5 d -mediated indirect exchange and effective spin Hamiltonians in Ce triangular-lattice delafossites

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 quasi-atomic 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 CsCeSe₂, KCeS₂, and RbCeO₂, 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 CsCeSe₂ and KCeS₂ evaluated from the calculated spin Hamiltonains are in good qualitative and quantitative agreement with experimental data.