Dynamics of molecular nanomagnets in time-dependent external magnetic fields:: Beyond the Landau-Zener-Stuckelberg model

The time evolution of the magnetization of a magnetic molecular crystal is obtained in an external time-dependent magnetic field, with sweep rates in the kT/s range. We present the "exact numerical" solution of the time-dependent Schrodinger equation, and show that the steps in the hysteresis curve can be described as a sequence of two-level transitions between adiabatic states. The multilevel nature of the problem causes the transition probabilities to deviate significantly from the predictions of the Landau-Zener-Stuckelberg model. These calculations allow the introduction of an efficient approximation method that accurately reproduces the exact results. When including phase relaxation by means of an appropriate master equation, we observe an interplay between coherent dynamics and decoherence. This decreases the size of the magnetization steps at the transitions, but does not modify qualitatively the physical picture obtained without relaxation.