  We computationally demonstrate Stoner-ferromagnetic half-metals and
antiferromagnetic Mott-Hubbard insulators in metal-free 2D polymers. Coupling
radicaloid (hetero)triangulene monomers via strong covalent bonds preserving
the in-plane conjugation of the electronic {\pi} system yields 2D crystals with
long-range magnetic order and magnetic couplings above the Landauer limit.
Dual-site honeycomb lattices produce both flat bands and Dirac cones. Depending
on the monomers, electron correlations lead to either a bandgap at the Dirac
points for antiferromagnetic Mott insulators, or Stoner ferromagnetism with
both spin-polarized Dirac cones and flat bands at the Fermi level. These
results pioneer a new type of Stoner and Mott-Hubbard magnetism emerging in the
electronic pi system of crystalline conjugated 2D polymers.
