Title: The phonon softening due to melting of the ferromagnetic order in elemental iron,
Abstract: 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 \textit{ab initio} Density Functional Theory(DFT)+embedded Dynamical
Mean-Field Theory(eDMFT) functional approach to address the dynamic stability
of iron polymorphs and the phonon softening with increased temperature. We show
that the non-harmonic 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 only thermodynamically unstable between
the BCC-$\alpha$ and the BCC-$\delta$ phase of iron.