Quantum-classical phase transition of escape rate in biaxial spin system with an arbitrarily directed magnetic field

We investigate the escape rate of a biaxial spin particle with an arbitrarily dierected magnetic field in the easy plane, described by Hamiltonian ${\cal H} = -AS_z^2 - BS_x^2 -H_x S_x -H_z S_z, (A>B>0)$. We derive an effective particle potential 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 escape rate we obtained various phase boundary curves depending on the anisotropy parameter $b\equiv B\mathrm{/}A$ and the field parameters $\alpha_{x,z} \equiv H_{x,z}/AS$:$\alpha_{zc}(b_c)'s, \alpha_{xc}(b_c)'s$,and$\alpha_{zc} = \alpha_{zc}(\alpha_{xc})$\mathrm{.}Itisfoundfrom$\alpha_{zc}(b_c)'s$and$\alpha_{xc}(b_c)'s$thatthe-first-orderregiondecreasesas$b$and$\alpha_x $(or$\alpha_z$)increase\mathrm{.}Thephaseboundaryline$\alpha_{zc} = \alpha_{zc}(\alpha_{xc}) shows that compared with the uniaxial system, both the first- and second-oredr regions are diminished due to the transverse anisotropy. Moreover, it is observed that, in the limit ${\alpha }_{xc}\to 0$, ${\alpha }_{zc}$ does not coinsides with the coercive field line, which yields more reduction in the first-order region. We have also computed the crossover temperatures at the phase boundary :$T_c(b_c),T_c({\alpha }_{xc},{\alpha }_{zc})$.