Ferromagnetic two-dimensional metal-chlorides MCl (M = Sc, Y, and La): Candidates for Weyl nodal line semimetals with small spin-orbit coupling gaps

Abstract

Currently, topological nodal line semimetals in two-dimensional (2D) materials, especially in ferromagnetic 2D materials, are still in urgent scarcity. Here, we report that 2D metal-chlorides MCl (M = Sc, Y, and La) are a family of such candidate materials. The 2D MCl are dynamic stable and show strong ferromagnetic ordering. They all possess a closed nodal line centering the Γ point in the 2D Brillouin zone. The nodal lines are quite close to the Fermi level with the linear energy range as large as 0.3 eV. Remarkably, the nodal lines identified here are time-reversal-breaking Weyl nodal lines, which are different from those reported previously in nonmagnetic 2D materials. Even more interestingly, we find the nodal lines in MCl monolayers can show both type-I (in LaCl and YCl) and type-II (in ScCl) band dispersions. These nodal lines open small gaps (<10 meV) under spin-orbit coupling (SOC), however, these gaps are much smaller than those in typical nodal line materials. Besides the nodal lines, ScCl and YCl also host three pairs of Weyl points in the Γ-K (K′) path. Our results indicate that these MCl materials are excellent candidates to investigate the novel properties of Weyl nodal lines and Weyl points with both type-I and type-II band dispersions in ferromagnetic 2D systems.