Quantum tunneling of magnetization in molecular spin

We examine the quantum tunneling of magnetization in molecular spin in weak interaction with a bath subject to Redfield master equation. By designing a microscopic model for a multilevel spin system using only a generic Hamiltonian and applying stationary approximation for excited doublets/singlets, we derive a key equation of motion for the quantum tunneling of magnetization process which is applicable in the whole temperature domain. From this equation, we find that in general three tunneling rates are needed to accurately describe the quantum tunneling process. More importantly, behavior of the quantum tunneling in the intermediate temperature domain where there exists a transition between incoherent and coherent quantum tunneling is also unraveled for the first time. Limiting cases at low and high temperature and/or low magnetic field are also worked out where some popular well-known results are reproduced. Last but not least, a new interpretation of the quantum tunneling of magnetization is proposed where we reveal the similarity between this relaxation process with a driven damped harmonic oscillator.