Quantum tunneling and quantum-classical transitions in large spin systems

We have studied quantum tunneling of large spins in a biaxial spin system and in a single-axial spin system with a transverse magnetic field. The asymptotically exact eigenvalues and eigenstates of the spin systems are obtained by solving the Mathieu equation. When the height 4q of energy barrier formed by the anisotropy and the magnetic field exceeds some critical values 4q(1T)(r), the ground states and the excited states split due to tunneling of large spins. We also have presented the phase diagram of these spin systems in the extremely weak spin-phonon coupling limit. The crossover from thermal to quantum regime is second order. With further decreasing temperature, the first-order phase transition occurs from a thermally-assisted resonant tunneling to thermal regime as q<q(1T)(s). Our theory agrees with recent experimental observations well.