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# Spin splitting of dopant edge state in magnetic zigzag graphene nanoribbons

## Abstract

Spin-ordered electronic states in hydrogen-terminated zigzag nanographene give rise to magnetic quantum phenomena1,2 that have sparked renewed interest in carbon-based spintronics3,4. Zigzag graphene nanoribbons (ZGNRs)—quasi one-dimensional semiconducting strips of graphene bounded by parallel zigzag edges—host intrinsic electronic edge states that are ferromagnetically ordered along the edges of the ribbon and antiferromagnetically coupled across its width1,2,5. Despite recent advances in the bottom-up synthesis of GNRs featuring symmetry protected topological phases6,7,8 and even metallic zero mode bands9, the unique magnetic edge structure of ZGNRs has long been obscured from direct observation by a strong hybridization of the zigzag edge states with the surface states of the underlying support10,11,12,13,14,15. Here, we present a general technique to thermodynamically stabilize and electronically decouple the highly reactive spin-polarized edge states by introducing a superlattice of substitutional N-atom dopants along the edges of a ZGNR. First-principles GW calculations and scanning tunnelling spectroscopy reveal a giant spin splitting of low-lying nitrogen lone-pair flat bands by an exchange field (~850 tesla) induced by the ferromagnetically ordered edge states of ZGNRs. Our findings directly corroborate the nature of the predicted emergent magnetic order in ZGNRs and provide a robust platform for their exploration and functional integration into nanoscale sensing and logic devices15,16,17,18,19,20,21.

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## Data availability

DFT code with pseudopotentials and GW code can be downloaded from the Quantum Espresso (https://www.quantum-espresso.org) and the BerkeleyGW (https://www.berkeleygw.org) websites, respectively. We used Quantum Espresso version 6.4.1 and BerkeleyGW version 2.1 for the theoretical calculations. All data presented in the main text and the supplementary information are available from the corresponding authors upon reasonable request.

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## Acknowledgements

This work was primarily funded by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), Materials Sciences and Engineering Division under contract no. DE-AC02-05-CH11231 (Nanomachine program KC1203) (molecular design, surface growth, calculations and analyses of surface–GNR interactions). Research was also supported by the Office of Naval Research under award no. N00014-19-1-2503 (STM characterization), the National Science Foundation under grant nos. DMR-1839098 (image analysis) and DMR-1926004 (GW calculations), the Center for Energy Efficient Electronics Science ECCS-0939514 (magnetic modelling), and the Office of Naval Research MURI under award no. N00014-16-1-2921 (molecular synthesis, ab initio DFT calculations). This research used resources of the National Energy Research Scientific Computing Center (NERSC), a US Department of Energy Office of Science User Facility operated under Contract No. DE-AC02-05-CH11231. Computational resources were also provided by the National Science Foundation through XSEDE resources at the NICS. R.E.B. acknowledges support through a National Science Foundation Graduate Research Fellowship under grant DGE-11064000. We thank the College of Chemistry for use of resources at their NMR facility, and we thank their staff for assistance. Instruments in CoC-NMR are supported in part by NIH S10OD024998.

## Author information

Authors

### Contributions

R.E.B., F.Z., S.G.L and F.R.F. initiated and conceived the research. E.B., I.P. and F.R.F designed, synthesized, and characterized the molecular precursors. R.E.B., S.W., J.Z., A.D. and F.R.F. performed on-surface synthesis and STM characterization and analysis. F.Z., Y.-L.L. and S.G.L. performed DFT and GW calculations as well as theoretical analyses, and assisted with data interpretation. R.E.B., F.Z., S.G.L. and F.R.F. wrote the manuscript. All authors contributed to the scientific discussion.

### Corresponding authors

Correspondence to Steven G. Louie or Felix R. Fischer.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature thanks Rémy Pawlak, Levente Tapaszto and Daniel Sanchez-Portal for their contribution to the peer review of this work.

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## Extended data figures and tables

### Extended Data Fig. 1 Height profiles of N-6-ZGNRs on Au(111).

a, STM topographic image of N-6-ZGNR on Au(111) (Vs = 50 mV, It = 20 pA; CO-functionalized tip). b, Height profile recorded along the arrows marked in a.

### Extended Data Fig. 2 dI/dV point spectroscopy of N-6-ZGNRs on Au(111).

a, dI/dV point spectra collected on bare Au(111) (Vac = 11 mV, f = 455 Hz). b, dI/dV point spectra collected on as grown segments of N-6-ZGNRs. c, dI/dV point spectra collected on decoupled segments of N-6-ZGNRs following the SPM tip-induced decoupling protocol.

### Extended Data Fig. 3 Tip induced decoupling of N-6-ZGNRs.

It/Vs plot showing in red the positive voltage sweep (Vs = +1.50 V to Vs = +2.50 V) used during the decoupling procedure. The respective return sweep (Vs = +2.50 V to Vs = +1.50 V) is depicted in grey and shows the irreversible shift in the tunnelling current It.

### Extended Data Fig. 4 Tip-induced decoupling of magnetic edge states in N-6-ZGNRs.

a, Topographic image of a fully cyclized N-6-ZGNR segment recorded with CO-functionalized STM tip. b, Constant-current dI/dV map recorded at a voltage bias of Vs = +0.5 V of N-6-ZGNR segment following tip-induced decoupling using a positive voltage sweep from Vs = 0.0 V to Vs = +2.5 V at the position marked by a red cross in a (Vac = 11 mV, It = 200 pA, f = 455 Hz, CO functionalized tip). c, Constant-current dI/dV map recorded at a voltage bias of Vs = +0.5 V of N-6-ZGNR segment following tip-induced decoupling using a negative voltage sweep from Vs = 0.0 V to Vs = –2.5 V at the position marked by a blue cross in a (Vac = 11 mV, It = 200 pA, f = 455 Hz, CO functionalized tip). Arrows mark the position of selected N-atom along the edge of the N-6-ZGNR.

