Ferromagnetic hybrid nodal loop and switchable type-I and type-II Weyl fermions in two dimensions

As a novel type of fermionic state, the hybrid nodal loop with the coexistence of both type-I and type-II band crossings has attracted intense research interest. However, it remains a challenge to realize the hybrid nodal loop in both two-dimensional (2D) materials and in ferromagnetic (FM) materials. Here, we propose a FM hybrid nodal loop in a 2D CrN monolayer. We show that the material has a high Curie temperature (>600 K) FM ground state, with the out-of-plane [001] magnetization. It shows a half-metallic band structure with two bands in the spin-up channel crossing each other near the Fermi level. These bands produce both type-I and type-II band crossings, which form a fully spin-polarized hybrid nodal loop. We find the nodal loop is protected by the mirror symmetry and robust against spin-orbit coupling. An effective Hamiltonian characterizing the hybrid nodal loop is established. We further find the configuration of the nodal loop can be shifted under external perturbations such as strain. Most remarkably, we demonstrate that both type-I and type-II Weyl nodes can be realized from such FM hybrid nodal loop by simply shifting the magnetization from out of plane to in plane. Our work provides an excellent candidate to realize a FM hybrid nodal loop and Weyl fermions in 2D material, and is also promising for related topological applications with their intriguing properties.