  Neutron-capture reactions on very neutron-rich nuclei are essential for
heavy-element nucleosynthesis through the rapid neutron-capture process, now
shown to take place in neutron-star merger events. For these exotic nuclei,
radiative neutron capture is extremely sensitive to their $\gamma$-emission
probability at very low $\gamma$ energies. In this work, we present
measurements of the $\gamma$-decay strength of $^{70}$Ni over the wide range
$1.3 \leq E_{\gamma} \leq 8 $ MeV. A significant enhancement is found in the
$\gamma$-decay strength for transitions with $E_\gamma < 3$ MeV. At present,
this is the most neutron-rich nucleus displaying this feature, proving that
this phenomenon is not restricted to stable nuclei. We have performed
$E1$-strength calculations within the quasiparticle time-blocking
approximation, which describe our data above $E_\gamma \simeq 5$ MeV very well.
Moreover, large-scale shell-model calculations indicate an $M1$ nature of the
low-energy $\gamma$ strength. This turns out to be remarkably robust with
respect to the choice of interaction, truncation and model space, and we
predict its presence in the whole isotopic chain, in particular the
neutron-rich $^{72,74,76}\mathrm{Ni}$.
