Polarization Functions

In this chapter we discuss the theoretical description of the muon spin polarization \( \vec {P}(t)\) for different types of static and dynamic local fields corresponding to different magnetic environments, with and without the application of external magnetic fields. Analytical expressions of \( \vec {P}(t)\) for specific configurations of static local fields (single-valued fields, continuous field distributions, short-range order, \(\ldots \) ) are derived, the information obtained is discussed, and corresponding experimental examples are shown. The effects of dynamical local fields on \( \vec {P}(t)\) are presented, and the extraction of parameters such as magnetic fluctuation times and spectral density of fluctuations from the \(\mu \) SR signal is shown.