Polymorphism control of superconductivity and magnetism in Cs
C 3 close to the Mott transition 60
(08 July 2010)
24 March 2010
27 April 2010
19 May 2010
The crystal structure of a solid controls the interactions between the electronically active units and thus its electronic properties. In the high-temperature superconducting copper oxides, only one spatial arrangement of the electronically active Cu
units—a two-dimensional square lattice—is available to study the competition between the cooperative electronic states of magnetic order and superconductivity 2+ . Crystals of the spherical molecular C 1 anion support both superconductivity and magnetism but can consist of fundamentally distinct three-dimensional arrangements of the anions. Superconductivity in the A 60 3- C 3 (A = alkali metal) fullerides has been exclusively associated with face-centred cubic (f.c.c.) packing of C 60 (refs 60 3- 2, 3), but recently the most expanded (and thus having the highest superconducting transition temperature, T ; ref. c 4) composition Cs C 3 has been isolated as a body-centred cubic (b.c.c.) packing, which supports both superconductivity and magnetic order 60 . Here we isolate the f.c.c. polymorph of Cs 5 , 6 C 3 to show how the spatial arrangement of the electronically active units controls the competing superconducting and magnetic electronic ground states. Unlike all the other f.c.c. A 60 C 3 fullerides, f.c.c. Cs 60 C 3 is not a superconductor but a magnetic insulator at ambient pressure, and becomes superconducting under pressure. The magnetic ordering occurs at an order of magnitude lower temperature in the geometrically frustrated f.c.c. polymorph (Néel temperature 60 T = 2.2 N K) than in the b.c.c.-based packing ( T = 46 N K). The different lattice packings of C change 60 3- T from 38 c K in b.c.c. Cs C 3 to 35 60 K in f.c.c. Cs C 3 (the highest found in the f.c.c. A 60 C 3 family). The existence of two superconducting packings of the same electronically active unit reveals that 60 T scales universally in a structure-independent dome-like relationship with proximity to the Mott metal–insulator transition, which is governed by the role of electron correlations characteristic of high-temperature superconducting materials other than fullerides. c
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Figure 1: Crystal structure and structural characterization of f.c.c. Cs 3C 60.
a, The crystal structure of f.c.c. Cs 3C 60 (ORTEP representation). The C 60 3- anions (carbon, dark grey) are orientationally disordered—only one orientation is shown for clarity. The mean C 60 3--C 60 3- near-neighbour contacts (3.59 Å through neighbouring hexagon:pentagon C–C bonds) are markedly shorter than those in the lower-anion-density (817.9 Å 3 per C 60 3-) A15 polymorph (3.80 Å through hexagon:hexagon faces: Supplementary Fig. 1b). The mean Cs …C distance (3.45 Å) for the tightly coordinated tetrahedral site of f.c.c. Cs 3C 60 is shorter than that in A15 Cs 3C 60 (3.66 Å). The more spacious octahedral Cs site in f.c.c. Cs 3C 60 supports a more expanded coordination environment—mean Cs …C distance, 3.90 Å. In common with all f.c.c. A 3C 60 phases , the Cs 20 + ion residing in the large octahedral interstices displays a very large isotropic thermal parameter, B iso ( = 11.65(7) Å 2), corresponding to a mean square fluctuation about the centre of the hole, = 0.665(2) Å. On cooling, the Debye–Waller factor decreases smoothly to low temperatures where considerable disorder (presumably of static origin) still persists ( = 0.373(1) Å at 30 K) ( Supplementary Fig. 2a). The Cs cations (red) residing in the tetrahedral and octahedral interstices are shown with 90% thermal ellipsoids to emphasize this disorder, which is absent in A15 Cs 3C 60 where the Cs ions reside in less spacious distorted tetrahedral holes. b, Main panel, final observed (red) and calculated (blue line) synchrotron X-ray ( λ = 0.40004 Å) powder diffraction profile for the f.c.c.-rich sample (85.88(2)%) at ambient temperature. The lower line (green) shows the difference profile, and the ticks show the reflection positions of the f.c.c. (top), A15 (3.31(5)%, upper middle), body-centred orthorhombic (b.c.o.) (6.7(2)%, lower middle), and CsC 60 (4.10(6)%, bottom) phases—refined parameters and agreement indices are given in Supplementary Table 1. Inset, expanded view of the diffraction profile (4.2-5.3°) with the observed reflections labelled by their ( hkl) Miller indices.
