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$\mathrm{Fe_{n=4,5}GeTe_2}$ exhibits quasi-two-dimensional properties as apromising candidate for a near-room-temperature ferromagnet, which hasattracted 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 bythree bipartite crystal lattices. By combining the model Hamiltonians ofbipartite crystal lattices and first-principles calculations, we investigatethe electronic structure and the magnetism of $\mathrm{Fe_{n=4,5}GeTe_2}$. Weconclude that flat bands near the Fermi level originate from the bipartitecrystal lattices and that these flat bands are expected to lead to theitinerant ferromagnetism in $\mathrm{Fe_{n=4,5}GeTe_2}$. Interestingly, we alsofind that the magnetic moment of the Fe5 atom in $\mathrm{Fe_5 Ge Te_2}$ isdistinct from the other Fe atoms and is sensitive to the Coulomb interaction$U$ and external pressure. These findings may be helpful to understand theexotic magnetic behavior of $\mathrm{Fe_{n=4,5} Ge Te_2}$.

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