### Extended Data Fig. 5 Bond resolved imaging of decoupled N-6-ZGNRs.

a, Constant-height BRSTM image of a N-6-ZGNR segment from (Vs = 0 mV, modulation voltage Vac = 11 mV, modulation frequency f = 455 Hz). b, Constant-height BRSTM image of the N-6-ZGNR segment in a following tip-induced decoupling using a positive voltage sweep from Vs = 0.0 V to Vs = +2.5 V at the position marked by a red cross in a (Vs = 0 mV, Vac = 11 mV, f = 455 Hz). Arrows mark the position of selected N-atom along the edge of the N-6-ZGNR. c, STM topographic image of as-grown N-6-ZGNRs with CO-modified tip. d, STM topographic image of N-6-ZGNR after decoupling the GNR on the left. (Vs = 50 mV, It = 20 pA).

### Extended Data Fig. 6 Calculated adsorption geometries of N-6-ZGNRs on Au(111).

a, Local minimum Adsorption Geometry I (E = +0.312 eV). Four C-atoms per unit cell interact through π-bonding (< 2.5 Å) with the Au(111) surface. The corrugation on opposing zigzag edges is in phase (φ = 0). b, Local minimum Adsorption Geometry II (E = +0.355 eV). Five C-atoms and one N-atom per unit cell interact through π-bonding (< 2.5 Å) with the Au(111) surface. The corrugation on opposing zigzag edges is phase shifted by φ = 1/3π. c, Global minimum Adsorption Geometry III (E = +0.000 eV). Four C-atoms and two N-atoms per unit cell interact through π-bonding (< 2.5 Å) with the Au(111) surface. The corrugation on opposing zigzag edges is phase shifted by φ = π. All calculations performed with ultrasoft pseudopotentials and 40 Ry cut-offs.

### Extended Data Fig. 7 Electronic structure of 6-ZGNR and N-6-ZGNRs.

a, GW band structure of freestanding 6-ZGNR (grey) and N-6-ZGNR (red) calculated using the same dimension unit cell. b, GW band structure of a freestanding N-6-ZGNR. The colour code shows the normalized contributions from C-atoms, N-atoms, and H-atoms to the wavefunction of each state. The number of pz + σ orbitals for C, N, and H atoms are 280, 8, and 10 per unit cell, respectively. The wavefunction projection of the state in the nth band and at wavevector k to the C, N, and H atoms is described by PnkC, PnkN, and PnkH, respectively. We define the normalized percentage weight PnkC, PnkN, and PnkH as the wavefunction projection on the C, N, and H atoms per atom in the unit cell: $$\bar{P}$$nkC = PnkC/280, $$\bar{P}$$nkN = PnkN/8, $$\bar{P}$$nkH = PnkH/10. The scale bar defines the mapping between the colour scale and the normalized percentage weight. c, Spatial distribution of the calculated spin polarized wavefunction for UNFB and LNFB. d, Spin unpolarized GW band structure of a freestanding N-6-ZGNR (with DFT within the local density approximation (LDA) as the starting point). In the spin unpolarized calculation the UNFB and LNFB form narrow non-splitting bands with a total band width smaller than 50 meV. e, Spatial distribution of the calculated spin unpolarized wavefunction for UNFB and LNFB.

### Extended Data Fig. 8 Spatial localization of spin split low-lying nitrogen dopant flat band states.

Waterfall plot of dI/dV point spectra collected along a line marked in the inset long the edge of a N-6-ZGNR (Vac = 11 mV, f = 455 Hz). When the STM tip is located immediately above the position of a nitrogen dopant atom the dI/dV point spectra show two characteristic peaks centred at Vs = –2.60 ± 0.02 V and Vs = –2.70 ± 0.02 V, corresponding to the UNFB and LNFB states, respectively.

### Extended Data Fig. 9 dI/dV point spectroscopy of spin split low-lying nitrogen dopant flat band states.

dI/dV point spectroscopy recorded on four different decoupled N-6-ZGNR/Au(111) at the position above the N atoms. Ten dI/dV point spectra were collected at each position (grey). The respective averaged dI/dV point spectra are highlighted in red, orange, yellow, and blue (spectroscopy: Vac = 11 mV, f = 455 Hz).

### Extended Data Fig. 10 Constant-current dI/dV maps of decoupled N-6-ZGNR.

dI/dV maps recorded at voltage biases of a, Vs = –2.000 V, b, Vs = –2.025 V, c, Vs = –2.050 V, d, Vs = –2.100 V, e, Vs = –2.125 V, f, Vs = –2.150 V, g, Vs = –2.200 V, h, Vs = –2.225 V, i, Vs = –2.250 V, j, Vs = –2.400 V, k, Vs = –2.500 V, and l, Vs = –2.800 V (Vac = 11 mV, It = 2 nA, f = 455 Hz).

## Supplementary information

### Supplementary Information

This file contains Supplementary Methods and Supplementary Figures 1–6.

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Blackwell, R.E., Zhao, F., Brooks, E. et al. Spin splitting of dopant edge state in magnetic zigzag graphene nanoribbons. Nature 600, 647–652 (2021). https://doi.org/10.1038/s41586-021-04201-y

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• DOI: https://doi.org/10.1038/s41586-021-04201-y

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