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Muons come to rest inside the sample and, in most cases, this happens without loss of spin polarization. The initial energy of the muon, of the order of 4 MeV, is huge compared to the typical energies of the electrons with whom it collides (from few eV, for valence shells, to several hundred keV for inner shells in heavy elements. Therefore the initial collisions are due to ionization processes (Coulomb scattering).
In this process the muons leave behind a wake of ions and electrons. When below the ionization threshold the muons generally travel quite a long way away from this region and the final thermalization depends on solis state or chemical details of the environment. In this context the positive muon may be regarded as a light isotope of hydrogen, whose complex epithermal chemistry reactions in the host material determine its successive fate.
Muons seldom replace an atom of the host compound: this may be the case when cation vacancies are abundant or when a MU-H exchange takes place, e.g. in organic compounds. More often the muon ends up at interstitial sites, in crystals, or equivalently, at addition sites, in molecules. The spin dynamics of the thermalized muon depends dramatically on whether it ends up in a coherent or in an incoherent spin state with its environment. Coherent spin states are formed:
- when the muon is attached to a paramagnetic molecule (in the chemical sense), that is when a MO state with an unpaired electron, also called free radical, is formed; this instance is characteristic of unsaturated organic molecules and the prototype of such a free radical is notably muonium, a hydrogen atom with the proton replaced by the muon.
- when the muon is bound to a diamagnetic molecule; a molecular orbital (MO) type of state is formed in which two electrons of opposite spin occupy a bond between an atom and this light hydrogen isotope; the only influence of the host on the muon would be a chemical shift?, which is however generally too feeble to be measured within a few muon lifetimes.
- when the muon is localized interstitially in a magnetically ordered environment where it experiences hyperfine and dipolar couplings to the ordered magnetic moments of the electron.
- when the muon is in close dipolar interaction with few isolated nuclei having non vanishing magnetic moment. This is typically the case of the F-Mu-F center formed in several flurides.
Incoherent spin environments are those where the magnetic moments of the electrons fluctuate rapidly on the time-scale of the muon spin dynamics. This are the paramagnetic cases, in the condesed matter sense:
- in metals, where free electrons (the Fermi liquid) are characterized by Pauli paramagnetism; in this case electron charge screening would generally prevent the formation of a bound state, and spin dependent scattering with the electon liquid would prevent the observation of a bound state, if it did form. Knight shift may be measured for metals, although high fields are required to observe it within a few muon lifetimes.
- in the disordered state above the magnetic ordering temperature of a magnetic material.
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We may consider that a magnetic molecule (like Fe8, shown here to the right), with a muon attached to it is, in a sense, a special case of radical. In this case, intermediate between that of an organic muonic radical an that of a muon implanted in a magnetic material, the free radical will have more than one unpaired electron.
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