Design Principles for Quasi-Isotropic Exchange in Rare-Earth Quantum Magnets

Abstract

Rare-earth quantum materials provide a promising platform for emergent phenomena ranging from quantum spin liquids with long-range entanglement to topological magnetic textures. However, the strong spin-orbit coupling that stabilizes their low-energy pseudospin degrees of freedom also tends to generate strongly anisotropic exchange interactions, complicating the realization of quasi-isotropic Heisenberg magnetism. Here we investigate the microscopic origin of superexchange in $\mathrm{Ce}^{3+}$- and $\mathrm{Yb}^{3+}$-based insulators with edge-sharing octahedral geometry. Using degenerate perturbation theory for a multiorbital Hubbard model, we show that isotropic exchange originates predominantly from virtual hopping within the ground-state Kramers doublet, whereas anisotropic interactions arise primarily from processes involving excited multiplets. This leads to a simple orbital design principle: quasi-isotropic exchange is promoted when the ground-state doublet has a strong maximal-angular-momentum character with respect to the quantization axis perpendicular to the superexchange plane spanned by rare-earth and ligand ions. We demonstrate this mechanism for both ideal and distorted geometries and show that it is broadly consistent with experimentally studied Yb-based insulators. Our results establish a practical framework for engineering quasi-isotropic interactions in rare-earth quantum materials.