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Fabrication of spin-1/2 Heisenberg antiferromagnetic chains via combined on-surface synthesis and reduction for spinon detection

Abstract

Spin-1/2 Heisenberg antiferromagnetic chains are one-dimensional platforms that are excellent for exploring quantum magnetic states and quasiparticle fractionalization. Understanding quantum magnetism and quasiparticle excitation at the atomic scale is crucial for manipulating the quantum spin systems. Here we report the fabrication of spin-1/2 Heisenberg chains through on-surface synthesis and in situ reduction. A closed-shell nanographene is employed as a precursor for Ullmann coupling to avoid side reactions, thus obtaining oligomer chains. Following exposure to atomic hydrogen and tip manipulation, the closed-shell polymers are transformed into spin-1/2 chains with controlled lengths by reducing ketone groups and subsequent hydrogen desorption. The spin excitation gaps are found to decrease in a power law as the chain lengthens, suggesting a gapless feature in the thermodynamic limit. Interestingly, the spinon dispersion is extracted from the inelastic spectroscopic spectra, agreeing well with calculations. Our results demonstrate the great potential of fabricating desired quantum systems through a combined on-surface synthesis and reduction approach.

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Fig. 1: Spin-1/2 Heisenberg chains fabricated through a stepwise solution/on-surface synthetic process.
Fig. 2: dI/dV spectra measured on OSCs with different numbers of olympicene units.
Fig. 3: Calculated ground state and spin excitations of OSCs with different numbers of olympicene units.
Fig. 4: Spinon dispersion in OSCs.

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Data availability

All data generated in this study are available via figshare at https://doi.org/10.6084/m9.figshare.28091300 (ref. 48).

Code availability

The relevant codes are available via GitHub at https://github.com/Suxl1994/spin_chain_ED.

References

  1. Haldane, F. D. M. Nonlinear field theory of large-spin heisenberg antiferromagnets: semiclassically quantized solitons of the one-dimensional easy-axis Néel state. Phys. Rev. Lett. 50, 1153–1156 (1983).

    Article  Google Scholar 

  2. Affleck, I., Kennedy, T., Lieb, E. H. & Tasaki, H. in Condensed Matter Physics and Exactly Soluble Models (eds Nachtergaele, B. et al.) Ch. 18, 249–252 (Springer, 2004).

  3. White, S. R. & Huse, D. A. Numerical renormalization-group study of low-lying eigenstates of the antiferromagnetic S = 1 Heisenberg chain. Phys. Rev. B 48, 3844–3852 (1993).

    Article  CAS  Google Scholar 

  4. White, S. R. Density-matrix algorithms for quantum renormalization groups. Phys. Rev. B 48, 10345–10356 (1993).

    Article  CAS  Google Scholar 

  5. Kenzelmann, M. et al. Structure of end states for a Haldane spin chain. Phys. Rev. Lett. 90, 087202 (2003).

    Article  CAS  PubMed  Google Scholar 

  6. Bethe, H. Zur theorie der metalle: I. Eigenwerte und eigenfunktionen der linearen atomkette. Z. Phys. 71, 205–226 (1931).

    Article  CAS  Google Scholar 

  7. Lieb, E., Schultz, T. & Mattis, D. Two soluble models of an antiferromagnetic chain. Ann. Phys. 16, 407–466 (1961).

    Article  Google Scholar 

  8. Affleck, I. & Lieb, E. H. A proof of part of Haldane’s conjecture on spin chains. Lett. Math. Phys. 12, 57–69 (1986).

    Article  Google Scholar 

  9. Mourigal, M. et al. Fractional spinon excitations in the quantum Heisenberg antiferromagnetic chain. Nat. Phys. 9, 435–441 (2013).

    Article  CAS  Google Scholar 

  10. Schlappa, J. et al. Probing multi-spinon excitations outside of the two-spinon continuum in the antiferromagnetic spin chain cuprate Sr2CuO3. Nat. Commun. 9, 5394 (2018).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  11. Choi, D. J. et al. Colloquium: atomic spin chains on surfaces. Rev. Mod. Phys. https://doi.org/10.1103/RevModPhys.91.041001 (2019).

  12. Toskovic, R. et al. Atomic spin-chain realization of a model for quantum criticality. Nat. Phys. 12, 656–660 (2016).

    Article  CAS  Google Scholar 

  13. Yang, K. et al. Probing resonating valence bond states in artificial quantum magnets. Nat. Commun. 12, 993 (2021).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  14. Clair, S. & de Oteyza, D. G. Controlling a chemical coupling reaction on a surface: tools and strategies for on-surface synthesis. Chem. Rev. 119, 4717–4776 (2019).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  15. Ruffieux, P. et al. On-surface synthesis of graphene nanoribbons with zigzag edge topology. Nature 531, 489–492 (2016).

