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

Abstract

We have found a novel feature of the bistable large-spin model described by the Hamiltonian $H{\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}DS}_{z}^{2}{\ensuremath{-}H}_{x}{S}_{x}$. The crossover from thermal to quantum regime for the escape rate can be either first $({H}_{x}<SD/2)$ or second $(SD/2<{H}_{x}<2\mathrm{SD})$ order, that is, sharp or smooth, depending on the strength of the transverse field. This prediction can be tested experimentally in molecular magnets like ${\mathrm{Mn}}_{12}\mathrm{Ac}$.