Exploring the coexistence of multiple quantum states in two-dimensional materials is a major goal in condensed matter physics. In this study, we theoretically predicted that the quasilayered hexagonal ${\mathrm{V}}_2{\mathrm{N}}_2$ (h-${\mathrm{V}}_2{\mathrm{N}}_2$) monolayer simultaneously hosts metal-insulator antiferromagnetic (AFM) Mott phase transition, higher-order topological insulator (HOTI) state, and tunable in-plane valley polarization (VP) effect. The synergistic effects of temperature modulation of Hubbard parameter ($U$) and force field modulation of hopping integral ($t$) can drive a phase transition from nonmagnetic Dirac metal to AFM Mott insulator, concurrently accompanied by a topological phase transition, which is topologically protected by corner states with a quantized fractional charge in both spin channels. An out-of-plane electric field can break $\mathit{PT}$ symmetry, driving the system into an electric potential difference antiferromagnet with spin-layer-polarized topological corner states. Furthermore, the system exhibits odd-even layer-dependent magnetism with ferromagnetic (FM) and AFM states, enabling effective magnetic control and preserving structural stability until the bulk material (AFM) is reached, providing feasibility for experimental synthesis. Remarkable, different from the conventional FM VP effect with out-of-plane magnetization, we introduce the AFM VP effect with in-plane magnetization in h-${\mathrm{V}}_2{\mathrm{N}}_2$ monolayer to further realize the spin-valley Hall effect, which is governed by $C_2$ symmetry breaking, and can be accurately described by our theoretical model (up to 15.5 meV), providing new ideas for exploring the future valleytronic applications.

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• Electronic structure
• Magnetism
• Valley degrees of freedom
• 2-dimensional systems
• Mott insulators
• Topological materials
• Density functional theory
• First-principles calculations
• Hubbard model