Magnetism and magnetocrystalline anisotropy in single-layer PtSe₂: Interplay between strain and vacancy

The exploration of the magnetism is a hot topic in the field of 2D materials research because most of the well known 2D materials such as graphene, h-BN, single-layer (1L) transition-metal dichalcogenide (TMD) are intrinsically nonmagnetic. In our recent work, using the first-principles calculations, we systematically studied the magnetic and electronic properties of the newly synthesized 1L-TMD PtSe₂. We found the selenium vacancy (V_Se) or strain alone could not induce the magnetism. However, an interplay between V_Se and strain led to the magnetism due to the breaking of Pt-Pt metallic bonds. Different from the case of 1L-MoS₂ with V_S, the defective 1L-PtSe₂ had the spatially extended spin density, which was responsible for the obtained long range ferromagnetic coupling. Moreover, the 1L-PtSe₂ with V_Se underwent a spin reorientation transition from out-of-plane to in-plane magnetization, accompanying a maximum magnetocrystalline anisotropy energy of 9～10.6 meV/V_Se. Our work show that the strain not only can effectively tune the magnetism but also can manipulate the magnetization direction of 1L-TMDs.