Effects of spin inertia on ground-state energies: the spin-instanton

Abstract

Recent experiments have shown that spin dynamics depend on spin inertia. If the spin dynamics are dependent on spin inertia, the energy levels of a single spin could have an inertia-dependence too. In this thesis, we investigate how spin inertia affects the lowest energy levels of a single spin. To find this result, we consider a model of a large spin, with easy-axis anisotropy. Furthermore, the spin is influenced by a magnetic field and we place the spin in a bath of harmonic oscillators, to induce non-zero spin inertia. We consider a spin which can have values in a single direction. We call this model the circular-spin model. To find these lowest energy levels and their eigenenergies, we use instanton calculus. For the circular-spin model, we find the lowest energy levels. This new result tells us how spin inertia affects the lowest energy levels of a spin. We found that these energy levels have a similar dependence on spin inertia as the lowest energy levels of a particle in a double-well potential, depends on the mass of the particle. With this result, we have a better fundamental understanding of the lowest energy levels of spins. Furthermore, this result may provide a new way to experimentally detect spin inertia.