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We present a comparative electronic structure study using DFT and variousbeyond-DFT (DFT+$U$, $G_0W_0$, DFT+DMFT) methods for ferromagnetic Iron (Fe) tofind better approach for describing the spectral properties of correlatedmagnetic 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 withexperimental spectra (ES) for peaks' positions. But, the proper line shape isonly found from DFT+DMFT with correct estimation of incoherent states, whichdepends on $J$ and form of local Coulomb interactions. The estimation ofreduced magnetization as function of reduced temperature using DFT+DMFT showsgood agreement with the experimental data. The insight of paramagneticelectronic structure of Fe is also explored. This work suggests that even forsimple correlated magnetic metal, we need DFT+DMFT method to reproduce the ESwith great accuracy.

Exploring the suitable theoretical approach for understanding the electronic and magnetic properties of $\alpha$-Iron