We develop a fully first-principles approach for topological magnons within the framework of time-dependent density functional perturbation theory. Spin dynamics equations are accurately solved to obtain magnon energies and corresponding density fluctuations. We demonstrate that magnon wave function can be expressed by a collection of perturbed electronic wave functions obtained from the decomposition of density fluctuation, enabling direct calculation of magnonic quantities including Berry curvature and Chern number. As a concrete example, we show that monolayer ${\mathrm{CrI}}_3$ can host topological magnons driven by spin-orbit coupling. Our model-free approach paves the way for comprehensive studies of topological magnons in real materials.

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• First-principles calculations
• Magnons
• Spin dynamics
• Topological materials