Flat bands and magnetism in Fe4GeTe2 and Fe5GeTe2 due to bipartite crystal lattices

${\mathrm{Fe}}_{n=4,5}{\mathrm{GeTe}}_{2}$ 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 ${\mathrm{Fe}}_{n=4,5}{\mathrm{GeTe}}_{2}$ 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 ${\mathrm{Fe}}_{n=4,5}{\mathrm{GeTe}}_{2}$. 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 ${\mathrm{Fe}}_{n=4,5}{\mathrm{GeTe}}_{2}$. Interestingly, we also find that the magnetic moment of the Fe5 atom in ${\mathrm{Fe}}_{5}{\mathrm{GeTe}}_{2}$ 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 ${\mathrm{Fe}}_{n=4,5}{\mathrm{GeTe}}_{2}$.