  The remarkable and fascinating properties of two-dimensional materials have
raised them to the rank of most promising candidates for technological
applications. In particular, the possibility of long-range ferromagnetic order
in 2D materials is generating a growing excitement. Here, we demonstrate that
flat bands (FBs) may pave the way to room temperature ferromagnetism in 2D
compounds. Indeed, the magnetic exchanges between localized spins are largely
dominated by the FB-FB contribution. This contribution is ferromagnetic and
scales linearly with the local coupling, thus leading to cross-over
temperatures (ferromagnetic phase/ paramagnetic phase) higher by an order of
magnitude than those currently reported in experiments. Cross-over temperatures
as high as $600~ K$ could be reached in micrometer-sized FB systems.
