Anisotropic intersite exchange interactions in frustrated rare-earth magnets are difficult to assess both theoretically and experimentally. Here, we propose an ab initio force-theorem framework combining the quasiatomic Hubbard-I approach to $4f$ correlations with a static mean-field treatment of the on-site intershell Coulomb interaction between rare-earth $4f$ and $5d$ states to simultaneously capture both $4f$ superexchange and $5d$-mediated indirect exchange. Applying it to the triangular lattice Ce delafossites ${\mathrm{CsCeSe}}_2, {\mathrm{KCeS}}_2$, and ${\mathrm{RbCeO}}_2$, we find that the indirect exchange dominates in the selenide, the superexchange in the oxide, while both mechanisms contribute almost equally in the sulfide. The magnetic exciation spectra of ${\mathrm{CsCeSe}}_2$ and ${\mathrm{KCeS}}_2$ evaluated from the calculated spin Hamiltonains are in good qualitative and quantitative agreement with experimental data.

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• Exchange interaction
• Frustrated magnetism
• RKKY interaction
• Antiferromagnets
• Rare-earth magnetic materials
• Triangular lattice
• Dynamical mean field theory