Topological frustration induces unconventional magnetism in a nanographene

A Publisher Correction to this article was published on 17 December 2019

This article has been updated


The chemical versatility of carbon imparts manifold properties to organic compounds, where magnetism remains one of the most desirable but elusive1. Polycyclic aromatic hydrocarbons, also referred to as nanographenes, show a critical dependence of electronic structure on the topologies of the edges and the π-electron network, which makes them model systems with which to engineer unconventional properties including magnetism. In 1972, Erich Clar envisioned a bow-tie-shaped nanographene, C38H18 (refs. 2,3), where topological frustration in the π-electron network renders it impossible to assign a classical Kekulé structure without leaving unpaired electrons, driving the system into a magnetically non-trivial ground state4. Here, we report the experimental realization and in-depth characterization of this emblematic nanographene, known as Clar’s goblet. Scanning tunnelling microscopy and spin excitation spectroscopy of individual molecules on a gold surface reveal a robust antiferromagnetic order with an exchange-coupling strength of 23 meV, exceeding the Landauer limit of minimum energy dissipation at room temperature5. Through atomic manipulation, we realize switching of magnetic ground states in molecules with quenched spins. Our results provide direct evidence of carbon magnetism in a hitherto unrealized class of nanographenes6, and prove a long-predicted paradigm where topological frustration entails unconventional magnetism, with implications for room-temperature carbon-based spintronics7,8.

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Fig. 1: Synthesis and structural characterization of Clar’s goblet.
Fig. 2: Electronic and magnetic characterization of Clar’s goblet.
Fig. 3: Spin decoupling in a fused dimer.
Fig. 4: Spin quenching and switching of magnetic ground states in 1′ and 2H-1.

Data availability

The data that support the findings of this study are available from the corresponding authors on reasonable request.

Code availability

The TB calculations were performed using a custom-made code on the WaveMetrics Igor Pro platform. Details of the TB code can be obtained from the corresponding authors on reasonable request.

Change history

  • 17 December 2019

    An amendment to this paper has been published and can be accessed via a link at the top of the paper.


  1. 1.

    Yazyev, O. V. Emergence of magnetism in graphene materials and nanostructures. Rep. Prog. Phys. 73, 056501 (2010).

    Google Scholar 

  2. 2.

    Clar, E. The Aromatic Sextet (Wiley, 1972).

  3. 3.

    Clar, E. & Mackay, C. C. Circobiphenyl and the attempted synthesis of 1:14, 3:4, 7:8, 10:11-tetrabenzoperopyrene. Tetrahedron 28, 6041–6047 (1972).

    CAS  Google Scholar 

  4. 4.

    Wang, W. L., Yazyev, O. V., Meng, S. & Kaxiras, E. Topological frustration in graphene nanoflakes: magnetic order and spin logic devices. Phys. Rev. Lett. 102, 157201 (2009).

    Google Scholar 

  5. 5.

    Landauer, R. Irreversibility and heat generation in the computing process. IBM J. Res. Dev. 5, 183–191 (1961).

    Google Scholar 

  6. 6.

    Cyvin, S. J., Brunvoll, J. & Cyvin, B. N. The hunt for concealed non-Kekuléan polyhexes. J. Math. Chem. 4, 47–54 (1990).

    CAS  Google Scholar 

  7. 7.

    Agarwal, H., Pramanik, S. & Bandyopadhyay, S. Single spin universal Boolean logic gate. New J. Phys. 10, 015001 (2008).

    Google Scholar 

  8. 8.

    Han, W., Kawakami, R. K., Gmitra, M. & Fabian, J. Graphene spintronics. Nat. Nanotechnol. 9, 794–807 (2014).

    CAS  Google Scholar 

  9. 9.

    Nakada, K., Fujita, M., Dresselhaus, G. & Dresselhaus, M. S. Edge state in graphene ribbons: nanometer size effect and edge shape dependence. Phys. Rev. B 54, 17954–17961 (1996).

    CAS  Google Scholar 

  10. 10.

    Fernández-Rossier, J. & Palacios, J. J. Magnetism in graphene nanoislands. Phys. Rev. Lett. 99, 177204 (2007).

    Google Scholar 

  11. 11.

