As the bulk single-crystal MoN2/ReN2 with a layered structure was successfully synthesized in experiment, transition-metal dinitrides have attracted considerable attention in recent years. Here, we focus on rare-earth-metal (Rem) elements and propose seven stable Rem dinitride monolayers with a 1T structure, namely 1T-RemN2. These monolayers have a ferromagnetic ground state with in-plane magnetization. Without spin-orbit coupling (SOC) effect, the band structures are spin-polarized with Dirac points at the Fermi level. Remarkably, the 1T-LuN2 monolayer shows an isotropic magnetic anisotropy energy in the xy-plane with in-plane magnetization, indicating easy tunability of the magnetization direction. When rotating the magnetization vector in the xy-plane, our proposed model can accurately describe the variety of the SOC band gap and two topological states (Weyl-like semimetal and Chern insulator states) appear with tunable properties. The Weyl-like semimetal state is a critical point between the two Chern insulator states with opposite sign of the Chern numbers (±1). The large nontrivial band gap (up to 60.3 meV) and the Weyl-like semimetal state are promising for applications in spintronic devices.

Two-dimensional (2D) transition metal trihalide (TMX3, X = Cl, Br, I) family has attracted considerable attention in recent years due to the realizations of CrCl3, CrBr3, and CrI3 monolayers. Up to now the main focus of the theoretically predicted TMX3 monolayers has been on the Chern insulator states, which can realize the quantum anomalous Hall effect. Here, using first-principles calculations, we theoretically demonstrate that the stable OsCl3 monolayer has a ferromagnetic ground state and a spinpolarized Dirac point without spin-orbit coupling (SOC), which disappears in the band structure of Janus OsBr1.5Cl1.5 monolayer. We find that OsCl3 exhibits in-plane magnetization when SOC is included. By manipulating the magnetization direction along the C2 symmetry axis of the OsCl3 structure, a gapless half-Dirac semimetal state with SOC can be achieved, which is different from the gapped Chern insulator state.Both semimetal states of OsCl3 monolayer without and with SOC exhibit a linear half-Dirac point (twofold degenerate) with high Fermi velocities. The achievement of the 2D semimetal state with SOC is expected to be found in other TMX3 monolayers, and we confirm it in TiCl3 monolayer. This provides a different perspective to study the band structure with SOC of the 2D TMX3 family.