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 $H{=-DS}_z^2{-H}_x{S}_x$. The crossover from thermal to quantum regime for the escape rate can be either first $(H_x<SD/2\mathrm{})$ or second $(SD/2<H_x<2\mathrm{SD})$ order, that is, sharp or smooth, depending on the strength of the transverse field. This prediction can be tested experimentally in molecular magnets like ${\mathrm{Mn}}_{12}\mathrm{Ac}$.