Single Spin Localization and Manipulation in Graphene Open-Shell Nanostructures

Predictions state that graphene can spontaneously develop magnetism from the Coulomb repulsion of its $\pi$-electrons, but its experimental verification has been a challenge. Here, we report on the observation and manipulation of individual magnetic moments localized in graphene nanostructures on a Au(111) surface. Using scanning tunneling spectroscopy, we detected the presence of single electron spins localized around certain zigzag sites of the carbon backbone via the Kondo effect. Two near-by spins were found coupled into a singlet ground state, and the strength of their exchange interaction was measured via singlet-triplet inelastic tunnel electron excitations. Theoretical simulations demonstrate that electron correlations result in spin-polarized radical states with the experimentally observed spatial distributions. Hydrogen atoms bound to these radical sites quench their magnetic moment, permitting us to switch the spin of the nanostructure using the tip of the microscope.

Among the many applications predicted for graphene, its use as a source of magnetism is the most unexpected one, and an attractive challenge for its active role in spintronic devices 1 .
Generally, magnetism is associated to a large degree of electron localization and strong spinorbit interaction.Both premises are absent in graphene, a strongly diamagnetic material.The simplest method to induce magnetism in graphene is to create an imbalance in the number of carbon atoms in each of the two sublattices, what, according to the Lieb's theorem for bipartite lattices 2 , causes a spin imbalance in the system.This can be done by either inserting defects that remove a single p z orbital [3][4][5][6] or by shaping graphene with zigzag edges 7,8 .However, magnetism can also emerge in graphene nanostructures where Lieb's theorem does not apply 9, 10 .For example, in π-conjugated systems with small band gaps, Coulomb repulsion between valence electrons forces the electronic system to reorganize into open-shell configurations 11 with unpaired electrons (radicals) localized at different atomic sites.Although the net magnetization of the nanostructures may be zero, each radical state hosts a magnetic moment of size µ B , the Bohr magneton, turning the graphene nanostructure paramagnetic.This basic principle predicts, for example, the emergence of edge magnetization originating from zero-energy modes in sufficiently wide zigzag [12][13][14] and chiral 15,16 graphene nanoribbons (GNRs).
The experimental observation of spontaneous magnetization driven by electron correlations is still challenging, because, for example, atomic defects and impurities in the graphene structures 17,18 hide the weak paramagnetism of radical sites 19 .Scanning probe microscopies can spatially localize the source states of magnetism, but they require both atomic-scale resolution and spin-sensitive measurements.Here we achieve these conditions to demonstrate that atomically-defined graphene nanostructures can host localized spins at specific sites and give rise to the Kondo effect 20,21 , a many-body phenomenon caused by the interaction between a localized spin and free conduction electrons in its proximity.Using a low-temperature scanning tunneling microscope (STM) we use this signal to map the spin localization within the nanostructure and to detect spin-spin interactions.The graphene nanostructures studied here are directly created on a Au(111) surface by cross-dehydrogenative coupling of adjacent chiral GNRs (chGNRs) 22 .We deposited the organic molecular precursors 2,2'-dibromo-9,9'-bianthracene (Fig. 1a) on a clean Au(111) surface, and annealed stepwisely to 250 • C (step 1 in Fig. 1a) to produce narrow chGNRs 14,23 .The chiral ribbons are semiconductors with a band-gap of 0.7 eV (Supplementary Figs.S7 and S8) and show two enantiomeric forms on the surface 24 .By further annealing the substrate to 350 • C (step 2 in Fig. 1a), chGNRs fuse together into junctions, as shown in Fig. 1b.The chGNR junctions highlighted by dashed rectangles are the most frequently found in our experiments.They consist of two chGNRs with the same chirality linked together by their termination (Fig. 1c).The creation of this stable nanostructure implies the reorganization of the carbon atoms around the initial contact point 25 into the final structure shown in Fig. 1d, as described in Supplementary Fig. S1.
In Fig. 1b, certain regions of the junctions appear brighter when recorded at low sample bias, reflecting enhancements of the local density of states (LDOS) close to the Fermi level.
