According to the Lieb's theorem the ferromagnetic interaction in
graphene-based materials with bipartite lattice is a result of disbalance
between the number of sites available for pzβ electrons in different
sublattices. Here, we report on another mechanism of the ferromagnetism in
functionalized graphene that is the direct exchange interaction between spin
orbitals. By the example of the single-side semihydrogenated (C2βH) and
semifluorinated (C2βF) graphene we show that such a coupling can partially or
even fully compensate antiferromagnetic character of indirect exchange
interactions reported earlier [Phys. Rev. B {\bf 88}, 081405(R) (2013)]. As a
result, C2βH is found to be a two-dimensional material with the isotropic
ferromagnetic interaction and negligibly small magnetic anisotropy, which
prevents the formation of the long-range magnetic order at finite temperature
in accordance with the Mermin-Wagner theorem. This gives a rare example of a
system where direct exchange interactions play a crucial role in determining a
magnetic structure. In turn, C2βF is found to be at the threshold of the
antiferromagnetic-ferromagnetic instability, which in combination with the
Dzyaloshinskii-Moriya interaction can lead to a skyrmion state.Comment: 10 page