A generalized Kubo-Toyabe formula for muon spin relaxation in crystals with uniaxial symmetry

The Kubo-Toyabe semiclassical formula, describing the time development of the polarization of a particle in zero external field at a lattice site with cubic local environment, is generalized for uniaxial site symmetry. The relaxation function and, in particular, its first moments and long time asymptotics obtained in a closed form depend on the angle between polarization and the crystalc-axis and are shown to vary sensitively with the asymmetry of the field distribution at the particular muon site. Besides the exact uniaxial variant of the Kubo-Toyabe relaxation function, an approximate simple interpolation formula is also derived, which is correct for both short times and in its long time asymptotics. The two parameters (, ₁) in the uniaxial formulae can be determined by using the observed values of the second momentM ₂ for two different crystal orientations.