Interestingly, the precise location of the bright regions is not unique, but can be localized over the pentagon cove (PC) site (Type 1, Fig. 1e), over the terminal zigzag (ZZ) site of the junction (Type 2, Fig. 1f), or over both (Type 3, Fig. 1g).Despite these different LDOS distributions in the three types of junctions, they have identical carbon arrangement (Fig. 1d).
To understand the origin of the enhanced LDOS at the ZZ and PC sites, we recorded differential conductance spectra (dI/dV ) on the three types of junctions.Spectra on the bright sites of Type 1 and 2 junctions show very pronounced zero-bias peaks (Fig. 2a,b) localized over the bright sites (spectra 1 to 4, and 6 to 8), and vanishing rapidly in neighbor rings (spectra 5, 9, and 10).These are generally ascribed as Abrikosov-Suhl resonances due to the Kondo effect, and named as Kondo resonances 20,21 .Their observation is a proof of a localized magnetic moment screened by conduction electrons 26,27 .The resonance line width increases with temperature (Fig. 2d) and magnetic field (Fig. 2e) following the characteristic behavior of a spin-½ system with a Kondo Temperature T K ∼ 6 K 27,28 .
Junctions with two bright regions (Type 3) show different low-energy features: two peaked steps in dI/dV spectra at ∼ ±10 meV (Fig. 2c).The peaks appear at the same energies over the terminal ZZ segment and over the PC region for a given nanostructure, and vanish quickly away from these sites.Based on the existence of localized spins on bright areas of Type 1 and 2 junctions, we attribute the double-peak features to excitation of two exchange coupled spins localized at each junction site.The exchange interaction tends to freeze their relative orientation, in this case antiferromagnetically into a singlet ground state.Electrons tunneling into the coupled spin system can excite a spin reversal in any of them when their energy equals the exchange coupling energy between the spins, i.e., eV ≥ J. Usually, this inelastic process is revealed in dI/dV spectra as steps at the onset of spin excitations 31 , from which one can directly determine the strength of the exchange coupling J between the spins.Here, the spectra additionally show asymmetric peaks on top of the excitation onsets characteristic of Kondolike systems with particle-hole asymmetry, when spin fluctuations are hindered in the ground state 30,[32][33][34] .Hence, the gap between dI/dV peaks in Fig. 2c is a measure of the interaction strength between the two localized spins.
Interestingly, the spectral gap in Type 3 junctions increases with the length of the connecting ribbons (See Supplementary Fig. 15b).In Fig. 2f we compare low-energy spectra of two junctions with different chGNR lengths.Although the atomic structures of both junctions are identical, the one with shorter ribbons (upper curve; 9 and 2 precursor units) displays a smaller gap than the junction of longer chGNRs (lower curve; > 8 and 7 units).Fitting the spectra with a model of two coupled spin-½ systems 30 , one obtains the exchange coupling J = 2.7 (9.9) meV for the upper (lower) spectrum.
To explain the emergence of localized spins, we simulated the spin-polarized electronic structure of chGNR junctions using both density functional theory (DFT) and mean-field Hub- The full width at half maximum (FWHM) at each temperature is extracted by fitting a Frota function (red dashed lines) 29 , and corrected for the thermal broadening of the tip 27 .The temperature dependence of FWHM was fit by the empirical expression (αk B T ) 2 + (2k B T K ) 228 , resulting in a Kondo temperature T K ∼ 6 K and α = 9.5.e, Magnetic field dependence of a Kondo resonance (over the same PC site) at the field strengths indicated in the figure.f, Split-peak dI/dV features for nanostructures with different sizes, determined by the number of precursor units in each chGNR, labeled L and R in panel c.The gap width increases with the length of the ribbons (Supplementary Section 7).The red dashed lines are fits to our spectra using a model for two coupled spin-½ systems 30 .The spectra in d and e were acquired with a metal tip, while the others with a CO-terminated tip.bard (MFH) models (see Supplementary Sections 5 and 6).Fig. 3a shows the spin-polarization of a junction of Fig. 1d.The ground state exhibits a net spin localization at the ZZ and PC regions with opposite sign, which is absent in the bare ribbons.This spin distribution agrees with the observations for Type 3 junctions.The origin of the spontaneous magnetization can be rationalized by considering the effect of Coulomb correlations between π-electrons as described within a tight-binding (TB) model.The spin distribution is related to the appearance of two junction states inside the gap of the (3,1)-chGNR electronic bands, localized at the PC and ZZ sites, respectively.In the absence of electron-electron correlations, these two states conform the highest occupied (HO) and lowest unoccupied (LU) molecular states of the nanostructure (Fig. 3e).Due to the large degree of localization (Supplementary Figs.S10-S11), the Coulomb repulsion energy U HH between two electrons in the HO state becomes comparable with the energy difference δ between the two localized levels.Hence, in a simplified picture, the two electrons find a lower-energy configuration by occupying each a different, spatially separated in-gap state.These two states become singly occupied (SO), spin-polarized (i.e., they have a net magnetic moment), and exchange coupled as schematically illustrated in Fig. 3c.Similar conclusions regarding the emergence of radical states at PC and ZZ sites can also be reached using the empirical Clar's aromatic π-sextet rule (Supplementary Section 3).
