Nonlocal correlations in the vicinity of the $\alpha$-$\gamma$ phase transition in iron within a DMFT plus spin-fermion model approach

We consider nonlocal correlations in iron in the vicinity of the $\alpha$-$\gamma$ phase transition within the spin-rotationally-invariant dynamical mean-field theory (DMFT) approach, combined with the recently proposed spin-fermion model of iron. The obtained nonlocal corrections to DMFT yield a decrease of the Curie temperature of the $\alpha$ phase, leading to an agreement with its experimental value. We show that the corresponding nonlocal corrections to the energy of the $\alpha$ phase are crucially important to obtain the proximity of energies of $\alpha$ and $\gamma$ phases in the vicinity of the iron $\alpha$-$\gamma$ transformation.