Fully generalized spin models with strain effects of Kitaev spin liquid candidate materials

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. The $$KJ\Gamma {\Gamma }^{{\prime} }$$ model, based on ideal symmetries, has been central to realizing Kitaev quantum spin liquids (KQSLs), but real materials often break these symmetries, requiring a more general framework. Here the authors develop a generalized spin model incorporating arbitrary lattice deformations and show that strain drives topological transitions and stabilizes KQSLs in real materials.