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.
Subscribe to Journal
Get full journal access for 1 year
only $14.08 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Rent or Buy article
Get time limited or full article access on ReadCube.
All prices are NET prices.
The data that support the findings of this study are available from the corresponding authors on reasonable request.
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.
Yazyev, O. V. Emergence of magnetism in graphene materials and nanostructures. Rep. Prog. Phys. 73, 056501 (2010).
Clar, E. The Aromatic Sextet (Wiley, 1972).
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).
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).
Landauer, R. Irreversibility and heat generation in the computing process. IBM J. Res. Dev. 5, 183–191 (1961).
Cyvin, S. J., Brunvoll, J. & Cyvin, B. N. The hunt for concealed non-Kekuléan polyhexes. J. Math. Chem. 4, 47–54 (1990).
Agarwal, H., Pramanik, S. & Bandyopadhyay, S. Single spin universal Boolean logic gate. New J. Phys. 10, 015001 (2008).
Han, W., Kawakami, R. K., Gmitra, M. & Fabian, J. Graphene spintronics. Nat. Nanotechnol. 9, 794–807 (2014).
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).
Fernández-Rossier, J. & Palacios, J. J. Magnetism in graphene nanoislands. Phys. Rev. Lett. 99, 177204 (2007).
Tao, C. et al. Spatially resolving edge states of chiral graphene nanoribbons. Nat. Phys. 7, 616–620 (2011).
Ruffieux, P. et al. On-surface synthesis of graphene nanoribbons with zigzag edge topology. Nature 531, 489–492 (2016).
Li, J. et al. Single spin localization and manipulation in graphene open-shell nanostructures. Nat. Commun. 10, 200 (2019).
Lieb, E. H. Two theorems on the Hubbard model. Phys. Rev. Lett. 62, 1201–1204 (1989).
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).
Nair, R. R. et al. Spin-half paramagnetism in graphene induced by point defects. Nat. Phys. 8, 199–202 (2012).
Zhang, Y. et al. Scanning tunneling microscopy of the π magnetism of a single carbon vacancy in graphene. Phys. Rev. Lett. 117, 166801 (2016).
González-Herrero, H. et al. Atomic-scale control of graphene magnetism by using hydrogen atoms. Science 352, 437–441 (2016).
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).
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).
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).
Pavliček, N. et al. Synthesis and characterization of triangulene. Nat. Nanotechnol. 12, 308–311 (2017).
Mishra, S. et al. Synthesis and characterization of π-extended triangulene. J. Am. Chem. Soc. 141, 10621–10625 (2019).
Su, J. et al. Atomically precise bottom-up synthesis of π-extended triangulene. Sci. Adv. 5, eaav7717 (2019).
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).
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).
Sharpe, A. L. et al. Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene. Science 365, 605–608 (2019).
Cyvin, B. N., Brunvoll, J. & Cyvin, S. J. in Advances in the Theory of Benzenoid Hydrocarbons II (ed. Gutman, I.) 65–180 (Springer, 1992).
Kang, J., Wu, F. & Li, J. Spin filter and molecular switch based on bowtie-shaped graphene nanoflake. J. Appl. Phys. 112, 104328 (2012).
Zhou, A., Sheng, W. & Xu, S. J. Electric field driven magnetic phase transition in graphene nanoflakes. Appl. Phys. Lett. 103, 133103 (2013).
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).
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).
Pogodin, S. & Agranat, I. Clar goblet and related non-Kekulé benzenoid LPAHs. A theoretical study. J. Org. Chem. 68, 2720–2727 (2003).
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).
Ortiz, R. et al. Exchange rules for diradical π-conjugated hydrocarbons. Nano Lett. 19, 5991–5997 (2019).
Hirjibehedin, C. F., Lutz, C. P. & Heinrich, A. J. Spin coupling in engineered atomic structures. Science 312, 1021–1024 (2006).
Ternes, M. Spin excitations and correlations in scanning tunneling spectroscopy. New J. Phys. 17, 063016 (2015).
Ternes, M., Heinrich, A. J. & Schneider, W.-D. Spectroscopic manifestations of the Kondo effect on single adatoms. J. Phys. Condens. Matter 21, 053001 (2008).
van der Lit, J. et al. Suppression of electron–vibron coupling in graphene nanoribbons contacted via a single atom. Nat. Commun. 4, 2023 (2013).
Horcas, I. et al. WSXM: a software for scanning probe microscopy and a tool for nanotechnology. Rev. Sci. Instrum. 78, 013705 (2007).
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).
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).
Pickett, W. E. Pseudopotential methods in condensed matter applications. Comput. Phys. Rep. 9, 115–197 (1989).
VandeVondele, J. & Hutter, J. Gaussian basis sets for accurate calculations on molecular systems in gas and condensed phases. J. Chem. Phys. 127, 114105 (2007).
Goedecker, S., Teter, M. & Hutter, J. Separable dual-space Gaussian pseudopotentials. Phys. Rev. B 54, 1703–1710 (1996).
Lee, C.-C., Yamada-Takamura, Y. & Ozaki, T. Unfolding method for first-principles LCAO electronic structure calculations. J. Phys. Condens. Matter 25, 345501 (2013).
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).
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).
Neaton, J. B., Hybertsen, M. S. & Louie, S. G. Renormalization of molecular electronic levels at metal–molecule interfaces. Phys. Rev. Lett. 97, 216405 (2006).
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).
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).
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.
The authors declare no competing interests.
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.
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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-1 (ΔES-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 1´ 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 1´ 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 1´ 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.
About this article
Cite this article
Mishra, S., Beyer, D., Eimre, K. et al. Topological frustration induces unconventional magnetism in a nanographene. Nat. Nanotechnol. 15, 22–28 (2020). https://doi.org/10.1038/s41565-019-0577-9
Chemical Society Reviews (2021)
Angewandte Chemie (2021)
Spiers Memorial Lecture : Carbon nanostructures by macromolecular design – from branched polyphenylenes to nanographenes and graphene nanoribbons
Faraday Discussions (2021)
Probing the ‘elephant’: On the essential difference between graphenes and polycyclic aromatic hydrocarbons