  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.
