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

Abstract

We investigate the escape rate of a biaxial spin particle with an arbitrarily directed magnetic field in the easy plane, described by Hamiltonian $\mathcal{H}=\ensuremath{-}{\mathrm{AS}}_{z}^{2}\ensuremath{-}{\mathrm{BS}}_{x}^{2}\ensuremath{-}{H}_{x}{S}_{x}\ensuremath{-}{H}_{z}{S}_{z},$ $(A>B>0).$ 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 $b\ensuremath{\equiv}B/A$ and the field parameters ${\ensuremath{\alpha}}_{x,z}\ensuremath{\equiv}{H}_{x,z}/AS:$ ${\ensuremath{\alpha}}_{\mathrm{zc}}{(b}_{c})$'s, ${\ensuremath{\alpha}}_{\mathrm{xc}}{(b}_{c})$'s, and ${\ensuremath{\alpha}}_{\mathrm{zc}}={\ensuremath{\alpha}}_{\mathrm{zc}}({\ensuremath{\alpha}}_{\mathrm{xc}}).$ It is found from ${\ensuremath{\alpha}}_{\mathrm{zc}}{(b}_{c})$'s and ${\ensuremath{\alpha}}_{\mathrm{xc}}{(b}_{c})$'s that the first-order region decreases as b and ${\ensuremath{\alpha}}_{x}$ (or ${\ensuremath{\alpha}}_{z})$ increase. The phase boundary line ${\ensuremath{\alpha}}_{\mathrm{zc}}={\ensuremath{\alpha}}_{\mathrm{zc}}({\ensuremath{\alpha}}_{\mathrm{xc}})$ shows that compared with the uniaxial system, both the first- and second-order regions are diminished due to the transverse anisotropy. Moreover, it is observed that, in the limit ${\ensuremath{\alpha}}_{\mathrm{xc}}\ensuremath{\rightarrow}0,$ ${\ensuremath{\alpha}}_{\mathrm{zc}}$ does not coincide 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: ${T}_{c}{(b}_{c}),$ ${T}_{c}({\ensuremath{\alpha}}_{\mathrm{xc}},{\ensuremath{\alpha}}_{\mathrm{zc}}).$