    Tao, C. et al. Spatially resolving edge states of chiral graphene nanoribbons. Nat. Phys. 7, 616–620 (2011).

    CAS  Google Scholar 

  12. 12.

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

    CAS  Google Scholar 

  13. 13.

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

    Google Scholar 

  14. 14.

    Lieb, E. H. Two theorems on the Hubbard model. Phys. Rev. Lett. 62, 1201–1204 (1989).

    CAS  Google Scholar 

  15. 15.

    Ugeda, M. M., Brihuega, I., Guinea, F. & Gómez-Rodríguez, J. M. Missing atom as a source of carbon magnetism. Phys. Rev. Lett. 104, 096804 (2010).

    CAS  Google Scholar 

  16. 16.

    Nair, R. R. et al. Spin-half paramagnetism in graphene induced by point defects. Nat. Phys. 8, 199–202 (2012).

    CAS  Google Scholar 

  17. 17.

    Zhang, Y. et al. Scanning tunneling microscopy of the π magnetism of a single carbon vacancy in graphene. Phys. Rev. Lett. 117, 166801 (2016).

    Google Scholar 

  18. 18.

    González-Herrero, H. et al. Atomic-scale control of graphene magnetism by using hydrogen atoms. Science 352, 437–441 (2016).

    Google Scholar 

  19. 19.

    Morita, Y., Suzuki, S., Sato, K. & Takui, T. Synthetic organic spin chemistry for structurally well-defined open-shell graphene fragments. Nat. Chem. 3, 197–204 (2011).

    CAS  Google Scholar 

  20. 20.

    Goto, K. et al. A stable neutral hydrocarbon radical: synthesis, crystal structure, and physical properties of 2,5,8-Tri-tert-butyl-phenalenyl. J. Am. Chem. Soc. 121, 1619–1620 (1999).

    CAS  Google Scholar 

  21. 21.

    Inoue, J. et al. The first detection of a Clar’s hydrocarbon, 2,6,10-Tri-tert-butyltriangulene: a ground-state triplet of non-Kekulé polynuclear benzenoid hydrocarbon. J. Am. Chem. Soc. 123, 12702–12703 (2001).

    CAS  Google Scholar 

  22. 22.

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

    Google Scholar 

  23. 23.

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

    CAS  Google Scholar 

  24. 24.

    Su, J. et al. Atomically precise bottom-up synthesis of π-extended [5]triangulene. Sci. Adv. 5, eaav7717 (2019).

    Google Scholar 

  25. 25.

    Small, D. et al. Intermolecular π-to-π bonding between stacked aromatic dyads. Experimental and theoretical binding energies and near-IR optical transitions for phenalenyl radical/radical versus radical/cation dimerizations. J. Am. Chem. Soc. 126, 13850–13858 (2004).

    CAS  Google Scholar 

  26. 26.

    Suzuki, S. et al. Aromaticity on the pancake-bonded dimer of neutral phenalenyl radical as studied by MS and NMR spectroscopies and NICS analysis. J. Am. Chem. Soc. 128, 2530–2531 (2006).

    CAS  Google Scholar 

  27. 27.

    Sharpe, A. L. et al. Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene. Science 365, 605–608 (2019).

    CAS  Google Scholar 

  28. 28.

    Cyvin, B. N., Brunvoll, J. & Cyvin, S. J. in Advances in the Theory of Benzenoid Hydrocarbons II (ed. Gutman, I.) 65–180 (Springer, 1992).

  29. 29.

    Kang, J., Wu, F. & Li, J. Spin filter and molecular switch based on bowtie-shaped graphene nanoflake. J. Appl. Phys. 112, 104328 (2012).

    Google Scholar 

  30. 30.

    Zhou, A., Sheng, W. & Xu, S. J. Electric field driven magnetic phase transition in graphene nanoflakes. Appl. Phys. Lett. 103, 133103 (2013).

    Google Scholar 

  31. 31.

    Temirov, R., Soubatch, S., Neucheva, O., Lassise, A. C. & Tautz, F. S. A novel method achieving ultra-high geometrical resolution in scanning tunnelling microscopy. New J. Phys. 10, 053012 (2008).

    Google Scholar 

  32. 32.

    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).

    CAS  Google Scholar 

  33. 33.