    Article  CAS  PubMed  Google Scholar 

  16. de Oteyza, D. G. et al. Direct imaging of covalent bond structure in single-molecule chemical reactions. Science 340, 1434–1437 (2013).

    Article  PubMed  Google Scholar 

  17. Rizzo, D. J. et al. Topological band engineering of graphene nanoribbons. Nature 560, 204–208 (2018).

    Article  CAS  PubMed  Google Scholar 

  18. Groning, O. et al. Engineering of robust topological quantum phases in graphene nanoribbons. Nature 560, 209–213 (2018).

    Article  CAS  PubMed  Google Scholar 

  19. Cirera, B. et al. Tailoring topological order and pi-conjugation to engineer quasi-metallic polymers. Nat. Nanotechnol. 15, 437–443 (2020).

    Article  CAS  PubMed  Google Scholar 

  20. Li, J. et al. Topological phase transition in chiral graphene nanoribbons: from edge bands to end states. Nat. Commun. 12, 5538 (2021).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  21. Mishra, S. et al. Synthesis and characterization of pi-extended triangulene. J. Am. Chem. Soc. 141, 10621–10625 (2019).

    Article  CAS  PubMed  Google Scholar 

  22. Cheng, S. et al. On-surface synthesis of triangulene trimers via dehydration reaction. Nat. Commun. 13, 1705 (2022).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  23. Du, Q. et al. Orbital-symmetry effects on magnetic exchange in open-shell nanographenes. Nat. Commun. 14, 4802 (2023).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  24. Hieulle, J. et al. On-surface synthesis and collective spin excitations of a triangulene-based nanostar. Angew. Chem. Int. Ed. 60, 25224–25229 (2021).

    Article  CAS  Google Scholar 

  25. Song, S. et al. Highly entangled polyradical nanographene with coexisting strong correlation and topological frustration. Nat. Chem. 16, 938–944 (2024).

    Article  CAS  PubMed  Google Scholar 

  26. Zheng, Y. et al. Designer spin order in diradical nanographenes. Nat. Commun. 11, 6076 (2020).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  27. Zhao, Y. et al. Quantum nanomagnets in on-surface metal-free porphyrin chains. Nat. Chem. https://doi.org/10.1038/s41557-022-01061-5 (2022).

  28. Zhao, C. et al. Tunable topological phases in nanographene-based spin-1⁄2 alternating-exchange Heisenberg chains. Nat. Nanotechnol. 19, 1789–1795 (2024).

    Article  CAS  PubMed  Google Scholar 

  29. Lado, J. L. & Fernández-Rossier, J. Magnetic edge anisotropy in graphenelike honeycomb crystals. Phys. Rev. Lett. 113, 027203 (2014).

    Article  CAS  PubMed  Google Scholar 

  30. Fu, X. et al. Building spin-1/2 antiferromagnetic Heisenberg chains with diaza-nanographenes. Preprint at https://doi.org/10.48550/arXiv.2407.20511 (2024).

  31. Sun, K. et al. Heisenberg spin-1/2 antiferromagnetic molecular chains. Preprint at https://doi.org/10.48550/arXiv.2407.02142 (2024).

  32. Xiang, Q., Ye, L., Ma, L. & Sun, Z. The olympicenyl radical and its derivatives. ChemPlusChem 89, e202300571 (2024).

    Article  CAS  PubMed  Google Scholar 

  33. Zhu, X. et al. Topological structure realized in cove-edged graphene nanoribbons via incorporation of periodic pentagon rings. J. Am. Chem. Soc. 146, 7152–7158 (2024).

    Article  CAS  PubMed  Google Scholar 

  34. Lawrence, J. et al. Circumventing the stability problems of graphene nanoribbon zigzag edges. Nat. Chem. 14, 1451–1458 (2022).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  35. Wang, T. et al. Aza-triangulene: on-surface synthesis and electronic and magnetic properties. J. Am. Chem. Soc. 144, 4522–4529 (2022).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  36. Gross, L., Mohn, F., Moll, N., Liljeroth, P. & Meyer, G. The chemical structure of a molecule resolved by atomic force microscopy. Science 325, 1110–1114 (2009).

