Muon spin relaxation studies of interstitial and molecular motion

The unusual methods of preparation and analysis of spin polarization in muSR spectroscopy, which exploit the unique properties of the positive muon, are introduced in this article. Following a summary overview of applications, particular attention is paid to the problem of spin-lattice relaxation for a muon experiencing a hyperfine interaction with a single unpaired electron. The specific cases considered are the interstitial diffusion of muonium--the 1-electron atom which may be considered as a light isotope of hydrogen-and the molecular dynamics of organic radicals labelled by muonium. Rate equations for the evolution of population in the hyperfine-coupled spin states are solved numerically for various relaxation mechanisms. The formalism is equally valid for conventional ESR studies of paramagnetic states but is pursued specifically to simulate T1-relaxation in muSR. The simulations are compared with literature data. Also treated is the case of intermittent hyperfine coupling, appropriate to electron capture and loss in semiconductors or soliton motion in polymers; for this, a Monte Carlo approach is used to simulate the muon response. (For low-dimensional motion, the relaxation function is not exponential, so that a unique value of T1 cannot be defined.) Finally, a proposal is made to implement muon-T1 measurements in the rotating frame; this is designed for the selective study of electronically diamagnetic muonium states (i.e., those without hyperfine coupling) in the presence of a paramagnetic muonium or radical fraction.