Études de l'effet tunnel des spins quantiques macroscopiques
Studies of the macroscopic quantum tunneling of spins
The study of molecular magnets has captivated the attention of many researchers in recent years. It has proven be a ubiquitous research area in physics, with applications ranging from quantum information processing, molecular spintronics to molecule-based magnetic coolers (magnetocaloric effects). Indeed, these molecular magnets are composed of very large spins with large anisotropy, which makes their application to technology more feasible. We present theoretical analyses together with experimental observations on macroscopic quantum tunneling and quantum-classical phase transitions of the escape rate in molecular magnets. We consider biaxial ferromagnetic spin systems. Using the coordinate dependent spin coherent state path integral, we obtain the quantum phase interference and the energy splitting of these systems. We also present a lucid exposition of tunneling in antiferromagnetic exchange-coupled dimer, with easy-axis anisotropy. Indeed, we obtain the ground state, the first excited state, and the energy splitting, for both integer and half-odd integer spins. These results are then corroborated using perturbation theory and the coordinate independent spin coherent state path integral. We further present a lucid explication of the effective potential method, which enables one to map a spin Hamiltonian onto a particle Hamiltonian; we employ this method to our models, however, in the presence of an applied magnetic field. This method enables us to investigate quantum-classical phase transitions of the escape rate of these systems. We obtain the phase boundaries, as well as the crossover temperatures of these phase transitions. Furthermore, we extend our analysis to one-dimensional anisotropic Heisenberg antiferromagnet, with N periodic sites. For even N, we show that the ground state is non-degenerate and given by the coherent superposition of the two Neél states. For odd N, however, the Neél state contains a soliton; as the soliton can be placed anywhere along the ring, the ground state is, indeed, N-fold degenerate. In the perturbative limit (weak exchange interaction), quantum fluctuation stemming from the interaction term lifts this degeneracy and reorganizes the states into a band. We show that this occurs at order 2s in (degenerate) perturbation theory. The ground state is non-degenerate for integer spin, but degenerate for half-odd integer spin, in accordance with Kramers’ theorem.
