Quantum-classical transition of the escape rate of a uniaxial spin system in an arbitrarily directed field

The escape rate Gamma of the large-spin model described by the Hamiltonian H = -DSz2-HzSz - HxSx is investigated with the help of the mapping onto a particle moving in a double-well potential U(x). The transition-state method yields Gamma in the moderate-damping case as a Boltzmann average of the quantum transition probabilities. We have shown that the transition from the classical to quantum regimes with lowering temperature is of the first order (d Gamma/dT discontinuous at the transition temperature T-0) for h(x) below the phase boundary line h(x) = h(xc)(h(z)), where h(x,z) = H-x,H-z /(2SD), and of the second order above this line. In the unbiased case (H-z = 0) the result is h(xc)(0) = 1/4, i.e., one fourth of the metastability boundary h(xm) = 1, at which the barrier disappears. In the strongly biased limit delta=1-h(z) much less than 1, one has h(xc) congruent to(2/3)(3/4)(root 3-root 2) delta(3/2) congruent to 0.2345 delta(3/2), which is about one half of the boundary value h(xm) congruent to(2 delta/3)(3/2) congruent to 0.5443 delta(3/2). The latter case is relevant for experiments on small magnetic particles, where the barrier should be lowered to achieve measurable quantum escape rates.