Resonant magnetic quantum tunneling through thermally activated states

Abstract

We present a theory of resonant quantum tunneling of large spins through thermally activated states. It gives numerical results that are in good agreement with data from recent magnetic quantum tunneling experiments in Mn acetate. We show that neither dipolar fields nor crystal-field perturbations, acting separately, can account for the resonances observed. However, we find that these two perturbations acting jointly produce a highly nonlinear effect that enhances tunneling rates up to their observed values. Resonant tunneling through low-lying energy-state pairs is blocked. We show that the tunneling frequency ${\ensuremath{\omega}}_{T}$ and the lifetime ${\ensuremath{\tau}}_{0}$ of the thermally populated pairs of states through which tunneling proceeds fulfils ${\ensuremath{\omega}}_{T}{\ensuremath{\tau}}_{0}\ensuremath{\gg}1$. A superposition of these two states becomes incoherent approximately in time $1/{\ensuremath{\omega}}_{T}.$ Using the master equation that follows, and spin-phonon-induced transition rates that we calculate, we obtain relaxation rates and magnetization hysteresis curves that agree reasonably well with experiment.