Muons muon-electron spin

Out of the many variants of xSR, it is the Muon Spin Relaxation that has been utilized up to now for the study of dynamic processes in organometallic systems, and therefore only this aspect will be discussed here. Interested readers should find ample descriptions of the other aspects of xSR in the references provided at the end of this chapter. For the unpaired electron occupying a Is hydrogenic orbital about the muon, the electron spin S and muon spin I are coupled by a scalar product to give the Hamiltonian for the so-called hyperfine, Fermi or contact interaction. 

Molecular dynamic information is obtained from a study of the variation of the muon spin relaxation rate with temperature. Reorientation depolarizes the muons by causing anisotropic or dipolar terms in the electron-muon hyperhne interaction to fluctuate. Peaks in the relaxation rate (analogous to 2i minima in NMR) occur when the reorientation rate matches the frequency of the dominant transition between the coupled muon-electron spin states. The correlation time, T, at each temperature can be obtained using the derivations of Cox and Sivia [14]. The measured relaxation rate X is given by the following expression ... 

Second Quantized Description of a System of Noninteracting Spin Particles.—All the spin particles discovered thus far in nature have the property that particles and antiparticles are distinct from one another. In fact there operates in nature conservation laws (besides charge conservation) which prevent such a particle from turning into its antiparticle. These laws operate independently for light particles (leptons) and heavy particles (baryons). For the light fermions, i.e., the leptons neutrinos, muons, and electrons, the conservation law is that of leptons, requiring that the number of leptons minus the number of antileptons is conserved in any process. For the baryons (nucleons, A, E, and S hyperons) the conservation law is the... 

It is common in the interpretation of electron spin resonance spectroscopy of organic radicals to draw classical structures to rationalise the observed distribution of spin. In this spirit the number of possible classical structures of CeoMu, with the muon... 

Consider for example the simplest possible system consisting of the muon, an electron, and a single spin nucleus labelled i = n. Take the muon and nuclear hyperfine interactions to be istoropic. The level crossing of interest occurs near the field... 

The muon and 29Si hyperfine parameters provide compelling evidence in support of the BC model. In the simple molecular-orbital model proposed by Cox and Symons (1986) the muon is located at the center of a Si—Si bond near a node in the unpaired electron spin density, which is... 

The triplet of frequencies gives rise to a beating in the time-domain spectrum as seen for a powder sample of ZnO in Figure 1. The separation of the two satellite lines provides a direct measure of the hyperfme coupling constant between the muon and the electron. This is 500 20 kHz, which is 0.011% of the free-muonium value of 4463 MHz, indicating immediately a small electron spin density at the site of the muon and an extended waveflmction associated with a shallow donor state. 

First of all what is muonium, what is its source, how do we observe it, and why is it useful Muonium (Mu) is an atom comprised of a positive muon nucleus, (y" ), and a bound electron. This bound electron can have its spin parallel or antiparallel to the muon nuclear spin resulting in triplet and singlet muonium atoms, respectively. The atom has a mass 1/9 that of the hydrogen atom, H but because the reduced masses are... 

A similar result was reported on the electronic spin (polaron) created by the muon in the undoped-PPy and... 

H-fi, are the Bohr magneton and the muon magneton, B is the external field, in the electron spin, T is the muon spin, and A is the strength of the Fermi contact interaction, proportional to the electron density at the... 

Both terms originate from the same set of dipoles. Bdip is the direct dipolar field of the moments surroimding the muon. We will return to it shortly. The term Bcon is called the Fermi contact field and is produced by the net spin density of conduction electrons in contact with the muon. The spin polarization of the conduction electrons in turn is induced by the dipole moments on lattice sites. One finds... 

An influence of electronic moments on the muon spin depolarization rate could not be detected. This is in full keeping with the notion of YC02 being a spin fluctuator. As in the archetypal spin fluctuator UAI2 (see paragraph on AnAl2, above) fluctuations of electronic spins are so fast even at low temperatures that full motional narrowing is in effect (reviewers remark). 

The hyperfine constant for the free-atom or vacuum-state muonium is, 4) = 4.46 GHz. This is approximately equal to the value for hydrogen, when scaled by the ratio of magnetic moments of the muon and the proton, i.e. 3.18. This implies essentially the same electron spin density at the nucleus for muonium and hydrogen, providing further justification for considering muonium as an isotope of hydrogen. 

In addition to Fukuzumi s early contribution, NHC-muonium radical 169 was first observed by Percival and Clybume using muon spin resonance (pSR) spectroscopy (which is similar to electron spin resonance (FSR) spectroscopy) in 2003 (Figure 5.19). The muonium (Mu = [p" e ]) could be used as a hydrogen atom (H-) equivalent and readily reacted with carbenes and carbene-main group complexes to obtain paramagnetic complexes vide infra). Unlike the aforementioned carbene-acyl radicals, 169 was not a stable... 

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. 

Although simple /rSR spectra that do not depend on the nuclear terms in the spin Hamiltonian are the easiest to observe, one loses valuable information on the electronic structure. Under certain circumstances it is possible to use conventional /rSR to obtain a limited amount of information on the largest nuclear hyperfine parameters. The trick is to find an intermediate field for which the muon is selectively coupled to only the nuclei with the largest nuclear hyperfine parameters. Then a relatively simple structure is observed that gives approximate nuclear hyperfine parameters. A good example of this is shown in Fig. 3a for one of the /xSR... 

The Mu spin Hamiltonian, with the exception of the nuclear terms, was first determined by Patterson et al. (1978). They found that a small muon hyperfine interaction axially symmetric about a (111) crystalline axis (see Table I for parameters) could explain both the field and orientation dependence of the precessional frequencies. Later /xSR measurements confirmed that the electron g-tensor is almost isotropic and close to that of a free electron (Blazey et al., 1986 Patterson, 1988). One of the difficulties in interpreting the early /xSR spectra on Mu had been that even in high field there can be up to eight frequencies, corresponding to the two possible values of Ms for each of the four inequivalent (111) axes. It is only when the external field is applied along a high symmetry direction that some of the centers are equivalent, thus reducing the number of frequencies. 

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