Quenched Spin Tunneling and Diabolical Points in Magnetic Molecules: I. Symmetric Configurations

Abstract

The perfect quenching of spin tunneling that has previously been discussed in terms of interfering instantons, and has recently been observed in the magnetic molecule \Fe8, is treated using a discrete phase integral (or Wentzel-Kramers-Brillouin) method. The simplest model Hamiltonian for the phenomenon leads to a Schrödinger equation that is a five-term recursion relation. This recursion relation is reflection-symmetric when the magnetic field applied to the molecule is along the hard magnetic axis. A completely general Herring formula for the tunnel splittings for all reflection-symmetric five-term recursion relations is obtained. Using connection formulas for a new type of turning point that may be described as lying "under the barrier", and which underlies the oscillations in the splitting as a function of magnetic field, this Herring formula is transformed into two other formulas that express the splittings in terms of a small number of action and action-like integrals. These latter formulas appear to be generally valid, even for problems where the recursion contains more than five terms. The results for the model Hamiltonian are compared with experiment, numerics, previous instanton based approaches, and the limiting case of no magnetic field.

Revtex; 4 ps figures

References in corpus (9)

• Tunnel splittings for one dimensional potential wells revisited
• Landau Zener method to study quantum phase interference of Fe8 molecular nanomagnets
• Diabolical Points in Magnetic Molecules: An Exactly Solvable Model
• Oscillatory Tunnel Splittings in Spin Systems: A Discrete Wentzel-Kramers-Brillouin Approach
• Quantum Phase Interference for Quantum Tunneling in Spin Systems
• Large transverse field tunnel splittings in the Fe_8 spin Hamiltonian
• Application of the discrete Wentzel-Kramers-Brillouin method to spin tunneling
• Instanton picture of the spin tunneling in the Lipkin model
• Diabolical points in the magnetic spectrum of Fe_8 molecules

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