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

Abstract

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.

Figures (3)

• Figure 1: Calculated CF level splitting. The thick red lines are calculated CF levels; the dashed blue lines are CF excitations measured in inelastic neutron scattering (INS) from Refs. Bordelon2021Bastien2020Ortiz2022Bag2024. Note that three excitations are seen in INS spectra for the Ce compounds.
• Figure 2: Spin structure factors and low-energy spectrum for the YZGO ($a,b$) and KCeS$_2$ ($c,d$) compounds in a $36$-site cluster. The isotropic structure factor $\mathcal{S}\left(\boldsymbol{k} \right)$ in $a)$ is peaked at the $K$ points, indicating $120^\circ$ order, consistent with low-energy excitations at $K_0.\text{A}$ and $K_1.\text{B}$. The peak at $M_2$ of $\mathcal{S}^{yy}(\boldsymbol{k})$ in $c)$ indicates stripe-$\perp$ order, consistent with low-energy excitations at the $M$ points in $d)$.
• Figure 3: $a)$ and $d)$ - Approximate phase diagram of the effective magnetic Hamiltonian, inferred from the quantum number organization of the low-energy spectrum. Dark red marks the $120^\circ$ AFM phase, dark blue the stripy-$\parallel$ order, pale purple the stripy-$\perp$ order, and orange the regime with first non-zero momentum excitation in the $X_1.\text{A}$ irrep, suggesting a possible DSL phase. A typical classical ordering for each stripe phase is shown in the sketch in $d)$. The remaining panels show the static spin structure factor at selected momenta in the FBZ (see inset in $a$)): panel $b)$ and $e)$ at $Z$, while $c)$ and $f)$ show the average over the three inequivalent $M$ points. In $b)$ we identify the parameters compatible with the YZGO system. Parameters: $\Delta = 1.03J$, $J^\prime = 0.02J$ in $a)$–$c)$, and $J_{z\pm} = 0$ in $d)$–$f)$.