According to both DFT (Fig. 3a) and MFH (Supplementary Fig. S9) the magnetic moments are antiferromagnetically aligned into a singlet ground state.Therefore, the inelastic features in dI/dV spectra found over Type 3 junctions (Fig. 2c) are associated to singlet-triplet excitations induced by tunneling electrons.In fact, the smaller excitation energy found for the smaller ribbons in both theory and experiment (Supplementary Section 7) agrees with a weaker exchange interaction due to a larger localization of the spin-polarized states.Alternative scenarios for peaks around E F , such as single-particle states or Coulomb-split radical states 6 , would show the opposite trend with the system size.
To account for spin localization in only one of the two radical regions in Type 1 and 2 junctions, one of the two edge magnetic moments has to vanish.H-passivation of radical sites is a highly probable process occurring on the surface due to the large amount of hydrogen available during the reaction 35 .DFT simulations show that attaching an extra H atom into an edge carbon in either the ZZ (Type 1) or PC (Type 2) sites leads to its sp 3 hybridization and the removal of a p z orbital from the aromatic backbone.This completely quenches the magnetic moment of the passivated region, and leaves the junction with a single electron localized at the opposite radical site (Supplementary Fig. S6).The computed distributions for the two energetically most favorable adsorption sites (Fig. 3b) are in excellent agreement with the extension of the Kondo resonance mapped in Fig. 2a,b.
The presence of extra H atoms in Type 1 and 2 junctions was confirmed by electron induced H-atom removal experiments.Figure 4 a shows a structure formed by three chGNRs connected via Type 1 and 2 junctions.Accordingly, their dI/dV spectra (black curves in Figs.4c,d) show a Kondo resonance at the PC 1 and ZZ 2 regions.We placed the STM tip on top of the opposite sites ZZ 1 and PC 2 , and raised the positive sample bias well above 1 V.A step-wise decrease of the tunneling current indicated the removal of the extra H atom (inset in Fig. 4c).The resulting junction appeared with double bright regions in low-bias images (Fig. 4b), and the PC 1 and ZZ 2 spectra turned into dI/dV steps characteristic of Type 3 junctions (blue curves in Figs.4c,d).
Thus, the removal of H atoms activated the magnetic moment of the initially unpolarized ZZ 1 and PC 2 sites, converting Type 1 and 2 junctions into Type 3, and switching the total spin of the junction from spin ½ to zero.
The magnetic state of the junction was also changed by creating a contact between the STM tip apex and a radical site.In the experiments shown in Figure 5, the STM tip was approached to the ZZ sites of a Type 3 junction.A step in the conductance-distance plot (Fig. 5b) indicated the formation of a contact.The created tip-chGNR contact could be stretched up to 3 Å before breaking (retraction step in Fig. 5b), signaling that a chemical bond was formed.feature of Type 3 junctions (black spectrum in Fig. 5c).After the bond formation (blue and red points in Fig. 5b), the spectra changed to show Kondo resonances (blue and red spectra in Fig. 5c), persisting during contact retraction until the bond-breaking step, where double-peak features are recovered (green spectrum in Fig. 5c).The formation of a tip-chGNR bond thus removed the spin of the ZZ site, and the transport spectra reflect the Kondo effect due to the remaining spin embedded in the junction.If the STM tip contacts instead the ZZ radical site • C for 15 minutes in order to induce the polymerization of the molecular precursors by Ullmann coupling, then the sample was annealed at 250 • C for 5 minutes to trigger the cyclodehydrogenation to form chiral graphene nanoribbons (chGNRs).A last step annealing at 350 • C for 1 minute created nanostructure junctions.A tungsten tip functionalized with a CO molecule was used for high resolution images.All the images in the manuscript were acquired in constant height mode, at very small voltages, and junction resistances of typically 20 MΩ.The dI/dV signal was recorded using a lock-in amplifier with a bias modulation of V rms = 0.4 mV at 760 Hz.
