  We investigate spin dynamics in antiferromagnetic (AF) molecular rings at
finite temperature in the presence of spin-phonon (s-p) interaction. We derive
a general expression for the spin susceptibility in the weak s-p coupling limit
and then we focus on the low-frequency behavior, in order to discuss a possible
microscopic mechanism for nuclear relaxation in this class of magnetic
materials. To lowest order in a perturbative expansion, we find that the
susceptibility takes a Lorentzian profile and all spin operators ($S^x$, $S^y,
S^z$) contribute to spin dynamics at wave vectors $q\ne 0$. Spin anisotropies
and local s-p coupling play a key role in the proposed mechanism. Our results
prove that small changes in the spatial symmetry of the ring induce qualitative
changes in the spin dynamics at the nuclear frequency, providing a novel
mechanism for nuclear relaxation. Possible experiments are proposed.
