The stability of lattice dynamics and the magnetism of the ordered γ′-Fe4N crystalline alloy at high pressures were studied by first-principle calculations based on density-functional theory. The dynamical stable new phase P2/m-Fe4N at high pressures was found by conducting the softening phenomenon at the point M (0.5 0.5 0) of the acoustic phonon at 10 GPa in the γ′-Fe4N via soft-mode phase transition theory. Compared to the phonon spectrum of γ′-Fe4N without considering electronic spin polarization, the ground-state lattice dynamical stability of the ferromagnetic phase γ′-Fe4N is induced by the spontaneous magnetization at pressures below 1 GPa. However, P2/m-Fe4N is more thermodynamically stable than γ′-phase at pressures below 1 GPa, and the magnetic moments of the two phases are almost the same. The ground-state structure of P2/m phase is more stable than that of γ′-phase in the pressure range from 2.9 to 19 GPa. The magnetic moments of the two phases are almost the same in the pressure range from 20 to 214 GPa, but the ground-state structure of γ′-phase is more stable than that of P2/m phase in the pressure range from 143.8 to 214 GPa. On the contrary, the ground-state structure of P2/m phase is more stable when the pressure is above 214 GPa. In the pressure range from 214 to 300 GPa, the magnetic moment of P2/m phase is lower than that of γ′-phase, and the magnetic moments of the two phase tend to be consistent when the pressure exceeds 300 GPa.
