  We predict the magnetic and electronic properties of a novel metal-organic
framework. By combining density functional theory and density matrix
renormalization group approaches, we find the diatomic Kagome crystal structure
of the metal-semiquinoid framework (H$_2$NMe$_2$)$_2$M$_2$(Cl$_2$dhbq)$_3$ (M =
Ti, V, Cr, Mn, Fe, Co, Ni, Cu, and Zn) to host a rich variety of
antiferromagnetic (AFM) and ferromagnetic (FM) Dirac semimetallic,
spin-polarized Dirac fermions, and flat band magnetic insulators and metallic
phases. Concomitantly, the spin excitation spectrum of the various magnetic
systems display multiple Dirac-like and nodal-ring crossings. This suggests
that the metal-semiquinoid system is an ideal platform for examining the
intertwining of Dirac fermions and magnons.
