Quantum tunneling and quantum-classical transitions in large spin systems

We have studied quantum tunneling of large spins in a biaxial spin system a nd in a single-axial spin system with a transverse magnetic field. The asym ptotically exact eigenvalues and eigenstates of the spin systems are obtain ed by solving the Mathieu equation. When the height 4q of energy barrier fo rmed 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 syst ems in the extremely weak spin-phonon coupling limit. The crossover from th ermal to quantum regime is second order. With further decreasing temperatur e, the first-order phase transition occurs from a thermally-assisted resona nt tunneling to thermal regime as q<q(1T)(s). Our theory agrees with recent experimental observations well.