is shifted to lower energy. As shown in Fig.\[fig2\], bands around the Fermi level mainly derived from the $p_z$ state of the NN carbon atom, where the $p_z$ split to majority and minority band; and the majority bands shift higher energy, whereas the minority bands shift lower energy due to the effective *pd* hybridization. The magnetic exchange coupling in such system follows the like-Zener’s $p_z$-d exchange mechanism[@49; @50] as that presents in diluted magnetic semiconductor[@51]. However, because of the *d* states couples with not only the out-plane $p_z$ but also the in-plane $p_{x-y}$, the *pd* hybridization shows the coexistence of out-of plane $p_z$-d and in-plane $p_{x-y}$-d exchange. The results in Fig\[fig4\] clearly show that the $p_{x-y}$ states from *sp* and $d$ states of TM overlap each other below the Fermi level indicating the key role of $p_{x-y}$ states in the *pd* hybridization process. Similar coupling mechanism can be find in the V-, Cr-, Mn- and Co-chain-GY systems. To analyze the magnetic coupling behaviour of TM-chain-GY, based on the results of PDOS, we illustrate the energy level of $d$ orbitals of neighboring TM atoms under both FM and AFM states as shown in Fig.\[fig5\]. For example, the PDOS of V-chain-GY as 