Macroscopic quantum tunneling and quantum-classical phase transitions of the escape rate in large spin systems

This article presents a review on the theoretical and the experimental developments on macroscopic quantum tunneling and quantum classical phase transitions of the escape rate in large spin systems. A substantial amount of research work has been done in this area of research over the years, so this article does not cover all the research areas that have been studied, for instance the effect of dissipation is not discussed and can be found in other review articles. We present the basic ideas with simplified calculations so that it is readable to both specialists and nonspecialists in this area of research. A brief derivation of the path integral formulation of quantum mechanics in its original form using the orthonormal position and momentum basis is reviewed. For tunneling of a particle into the classically forbidden region, the imaginary time (Euclidean) formulation of path integral is useful, we review this formulation and apply it to the problem of tunneling in a double well potential. For spin systems such as single molecule magnets, the formulation of path integral requires the use of non-orthonormal spin coherent states in (2s + 1) dimensional Hilbert space, the coordinate independent and the coordinate dependent form of the spin coherent state path integral are derived. These two (equivalent) forms of spin coherent state path integral are applied to the tunneling of single molecule magnets through a magnetic anisotropy barrier. Most experimental and numerical results are presented. The suppression of tunneling for half-odd integer spin (spin-parity effect) at zero magnetic field is derived using both forms of spin coherent state path integral, which shows that this result (spin-parity effect) is independent of the choice of coordinate. At nonzero magnetic field we present both the experimental and the theoretical results of the oscillation of tunneling splitting as a function of the applied magnetic field applied along the spin hard anisotropy axis direction. The experimental and the theoretical results of the tunneling in antiferromagnetic exchange coupled dimer model are also reviewed. As the spin coherent state path integral formalism is a semi-classical method, an alternative exact mapping of a spin Hamiltonian to a particle Hamiltonian with a potential field (effective potential method) is derived. This effective potential method allows for the investigation of quantum-classical phase transitions of the escape rate in large spin systems. We present different methods for investigating quantum-classical phase transitions of the escape rate in large spin systems. These methods are applied to different spin models. (C) 2014 Elsevier B.V. All rights reserved.