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

Metal-free Stoner and Mott-Hubbard magnetism in 2D polymers with honeycomb lattice