  We studied the mechanism of half-metallicity (HM) formation in transition
metal doped (TM) conjugated carbon based structures by first-principles
electronic structure simulations. It is found that the HM is a rather complex
phenomenon, determined by the ligand field splitting of d-orbitals of the
transition metal (TM) atoms, the exchange splitting and the number of valence
electrons. Since most of the conjugated carbon based structures possess ligands
with intermediate strength, the ordering of the d-orbital splitting is similar
in all structures, and the HM properties evolve according to the number of
valence electrons. Based on this insight we predict that Cr-, Fe-, Co-doped
graphyne will show HM, while Mn- and Ni-doped graphyne will not. By tuning the
number of valence electron, we are thus able to control the emergence of HM and
control the energy gaps evolving in majority or minority spin channels.