Figure 2: Ambient pressure magnetic properties of f.c.c. Cs 3C 60.
a, Temperature dependence of the magnetic susceptibility, χ( T) (green circles), of f.c.c.-rich Cs 3C 60, obtained from the difference of the values at 5 T and 3 T. b, Temperature dependence of the spin–lattice relaxation rate, 1/ 13 T 1. Inset, below 100 K, there is a distribution of relaxation rates, giving stretched-exponential behaviour to the 13C magnetization relaxation curves, M( z τ) - M(0) z ∝ exp [-( τ/ T 1) α ], where M( z τ) is the z-component of the nuclear spin magnetization measured at time τ after a train of pulses saturated the 13C nuclear spin magnetization. The stretch exponent changes below ~15 α K. c, Temperature dependence of the spin–spin relaxation rate, 1/ 13 T 2. Gradual freezing of local magnetic moments gives a rapid increase below 15 K. d, 133Cs NMR spectra of f.c.c. Cs 3C 60 between 4 and 65 K. O and T are resonances for the octahedral and tetrahedral sites, T′ and O′ are associated with the anion disorder . 21 e, Temperature dependence of the second moment, 133 M 2 1/2 (red circles). Its increase at low T is ascribed to the increased width of the distribution of static local magnetic fields (see also Supplementary Fig. 7). For comparison, we show 133 M 2 1/2 in A15 Cs 3C 60 ( T N = 46 K). f, Temperature evolution of the ZF μ +-spin polarization, P ( μ t), for f.c.c.-rich Cs 3C 60 between 0.625 and 100 K. At high temperatures, the spectra imply the presence of weak static nuclear moments together with a slow relaxation arising from fluctuating electronic moments. Between 16.2 and 2.5 K, they are consistent with inhomogeneous magnetism: that is, co-existing spin frozen and paramagnetic domains. Below 2.2 K, they are dominated by a short-lived heavily damped oscillating signal. g, Temperature evolution of the ZF μ +-spin precession frequency, ν , below μ T N ≈ 2.2 K, and of the volume fraction and relaxation rate, λ 1, of the slowly relaxing (paramagnetic) component for temperatures where paramagnetic and spin frozen domains coexist. The lines through the points are guides to the eye. a.u., arbitrary units. Error bars, ±s.d.
Figure 3: Superconductivity under pressure in f.c.c. Cs 3C 60.
a, Temperature dependence of the magnetization, M (ZFC protocol, 20 Oe), at selected pressures. Inset, expanded view of the data near the onset of the metal-to-superconductor transition, T c. FC and ZFC data confirming the Meissner effect are shown in Supplementary Fig. 9. b, Pressure dependence of T c measured for three different f.c.c. Cs 3C 60 samples (blue/green/red circles). Filled (open) circles label data obtained with increasing (decreasing) pressure. T c is defined as the temperature at which M( T) in a begins to decrease. Inset, evolution of the shielding fraction with change in pressure. The data for A15 Cs 3C 60 (squares) are also included to emphasize the lower pressure onset of bulk superconductivity in the f.c.c. polymorph. 5 c, Pressure dependence of the unit cell volume of the f.c.c. Cs 3C 60 phase at 15 K up to an applied pressure of 13 GPa (different colours indicate different sample batches). A linear fit to the data up to 0.8 GPa gives a volume compressibility, κ = 0.053(1) GPa -1, comparable to that measured for A15 Cs 3C 60 ( κ = 0.054(5) GPa -1) . The line through the data points is a least-squares fit to the second-order Murnaghan equation of state, with an atmospheric pressure isothermal bulk modulus ( 6 K 0) of 13.7(3) GPa, and its pressure derivative K' 0 = 13.0(3).
Figure 4: Electronic phase diagrams shown as functions of volume occupied per fulleride anion and normalized conduction bandwidth in the two sphere packings of A 3C 60 superconductors.
a, Superconducting transition temperature, T c, as a function of volume occupied per fulleride anion, V, at low temperature. The red/green/blue circles and pink squares correspond to the bulk T c( V) behaviour observed in f.c.c.- and A15-structured Cs 3C 60, respectively. Open symbols represent data at pressures where trace superconductivity is observed and where in the A15 phase superconductivity coexists with antiferromagnetism. The yellow rhombi, dark blue triangles and brown inverted triangles correspond to the ambient pressure T c of f.c.c. C 60 3- anion packings with Li 2CsC 60, Pa symmetry, and Fm m symmetry, respectively. b, Normalized superconducting transition temperature, T c/ T c(max), as a function of the ratio ( U/ W) divided by the critical value ( U/ W) c required to produce localization in the A 3C 60 fulleride structures with f.c.c.- and bcc-sphere packings. W c is estimated as 0.55 eV for b.c.c.-structured A15 Cs 3C 60 and 0.35 eV for the f.c.c. phases. The symbols have the same meaning as in a. Inset, dependence of the t 1u conduction bandwidth on volume occupied per fulleride anion, V, for f.c.c.-sphere (red circles) and b.c.c.-sphere (pink squares) packings, as determined by electronic structure calculations . 12