show easy-axis anisotropy. However, the interaction between $|m_l|$=2 of HOMO and $|m_l|$=1 of LUMO by the ladder operator $\hat{L}_+$ is favorable for easy-plane anisotropy. The easy-axis anisotropy for Fe-chain-GY is derived from the competition effect between the operator $\hat{L}_+$ and $\hat{L}_z$ . From the $|m_l|$-resolved PDOS (Fig.\[fig7\](f)) of Co-chain-GY system one can see that the HOMO and LUMO are mainly contributed by $|m_l|$=2 and $|m_l|$=1 states. These states interact through the ladder operator $\hat{L}_+$ and $\hat{L}_z$. The energy-lowering associated with $\hat{H}_{SO}^{sc}$ approaches maximum when the $\theta$=90$^\circ$, i.e., the magnetization direction for Co-chain-GY is parallel to plane, indicating easy-plane anisotropy.\

Conclusion
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In summary, we have performed DFT+U calculations on the magnetic exchange coupling and anisotropy of a quasi 1D 3d-TM zigzag nanowire adsorbed on GY sheet. TM intra-chain magnetic coupling mediated by *sp* hybridized carbon atoms gives rise to robust long range ferromagnetic order except for Cr with anti-ferromagnetic order. The magnetic exchange interaction between TM adatom follows like-Zener’s $p_z$-d exchange mechanism due to the coexistence of out-of plane $p_z$-d and in-plane $p_{xy}$-d exchange. We find that the Fe and Co chains show considerable magnetic anisotropy energy (MAE) and orbital magnetic moment. V, Cr, Mn and Fe chains show easy-axis 