Dipole response in deformed halo nuclei $^{42}\mathrm{Mg}$ and $^{44}\mathrm{Mg}$

The quasiparticle finite amplitude method based on the deformed relativistic Hartree-Bogoliubov theory in continuum has been developed for the noncharge-exchange multipole response. Taking neutron-rich magnesium isotopes as examples, the isovector electric dipole response, especially in the low-lying region, is studied. It is found that the low-energy dipole strength increases with neutron number and becomes notably enhanced in the predicted deformed halo nuclei $^{42}\mathrm{Mg}$ and $^{44}\mathrm{Mg}$. In these isotopes, the $K^\pi=1^-$ states below 3 MeV are dominated by transitions from the ``halo" part of the single-neutron orbitals. Their transition densities reveal a low-frequency, out-of-phase oscillation between the neutron halo and the core. These results provide a microscopic picture for the soft dipole resonance in $^{42}\mathrm{Mg}$ and $^{44}\mathrm{Mg}$.