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For next-generation nanospintronic devices,it is highly desired to search new two-dimensional(2D) half-metallic materials.Recently,a new family of atomically thin 2D materials,transition-metal(TM)dinitrides which exhibit ferromagnetic metallicity or half-metallicity,has been proposed based on the synthesis of layered 3R-MoN2 with rhombohedral MoS2 structure.However,our first-principles calculations of dynamical and thermodynamic properties suggest that the proposed monolayer of 3R-TMN2 structure is unstable.Inspired by the structural phase diversities of transition-metal dichalcogenides(TMDs),we consider the octahedral coordinated phase(marked as T-TMN2)and find that the T-TaN2 monolayer is not only dynamically stable,but also possesses thermodynamic stability at room temperature.Although the magnetic ground state of T-TaN2 is nonmagnetism,both biaxial and uniaxial tensile strain(larger than 1%)can induce magnetic moment due to the competitive effect between through-bond and through-space interactions.Remarkably,when the biaxial tensile strain increases to 10%,the T-TaN2 monolayer becomes a fully spin-polarized half-metallicity.In contrast to the magnetic moments in TMDs,the magnetic moments in T-TaN2 are mainly originated from non-metal N atoms.Therefore,it will surmount the problem of short spin relaxation time caused by large spin coupling of TM atoms.The results obtained in this work highlight a new promising strain-controllable magnetic 2D material for nanospintronics application.