We predict a new family of two-dimensional (2D) material MXY3 monolayers (M=V, Mo, W; X=Al, Ga, In; Y=S, Se, Te), and we perform a comprehensive investigation into their structural, electronic, and magnetic properties. First-principles calculations confirm the dynamical and thermodynamic stability of 21 materials among this family, underscoring their feasibility for experimental realization. The rich tapestry of magnetic phenomena presented in the MXY3 family ranges from ferromagnetism to various forms of antiferromagnetism, including the intriguing noncollinear states. We provide a detailed explanation for the origins of the various magnetic ground states. Specifically, V-based materials are ferromagnets with in-plane magnetocrystalline anisotropy, whereas Mo-based materials show a robust out-of-plane anisotropy ferromagnetic state. Most W-based materials display stripelike antiferromagnetism with significant orbital magnetic moments (∼0.2µB) and strong in-plane magnetic anisotropy, and they exhibit substantial electronic structure variations depending on the spin orientation. These antiferromagnetic W-based compounds are characterized by high critical temperatures, reaching up to 506 K for WAlS3. Interestingly, a significant anomalous Hall conductivity is identified in nonlinear antiferromagnetic FeAlS3 and FeGaS3, which is absent in conventional linear counterparts. This study suggests the great potential of MXY3 monolayers serving as a versatile platform for exploring fundamental physics and searching for new 2D magnetic materials. locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon Physics Subject Headings (PhySH)First-principles calculationsMagnetic anisotropyMagnetic couplingMagnetic interactionsMagnetic order2-dimensional systemsDensity functional theory