Flat bands and magnetism in $\mathrm{\mathbf{Fe_4 Ge Te_2}}$ and $\mathrm{\mathbf{Fe_5GeTe_2}}$ due to bipartite crystal lattices

$\mathrm{Fe_{n=4,5}GeTe_2}$ exhibits quasi-two-dimensional properties as a promising candidate for a near-room-temperature ferromagnet, which has attracted great interest. In this work, we notice that the crystal lattice of $\mathrm{Fe_{n=4,5}GeTe_2}$ can be approximately regarded as being stacked by three bipartite crystal lattices. By combining the model Hamiltonians of bipartite crystal lattices and first-principles calculations, we investigate the electronic structure and the magnetism of $\mathrm{Fe_{n=4,5}GeTe_2}$. We conclude that flat bands near the Fermi level originate from the bipartite crystal lattices and that these flat bands are expected to lead to the itinerant ferromagnetism in $\mathrm{Fe_{n=4,5}GeTe_2}$. Interestingly, we also find that the magnetic moment of the Fe5 atom in $\mathrm{Fe_5 Ge Te_2}$ is distinct from the other Fe atoms and is sensitive to the Coulomb interaction $U$ and external pressure. These findings may be helpful to understand the exotic magnetic behavior of $\mathrm{Fe_{n=4,5} Ge Te_2}$.