Title: Exploring the suitable theoretical approach for understanding the electronic and magnetic properties of $α$-Iron

Abstract: We present a comparative electronic structure study using DFT and various beyond-DFT (DFT+$U$, $G_0W_0$, DFT+DMFT) methods for ferromagnetic Iron (Fe) to find better approach for describing the spectral properties of correlated magnetic system. The computed value of $U$ ($W$) is $\sim$5.4 ($\sim$0.8) eV. The calculated spectra of all methods are providing good agreement with experimental spectra (ES) for peaks' positions. But, the proper line shape is only found from DFT+DMFT with correct estimation of incoherent states, which depends on $J$ and form of local Coulomb interactions. The estimation of reduced magnetization as function of reduced temperature using DFT+DMFT shows good agreement with the experimental data. The insight of paramagnetic electronic structure of Fe is also explored. This work suggests that even for simple correlated magnetic metal, we need DFT+DMFT method to reproduce the ES with great accuracy.