Incoherent Zener tunneling and its application to molecular magnets

We generalize the Landau-Zener theory of coherent tunneling transitions by taking thermal relaxation into account. The evaluation of a generalized master equation containing a dynamic tunneling rate that includes the interaction between the relevant system and its environment leads to an incoherent Zener transition probability with an exponent that is twice as large as the one of the coherent Zener probability in the limit $\overrightarrow{T}0.$ We apply our results to molecular clusters, in particular to recent measurements of the tunneling transition of spins in ${\mathrm{Fe}}_8$ crystals performed by Wernsdorfer and Sessoli [Science 284, 133 (1999)].