Recent observations of novel spin-orbit coupled states have generated interest in 4 d /5 d transition metal systems. A prime example is the J eff = 1 2 state in iridate materials and α-RuCl ₃ that drives Kitaev interactions. Here, by tuning the competition between spin-orbit interaction (λ _SOC ) and trigonal crystal field (Δ _T ), we restructure the spin-orbital wave functions into a previously unobserved μ = 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 . Using perturbation theory, we present an explicit expression for the μ = 1 2 state in the limit Δ _T ≫ λ _SOC realized in Ag ₃ LiRh ₂ O ₆ , different from the conventional J eff = 1 2 state in the limit λ _SOC ≫ Δ _T realized in Li ₂ RhO ₃ . The change of ground state is followed by a marked 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 .