This article presents a review on the theoretical and the experimentaldevelopments on macroscopic quantum tunneling and phase transition of theescape rate in spin systems. We present the basic ideas with simplifiedcalculations so that it is readable to both specialists and nonspecialists inthis area of research. A brief derivation of the path integral formulation ofquantum mechanics in its original form using the orthonormal position andmomentum basis is reviewed. For spin systems such as single molecule magnets,the formulation of path integral requires the use of non-orthonormal spincoherent state in $(2s+1)$ dimensional Hilbert space, the coordinateindependent and the coordinate dependent form of the spin coherent state pathintegral is derived. These two forms of spin coherent state path integral areapplied to the tunneling of single molecule magnets through its magneticanisotropy barrier. Most experimental and numerical results are presented. Thesuppression of tunneling for half-odd integer spin (spin-parity effect) at zeromagnetic field is derived from both forms, which shows that this result(spin-parity effect) is independent of the coordinate. At nonzero magneticfield we present both the experimental and the theoretical results of theoscillation of tunneling splitting as a function of the applied magnetic fieldapplied along the spin hard anisotropy axis direction. The experimental and thetheoretical results of the tunneling in antiferromagnetic exchange coupleddimer model are also reviewed. As the spin coherent state path integralformalism is a semi-classical method, an alternative exact mapping of a spinsystem to a particle in a potential field (effective potential method) isderived. This effective potential method allows for the investigation of phasetransition of the escape rate in spin systems.
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