6.2 Muonium in A₁C₆₀

Because of the great success in using endohedral muonium to probe the electronic properties of A₃C₆₀ (Chapter 4), attempts were made[168] to find a similar signal in the metallic polymer phases of A₁C₆₀. The presence of Mu is suggested by the missing fraction $f_m \approx 15$% observed in transverse field in Rb₁C₆₀ and K₁C₆₀, for T<250K. No measurement has yet been attempted in Cs₁C₆₀.

An näive initial guess for the spin exchange rate of Mu@C₆₀ in A₁C₆₀ is that it would simply be scaled down by 1/3 (for the lower conduction electron density) from the equivalent sized A₃C₆₀ system at the same temperature. However, modifications to the electronic structure due to polymerization and possibly electron-electron interactions will likely alter this. Initial attempts to identify Mu by its spin exchange relaxation in LF (see Section 3.1), using this guess as a rough guide, were unsuccessful[168].

In the following the observation of muonium in the first metallic system other than the A₃C₆₀ materials is reported for the first time. In zero field, the relaxation function is nearly temperature independent, and contains a small approximately exponential relaxation superimposed on a larger, very slowly relaxing signal (see squares in Fig.6.36). This relaxation has been fit with the sum of an exponential and a slow gaussian. The resulting relaxation rates are temperature independent and are shown shown in Fig.6.37. The relaxation rate of the fast component in K₁C₆₀ is considerably less than that in Rb₃C₆₀ at 4K, which can be estimated from the inset of Fig.4.27 to be about 2.5$\mu$s^-1.

In order to confirm that this signal is due to Mu and also in attempt to measure its hyperfine parameter, decoupling curve measurements (of the Mu asymmetry as a function of applied LF, Eq. (4.4)) were made. The best two curves are shown in Fig.6.38. The behaviour is clearly different from that of Mu@C₆₀ in Rb₃C₆₀ (Fig.4.16), with the inflection occuring at much lower fields. The two data sets are fit to the isotropic expression Eq. (4.4), which yields hyperfine parameters of 500(100)MHz at 2K and 1070(100)MHz at 250K. This indicates that the chemical environment of the Mu is not the same as in Rb₃C₆₀, and, furthermore, it is temperature dependent. This is not really surprising, considering the distortion of the C₆₀ molecule caused by polymerization.

The quenching of the zero field relaxation (see chapter 5) shown in Fig.6.36 is likely due to the applied LF exceeding the internal fields due to randomly oriented ¹³C and ^39,40,41K nuclear dipoles. The exponential relaxation may be due to the rather dilute spatial distribution of these moments. Taking the quenching of the relaxation as a measure of the width of the random field distribution, e.g. 5G, we estimate an early time zero field exponential relaxation rate $\lambda$for diamagnetic muons sampling a lorentzian field distribution with w=5G (Eq. (5.4)) of $\frac{4}{3} \gamma_\mu w \approx 0.6 \mu$s^-1 (see [168]). The observed zero field relaxation exceeds this considerably. This may simply be due to the enhanced effect of the field distribution because of the large electron magnetic moment of Mu.

In addition, on the plateau of the decoupling curve, where the asymmetry is high, i.e. in 1kG LF, a temperature scan of the very slow T₁ relaxation of Mu was made. The temperature dependence of the relaxation rate for an exponential relaxation with amplitude fixed from the low temperature decoupling curve is shown in Figure 6.39. The value of the Korringa constant, (T₁T)^-1, for the linear regime above 50K is $1.0(2)\times 10^{-3} \mu$s^-1K^-1. For comparison the value of (T₁T)^-1 in K₃C₆₀, which is obtained from Fig.4.15 by extrapolating down in field from 2T to 0.1T using Eq. (3.4), is about 7.0 $\mu$s^-1K^-1. Thus the Korringa relaxation rate is $\sim 2000$ times slower than the näive guess discussed above. The extremely small Korringa rate is also consistent with the ZF relaxation rate being dominated by static fields. From this results we expect that the low temperature fast component in Rb₃C₆₀ (Fig.4.27), is due to Mu@C₆₀ relaxing via the (slow) low temperature Korringa mechanism in addition to a contribution from the (more dense) ^85,87Rb moments. The extremely slow LF relaxation observed here is likely the reason that earlier attempts to find Mu in Rb₁C₆₀ were unsuccessful.

The deviation, below 50K, from linear temperature dependence of the LF relaxation rate at 1kG may be due to one of several factors. The first is simply that the rates are very close to the minimum rate measureable (due to the muon lifetime), and hence any slight late time distortion, due, for example, to imperfect background correction (see Eq. 2.4), may be mistaken for a slow relaxation. Physically more interesting explanations are that at low temperature, there is some degree oflocalization and/or the electrons begin to behave in a 1d manner. We note that in 1d, the Korringa relaxation mechanism leads to temperature independent T₁ and is observed in the metallic polymer phases of both Rb₁C₆₀ and Cs₁C₆₀ [64]. At higher temperature, we note that ¹³C NMR finds Korringa behaviour in K₁C₆₀ down to 70K [64]. The results of Figure 6.39 suggest that similar NMR measurements be made below this temperature.

Finally, the results presented here are apparently inconsistent with other published $\mu {\cal SR}$ results on K₁C₆₀ [203]. I believe this inconsistency is entirely because the presence of two components in the ZF relaxation was not recognized in [203]. In [203], the ZF relaxation was fit to a single component gaussian relaxation. The temperature independence of the observed relaxation guarantees that such a fit will yield a temperature independent relaxation rate (such as that reported in [203]). A brief look at the raw data of the measurements of [203] indicates that there is no inconsistency between that data and the ZF data presented above.