Quantum-classical crossover of the escape rate in a biaxial spin system with an arbitrarily directed magnetic field

We investigate the escape rate of a biaxial spin particle with an arbitrari ly directed magnetic held in the easy plane, described by Hamiltonian H = - AS(z)(2) -BSx2- HxSx- HzSz, (A>B>0). We derive an effective particle potent ial by using the method of particle mapping. With the help of the criterion for the presence of a first-order quantum-classical transition of the esca pe rate we obtained various phase boundary curves depending on the anisotro py parameter b = B/A and the held parameters a(x,z) = H-x,H-z/AS: alpha(zc) (b(c))'s, alpha(xc)(b(c))'s, and alpha(zc) = alpha(zc)(alpha(xc)). It is fo und from alpha(zc)(b(c))'s and alpha(xc)(b(c))'s that the first-order regio n decreases as b and alpha(x) (or alpha(z)) increase. The phase boundary li ne alpha(zc) = alpha(zc)(alpha(xc)) shows that compared with the uniaxial s ystem, both the first- and second-order regions rue diminished due to the t ransverse anisotropy. Moreover, it is observed that, in the limit alpha(xc) -->0, alpha(zc) does not coincide with the coercive held line, which yields more reduction in the first-order region. We have also computed the crosso ver temperatures at the phase boundary: T-c(b(c)), T-c(alpha(xc),alpha(zc)) .