In the emerging field of two-dimensional (2D) intrinsic magnetic materials, the Dzyaloshinskii-Moriya interaction (DMI) has attracted wide attention for its crucial role in triggering exotic spin textures, provided that the Heisenberg exchange supplies the long-range magnetic order as a background. In this work, we predict that DMI alone can stabilize 2D long-range magnetism at finite temperatures. As a representative model, we propose a three-spin lattice considering only DMI, and analytically derive a twofold-degenerate long-range order, exhibiting both out-of-plane ferromagnetism and in-plane ${120}^{\circ }$ antiferromagnetism, which we term Dzyaloshinskii-Moriya magnetism (DMM). Using first-principles calculations combined with spin-wave spectrum calculations and Monte Carlo simulations, we predict that monolayer $\mathrm{Li}\text{−}{\left({\mathrm{IrI}}_3\right)}_2$ is a promising candidate for hosting such DMM, featuring a spin-wave excitation gap of 1.70 meV and a critical temperature of 2.61 K. Interestingly, the dynamics of chiral domain walls in the DMM are nearly frozen below $\sim 0.1$ K, which enables artificial imprinting of specific domain patterns. These findings expand the scope of 2D magnetism and open a unique avenue for DMI-based spintronics.

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• Dzyaloshinskii-Moriya interaction
• Magnetic domains
• Magnetism
• 2-dimensional systems
• Triangular lattice
• First-principles calculations
• Monte Carlo methods
• Spin lattice models