Muon implantation

This paper is concerned with the structures of the simplest possible adducts of the Ceo and C70 fullerenes, namely the monohydrides, CmH and C H. These open shell species or radicals may be considered as the product of the addition of one atom of hydrogen or one of its isotopes, among which we include specifically the light pseudoisotope of hydrogen known as muonium. Mu = pfe. Although Ceo//has been observed [1], the stimulus for these calculations arose from the experiments on muon implantation in solid [2,3] and C70 [4]. 

The muon spin relaxation rates Ay and Ax, observed in ZF measmements with muons implanted with initial spin polarization parallel and perpendicular to the c-axis, are given by... 

Similar set of experiments with a polycrystalline sample of cyclopentadi-enyl manganese tricarbonyl has shown very similar patterns of data to the above compound [18]. Longitudinal field relaxation of muons implanted into cyclopentadienyl manganese tricarbonyl was studied within the field range 0-400 mT at 300 K, and the temperature range 375-25 K at an applied field of 200 mT. The latter showed a relaxation maximum around 275 K, which was shown to be due to an Arrhenius process with an activation energy of... 

Figure 3 TF- SR spectra for positive muons implanted into benzene (A) the raw time-differential histogram recorded for the experiment (B) the Fourier transform of (A) showing the two transitions due to the CeHeMu radical (218.18 and 295.85 MHz, giving a hyperfine coupling constant of of 514.03 MHz) and the signal from muons in diamagnetic environments (27.1 MHz).

The muon spin relaxation technique uses the implantation and subsequent decay of muons, n+, in matter. The muon has a polarized spin of 1/2 [22]. When implanted, the muons interact with the local magnetic field and decay (lifetime = 2.2 ps) by emitting a positron preferentially in the direction of polarization. Adequately positioned detectors are then used to determine the asymmetry of this decay as a function of time, A t). This function is thus dependant on the distribution of internal magnetic fields within a... 

For the case of muonium, nonresonant spin precession in a magnetic field provides a copious source of information about its crystallographic sites and the associated unpaired electron distribution around them (see Chapter 15). Here, the concentration of muons is always too low for molecule formation, and migration to impurities and implantation defects can be kept small by the short muon lifetime and use of pure material and low temperature. 

The close correspondence between the properties of Mu in Si as determined by /u,SR and pLCR and those for the AA9 center produced by implanting hydrogen in silicon shows that Mu in silicon and the AA9 center are isostructural and in fact almost identical. They are neutral isolated bond-centered interstitials. Numerous theoretical studies support this conclusion. The observation of such similar centers for muonium and hydrogen supports the generalization that hydrogen analogs of many of the muonium centers exist. Of course, this assumes that the effects of the larger zero-point vibration of the muon relative to the proton do not make a major contribution to structural differences. The p-SR experiments, reinforced by theory, demonstrate that another structure also exists for muonium in silicon, called normal muonium or Mu. This structure is metastable and almost certainly is isolated neutral muonium at a tetrahedral interstitial site. 

The muon can be implanted as a local magnetic probe in any material that does not itself contain suitable magnetic nuclei. 

Basically, p.SR is the measurement of the temporal development of the spatial orientation of the spins of muons which have been implanted in the material of interest with all spins initially fixed in one direction (complete muon spin polarization). The three names covered by the acronym p,SR, namely muon spin rotation, relaxation or resonance, refer loosely to different means of observation. 

Muon Spin Relaxation refers to the observation of incoherent motions of the muon spins which result in a loss of polarization with time. This will occur if the magnetic field sensed by the ensemble of implanted muons is broadly distributed. If the local field each muon sees in addition fluctuates randomly during a muon s life we observe what is called dynamic depolarization , but also a stationary distributed field causes depolarization by phase incoherence ( static depolarization ). These two cases must be clearly distinguished. The situation corresponds to the two relaxation times Ty (spin-lattice) and Ti (spin-spin) in NMR. Muon Spin Relaxation measurements can be carried out without observing spin rotation and thus are possible in zero applied field or with a longitudinally applied field (i.e., a field applied parallel to the muon spin direction at the moment of implantation). Longitudinal field measurements are the most appropriate way to obtain a clear distinction between static and dynamic muon spin depolarization. Muon Spin Relaxation hence mostly refers to zero or longitudinal field (iSR. 

The interest of the p,SR physicist (or chemist) lies in determining how the muon spin moves due to its coupling to internal fields after the muon has been implanted into the material under study. One directs the beam of polarized muons onto a sample thick and large enough to stop all impinging muons. The proper selection of sample size depends on beam characteristics and will be discussed in sect. 2.5. 

Implantation involves the slowing down of muons from MeV energies to thermal energies which is an intricate process not fully understood in all details. The different steps involved are reviewed by Brewer et al. (1975). We shall forgo a discussion and just point out two basic features which must be satisfied ... 

One fairly simple solution is to surround the small sample with material in which implanted muons are quickly depolarized or in which muonium is formed, whose precession frequency (especially if sizable transverse fields are applied) is well beyond the time resolution of the spectrometer. Powdered high-quality Y-Fe203 is a material of choice. Still, this leads to a poor signal/background ratio in the p,SR spectra and hence to a severe loss in data accuracy. 

Fig. 15. The Lorentz construction. The case shown refers to a sample fully magnetized by an externally applied field. Symbols in the Lorentz sphere solid circle and arrow, paramagnetic ion open circle and arrow, implanted muon on interstitial site broken lines, dipolar field lines dots, conduction electron density.

The relaxation rates above were studied both by Barsov et al. (1986c) in a textured polycrystal, and Ekstrom et al. (1996, 1997) in a single-crystal sample. The muon relaxation rate is anisotropic, with larger values for A if the muons are implanted parallel to the c-axis. In fig. 34 (left) we show the result by Barsov et al. (1986c) expressed in terms of the relaxation fiinctions Gy and Gj. as introduced in sect. 4.1. It follows that... 

Muon states have been also implanted in porous silicon in order to perform pSR spectroscopy (Harris et al. 1997). 

Gross E, Kovalev D, Kiinzner N, Diener J, Koch F, Timoshenko VY, Fujii M (2003) Spectrally resolved electronic energy transfer from silicon nanocrystals to molecular oxygen mediated by direct electron exchange. Phys Rev B 68(11) 115405 1-115405 11 Harraz FA, Salem MS, Sakka T, Ogata YH (2008) Hybrid nanostructure of polypyrrole and porous silicon prepared by galvanostatic technique. Electrochim Acta 53 3734—3740 Harris PJ, Bayliss SC, Canham LT, Cottrell S (1997) Implanted muon states in porous silicon. Thin Solid Films 297 84-87... 

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