First- and Second-Order Transitions between Quantum and Classical Regimes for the Escape Rate of a Spin System

We have found a novel feature of the bistable large-spin model described by the Hamiltonian H = -DS_z^2 - H_xS_x.The crossover from thermal to quantum regime for the escape rate can be either first (H_x<SD/2) or second (SD/2<H_x<2SD) order, that is, sharp or smooth, depending on the strength of the transverse field. This prediction can be tested experimentally in molecular magnets like Mn_12Ac.