Collapse of N$=$28 magicity in exotic $^{40}$Mg -- Probe of deformed halo and 2n-radioactivity at Mg neutron drip-line

The exotic phenomenon of two-neutron halos and 2n-radioactivity are explored in the neutron-rich $^{40,42,44}$Mg by employing various variants of the relativistic mean-field approach. The extended tail of spatial density distributions including the enhanced neutron radii and skin thickness, pairing correlations, single-particle spectrum and wave functions predict $^{40,42,44}$Mg to be strong candidates for deformed neutron halos. Weakening of magicity at N$=$28 plays a significant role in the existence of a weakly bound halo in $^{40}$Mg which is currently the heaviest isotope of Mg accessible experimentally. Large deformation, mixing of f-p shell Nilsson orbitals and the valence neutron occupancy of p-states leads to a reduced centrifugal barrier and broader spatial density distributions that favour 2n-radioactivity in $^{42,44}$Mg.