First demonstration of tuning between the Kitaev and Ising limits in a honeycomb lattice

Recent observations of novel spin-orbit coupled states have generated tremendous interest in $4d/5d$ transition metal systems. A prime example is the $J_{\text{eff}}=\frac{1}{2}$ state in iridate materials and $\alpha$-RuCl$_{3}$ that drives Kitaev interactions. Here, by tuning the competition between spin-orbit interaction ($\lambda_{\text{SOC}}$) and trigonal crystal field splitting ($\Delta_\text{T}$), we restructure the spin-orbital wave functions into a novel $\mu=\frac{1}{2}$ state that drives Ising interactions. This is done via a topochemical reaction that converts Li$_{2}$RhO$_{3}$ to Ag$_{3}$LiRh$_{2}$O$_{6}$, leading to an enhanced trigonal distortion and a diminished spin-orbit coupling in the latter compound. Using perturbation theory, we present an explicit expression for the new $\mu=\frac{1}{2}$ state in the limit $\Delta_\text{T}\gg \lambda_{\text{SOC}}$ realized in Ag$_{3}$LiRh$_{2}$O$_{6}$, different from the conventional $J_\text{eff}=\frac{1}{2}$ state in the limit $\lambda_{\text{SOC}}\gg \Delta_\text{T}$ realized in Li$_{2}$RhO$_{3}$. The change of ground state is followed by a dramatic change of magnetism from a 6 K spin-glass in Li$_{2}$RhO$_{3}$ to a 94 K antiferromagnet in Ag$_{3}$LiRh$_{2}$O$_{6}$. These results open a pathway for tuning materials between the two limits and creating a rich magnetic phase diagram.