The diffusion of muons and muonium through solids has been studied over many years using the technique of spin relaxation. At low temperatures, the motion is due to tunneling between lattice sites, and the competition between tunneling rates and decoherence rates is important in determining the dynamics. Coherent propagation is seen in superconductors and insulators at low temperature where dissipation is small. At higher temperatures the motion undergoes a crossover from bandlike propagation to incoherent hopping between neighboring sites. This review covers both theory and experiment, emphasizing the mechanisms for dissipation, the role of barrier fluctuations, and effects of crystal disorder on the transport. The review of experimental data includes an analysis of barrier penetration bandwidths for muon and muonium diffusion in a variety of metals and insulators.

DOI:https://doi.org/10.1103/RevModPhys.70.929