Abstract
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.
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Acknowledgements
We thank Takasada Shibauchi, Kyusung Hwang, Heung-Sik Kim, and Jae Hoon Kim for their invaluable comments and discussions. This work was supported by 2022M3H4A1A04074153, the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (Grant Nos. RS-2025-00559042, RS-2023-00253716, and RS-2025-00559286), the Nano & Material Technology Development Program through the National Research Foundation of Korea (NRF) funded by Ministry of Science and ICT (RS-2023-00281839, RS-2024-00451261) and National Measurement Standards Services and Technical Support for Industries funded by Korea Research Institute of Standards and Science (KRISS-2025-GP2025-0015).
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P.N. and H.L. contributed equally to this work. P.N. conducted symmetry analysis, microscopic derivations, and theoretical analysis of topological phase transitions. H.L. performed density functional theory (DFT) calculations and analysis of strain-dependent band structures. M.J.H. co-supervised the project and contributed to the analysis of DFT calculation results. E.-G.M. conceived and supervised the project. All authors contributed to the interpretation of the data and the manuscript.
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Noh, P., Lee, H., Han, M.J. et al. Fully generalized spin models with strain effects of Kitaev spin liquid candidate materials. Commun Phys (2026). https://doi.org/10.1038/s42005-026-02607-6
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DOI: https://doi.org/10.1038/s42005-026-02607-6
