A dissipative quantum dynamic approach to magnetic hysteresis loop and magnetization relaxation for molecule magnet Mn₁₂

A new approach to the magnetic hysteresis loop and magnetization relaxation of molecule magnet, Mn₁₂, is presented. The method, so called "quasi-thermal equilibrium (QTE) + erase phase (EP)" (QTE + EP), leads the dissipation in state evolution. The method gives an method to approach an irreversible quantum dynamic tunnelling and time evolution of system and straightly leads the hysteresis loops. The QTE can work well for the double-well system and is able to be extended to the multi-wells quantum system. The EP is based on the physics of random interaction with the environment that results the phase de-coherence or say "re-initial" of the phase of quantum state during the time evolution. The stairs in the magnetic loops of Mn₁₂ we have obtained quantitatively show the quantum resonant tunnelling. The relaxation of magnetization from initial lowest state is calculated for different temperatures and well shows the exponential behavior. The theoretical results well agree with the experiments.