Multiple Weyl fermions and topological phase transition in two-dimensional ferromagnetic CrS₂

The study of topological states in two-dimensional (2D) systems, especially with magnetic properties, has recently gained significant attention owing to their potential in spintronics and nanotechnology. Here, we propose a 2D ferromagnetic (FM) material, CrS₂, which hosts multiple Weyl points (WPs) and can undergo a topological phase transition by rotating the magnetization direction. Based on first-principles calculations, we identify distinct Weyl points around the Fermi level: W₁, W₂, and W₃. These points appear in both spin channels and include various types: type-I, type-II and type-III WPs. Corresponding Fermi arcs are clearly observed at the material edges. CrS₂ displays a FM ground state with the easy magnetization direction along the c-axis. When the magnetization direction is rotated in the x-y plane, the W₁ and W₃ points open gaps, with the gap values remaining the same in all magnetization directions. The W₂ can maintain a crossing at specific in-plane magnetization directions, indicating that the material retains its Weyl state. Additionally, we examine the effects of biaxial and uniaxial strains on electronic properties. Weyl points remain stable under biaxial strain of less than ±5%, but they disappear under uniaxial strain. In summary, our work proposes a 2D FM material with multiple coexisting Weyl fermions, where the topological states can be tuned by an external magnetic field.