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We study the fundamental question of the lattice dynamics of a metallicferromagnet in the regime where the static long range magnetic order isreplaced by the fluctuating local moments embedded in a metallic host. We usethe \textit{ab initio} Density Functional Theory(DFT)+embedded DynamicalMean-Field Theory(eDMFT) functional approach to address the dynamic stabilityof iron polymorphs and the phonon softening with increased temperature. We showthat the non-harmonic and inhomogeneous phonon softening measured in iron is aresult of the melting of the long range ferromagnetic order, and is unrelatedto the first order structural transition from the BCC to the FCC phase, as isusually assumed. We predict that the BCC structure is dynamically stable at alltemperatures at normal pressure, and is only thermodynamically unstable betweenthe BCC-$\alpha$ and the BCC-$\delta$ phase of iron.

The phonon softening due to melting of the ferromagnetic order in elemental iron