Positive-muon spin depolarization in solids

A theory of positive-muon spin depolarization in solids is presented. Treating the interaction of the muon spin with the solid perturbatively, the depolarization rate is related to the temporal correlations of the local magnetic fields at the position of the muon. This general result encompasses both transverse and longitudinal spin depolarization. For some situations it is shown that the local-field correlations can be expressed in terms of two quantities, a muon self-diffusion function which contains the information regarding muon motion, and a function describing the spin dynamics of the solid. When applicable, this separation precisely identifies the aspects of muon motion that are studied by muon-spin-rotation experiments. The consequences of some simple models for muon motion are examined. The effect of the finite spread of the muon wave function when centered on a particular interstitial site is also included. The possible importance of this effect is suggested by calculations which account for the applied-magnetic-field dependence of the depolarization rate in copper.