  We investigate the sensitivity of nonintegrable large-spin quantum lattices
to small perturbations with a particular focus on the time reversal experiments
known in statistical physics as "Loschmidt echoes" and in nuclear magnetic
resonance (NMR) as "magic echoes". Our numerical simulations of quantum
spin-$7\frac{1}{2}$ clusters indicate that there is a regime, where Loschmidt
echoes exhibit nearly exponential sensitivity to small perturbations with
characteristic constant approximately equal to twice the value of the largest
Lyapunov exponent of the corresponding classical spin clusters. The above
theoretical results are verifiable by NMR experiments on solids containing
large-spin nuclei.
