Ab initio spin Hamiltonians and magnetism of Ce and Yb triangular-lattice compounds

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) RbCeO$_2$ and YbZn$_2$GaO$_5$ and the antiferromagnets KCeO$_2$ and 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.

💡 Research Summary

In this work the authors present a comprehensive first‑principles study of the crystal‑field (CF) spectra, ground‑state Kramers doublets, and inter‑site exchange interactions for a representative set of triangular‑lattice rare‑earth compounds containing Ce³⁺ (4f¹) and Yb³⁺ (4f¹³). The materials investigated are KCeO₂, KCeS₂, RbCeO₂—known antiferromagnets or putative quantum spin‑liquid (QSL) candidates—and the Yb‑based YbZn₂GaO₅ (YZGO), which has been proposed as a Dirac spin‑liquid (DSL) system.

The electronic structure is obtained using a charge‑self‑consistent DFT+DMFT scheme with the Hubbard‑I approximation, which treats the localized 4f shell in the high‑temperature paramagnetic limit. This approach yields accurate CF level schemes that agree well with inelastic neutron‑scattering data, reproducing the large CF splittings in the Ce oxides (≈60 % of the spin‑orbit gap) and the essentially pure J = 7/2 ground doublet in YZGO. The calculated g‑tensors show strong in‑plane anisotropy for the Ce compounds (g_ab ≫ g_c) and a nearly isotropic, larger g‑factor for YZGO, consistent with ESR and quantum‑chemistry results.

Exchange interactions are derived from the same paramagnetic electronic structure using the force‑theorem Hubbard‑I (FT‑HI) method, which includes all kinetic‑exchange pathways as well as classical dipole‑dipole contributions. The nearest‑neighbour (NN) couplings are antiferromagnetic for all four compounds, with a diagonal XXZ anisotropy Δ ≥ 1. In the Ce systems the off‑diagonal terms J_±± and J_z± are sizable, producing a pronounced exchange anisotropy, whereas in YZGO the NN exchange is almost isotropic and the next‑nearest‑neighbour (NNN) exchange is dominated by dipolar interactions, leading to a very large anisotropy Δ′ ≈ 6 despite a small magnitude (J′/J ≈ 0.003).

Using these ab‑initio parameters the authors construct effective spin‑½ Hamiltonians and solve them by exact diagonalization (ED) on clusters up to N = 36 sites (XDiag library). The static spin structure factors S_αα(k) and low‑energy spectra reveal that KCeO₂ and RbCeO₂ realize the conventional 120° antiferromagnetic order of the triangular Heisenberg model, while KCeS₂ stabilizes a collinear stripy (stripy⊥) phase. YZGO also shows 120° order, with a pronounced peak at the K point and a sizable gap at the X point, ruling out the gapless DSL scenario. The ED results are corroborated by symmetry analysis of the irreducible representations of the low‑lying states.

To explore the broader phase diagram, the authors vary the NN anisotropy (Δ, J_±±) and the isotropic NNN coupling J′. They find that a quantum spin‑liquid region can only be accessed when the antiferromagnetic NNN exchange is sufficiently strong; increasing NN anisotropy generally shrinks or eliminates the QSL region. This confirms that the DSL and related QSL phases are highly sensitive to exchange anisotropy and that realistic rare‑earth triangular lattices, which inevitably possess sizable anisotropic NN terms, are unlikely to host a robust QSL without additional mechanisms (e.g., disorder, further‑range couplings).

Finally, the calculated Curie–Weiss temperatures, obtained from high‑temperature susceptibility within a mean‑field treatment, agree well with experimental values for the Ce oxides, but underestimate the magnitude for KCeS₂, suggesting that in sulfides other exchange pathways (perhaps direct 4f–4f overlap) dominate over the kinetic exchange captured by FT‑HI.

Overall, the paper demonstrates that a DFT+DMFT/Hubbard‑I framework can reliably predict crystal‑field schemes and exchange tensors in strongly spin‑orbit‑coupled 4f systems, and it provides a clear microscopic rationale for why the examined Ce and Yb triangular‑lattice compounds order magnetically rather than forming a quantum spin liquid. The work highlights the crucial role of next‑nearest‑neighbour antiferromagnetic exchange and the detrimental effect of strong NN anisotropy, offering valuable guidance for future material design and theoretical modeling of frustrated rare‑earth magnets.