Uncovering the Triplet Ground State of Triangular Graphene Nanoflakes Engineered with Atomic Precision on a Metal Surface

Jingcheng Li, Sofia Sanz, Jesus Castro-Esteban, Manuel Vilas-Varela, Niklas Friedrich, Thomas Frederiksen, Diego Peña, and Jose Ignacio Pascual

Phys. Rev. Lett. 124, 177201 – Published 27 April 2020

Abstract

Graphene can develop large magnetic moments in custom-crafted open-shell nanostructures such as triangulene, a triangular piece of graphene with zigzag edges. Current methods of engineering graphene nanosystems on surfaces succeeded in producing atomically precise open-shell structures, but demonstration of their net spin remains elusive to date. Here, we fabricate triangulenelike graphene systems and demonstrate that they possess a spin $S = 1$ ground state. Scanning tunneling spectroscopy identifies the fingerprint of an underscreened $S = 1$ Kondo state on these flakes at low temperatures, signaling the dominant ferromagnetic interactions between two spins. Combined with simulations based on the meanfield Hubbard model, we show that this $S = 1$ $π$ paramagnetism is robust and can be turned into an $S = 1 / 2$ state by additional H atoms attached to the radical sites. Our results demonstrate that $π$ paramagnetism of high-spin graphene flakes can survive on surfaces, opening the door to study the quantum behavior of interacting $π$ spins in graphene systems.

Received 16 October 2019
Revised 17 February 2020
Accepted 2 April 2020

DOI:https://doi.org/10.1103/PhysRevLett.124.177201

Physics Subject Headings (PhySH)

Ferromagnetism Kondo effect Spintronics

Graphene

Hubbard model Scanning tunneling microscopy Scanning tunneling spectroscopy Tight-binding model

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Jingcheng Li ¹, Sofia Sanz ², Jesus Castro-Esteban³, Manuel Vilas-Varela³, Niklas Friedrich ¹, Thomas Frederiksen ^2,4,*, Diego Peña^3,†, and Jose Ignacio Pascual ^1,4,‡

¹CIC Nanogune BRTA, 20018 Donostia-San Sebastián, Spain
²Donostia International Physics Center (DIPC), 20018 Donostia-San Sebastián, Spain
³Centro Singular de Investigación en Química Biolóxica e Materiais Moleculares (CiQUS), and Departamento de Química Orgánica, Universidade de Santiago de Compostela, 15705 Santiago de Compostela, Spain
⁴Ikerbasque, Basque Foundation for Science, 48013 Bilbao, Spain

^*thomas_frederiksen@ehu.eus
^†diego.pena@usc.es
^‡ji.pascual@nanogune.eu

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Vol. 124, Iss. 17 — 1 May 2020

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Images

Figure 1
Chemical structures and synthetic route of extended triangulene and double triangulene. (a), (b) Atomic structures of ETRI and DTRI, which have spin 1 and 0, respectively. Red (black) open circles denote carbon atoms that belong to different sublattices, with the total number of carbon atoms indicated under the structures. (c), (d) Molecular precursors 2,6-dibromo-10-(2,6-dimethylphenyl)-9,9’-bianthracene (precursor 1) and 2,2’-dibromo-10,10’-bis(2,6-dimethylphenyl)-9,9’-bianthracene (precursor 2) used to synthesize ETRI and DTRI, respectively. (e), (f) STM overview images ( $V = 0.3 V$ , $I = 0.1 nA$ ) of the formed GNFs from precursors 1 and 2, respectively. The arrows in (e) indicate the ETRI monomers created. (g), (h) Constant height current images ( $V = 2 mV$ ) of ETRI and DTRI with a CO-terminated tip.
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Figure 2
Kondo resonances in extended triangulene. (a) $d I / d V$ spectra of ETRI (blue curve) and DTRI (red curve) measured at the sites indicated by the colored crosses in the inset. (b) Temperature dependence of the Kondo resonance for an ETRI molecule. The inset plots the half width at half maximum (HWHM) at each temperature, extracted by fitting a Frota function (red dashed lines) [39] and corrected for the thermal broadening of the tip [40]. The plot includes the empirical expression $\sqrt{(α k_{B} T)^{2} + (2 k_{B} T_{K})^{2}}$ [41], fitting the results with $T_{K} \sim 6 K$ and $α = 8.5$ . The temperature evolution of the zero-bias conductance, shown as SM [25], agrees with a spin-polarized state in the Kondo regime with energy scale of a few Kelvin. (c) Magnetic field dependence of the Kondo resonance with the field strength indicated in the figure, measured at $T = 1.3 K$ . The red dashed lines show the simulated curves using a model for a spin-1 system using the code of Ref. [38]. The inset shows the dependence of Zeeman splitting of the Kondo resonance with magnetic fields, determined from the bias position of steepest slope (indicated on the spectrum at 2.8 T). The dashed line fits the Zeeman splitting with a $g$ factor of $1.98 \pm 0.07$ . The spectra in (b), (c) are shifted vertically for clarity.
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Figure 3
Spin manipulation by electron-induced removal of extra H atoms. (a) Constant height current image ( $V = 2 mV$ ) of a 2H-ETRI, with its chemical structure shown in (b). (c), (e) Constant height current image ( $V = 2 mV$ ) of the same ETRI of (a) after the electron-induced removal of one and two passivating hydrogen atoms, respectively. The arrows in (a), (c) indicate the STM tip positions during the processes. The corresponding chemical structures are show in (d), (f). (g) Comparison of $d I / d V$ spectra taken on the three structures at the locations noted with numbers in (a), (c), (e). (h) Comparison of the HWHM from the Kondo resonance taken on 1H-ETRI (red data points) and ETRI (blue data points), respectively. The value of each data point is extracted by fitting the corresponding Kondo resonances with Frota functions [39]. Different data points stand for the measurements from different molecules. (i) Comparison of Kondo resonance taken on 1H-passivated ETRI (red curve) and ETRI (blue curve) at a magnetic field of 2.5 T. (j), (k), (l) Spin polarization of 2H-ETRI, 1H-ETRI, and ETRI from meanfield Hubbard simulations.
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Figure 4
Magnetic properties of dimers of ETRI. (a) Constant height current image ( $V = 2 mV$ ) of a ETRI dimer with its chemical structure shown in (b). (c) $d I / d V$ spectra taken on the dimer on the sites indicated with corresponding numbers in (a). (d) Temperature dependence of the Kondo resonance taken at site no.2. The spectra are shifted vertically for clarity. The inset plots the HWHM at each temperature, extracted by fitting a Frota function (red dashed lines) [39] and corrected for the thermal broadening of the tip [40]. The inset includes the simulation with the empirical expression $\sqrt{(α k_{B} T)^{2} + (2 k_{B} T_{K})^{2}}$ [41], fitting the results with $T_{K} \sim 7 K$ with $α = 15$ . For comparison, the temperature dependence of HWHM from the Kondo resonance taken on a single ETRI monomer (gray data points) is also shown. (e) Kondo resonance taken at location 2 at different magnetic fields at $T = 1.3 K$ . (f) Spin polarization of a ETRI dimer from MFH simulations.
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