<![CDATA[First-principles calculations are increasingly crucial in searching for new materials with customized properties or new functionality. First-principles calculations are superior in speed and cost, and comparable to experiments in terms of accuracy. Two-dimensional (2D) ferromagnetism materials were successfully fabricated experimentally in atomic thin films of CrI3. 2D intrinsic ferromagnetism with perpendicular magnetic anisotropy energy (PMAE) is an encouraging applicant compatible with high-density magnetic storage applications. In this study, spin density functional calculations are investigated on the magnetic anisotropy energy (MAE) in 2D monolayer ferromagnetic CrI3 using a first-principles electronic structure calculation. We include the MAE part calculation from the magnetocrystalline anisotropy energy (MCAE) that comes from the spin-orbit coupling (SOC). In the present calculation, the MCAE part, in addition to a usual scheme of total energy (TE), was evaluated using a grand-canonical force theorem (GCFT) scheme. The MCAE of 2D monolayer ferromagnetic CrI3 is 1.7 meV/unit cell and verified it has an easy-axis perpendicular to the crystal plane, which is a good agreement with experimental measurement. In the latter scheme, employing GCFT, we evaluated atom-resolved, k-resolved, and atomic k-resolved analyses for MCAE can be performed. From the GCFT result, the Cr atom indicates that it is the primary origin of PMAE in the atom-resolved MCAE. The negative MCAE contribution is in points, and the positive MCAE is mainly placed at the line in the 2D first Brillouin zone. Our systematic calculation in this work may also help design an effective structure of monolayer CrI3 in new 2D material magnetic sensor and spintronic device designs.]]>