    Pogodin, S. & Agranat, I. Clar goblet and related non-Kekulé benzenoid LPAHs. A theoretical study. J. Org. Chem. 68, 2720–2727 (2003).

    CAS  Google Scholar 

  34. 34.

    Das, A., Müller, T., Plasser, F. & Lischka, H. Polyradical character of triangular non-Kekulé structures, zethrenes, p-quinodimethane-linked bisphenalenyl, and the Clar goblet in comparison: an extended multireference study. J. Phys. Chem. A 120, 1625–1636 (2016).

    CAS  Google Scholar 

  35. 35.

    Ortiz, R. et al. Exchange rules for diradical π-conjugated hydrocarbons. Nano Lett. 19, 5991–5997 (2019).

    CAS  Google Scholar 

  36. 36.

    Hirjibehedin, C. F., Lutz, C. P. & Heinrich, A. J. Spin coupling in engineered atomic structures. Science 312, 1021–1024 (2006).

    CAS  Google Scholar 

  37. 37.

    Ternes, M. Spin excitations and correlations in scanning tunneling spectroscopy. New J. Phys. 17, 063016 (2015).

    Google Scholar 

  38. 38.

    Ternes, M., Heinrich, A. J. & Schneider, W.-D. Spectroscopic manifestations of the Kondo effect on single adatoms. J. Phys. Condens. Matter 21, 053001 (2008).

    Google Scholar 

  39. 39.

    van der Lit, J. et al. Suppression of electron–vibron coupling in graphene nanoribbons contacted via a single atom. Nat. Commun. 4, 2023 (2013).

    Google Scholar 

  40. 40.

    Horcas, I. et al. WSXM: a software for scanning probe microscopy and a tool for nanotechnology. Rev. Sci. Instrum. 78, 013705 (2007).

    CAS  Google Scholar 

  41. 41.

    Hutter, J., Iannuzzi, M., Schiffmann, F. & Vandevondele, J. CP2K: atomistic simulations of condensed matter systems. Wiley Interdiscip. Rev. Comput. Mol. Sci. 4, 15–25 (2014).

    CAS  Google Scholar 

  42. 42.

    VandeVondele, J. et al. QUICKSTEP: fast and accurate density functional calculations using a mixed Gaussian and plane waves approach. Comput. Phys. Commun. 167, 103–128 (2005).

    CAS  Google Scholar 

  43. 43.

    Pickett, W. E. Pseudopotential methods in condensed matter applications. Comput. Phys. Rep. 9, 115–197 (1989).

    Google Scholar 

  44. 44.

    VandeVondele, J. & Hutter, J. Gaussian basis sets for accurate calculations on molecular systems in gas and condensed phases. J. Chem. Phys. 127, 114105 (2007).

    Google Scholar 

  45. 45.

    Goedecker, S., Teter, M. & Hutter, J. Separable dual-space Gaussian pseudopotentials. Phys. Rev. B 54, 1703–1710 (1996).

    CAS  Google Scholar 

  46. 46.

    Lee, C.-C., Yamada-Takamura, Y. & Ozaki, T. Unfolding method for first-principles LCAO electronic structure calculations. J. Phys. Condens. Matter 25, 345501 (2013).

    Google Scholar 

  47. 47.

    Grimme, S., Antony, J., Ehrlich, S. & Krieg, H. A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H–Pu. J. Chem. Phys. 132, 154104 (2010).

    Google Scholar 

  48. 48.

    Wilhelm, J., Del Ben, M. & Hutter, J. GW in the Gaussian and plane waves scheme with application to linear acenes. J. Chem. Theory Comput. 12, 3623–3635 (2016).

    CAS  Google Scholar 

  49. 49.

    Neaton, J. B., Hybertsen, M. S. & Louie, S. G. Renormalization of molecular electronic levels at metal–molecule interfaces. Phys. Rev. Lett. 97, 216405 (2006).

    CAS  Google Scholar 

  50. 50.

    Kharche, N. & Meunier, V. Width and crystal orientation dependent band gap renormalization in substrate-supported graphene nanoribbons. J. Phys. Chem. Lett. 7, 1526–1533 (2016).

    CAS  Google Scholar 

  51. 51.

