  We study the one-dimensional quantum Heisenberg ferromagnet with exchange
couplings exhibiting long-range correlated disorder with power spectrum
proportional to $1/k^{\alpha}$, where $k$ is the wave-vector of the modulations
on the random coupling landscape. By using renormalization group, integration
of the equations of motion and exact diagonalization, we compute the spin-wave
localization length and the mean-square displacement of the wave-packet. We
find that, associated with the emergence of extended spin-waves in the
low-energy region for $\alpha > 1$, the wave-packet mean-square displacement
changes from a long-time super-diffusive behavior for $\alpha <1$ to a
long-time ballistic behavior for $\alpha > 1$. At the vicinity of $\alpha =1$,
the mobility edge separating the extended and localized phases is shown to
scale with the degree of correlation as $E_c\propto (\alpha -1)^{1/3}$.
