Ferromagnetism with in-plane magnetization, Dirac spin-gapless semiconducting properties, and tunable topological states in two-dimensional rare-earth metal dinitrides

Since the successful synthesis of bulk single crystals ${\mathrm{MoN}}_{2}$ and ${\mathrm{ReN}}_{2}$, which have a layered structure, 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, $1\mathrm{T}\text{\ensuremath{-}}{\mathrm{RemN}}_{2}$. We use first-principles calculations, and find that these monolayers have a ferromagnetic ground state with in-plane magnetization. Without spin-orbit coupling (SOC), the band structures are spin-polarized with Dirac points at the Fermi level. Remarkably, the $1\mathrm{T}\text{\ensuremath{-}}{\mathrm{LuN}}_{2}$ monolayer exhibits an isotropic magnetocrystalline 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, we propose a model that accurately describes the variation of the SOC band gap and the two possible topological states (Weyl-like semimetal and Chern insulator states) whose properties are tunable. The Weyl-like semimetal state is a critical point between the two Chern insulator states with opposite sign of the Chern numbers (\ifmmode\pm\else\textpm\fi{}1). The nontrivial band gap (up to 60.3 meV) and the Weyl-like semimetal state are promising for applications in spintronic devices.