivity in fullerides to be identified.

The “low-spin” S = ½ state shows the dominant energy for the (t1u)3 electrons localized on the C603– anion by U; the vibronic Jahn-Teller coupling overcomes the intramolecular Hund's rule electron repulsion to stabilize one of the three t1u orbitals, which is preferentially occupied by two electrons. The observed cubic metric symmetry of the AFI state shows that this Jahn-Teller distortion producing the S = ½ state must be dynamic, with the molecular distortion axis fluctuating among the three possible directions, and demonstrates that the long-range structure does not suppress the orbital degeneracy. The antiferromagnetic exchange (20) between neighboring C603– anions is produced by dynamic orbital order (21) with locally favored ferrodistortive intersite arrangement of distortion axes (22). The weak ferromagnetic component seen at low field may then arise either from an antiferrodistortive contribution to the local dynamical coupling of Jahn-Teller distortion axes (which will give ferromagnetic exchange) or from the Dzyaloshinskii-Moriya coupling arising from the absence of an inversion center (Fig. 1B) on the direct exchange pathway (23) between neighboring anions in the $Math$ space group of the A15 phase.

The AFI state is suppressed in favor of the superconducting state purely by the application of pressure without any complicating influence of disorder or change in crystal structure, and thus with the preservation of t1u orbital degeneracy. This symmetry retention is crucial to the stabilization of the metallic and superconducting state with increasing P; at the same volume per C603– anion (24, 25) found at ∼13 and 10.5 kbar for superconducting A15 Cs3C60, orthorhombic (NH3)K3C60 and (CH3NH2)K3C60, respectively, are antiferromagnetic insulators (17, 26, 27) because the lower point symmetry in these noncubic materials lifts the t1u degeneracy and allows U to localize the electrons. The orbitally degenerate cubic superconducting phase, formed by the suppression of the AFI state upon application of pressure and initially coexisting with it, has a Tc that initially increases with decreasing interfullerene separation to a maximum of 38 K (Fig. 4B). This is the clear signature of non-BCS behavior in the superconducting state emerging directly from the AFI state as the bare density of states in A15 Cs3C60 smoothly decreases with increasing P across this region, according to DFT calculations (18) based on the experimentally determined structures; this same effect would drive a decrease in Tc in the BCS-related models where N(EF) controls Tc exponentially. This experimental behavior is in stark contrast to the fcc A3C60 systems, where the decrease of Tc with increasing pressure is driven by the accompanying decrease of N(EF) as the interanion orbital overlap increases, and has its origin in the dominance of correlations in the parent AFI state.

The high symmetry of the C60 building unit imposes a robust cubic three-dimensional structure on A15 Cs3C60 free of positional, chemical, or orientational disorder, with a fixed charge state in which magnetism is transformed into superconductivity solely by changing an electronic parameter: the extent of overlap between the outer wave functions of the constituent anions. The pressure-induced transition in A15 Cs3C60 from a localized electron AFI state to a superconducting state with two distinct dependences of Tc on packing density is purely electronic in nature, driven by increased overlap between the C603– anions and the associated enhanced tendency to delocalize the t1u electrons. The unconventional nature of the superconducting state that emerges from the AFI state can be associated with its proximity to the metal-insulator transition where conventional Fermi liquid theories are not expected to be valid, and quasi-localized effects produced by electronic correlation enhancing the role of intramolecular Jahn-Teller (electron-phonon) and Hund's rule (electron-electron) coupling are directly controlled by the persistent orbital degeneracy in both the insulating and superconducting states, clearly traceable to the molecular origin of the electron states. The observed maximum in the dependence of Tc on P is consistent with modern theoretical treatments (57) that explicitly take into account the orbital degeneracy and the repulsion between the electrons as well as the classical electron-phonon coupling. These effects are not seen in the conventional fcc A3C60 systems, which are too far from the metal-insulator transition for differences from the conventional BCS predictions of the dependence of Tc on N(EF) to become apparent. A15 Cs3C60 is an ideal material for understanding the interactions producing superconductivity in structurally and chemically complex correlated electron systems such as the cuprates and oxyarsenides, as it allows the isolation of the influence of only electronic factors (including orbital degeneracy) without any other complications.

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Materials and Methods

Figs. S1 to S4

References

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