  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.
