Designing Kitaev Spin Liquids in Metal-Organic Frameworks

Kitaev’s honeycomb lattice spin model is a remarkable exactly solvable model, which has a particular type of spin liquid (Kitaev spin liquid) as the ground state. Although its possible realization in iridates and $\alpha \text{−}{\mathrm{RuCl}}_3$ has been vigorously discussed recently, these materials have substantial non-Kitaev direct exchange interactions and do not have a spin liquid ground state. We propose metal-organic frameworks (MOFs) with ${\mathrm{Ru}}^{3+}$ (or ${\mathrm{Os}}^{3+}$), forming the honeycomb lattice as promising candidates for a more ideal realization of Kitaev-type spin models, where the direct exchange interaction is strongly suppressed. The great flexibility of MOFs allows generalization to other three-dimensional lattices for the potential realization of a variety of spin liquids, such as a Weyl spin liquid.

Figure 1

(a) Geometric structure of the honeycomb Ru-oxalate framework. White octahedra are ${\mathrm{RuO}}_6$ octahedra, and carbon atoms are shown in brown. The color of the bond between the Ru atoms means which plane the bridging oxalate belongs to (red: $yz$ plane, green: $zx$ plane, blue: $xy$ plane). (b) Two superexchange pathways between two neighboring ${\mathrm{Ru}}^{3+}$ through an oxalate ion, belonging to the $xy$ plane [one of the blue bonds in (a)]. $t_{\pi \pi }$ is a hopping parameter between the two distinct pathways.

Figure 2

Chemical formulae for the proposed metal-organic frameworks. (a) Possible organic molecules to realize a honeycomb structure with octahedral coordination. (1) Oxalate-based molecules ($E=\mathrm{O}$, S, NH). (2) Quinoid-based molecules ($E=\mathrm{O}$, S, NH; $X=\mathrm{H}$, Cl, Br, I, etc.). (3) Tetraaminopyrazine-based molecule. (b) Honeycomb structure of metal-oxalate frameworks ($M=\mathrm{Ru}$, Os).