Spin-wave dynamics in the ${\mathrm{KCeS}}_2$ delafossite: A theoretical description of powder inelastic neutron-scattering data

Layered rare-earth delafossites $AR{X}_2$ with $R=\text{Yb}$(III) or Ce(III) received a lot of interest as potential hosts for a quantum spin-liquid ground state. Some systems of this family that show no long-range order down to the lowest-measured temperatures, such as ${\mathrm{NaYbO}}_2$, ${\mathrm{NaYbS}}_2$, and ${\mathrm{NaYbSe}}_2$, are presumed to be in a quantum spin-liquid state. However, other isostructural compounds are known to order antiferromagnetically at subkelvin temperatures. Among them, ${\mathrm{KCeS}}_2$ exhibits stripe-yz magnetic order in the triangular-lattice planes that sets in below 400 mK. Here we investigate the spin-wave spectrum of this ordered phase with powder inelastic neutron scattering and describe it using a model Hamiltonian obtained from first-principles calculations based on the complete $|J,m_J\rangle$ multiplet description of the Ce sites with an anisotropic nearest-neighbor exchange interaction. Combining the current understanding of the exchange interaction in the systems with the effects of texturing in the powder, we are able to model the inelastic neutron scattering spectrum with high fidelity.

Figure 1

(a) Delafossite $AR{X}_2$ atomic structure in the ac-plane with the $A^{+}$ and $R^{3+}$ cation sites indicated. (b) Top view of the $R$-layer forming a triangular lattice, with the $R{X}_6$ polyhedron highlighted. (c) On-site total moments and the 4f charge density isofurface in the stripe-yz AFM ordered state. (d) A sketch of the powder holder used in INS experiments, with the platelike microcrystals packed so that their $c$-axes point preferentially orthogonal to the $z$-axis of the laboratory frame, as we found in the work (see text for details).

Figure 2

The powder INS spectra of ${\mathrm{KCeS}}_2$ at $T=0.04$, 0.2, 0.5, and 5.0 K, measured on IN5 with the incident neutron energy $E_{\text{i}}=1.67$ meV. (a)–(d) Powder-averaged intensity maps. The black and red dots above the bottom axis show the position of the structural (003) and four magnetic Bragg peaks $\left(0\frac{\overline{1}}{2}\frac{1}{2}\right)$, $\left(0\frac{\overline{1}}{2}\frac{\overline{5}}{2}\right)$, $\left(0\frac{\overline{1}}{2}\frac{\overline{7}}{2}\right)$, and $\left(1\frac{\overline{1}}{2}\frac{\overline{3}}{2}\right)$, respectively, with their Bragg intensities encoded with color saturation. (e, f) Comparison of the INS spectra that were integrated within the two momentum windows shown in the top panels with horizontal white bars.

Figure 3

(a) Top view of the $\left[{\mathrm{Ce}}_2{\mathrm{S}}_{10}\right]$ system considered in the dimer modeling at the CASSCF(2,14)/ANO-RCC-VDZP level, with isosurfaces of the natural spin density for the ground state. (b) Computed dispersion of the spin waves along the high-symmetry lines ($\mathrm{\Gamma }$–$M$–$M^{\prime }$–$\mathrm{\Gamma }$), with the line thickness and color saturation proportional to $I_{\text{dip}}$. Here $M^{\prime }$ denotes the $M$ point spontaneously chosen as the magnetic ordering vector in the $ab$ plane. (c) Theoretical INS powder spectra for the different values of aspect ratios ($\text{ar}=0.1$, 1.0, 5.0 and 10.0). The bottom row of panels shows the corresponding momentum-integrated spectra taken in the $\left|\mathbf{Q}\right|$ windows $R_1=[0.28,0.43]$ ${\AA }^{-1}$ and $R_2=[1.0,1.3]$ ${\AA }^{-1}$.