4.3.2 T₁(T) and Quench Rate Dependence in Na₂Cs

In two separate measurements on the same sample of Na₂Cs, we observed very different behaviour. In the initial run, we found no broadening of the TF precession signal associated with T_c. We did, however, observe the expected Mu@C₆₀ T₁ relaxation. The temperature dependence of this relaxation rate remained Korringa like (Fig. 4.28a) down to about 8K, below which it began to increase. To ensure that the sample hadn't deteriorated, it was recharacterized by x-ray diffraction after this run. In the subsequent run, we observed T_c in TF (Fig. 4.20) and in LF (Fig. 4.29a). Because of the low temperature of the structural phase transition in this material[44] (299 K), we suspected a quench-rate dependence, possibly due to frozen orientational disorder. We attempted a fast-quench (sample at 300K for 20 minutes, then quenched to 200K in 5.5 m and to 5K in about 20 minutes), and found that this cooling procedure did not affect the height of the coherence peak, but it did reduce the low temperature T₁ rates at 2.7K in both 1T and 0.3T (stars in Fig.4.29). However, with no evidence at the time for ambient pressure polymerization, we did not attempt a slow quench or anneal, and, only for the last three points, did we record the cooling procedure in sufficient detail. It now seems likely that, as in the case of Na₂Rb, there exists another stable ambient pressure low temperature phase of Na₂Cs, which may involve C₆₀ polymerization. According to our measurements (Fig.4.28) this phase is metallic, non-superconductig and appears to exhibit a low temperature (possibly magnetic) phase transition. We note that attempts by another group has not produced a polymerized phase in Na₂Cs.[133] The unusually small value of (T₁T)^-1 in Na₂Cs (discussed in section V) cannot be explained by the coexistence of the superconducting (s-Na₂Cs) and non-superconducting (ns-Na₂Cs) phases, as the values of (T₁T)^-1 are indistinguishable except below $\sim$8K. However, as the fast-quench procedure suggests, a small fraction of the non-superconducting phase could explain the finite low temperature rate in Fig. 4.29. The field dependence of T₁^-1 in the ns-Na₂Cs was also indistinguishable from the superconductor at 35K (Fig. 4.15a), but at 3K, appeared to fall more sharply with field. In addition there was a small peak in the linewidth of the diamagnetic precession at $\sim7.5$K in ns-Na₂Cs. The weak low T dependence of the diamagnetic signal compared to the T₁ of Mu@C₆₀ is consistent with the enhanced sensitivity of Mu due to the bound electron moment. One possible explanation for the feature in TF, is that ns-Na₂CsC₆₀ is superconducting over a narrow range in temperature, and is re-entrant at about 7K to a low temperature non-superconducting phase.

  

Figure 4.28: Probable quench rate dependence of the Mu@C₆₀ T₁ relaxation rate in Na₂CsC₆₀. triangles: non-superconducting run, circles: superconducting run, stars: fast quench. Note that above about 10K, the values of T₁T in both runs are about the same. The line is the same fit as in Fig. 4.29a.

Despite the complications due to the presence of some fraction of ns-Na₂CsC₆₀ in the superconducting run, we can compare the temperature dependence of T₁ with the cubic Fm$\bar{3}$m materials discussed above. In order to account for an ns-Na₂CsC₆₀ fraction, we model (T₁T)^-1 as the sum of the Hebel-Slichter integral (3.9) with an additional T independent term. Such fits are shown in Fig. 4.29.

The fast quench points indicate that for s-Na₂Cs, the values of $\Delta$(Table 4.6) are not reliable. The size of the coherence peak, relative to the normal state, though, is not dramatically different than in the Fm$\bar{3}$m materials. This implies that orientational disorder is not likely to be the cause of the broadening of the coherence peak (or g_S).

  

Figure 4.29: The coherence peak and low temperature fall off in superconducting Na₂Cs. The solid stars indicate fast quench runs (described in the text).

These results clearly indicate the need for further experiments< on Na₂CsC₆₀ with careful attention paid to the cooling procedure. The rapid quench points suggest that one should be able to make a much more reliable estimate of the paramaters of s-Na₂Cs. It also seems likely that in order to study ns-Na₂Cs, it will probably be necessary to investigate temperatures lower than those accessible by pumped liquid Helium cryostats.

 

$$\nu_{SE}(35K) \mu \rho_{35K}^x \rho^x$$

Rb₃C₆₀ 587(47) 0.217(70) 1 1

K₃C₆₀ 572(63) 0.215(50) 0.987(94) 0.950(31)

Na₂CsC₆₀ 132(4) 0.0000(2) 0.474(25) 0.506(20)

 

$$\sigma_N/\sqrt{2} \mu \sigma_S(0)/\sqrt{2} \mu \varpi \Delta \lambda \Delta_0/kT_c$$ Sample(B[T]) T_c [K]

Rb₃C₆₀-1(1.0) 0.076(1) 0.4315(10) 29.3(8) 2.93(4) 0.717 4200 1.37(5)

Rb₃C₆₀-2(0.27) 0.093(1) 0.2068(10) 28.9(2) 3.36(8) 0.343 6100 1.56(5)

K₃C₆₀(1.0) 0.087(1) 0.2570(20) 18.6(2) 2.83(9) 0.427 5400 1.39(6)

Na₂CsC₆₀(0.01) 0.133(1) 0.0769(10) 11.3(3) 7.5(1.0) 0.128 9900 --

 

Data Set(B_app [T]) I II III IV

Rb₃C₆₀-1(1.5) - - 3.8 4.6-4.8

Rb₃C₆₀-2(1.5) - - 3.2 4.0-4.2

K₃C₆₀(2.0) - - 3.6 4.4

Na₂CsC₆₀(1.0) - - 3.8^* 4.0^*

Rb₃C₆₀-1(0.3) 2.7 3.1 3.2-3.8 3.6-3.8

Rb₃C₆₀-2(0.3) 2.4 2.7 2.8-3.2 3.0-3.2

K₃C₆₀(0.3) 2.7 3.0 3.2-4.0 3.2-3.6

Na₂CsC₆₀(0.3) 1.1 1.5 - 3.0-3.2^*