Geometrical Frustration in the Spin Liquid ${\beta }^{\prime }\mathrm{\text{−}}{\mathrm{Me}}_3\mathrm{EtSb}[\mathrm{Pd}(\mathrm{dmit}{)}_2{]}_2$ and the Valence-Bond Solid ${\mathrm{Me}}_3\mathrm{EtP}[\mathrm{Pd}(\mathrm{dmit}{)}_2{]}_2$

We show that the electronic structures of the title compounds predicted by density functional theory are well described by tight binding models. We determine the frustration ratio, $J^{\prime }/J$, of the Heisenberg model on the anisotropic triangular lattice, which describes the spin degrees of freedom in the Mott insulating phase for a range of $\mathrm{Pd}(\mathrm{dmit}{)}_2$ salts. All of the antiferromagnetic materials studied have $J^{\prime }/J\lesssim 0.5$ or $J^{\prime }/J\gtrsim 0.9$, and all salts with $0.5\lesssim J^{\prime }/J\lesssim 0.9$ are known, experimentally, to be charge ordered valence-bond solids or spin liquids.

Figure 1

In-plane crystal structures and interdimer hopping integrals for Sb-1 (left) and P-1 (right). Rings indicate the dimers. The conventional unit cell is marked.

Figure 2

Band structure of Sb-1 calculated from DFT (points) and fit to the dimer tight-binding model (curves). The corresponding Fermi surface and the locations of high symmetry points are shown in Fig. 5 of the Supplemental Material [32]. The values of the dimer tight-binding fit (in meV) for the HOMO band are $t_1=37$, $t_2=49$, $t_3=45$, $t_{\perp }=-2.1$, and the parameters for the LUMO band are $t_1=7.2$, $t_2=-15$, $t_3=-0.2$, $t_{\perp }=-1.5$.

Figure 3

Band structure of P-1 calculated from DFT (points) and fit to the dimer tight-binding model (curves). The corresponding Fermi surface and the locations of high symmetry points are shown in Fig. 6 of the Supplemental Material [32]. The values of the dimer tight-binding fit (in meV) for the HOMO band are $t_1=45$, $t_2=52$, $t_3=52$, $t_{\perp }=6.7$, $\delta =16$, and the fit to the LUMO band yields $t_1=6.6$, $t_2=-11$, $t_3=-8$, $t_{\perp }=-8.0$, $\delta =0$.