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Magnetic Exchange Coupling and Anisotropy of 3d Transition-Metal Nanowire on the Surface of Graphyne Sheet

Using density functional theory plus Hubbard-U (DFT+U) approach, we find that quasi one-dementation(1D) 3d transition metal(TM) zigzag nanowire can be constructed by TM adsorbed on the surface of graphyne sheet. The results show that the TM exchange coupling of the zigzag nanowire mediated by sp hybridized carbon atoms gives rise to long range ferromagnetic order except for Cr with anti-ferromagnetic order. The magnetic exchange interaction of TM chains follows like-Zener's p_z-d exchange mechanism: the coexistence of out-of plane p_z-d and in-plane p_x-y-d exchange. Finally, by including spin-orbit interactions within spin-DFT, we calculate the magnetic anisotropy energy of the TM chain on graphyne. We find that the Fe and Co chains show considerable magnetic anisotropy energy (MAE) and orbital magnetic moment. The easy axis of V, Cr, Mn and Fe chains is perpendicular to the surface, whereas the easy axis of Co lies in the surface. Moreover, only V chain shows relatively larger in-plane anisotropy. Our results open a new route to realize the applications of graphyne in spintronics.