Computer simulation of muon spin evolution

Abstract

This paper describes an exact numerical method for simulating the response of the muon polarisation in a variety of experimental situations. It models the muon together with nearby spins such as electrons and nuclei, interacting via dipolar, hyperfine and quadrupolar interactions. It also takes account of Zeeman interaction with both static and RF magnetic fields, and spin flips and site changes. For the simple case of a static environment a Hamiltonian is calculated and diagonalised. External RF fields are modelled by calculating an effective Hamiltonian for the evolution over one RF cycle. For spin flips and site changes the evolution of the density matrix is used, and the solution contains exponential terms representing the relaxation rate. The program uses Monte-Carlo averaging to model powder samples. It can plot out results as a function of field, frequency or hop rate, or vary any parameter to fit experimental data. The output can be as a time domain signal, a frequency spectrum or a calculated quantity such as integral asymmetry, relaxation rate or linewidth.