Single-site magnetic anisotropy governed by interlayer cation charge imbalance in triangular-lattice $A\mathrm{Yb}{X}_2$

The behavior in magnetic field of a paramagnetic center is characterized by its $g$ tensor. An anisotropic form of the latter implies different kind of response along different crystallographic directions. Here we shed light on the anisotropy of the $g$ tensor of ${\mathrm{Yb}}^{3+}4f^{13}$ ions in ${\mathrm{NaYbS}}_2$ and ${\mathrm{NaYbO}}_2$, layered triangular-lattice materials suggested to host spin-liquid ground states. Using quantum chemical calculations we show that, even if the ligand-cage trigonal distortions are significant in these compounds, the decisive role in realizing strongly anisotropic, noncubic $g$ factors is played by interlayer cation charge imbalance effects. The latter refer to the asymmetry experienced by a given Yb center due to having higher ionic charges at adjacent metal sites within the magnetic $ab$ layer, i.e., $3+$ nearest neighbors within the $ab$ plane versus $1+$ species between the magnetic layers. According to our results, this should be a rather general feature of $4f^{13}$ layered delafossites: less interlayer positive charge is associated with stronger in-plane magnetic response.

Figure 1

Crystal structure of ${\mathrm{NaYbX}}_2$: (a) Stacking of ${\mathrm{YbX}}_2$ triangular layers on top of each other. (b) The reference ${\mathrm{YbX}}_6$ octahedron, the six NN Yb atoms, and the adjacent Na ions explicitly included in the calculations. As our study is focused on single-site properties (${\mathrm{Yb}}_1$ central site), the adjacent six Yb ions (${\mathrm{Yb}}_2$) enter the calculations as large-core pseudopotentials [23] that include as well the $f$ electrons (see text for more details). The extended solid-state surroundings were modeled as an effective embedding potential.