▎ 摘　　要

One of the most important tasks in the development of high-performance spintronic devices is the preparation of two-dimensional (2D) magnetic layers with long-range exchange interactions. MN4 embedded graphene (MN4-G) layers, with M being transition metal elements, are experimentally accessible 2D layers which exhibit interesting magnetic properties. In this paper, by employing the spin-polarized density functional theory (SP-DFT), we study MN4-G layers with a special focus on the behavior of the indirect M-M exchange interactions and demonstrate that the MN4-G layers with M = Fe, Mn, and Co, are 2D anisotropic magnetic layers with Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction. By examining the electronic configurations of the M atoms for various M-M spacers, we demonstrate that the RKKY interaction in such layers are tunable and exhibit an unusual, prolonged decay (r(-n), with 0.5