Spin tunneling and topological selection rules for integer spins

We present topological interference effects for the tunneling of a single large spin, which are caused by the symmetry of a general class of magnetic anisotropies. The interference originates from spin Berry phases associated with different tunneling paths exposed to the same dynamics. Introducing a generalized path integral for coherent spin states, we evaluate transition amplitudes between ground as well as low-lying excited states. We show that these interference effects lead to topological selection rules and spin-parity effects for integer spins that agree with quantum selection rules and which thus provide a generalization of the Kramers degeneracy to integer spins. Our results apply to the molecular magnets ${\mathrm{Mn}}_{12}$ and ${\mathrm{Fe}}_8.$