Tunneling of quantum spins

Abstract

A WKB formalism is presented whereby the tunneling rate of a quantum spin is obtained in the semiclassical limit when h ̷ → 0 and the spin quantum number S → ∞ in such a way that h ̷ S remains constant. The main idea is to single out one of t anisotropy axes, say the z-axis, to work in a representation with S z , the z-component of the spin, diagonal and to describe quantum tunneling as a hopping process on the spectrum of S z . This formalism enables us to efficiently handle tunneling problems, to incorporate dissipation, and to prove that the tunneling rate is universal, i.e. independent of the particular form of the anisotropy.