TM adsorption. All calculation parameters in present work are systematically optimized. As for the calculations within DFT+U, the rotationally invariant DFT+U formalism proposed by Dudarev et al.[@44] is used, where only $U_{eff} =U-J$ value is meaningful instead of individual U and J values. We assign the value $U_{eff}$=4.84eV, 3.55eV, 5.01eV, 5.03eV and 6.31eV for V, Cr, Mn, Fe and Co adatom based on our earlier calculations[@19] with linear response method[@45]. The appropriateness of the uniform $U_{eff}$ value for single TM, TM dimer and TM chain is due to the localization of coupling effect of TM adatoms in TM dimer and TM chain, which will be discussed below. For the magnetic anisotropy calculations, the spin-orbit coupling (SOC) is included self-consistently. The MAE is calculated from the ground state energies for magnetization aligned in the most relevant directions. The total energies are converged to a precision of $10^{-7}$ eV.\
To evaluate the stability of adsorption configuration, adsorption energy per TM atom E$_a$ is adopted which is defined as, $$E_{a}=\frac{1}{n}[({E_{GY}+nE_{TM})-E_{TM+GY}}]$$ where $E_{TM+GY}$ denotes spin-polarized total energy of TM adsorbed GY sheet, $E_{GY}$ is the total energy of isolated pure GY sheet, and $E_{TM}$ is the spin-polarized total energy of corresponding free TM atom.\
