Quantum tunneling and quantum-classical transitions in large spin systems

Abstract

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.