Oscillatory Tunnel Splittings in Spin Systems: A Discrete Wentzel-Kramers-Brillouin Approach

TL;DR

This paper introduces a discrete WKB method to analyze oscillatory tunnel splittings in spin systems, providing new formulas and insights, especially for the ext{Fe}_8 system, extending previous results to higher energy levels.

Contribution

A novel discrete WKB approach is developed to study tunnel splittings in spin systems, including analysis of a new turning point and application to ext{Fe}_8, extending prior results.

Findings

Derived a general formula for tunnel splittings with oscillations.

Analyzed a new turning point inside the forbidden region.

Extended previous magnetic field oscillation results to higher energy levels.

Abstract

Certain spin Hamiltonians that give rise to tunnel splittings that are viewed in terms of interfering instanton trajectories, are restudied using a discrete WKB method, that is more elementary, and also yields wavefunctions and preexponential factors for the splittings. A novel turning point inside the classically forbidden region is analysed, and a general formula is obtained for the splittings. The result is appled to the \Fe8 system. A previous result for the oscillation of the ground state splitting with external magnetic field is extended to higher levels.