Abstract
It is shown that in experiments on single molecule magnets in which transitions between two lowest spins states are induced by sweeping the applied magnetic field along the easy axis; the transitions are fully incoherent. Nuclear spins and the dipolar coupling of molecular spins are identified as the main sources of decoherence, and the form of the decoherence is calculated. The Landau-Zener-St\"uckelberg (LZS) process is examined in light of this decoherence, and it is shown that the correct formula for the spin-flip probability is better given by a more recent formula of Kayanuma than that of LZS. The two formulas are shown to be identical in the limit of rapid sweeps. An approximate way of incorporating the molecular spin dipole field into the rate equations for this process is developed.
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