focus on the magnetic anisotropy of TM chain on the surface of GY. Section IV gives a brief summary of this work.\

![image](Fig1.eps){width="4.5in"}

METHOD AND COMPUTATIONAL DETAILS
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The unit cells of GY with TM adatom dimer and chain adopted in present work are shown in Fig.\[fig1\]. A vacuum space of $13\AA$ perpendiculars to the GY plane is chosen to avoid the interactions between the neighboring images. The first-principles calculations are performed using the Vienna ab initio simulation package (VASP)[@35; @36] within spin-polarized DFT.[@37; @38] To account for the correlation energy of the strongly localized *3d* orbital of TM, Hubbard U correction (DFT+U)[@39] is employed based on the generalized gradient approximation of Perdew-Burke-Ernzerhof (PBE).[@40] We choose the projector augmented wave (PAW) potentials[@41; @42] to describe the electron-ionic core interaction. A plane-wave basis set with the kinetic energy cutoff of 400 eV is employed. The Brillouin zone (BZ) is sampled using 5$\times$3$\times$1 and 9$\times$5$\times$1 Gamma-centered Monkhorst-Pack grids for the calculations of relaxation and electronic structures, respectively. The criteria of energy and atom force convergence are set to $10^{-5}$ eV/unit cell and 0.01 eV/$\AA$, respectively. The dipole correction[@43] is considered to deal with the impact of variety of potential distribution introduced by 