Stable room-temperature ferromagnetism and gate-tunable quantum anomalous Hall effect of two-dimensional 5d transition-metal trihalide OsX ₃ (X = Cl, Br, I) monolayers

5d transition-metal compounds are usually not expected to exhibit distinct magnetic ordering owing to their substantial binding energy associated with 5d electrons. In this study, we demonstrate that two-dimensional (2D) 5d transition-metal Os trihalide OsX₃ monolayers can exhibit room-temperature ferromagnetism and quantum anomalous Hall effect (QAHE) by utilizing density functional theory and Monte Carlo simulation. Our calculation results of coexisting Raman and infrared activities of lattice vibration reveal the structural stability of 2D OsX₃ (X = Cl, Br, I) and structural instability of 2D OsX₃ (X = F). Furthermore, all 2D OsX₃ trihalides (X = Cl, Br, I) are half-metals, and their ferromagnetism remains stable under ambient temperature, where 2D OsCl₃ and OsBr₃ have an in-plane easy axis while 2D OsI₃ has an out-of-plane easy axis. Notably, when spin-orbit coupling is included, the gate-tunable QAHE could emerge in ferromagnetic 2D OsI₃, while 2D OsCl₃ and OsBr₃ are topologically trivial. Additionally, the magnon bands of 2D OsX₃ (X = Cl, Br, I) possess two spin-wave branches with dispersion similar to that of the Dirac cone in the electronic structure of graphene, which are attributed to the unique ferromagnetic honeycomb sublattice of osmium atoms.