Crossover temperature for quantum tunnelling in spin systems

We derive an analytical expression for the crossover temperature corresponding to the transition from classical activation mechanism to temperature assisted quantum tunnelling in spin systems. The crossover temperature depends on the magnetic configuration and Hessian at the first order saddle point on the energy surface of the system. The theory is applied to several single spin models, including a system with four-fold anisotropy. Good agreement is obtained with experimental results for a molecular magnet containing Mn₄.