Muon spin relaxation in strongly coupled systems

In many materials there is a strong magnetic dipolar or quadrupolar interaction between an implanted muon and a small number of nearby nuclei, which is not well described by the usual 'classical' approximations such as the Kubo-Toyabe function. In this paper we show how the polarisation P(t) of the muon at any time t greater than or equal to 0 can be calculated by the density matrix method. For zero-field and single-crystal measurements we can obtain an analytical solution, while powder samples in applied fields need Monte Carlo averaging. Examples of simulated fits to measured zero-field relaxation are given: in Mg(OH)(2) where the muon substitutes into a hexagonal lattice of protons, and in gypsum CaSO4.2H(2)O where the muon replaces a proton in a water molecule. (C) 2000 Elsevier Science B.V. All rights reserved.