    Pizzi, G., Cepellotti, A., Sabatini, R., Marzari, N. & Kozinsky, B. AiiDA: automated interactive infrastructure and database for computational science. Comput. Mater. Sci. 111, 218–230 (2016).

    Google Scholar 

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We thank M. N. Huda for assistance with STM measurements, T. Lübken for assistance with nuclear magnetic resonance measurements, and R. Ortiz, J. Fernández-Rossier and D. Passerone for discussions. This work was supported by the Swiss National Science Foundation (grant nos 200020-182015 and IZLCZ2-170184), the NCCR MARVEL funded by the Swiss National Science Foundation (grant no. 51NF40-182892), the European Union’s Horizon 2020 research and innovation programme under grant agreement nos 696656 and 785219 (Graphene Flagship Core 2), the Office of Naval Research (N00014-18-1-2708), ERC Consolidator grant (T2DCP, no. 819698), the German Research Foundation (DFG) within the Cluster of Excellence Center for Advancing Electronics Dresden (cfaed) and EnhanceNano (no. 391979941), and the European Social Fund and the Federal State of Saxony (ESF-Project GRAPHD, TU Dresden). We acknowledge computational support from the Swiss Supercomputing Center (CSCS) under project ID s904; S.K. and P.L. acknowledge funding from the Academy of Finland (grant nos 309975 and 318995) and the European Research Council (ERC-AdG no. 788185) and the facilities of the Aalto Nanomicroscopy Centre.

Author information




K.M., X.F., P.R. and R.F. conceived the project; D.B. and R.B. synthesized and characterized the precursor molecules; S.M. performed the on-surface synthesis and STM experiments; S.M. and S.K. performed the magnetic field STM experiments under the supervision of P.L.; S.M. and O.G. performed TB calculations; K.E. performed DFT and GW calculations under the supervision of C.A.P.; the manuscript was written by S.M., with contributions from all co-authors.

Corresponding authors

Correspondence to Xinliang Feng or Roman Fasel.

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The authors declare no competing interests.

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Peer review information Nature Nanotechnology thanks Manuel Melle-Franco and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 MFH-calculated singlet-triplet gaps of 1 and di-1.

a, Schematic representations of 1 and di-1. b, Calculated singlet-triplet gaps (ΔES-T) of 1 (blue filled circles) and di-1 (red filled circles) as a function of the on-site Coulomb repulsion U, within the MFH model. Over a wide range of U/t (where t = 2.7 eV is the nearest-neighbour hopping parameter), ΔES-T, 1 is much larger than ΔES-T, di-1. c, Same as (b), with U/t ranging between 0.5 and 1.5, where it is evident that ΔES-T, di-1 values are essentially zero over the considered range of U, while ΔES-T, 1 shows a monotonic increase with increasing U. This is in support of the experimentally observed cases of spin excitations in 1 (finite ΔES-T) and Kondo resonances in di-1ES-T ≈ 0). ΔES-T values for both species are calculated as the mean-field energy difference between the converged electronic structures of the open-shell triplet (where n = n + 2) and open-shell singlet configurations (where n = n).

Extended Data Fig. 2 Analyses of temperature-dependent characteristics of zero-bias peak at the unbound end of 1´.

a, HR STM image showing two molecules towards the top and bottom of the scan frame, along with di-1 and a dimer where the constituent molecules are fused in an off-centre configuration (V= −100 mV, I= 50 pA). The lower end of each molecule is bound to the elbow site, leading to a distinct topographic appearance of the molecules. b, Temperature evolution of the ZBP at the unbound end of the upper molecule with fit to the experimental data with the Frota function (V= −20 mV, I= 300 pA, Vrms = 400 μV). Tip position is marked by a filled circle in (a). c, Extracted HWHM of the ZBP as a function of temperature, with corresponding fit using the Fermi-liquid model. As seen from the fit data in (b) and (c), the ZBP exhibits the expected lineshape and resonance linewidth broadening characteristic of a Kondo resonance, with the Kondo temperature TK = 57 ± 2 K. Scale bar: 2 nm.

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Supplementary Figs. 1–35, Notes 1–5, Schemes 1–8 and refs. 1–6.

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Mishra, S., Beyer, D., Eimre, K. et al. Topological frustration induces unconventional magnetism in a nanographene. Nat. Nanotechnol. 15, 22–28 (2020).

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