chain on GY show antiferromagnetic coupling with zero net magnetic moment and its exchange energy is -42meV. The above results indicate that the TM chain on the surface of GY have robust FM and AFM order. To clearly show the magnetic coupling, we calculate the SCD and the results of typical ferromagnetic Fe-chain-GY and antiferromagnetic Cr-chain-GY are shown in Fig.\[fig3\]. The results show that the magnetic moment of TM-chain-GY is mainly contributed by the TM adatom. Moreover, the SCD results indicate that the spin polarized charge density mainly localizes within the region of TM chain suggesting the coupling between neighbor chains is weak, which is crucial for achievement of a perfect spin-polarized current with TM chain in practical spintronic applications.\

![Band structures of V-chain-GY (a), Cr-chain-GY (c), Mn-chain-GY (d) Fe -chain-GY(e), Co-chain-GY(f) under FM magnetic state, and Cr-chain-GY(b) under FM magnetic state, respectively. The solid (red) and dashed (blue) lines represent the majority and minority spin channels, respectively. The Fermi level is set to zero.[]{data-label="fig2"}](Fig2.eps "fig:"){width="3.5in"}\

![Spin-polarized charge density (SCD) distribution for Cr-chain-GY (a) and Fe-chain-GY (b). The dark (red) and light (green) isosurfaces denote the spin-up and spin-down charge density, respectively. The isosurface of SCD is 0.004 e$/\AA^3$.[]{data-label="fig3"}](Fig3.eps "fig:"){width="3.5in"}\

