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The time evolution of the magnetization of a magnetic molecular crystal isobtained in an external time-dependent magnetic field, with sweep rates in thekT/s range. We present the 'exact numerical' solution of the time dependentSchr\"{o}dinger equation, and show that the steps in the hysteresis curve canbe described as a sequence of two-level transitions between adiabatic states.The multilevel nature of the problem causes the transition probabilities todeviate significantly from the predictions of the Landau-Zener-St\"{u}ckelbergmodel. These calculations allow the introduction of an efficient approximationmethod that accurately reproduces the exact results. When including phaserelaxation by means of an appropriate master equation, we observe an interplaybetween coherent dynamics and decoherence. This decreases the size of themagnetization steps at the transitions, but does not modify qualitatively thephysical picture obtained without relaxation.Comment: 8 pages, 7 figure

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