The \(KJ\Gamma {\Gamma }^{{\prime} }\) spin model-originally derived for an ideal \({{{\rm{P}}}}\bar{3}1{{{\rm{m}}}}\) symmetric geometry-has long served as a central framework for understanding candidate Kitaev materials. In realistic crystals, however, this ideal geometry is seldom realized, either at low temperatures or under external perturbations, limiting the model’s quantitative applicability. Here we introduce a fully generalized spin model, denoted ϵ- \(KJ\Gamma {\Gamma }^{{\prime} }\) , that explicitly incorporates arbitrary lattice deformations ϵ. All spin-exchange interactions and their strain-dependent coefficients are obtained from density functional theory (DFT) calculations and a microscopic derivation of coupling constants for materials based on d5 transition-metal ions. For α-RuCl3 under a strain of 3%, new emergent exchange channels acquire magnitudes comparable to their unstrained counterparts. Building on these parameters, we investigate strain-driven quantum phase transitions between competing magnetic states-including the zigzag order and the Kitaev quantum spin liquid (KQSL)-and identify a strain-induced topological transition within the KQSL states that offers a practical diagnostic of Kitaev physics. Furthermore, our symmetry analysis of the ϵ- \(KJ\Gamma {\Gamma }^{{\prime} }\) model is applicable to both d5 ions, such as α-RuCl3, and d7 systems, including cobalt-based compounds.
