Theory of muon spin relaxation due to the hopping of positive muons in ferromagnets

The interaction of the magnetic moments of spin-polarized positive muons with the magnetic fields at the interstices in ferromagnetic (or ferrimagnetic) materials may be used to study the localization and the hopping motion of thermalized muons by observing the relaxation of the longitudinal or transverse spin polarization or the shift of the muon spin precession frequency as a function of the orientation of a strong applied magnetic field. The general theory is developed and applied to the special cases of muon diffusion between two types of interstice of tetragonal symmetry in body-centred-cubic metals (α-Fe) or of cubic symmetry in facecentred-cubic metals (Ni). It is shown that by a suitable choice of the strength and the crystallographic direction of the applied magnetic field, quite detailed information on the quantum diffusion of positively charged light particles in crystals may be obtained