According to the WHH formula values of Hc2(0) at T = 0 can be estimated from Hc2 measurements predominately near Tc. The results presented in Fig. 15.8 show that (SHc2/ST) is constant near Tc, and Hc2 has a linear T dependence near Tc in accordance with Ginzburg-Landau theory. Justifi-

Fig. 15.8. Temperature dependence of the upper critical field Hc2 for ^C^. The dots are experimental points taken at relatively low magnetic fields and the solid curve is a fit of these data to the WHH model (see text) [15.70],

Fig. 15.8. Temperature dependence of the upper critical field Hc2 for ^C^. The dots are experimental points taken at relatively low magnetic fields and the solid curve is a fit of these data to the WHH model (see text) [15.70],

cation for use of the WHH formula for fullerene superconductors comes from measurements on powder samples of K3C60 and Rb3C60 extending to very high magnetic fields and including Pauli-limiting spin effects [15.61]. An independent determination of the dHcl/dT has been made from analysis of the measured jump in the specific heat at Tc, yielding a value of dHc2/dT = -3.5 ± 1.0 T/K (see §14.8.3) [15.67]. The high-field determinations of Hc2(0) yielding 30 T and 55 T for K3C60 and Rb3C60, respectively, represent the most detailed experimental determinations of Hc2{0) that are presently available, although the high-field measurements were not made on high-quality single crystals. Although prior work suggested departures from the WHH formula on samples taken to high fields [15.62] due to sample granularity and Fermi surface anisotropy, it seems to be generally believed on the basis of more detailed high-field measurements [15.61] that the WHH model provides a good first approximation for describing the functional form of Hc2(T) for fullerene superconductors. Generally, Hc2(0) for single-crystal Rb3C60 is reported to be higher than that for an Rb3C60 film [15.17,23,61,72], although the opposite trend was reported for K3C60 (see Table 15.1). Further systematic studies are needed to clarify the dependence of the superconducting parameters on grain size and microstructure.

Typical values for Hcl(0) are very high, as given in Table 15.1 for powder, film, and single-crystal KjQo and Rb3C60 samples. Also given in Table 15.1 is the range of values for £0, which are typically found from Hc2{0) [see Eq. (15.6)] and therefore reflect the corresponding range of values for Hc2{0). Also shown in Table 15.1 are values for the London penetration depth kL which is measured through magnetic field penetration studies. Microwave experiments for K3C60 and Rb3C60 have yielded values near 2000 A [15.60,73], while muon spin resonance studies [15.57,64,74] have yielded values of kL about a factor of 2 greater (~4000 A), and far-infrared optical experiments have reported even larger values of kL (~8000 A) [15.65], The reason for this discrepancy in the value for kL is not presently understood, and this remains one of the areas where further systematic work is needed.

Measurements for Hc2{0) show on the basis of Eq. (15.5) that £0 is only slightly larger than a lattice constant for the fee unit cell of the fullerene superconductors. In contrast, the measured kL values are very much larger than both and I (see Table 15.1), especially near Tc. Magnetization studies on powder samples of Rb3C60 show that the temperature dependence of the London penetration depth is well fit by the empirical relation [15.44]

where AGL(0) is the Ginzburg-Landau penetration depth at T = 0. The values of \L in Table 15.1 correspond to extrapolations of the measured Al(T) to T 0, i.e., to Agl(0), if Eq. (15.8) is used to fit the data.

Measurements of the lower critical field Hcl, where magnetic flux penetration initially occurs, show that Hcl(0) for superconducting fullerene solids has a very small value [15.17]. Microwave measurements indicate that Hcl(T) follows the simple empirical formula [15.17,73]

Values for Hcl(0) are also given in Table 15.1, and through Eq. (15.5) the values for //cl(0) provide consistency checks for determinations of AL and fo-

More detailed studies of the superconducting state for the M3C60 type II superconductors reveal a phase diagram akin to that of high-rc cuprates, consisting of a Meissner phase (with no vortices), a vortex glass phase with pinned vortices, and a vortex fluid phase [15.75]. The inset to Fig. 15.9 shows the temperature dependence of the magnetic susceptibility x(T) for a powder sample of K3C60 (Tc — 19.0 K) under zero-field-cooling (ZFC) and field-cooling (FC) conditions for an applied field of 10 G. Comparing

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