Derivation of effective spin Hamiltonians for heavy-fermion materials

We derive effective the spin Hamiltonians that capture the interaction among the effective magnetic moments by utilizing a multi-orbital periodic Anderson model with parameters obtained from ab initio band structure calculations, combined with degenerate perturbation theory. This derivation encompasses fluctuations via both nonmagnetic 4f⁰ and magnetic 4f² virtual states, and its accuracy is confirmed through comparison with experimental data obtained from CeIn₃. The agreement observed between experimental results and theoretical predictions highlights the potential of deriving minimal models from first-principles calculations for achieving a quantitative description of 4f materials. Moreover, regardless of the metallic or insulator character of the system, our microscopic derivation unveils the underlying origin of anisotropy in the exchange interaction between Kramers doublets, shedding light on the conditions under which this anisotropy may be weak compared to the isotropic contribution.