Muon diffusion

Muon generation and decay 67 3.8. Muon diffusion and magnetism (site ... 

Thermal energies may be enough to initiate muon diffusion, e ecially in elemental metals with simple crystal structures. That is to say, the muon hops firom one interstitial site to a neighboring one on a time scale less than a ps. It is often trapped after some diffusional motion at a lattice imperfection. The study of muon diffusion has already been mentioned as a major application of pSR spectroscopy. From the point of view of magnetic studies, muon diffusion is usually an undesirable complication. It is good practice for magnetic studies to check on the mobility status of the muon, at least in the temperature regime of interest. 

The jxSR study by Grosse et al. (1999) used mosaics of oriented single-crystal platelets. LaS, the lower concentration limit (x = 0), is diamagnetic. The ZF spectra are static Gaussian Kubo-Toyabe patterns originating from the nuclear moments on La. Full decoupling needs only LF=10G. Between 300 K and 4K only a minute change in static width is seen, which can be accounted for by thermal contraction. These data show that effects of muon diffusion are not discemable. US, the upper concentration limit (x = 1) is a FM (7c = 177 K and fiu = 1.7 Ub). The reduction in moment was... 

Work by Charrier et al. (1999) was carried out at the ISIS pulsed source and thus suffered more severely from losses of asymmetry in the initial dead time. The resiJts for the Gd and Tb compoimds are quite comparable to those of Noakes et al. (1998) when this limitation is taken into accoimt In particular, the (unexplained) two-signal spectra (rapidly and slowly relaxing) are observed as well. The study also includes measurements on the Dy and Y compounds. The former behaves much like the Tb quasicrystal, as expected. The Y material is nonmagnetic and muon spin depolarization arises solely from nuclear dipole moments. The fact that no sudden change in the rather weak depolarization rate ( 0.01 p,s ) was seen between 300 K and 10K makes muon diffusion unlikely in this structure. 

The motion of a heavy particle when accompanied by a screening cloud of band electrons was first studied by Kondo (1984) and later by Kagan and Prokofev (1986) as a model for muon diffusion in metals. Liu (1987) and Kagan and Prokofev (1987) independently proposed that the same mechanism applies in heavy-fermion systems. The idea is that the f band is formed by the hopping of an f hole whose motion is accompanied by the screening cloud. Just like the band problem in the spin fluctuation resonance model, the hopping is the result of the hybridization interaction. Consequently, the dispersion of the f band is again solved from eq. (52) where Gf(to) is now calculated from the f hole spectrum in eq. (57) (Liu 1987, 1988) ... 

The simulation of hydrogen by muons has proved to be extremely valuable in the identification of potential sites for hydrogen in semiconductors and insulators. Although the muon has a mass one-ninth that of the proton, its interaction with the host lattice, both electronically and chemically, is virtually identical to that of a proton. During its 2.2 microsecond lifetime (experiments are frequently undertaken over a timescale of up to ten lifetimes), the muon can diffuse, interact with, and adopt positions in the lattice that protons themselves would occupy. If the temperature is sufficiently low, muons can capture electrons to form muonium atoms. The reduced mass of muonium is within 0.5% of that of... 

Studies in magnetism are but one application of p,SR. Other fields where pSR has given important information is the diffusion of light interstitials, especially with regard to quantum diffusion in metals, semiconductors and insulators (Kehr et al. 1982, Kondo 1986, Kadono 1990, Prokof ev 1994, Storchak et al. 1996, Karlsson 1996). Other very active fields are applications to chemistry with emphasis on chemical kinetics especially in connection with radical formation (Brewer et al. 1975, Walker 1983, Fischer 1984, S.F.J. Cox and Symons 1986, Roduner 1990, 1999, Fleming and Senba 1992) and also the study of hydrogen states in semiconductors (Chow et al. 1995). pSR in life sciences is discussed by Nagamine (1999) in an article on Exotic applications of muons. 

One can imagine influences of the muon also on B. Firstly, the muon distorts the lattice aroimd its position (self-trapping, small polaron). This can change the dipolar sum over the first neighbor shell. Secondly, the muon may not be that well localized at r = 0, even if it does not diffuse from site to site. The muon could have an extended wave... 

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