Escape rate of a biaxial nanospin system in a magnetic field : first- and second-order transition between quantum and classical regimes

We investigate the escape rate of the biaxial nanospin particle with a magnetic field applied along the easy axis. The model studied here is described by the Hamiltonian ${\cal H} = -AS_z^2 - BS_x^2 - HS_z, (A>B>0)$. By reducing this Hamiltonian to a particle one, we derive, for the first time, an effective particle potential for this model and find an analytical form of the phase boundary line between first- and second-order transitions, from which a complete phase diagram can be obtained. We also derive an analytical form of the crossover temperature as a function of the applied field at the phase boundary.