Phonon Softening due to Melting of the Ferromagnetic Order in Elemental Iron

We study the fundamental question of the lattice dynamics of a metallic ferromagnet in the regime where the static long-range magnetic order is replaced by the fluctuating local moments embedded in a metallic host. We use the ab initio density functional theory + embedded dynamical mean-field theory functional approach to address the dynamic stability of iron polymorphs and the phonon softening with an increased temperature. We show that the nonharmonic and inhomogeneous phonon softening measured in iron is a result of the melting of the long-range ferromagnetic order and is unrelated to the first-order structural transition from the bcc to the fcc phase, as is usually assumed. We predict that the bcc structure is dynamically stable at all temperatures at normal pressure and is thermodynamically unstable only between the bcc-α and the bcc-δ phases of iron.