    Article  CAS  PubMed  Google Scholar 

  37. Pavlicek, N. et al. Synthesis and characterization of triangulene. Nat. Nanotechnol. 12, 308–311 (2017).

    Article  CAS  PubMed  Google Scholar 

  38. Mistry, A. et al. The synthesis and STM/AFM imaging of ‘olympicene’ benzo[cd]pyrenes. Chemistry 21, 2011–2018 (2015).

    Article  CAS  PubMed  Google Scholar 

  39. Li, J. et al. Single spin localization and manipulation in graphene open-shell nanostructures. Nat. Commun. 10, 200 (2019).

    Article  PubMed  PubMed Central  Google Scholar 

  40. Su, X. et al. Atomically precise synthesis and characterization of heptauthrene with triplet ground state. Nano Lett. 20, 6859–6864 (2020).

    Article  CAS  PubMed  Google Scholar 

  41. Zhao, C. et al. Gapless spin excitations in nanographene-based antiferromagnetic spin-1/2 Heisenberg chains. Preprint at https://doi.org/10.48550/arXiv.2408.10045 (2024).

  42. Jiménez-Martín, A. et al. Atomically precise control of topological state hybridization in conjugated polymers. ACS Nano 18, 29902–29912 (2024).

    Article  PubMed  PubMed Central  Google Scholar 

  43. Ternes, M. Spin excitations and correlations in scanning tunneling spectroscopy. New J. Phys. https://doi.org/10.1088/1367-2630/17/6/063016 (2015).

  44. des Cloizeaux, J. & Pearson, J. J. Spin-wave spectrum of the antiferromagnetic linear chain. Phys. Rev. 128, 2131–2135 (1962).

    Article  Google Scholar 

  45. Fernández-Rossier, J. Theory of single-spin inelastic tunneling spectroscopy. Phys. Rev. Lett. 102, 256802 (2009).

    Article  PubMed  Google Scholar 

  46. Yuan, Z. et al. Fractional spinon quasiparticles in open-shell triangulene spin-1/2 chains. J. Am. Chem. Soc. https://doi.org/10.1021/jacs.4c14712 (2025).

  47. Renard, J. P., Regnault, L. P. & Verdaguer, M. in Magnetism: Molecules to Materials (eds Miller, J. S. & Drillon, M.) Ch. 2, 49–93 (Wiley, 2002).

  48. Su, X., et al. Dataset for ‘Fabrication of spin-1/2 Heisenberg antiferromagnetic chains via combined on-surface synthesis and reduction for spinon detection’. figshare https://doi.org/10.6084/m9.figshare.28091300 (2024).

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Acknowledgements

P.Y. gratefully acknowledges the financial support from the National Natural Science Foundation of China (22472098), Science and Technology Commission of Shanghai Municipality (24ZR1452100) and ShanghaiTech start-up funding. X.S. acknowledges the Postdoctoral Science Foundation of China (2021M702188). C.L. acknowledges the NSFC grant 12304230 and Postdoctoral Science Foundation of China (grant GZB20230422). Y.-F.J. acknowledges support from the National Program on Key Research Project (grant no. 2022YFA1402703). We also thank Fermion Instruments for supplying the hydrogen cracker source.

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Authors and Affiliations

Contributions

X.S., Z.D., Y.H. and P.Y. conceived the project. X.S., Z.D. and P.Y. acquired and analysed the experimental data. N.K., C.L. and Y.-F.J. performed all the calculations. Y.H. and K.Y. designed and synthesized the molecular precursors. All the authors discussed and contributed to the paper writing.

Corresponding authors

Correspondence to KaKing Yan, Can Li, Yi-Fan Jiang or Ping Yu.

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Nature Synthesis thanks Jiong Lu, Shiyong Wang and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Primary Handling Editor: Peter Seavill, in collaboration with the Nature Synthesis team.

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Supplementary information

Supplementary Information

Supplementary Figs. 1–18 and experimental details.

Supplementary Data

The source data for Supplementary Figs. 11, 15b and 17a–c.

Source data

Source Data Fig. 1

The source data for STM and AFM images in Fig. 1.

Source Data Fig. 2

The source data for AFM images, STS and simulated spectra in Fig. 2.

Source Data Fig. 3

The source data for calculated and experimental spin excited energies of OSCs in Fig. 3.

Source Data Fig. 4

The source data for AFM images, STM images, STS, and experimental and calculated spinon dispersion in Fig. 4.

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Su, X., Ding, Z., Hong, Y. et al. Fabrication of spin-1/2 Heisenberg antiferromagnetic chains via combined on-surface synthesis and reduction for spinon detection. Nat. Synth 4, 694–701 (2025). https://doi.org/10.1038/s44160-025-00744-4

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