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. The large nontrivial band gap (up to 60.3 meV) and the Weyl-like semimetal state are promising for applications in spintronic devices.
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