Chromium trihalides ($\mathrm{Cr}{X}_3$, with $X=\mathrm{I},\mathrm{Br},\mathrm{Cl}$) are layered ferromagnetic materials with rich physics and possible applications. Their structure consists of magnetic Cr atoms sandwiched between two layers of halide atoms. Different halide atoms result in distinct magnetic properties, but their effect on spin-wave (magnon) excitations is not fully understood. Here we show first-principles calculations of magnon dispersions and wave functions in monolayer Cr trihalides using the finite-momentum Bethe-Salpeter equation (BSE) to describe collective spin-flip excitations. We study the dependence of magnon dispersions on the halide species and resolve the small topological gap at the Dirac point in the magnon spectrum by including spin-orbit coupling. Analysis of magnon wave functions reveals that magnons are made up of electronic transitions with a wider energy range than excitons in $\mathrm{Cr}{X}_3$ monolayers, providing insight into magnon states in real and reciprocal space. We analyze Heisenberg exchange parameters extracted from the BSE and discuss the convergence of BSE magnon calculations. Our work advances the quantitative modeling of magnons, providing the starting point for studying magnon interactions in a first-principles BSE framework.

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• Magnons
• Spin waves
• Spin-orbit coupling
• Magnetic insulators
• van der Waals systems
• Bethe-Salpeter equation
• Density functional theory
• GW method