Quantum-classical transition of the escape rate of a biaxial ferromagnetic spin with an external magnetic field

We study the model of a biaxial single ferromagnetic spin Hamiltonian with an external magnetic field applied along the medium axis. The phase transition of the escape rate is investigated. Two different but equivalent methods are implemented. Firstly, we derive the semi-classical description of the model which yields a potential and a coordinate dependent mass. Secondly, we employ the method of spin-particle mapping which yields a similar potential to that of semi-classical description but with a constant mass. The exact instanton trajectory and its corresponding action, which have not been reported in any literature is being derived. Also, the analytical expressions for the first- and second-order crossover temperatures at the phase boundary are derived. We show that the boundary between the first-and the second-order phase transitions is greatly influenced by the magnetic field.