those of corresponding TM free standing state, the charge transfer between TM and GY can be qualitatively determined. The electron transfer from TM adatom to GY sheet ($T_e$) as listed in Tab.\[tab1\] indicates that there are considerable electron exchange from TM to GY sheet. Such electron exchange derives from the strong coupling between the *d* states and *p* states of the NN carbon, which is determined the magnetic states and magnetic moments of TM chain.\

![PDOS for V (a), Cr (c), Mn (d), Fe (e), and Co (f) under FM state and Cr (b) under AFM states. The solid (red) and dash (blue) lines represent the majority and minority spin channels, respectively. The Fermi level is set to zero.[]{data-label="fig4"}](Fig4.eps "fig:"){width="3.5in"}\

![Illustration of energy level of $d$ orbital for V (a), Cr (b), Mn (c), Fe (d), and Co (e) and their virtual hopping mechanism. In each picture, left panel: virtual hopping under FM state; Right panel: virtual hopping under AFM state. Blue and red lines represent spin-up and spin-down level, respectively. Solid(dashed) line indicate occupied(unoccupied) states[]{data-label="fig5"}](Fig5.eps "fig:"){width="3.5in"}\

             MAE\[x-z\](meV)   MAE\[y-z\](meV)   $m_s$($\mu_B$)   $m_o$(easy)($\mu_B$)   $m_o$(hard)($\mu_B$)   Easy axis($\theta$,$\phi$)   Hard axis($\theta$,$\phi$)
  --------- ----------------- ----------------- ---------------- ---------------------- ---------------------- ---------------------------- ----------------------------
      V           0.294             0.816             3.37               0.094                  0.047                     