Quenched spin tunneling and diabolical points in magnetic molecules. II. Asymmetric configurations

The perfect quenching of spin tunneling first predicted for a model with biaxial symmetry, and recently observed in the magnetic molecule (formula presented) is further studied using the discrete phase integral or WKB (Wentzel-Kramers-Brillouin) method. The analysis of the previous paper is extended to the case where the magnetic field has both hard and easy components, so that the Hamiltonian has no obvious symmetry. Herring’s formula is now inapplicable, so the problem is solved by finding the wave function and using connection formulas at every turning point. A general formula for the energy surface in the vicinity of the diabolo is obtained in this way. This formula gives the tunneling amplitude between two wells unrelated by symmetry in terms of a small number of action integrals, and appears to be generally valid, even for problems where the recursion contains more than five terms. Explicit results are obtained for the diabolical points in the model for (formula presented) that closely parallel the experimental observations. The leading semiclassical results for the diabolical points are found to agree precisely with exact results.