Theory of Mesoscopic Quantum Tunneling in Magnetism: A WKB Approach

Abstract

This is a comprehensive and self-contained review of WKB theory for mesoscopic quantum tunneling in magnetism. It describes the behavior of a large quantum spin, e.g., a magnetic moment, in an anisotropic surroundings and its penetration into a classically forbidden region. The tunneling rate of a quantum spin is obtained in the semiclassicaJ limit when ħ → 0 and the spin quantum number S → ∞ in such a way that ħS remains constant. The key idea is to single out one of the anisotropy axes, say the z-axis, to work in a representation with S z diagonal, and to describe quantum tunneling as a hopping process on the spectrum of S z . We sketch the original motivation of our theory, present the WKB basics, compute the tunneling rate, prove its universal power-law dependence upon the anisotropy constants which is independent of the specific form of the anisotropy, and discuss the underlying physics. We treat several examples, including antiferromagnetic tunneling. In addition, we provide a general theory of quantum coherence, including Kramers degeneracy.