Single-and few-layer chromium triiodide (CrI3), which has been intensively investigated as a promising platform for two-dimensional magnetism, was usually prepared by mechanical exfoliation. Here, we report on the growth of single-layer CrI3 by molecular beam epitaxy under ultrahigh vacuum. The atomic structures and local density of states have been revealed by scanning tunneling microscopy (STM). Iodine trimers, each of which consists of three I atoms surrounding a three-fold Cr honeycomb center, have been identified as the basic units of the topmost I layer. Different superstructures of single-layer CrI3 with characteristic periodicity around 2-4 nm were obtained on Au(111), but only pristine structure was observed on graphite.At elevated temperatures (423 K), CrI3 was partially decomposed, resulting in the formation of single-layer chromium diiodide. Our bias-dependent STM images suggest that the unoccupied and occupied states are distributed spatial-separately, which is consistent with our density functional theory calculations. The effect of charge distribution on the superexchange interaction in single-layer CrI3 was discussed.Keywords: two-dimensional magnetic materials, CrI3, molecular beam epitaxy, scanning tunneling microscopy 2 / 18 Two-dimensional (2D) magnetic materials, which serve as ideal platforms for investigating spin-related emergent phenomena at reduced dimensions and exhibit potential applications in optoelectronics and spintronics, 1,2 have long been sought. However, as revealed by Mermin-Wagner theorem, long-range magnetic order in 2D systems with isotropic local magnetic interactions are thermodynamically instable at finite temperatures owing to enhanced thermal fluctuations. 3 By introducing magnetic anisotropy, on the other hand, 2D magnetism may exist in a number of layered van der Waals (vdW) materials, for example, transition metal chacogenides and halides. 4-6 Among them, single-and bi-layer chromium triiodide (CrI3) has been recently confirmed with intralayer ferromagnetism (FM) and interlayer antiferromagnetism (AFM). 7,8 The FM coupling in single-layer CrI3, which exhibits a Curie temperature of 45 K, slightly lower than that of the bulk counterpart (61 K), is mainly ascribed to the superexchange interaction between the neighboring Cr atoms mediated by the bridging I atoms. 9 The easy magnetization direction is out of plane with an anisotropy energy about 0.50-0.69 meV/Cr, according to density functional theory (DFT) calculations. 10,11 The magnetic tunneling junction consisting of four-layer CrI3 sandwiched with two graphene layers as the electrodes performs a magnetoresistance change as large as 19,000%, 12 demonstrating the advantages of layered vdW materials for fabricating advanced spintronic devices. [12][13][14][15] Besides CrI3, other layered materials, such as Cr2Ge2Te6, CrCl3, CrBr3, Fe3GeTe2 and FePS3, have been already obtained and verified with long-range magnetic order. [16][17][18][19][20][21] So far, mechanical exfoliation is the major method for preparing 2D magn...