  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 Mn12 and Fe8.
