Spin tunneling in magnetic molecules: Quasisingular perturbations and discontinuous SU(2) instantons

Spin coherent state path integrals with discontinuous semiclassical paths are investigated with special reference to a realistic model for the magnetic degrees of freedom in the (formula presented) molecular solid. It is shown that such paths are essential to a proper understanding of the phenomenon of quenched spin tunneling in these molecules. In the (formula presented) problem, such paths are shown to arise as soon as a fourth-order anisotropy term in the energy is turned on, making this term a singular perturbation from the semiclassical point of view. The instanton approximation is shown to quantitatively explain the magnetic field dependence of the tunnel splitting, as well as agree with general rules for the number of quenching points allowed for a given value of spin. A fairly accurate approximate formula for the spacing between quenching points is derived.