We calculate the crystal-field splitting, ground-state Kramers doublet, and intersite exchange interactions within the ground-state doublet manifold using an ab initio Hubbard-I based approach for a representative set of Ce and Yb triangular-lattice compounds. These include the putative quantum spin liquids (QSL) ${\mathrm{RbCeO}}_2$ and ${\mathrm{YbZn}}_2{\mathrm{GaO}}_5$ and the antiferromagnets ${\mathrm{KCeO}}_2$ and ${\mathrm{KCeS}}_2$. The calculated nearest-neighbor (NN) couplings are antiferromagnetic and exhibit noticeable anisotropy. The next-nearest-neighbor (NNN) couplings are ferromagnetic in the Ce systems and dominated by classical dipole-dipole interactions in the Yb case. Solving the resulting effective spin-1/2 models by exact diagonalization up to $N=36$ sites, we predict ordered magnetic ground states for all systems, including the two QSL candidates. We explore the phase space of an anisotropic NN $+$ isotropic NNN triangular-lattice model finding that a significant antiferromagnetic NNN coupling is required to stabilize QSL phases, while the NN exchange anisotropy is detrimental to them. Our findings highlight a possibly important role of deviations from the perfect triangular model—like atomic disorder—in real triangular-lattice materials.

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• Antiferromagnetism
• Dipolar interaction
• Exchange interaction
• First-principles calculations
• Quantum spin liquid
• Layered crystals
• Rare-earth magnetic materials
• Strongly correlated systems
• Density functional theory
• Dynamical mean field theory
• Exact diagonalization
• Spin lattice models