  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.
