Transforming from Kitaev to Disguised Ising Chain: Application to CoNb₂O₆

For many years, CoNb₂O₆ has served as an exemplar of the one-dimensional Ising model. However, recent experimental and theoretical analyses challenge its applicability to this material. Prior to that, a tailored spin model for 3d⁷ systems such as Co²⁺, known as the JKΓ model, has emerged, featuring Heisenberg $(J)$, Kitaev $(K)$, and Gamma (Γ) interactions. While these interactions are permitted by the symmetry of the system, their role in CoNb₂O₆ remains enigmatic. We present a microscopic theory based on spin-orbit entangled Jeff = 1/2 states, aimed at elucidating the roles of Kitaev and Gamma interactions in shaping Ising anisotropy. Leveraging strong coupling theory, we identify a dominant ferromagnetic Kitaev interaction. Furthermore, by comparing dynamical structure factors obtained via exact diagonalization with those from inelastic neutron scattering experiments, we find an antiferromagnetic Γ interaction, which dictates the Ising axis and explains the mechanism behind moment pinning. Our theory suggests that CoNb₂O₆ represents a rare one-dimensional Kitaev chain with significant ferromagnetic Kitaev and antiferromagnetic Gamma interactions.