Ferrimagnetism in 2D networks of porphyrin-X and -XO (X=Sc,...,Zn) with acetylene bridges

Magnetism in 2D networks of the acetylene-bridged transition metal porphyrins M(P)-2(C-C)-2 (denoted P-TM), and oxo-TM-porphyrins OM(P)-2(C-C)-2 (denoted P-TMO), is studied with the density functional theory (DFT) and the self-interaction corrected pseudopotential scheme (pSIC). Addition of oxygen lowers magnetism of P-TMO with respect to the corresponding P-TM for most of the first-half $3d$-row TMs. In contrast, binding O with the second-half $3d$-row TMs or Sc increases the magnetic moments. Ferrimagnetism is found for the porphyrin networks with the TMs from V to Co and also for these cases with oxygen. This is a long-range effect of the delocalized spin-polarization, extended even to the acetylene bridges.