  A low-energy enhancement (LEE), observed experimentally in the $\gamma$-ray
strength function ($\gamma$SF) describing the decay of compound nuclei, would
have profound effects on $r$-process nucleosynthesis if it persists in heavy
neutron-rich nuclei. The LEE was shown to be a feature of the magnetic dipole
($M1)$ strength function in configuration-interaction shell-model calculations
in medium-mass nuclei. However, its existence in heavy nuclei and its evolution
with neutron number remain open questions. Here, using a combination of
many-body methods, we find the LEE in the $M1$ $\gamma$SFs of heavy samarium
nuclei. In particular, we use the static-path plus random-phase approximation
(SPA+RPA), which includes static and small-amplitude quantal fluctuations
beyond the mean field. Using the SPA+RPA strength as a prior, we apply the
maximum-entropy method (MEM) to obtain finite-temperature $M1$ $\gamma$SFs from
exact imaginary-time response functions calculated with the shell model Monte
Carlo (SMMC) method. We find that the slope of the LEE in samarium isotopes is
roughly independent of the average initial energy over a wide range below the
neutron separation energy. As the neutron number increases, strength transfers
to a low-energy excitation, which we interpret as the scissors mode built on
top of excited states.
