  By coupling a first-principles, spin-density functional calculation with an
exact diagonalization study of the Hubbard model, we have searched over various
functional groups for the best case for the flat-band ferromagnetism proposed
by R. Arita et al. [Phys. Rev. Lett. {\bf 88}, 127202 (2002)] in organic
polymers of five-membered rings. The original proposal (poly-aminotriazole) has
turned out to be the best case among the materials examined, where the reason
why this is so is identified here. We have also found that the ferromagnetism,
originally proposed for the half-filled flat band, is stable even when the band
filling is varied away from the half-filling. All these make the ferromagnetism
proposed here more experimentally inviting.
