Nuclear spin bath effects on Landau-Zener transitions in nanomagnets

We study how coupling between the electronic and nuclear spins modifies tunneling transitions in nanomagnets in time-dependent external fields. The limit of very fast sweeping rates is correctly described by the ideal Landau-Zener formula even when in static fields the environmental spins render the magnetization dynamics incoherent. On one hand, this result justifies the experimental technique based on Landau-Zener formula for measuring the tunneling amplitude, on the other hand, it makes the origin of the isotope effect in such experiments puzzling. We also consider tunneling transitions on the Landau-Zener grid in slowly varying fields.