Simulations.We performed calculations with the SIESTA implementation 38 of density functional theory (DFT).Exchange and correlation (XC) were included within either the local (spin) density approximation (LDA) 39 or the generalized gradient approximation (GGA) 40 .We used a 400 Ry cutoff for the real-space grid integrations and a double-zeta plus polarization (DZP) basis set generated with an 0.02 Ry energy shift for the cutoff radii.The molecules, represented with periodic unit cells, were separated by a vacuum of at least 10 Å in any direction.The electronic density was converged to a stringent criterion of 10 5 .The force tolerance was set to 0.002 eV/ Å.Here is a description of a specific method used.To complement the DFT simulations described above we also performed simulations based on the mean-field Hubbard (MFH) model, known to provide a good description for carbon π-electron systems 7,8,15,16,41 .
the chGNR molecular precursor.J.L. realized the measurements.S.S. and T.F. did the theoretical simulations.All the authors discussed the results.J.L., T.F., and J.I.P. wrote the manuscript.

Statistics of different types of junctions
In the main text we studied three different nanostructure junctions (Figs. 1 and 2).Here we show the frequency statistics of the three types.From the 45 different junctions studied, 30 of them are identified as Type 3 junctions, while 9 and 5 of them are identified as Type 1 and Type 2 junctions respectively (Figure S2a).From this statistics, we deduced that the ZZ sites are more favorable to incorporate an extra hydrogen atom and get passivated (22% of the radicals).The PC sites had an extra atom only in 13% of the cases.The overall percentage of H-passivation observed here is comparable to the value found at the termination of armchair GNRs [1], which was happened in a 15% of the occasions.
In one of the 45 nanostructures inspected, we observed a junction with same backbone structure as the other three types, but with neither bright sites, nor zero-bias features in the spectra.Figure S2b shows a constant height current image of the junction, where its ring structure can be now nicely resolved.It corresponds to the carbon backbone sketch in Fig. 1d of the main text but with two extra H atoms saturating the radical sites.3 Understanding the appearance of spins in the junctions from Clar's theory In the main text, we used both DFT and Hubbard Mean Field simulations to show that the spins in Type 3 junctions comes from two in-gap states, simply occupied as a result of electronelection correlations.An alternative and intuitive chemical picture behind the emergence of singly occupied radical states can be drawn bearing in mind Clar's aromatic pi-sextet rule [2].In Fig. 5 of the main text, we studied the behaviour of a spin localized at the PC site in a transport measurement, when a Type 3 junction was contacted with the STM tip at the neighbour ZZ site and lifted.Electrons injected through the conjugated backbone reproduced the Kondo resonance observed in tunneling regime.For comparison, here we show similar transport measurement for a Type 2 junction, i.e. when there is no spin in the graphene nanostructure.As in the other case, the STM tip was approached to the radical at the ZZ site to make a bond between nanostructure and STM tip (illustrated in Figure S4).Before bond formation, the characteristic Kondo resonance of Type 2 junctions is observed in the dI/dV spectra (point 1 in the figure).
However, once the radical bonded to the tip (signalled by the characteristic jump-to-contact step), the junction bridged tip and substrate and the Kondo resonance disappeared.This proves that the tip-radical contact quenches the magnetic moment of this site, as presumed in Fig. 5.It also proves that the Kondo feature observed in Fig. 5 for the lifted junction correspond to the PC spin embedded in the cGNR junction.

DFT simulations
We performed calculations with the SIESTA implementation [3] of density functional theory (DFT).Exchange and correlation (XC) were included within either the local (spin) density approximation (LDA) [4] or the generalized gradient approximation (GGA) [5].We used a 400 Ry cutoff for the real-space grid integrations and a double-zeta plus polarization (DZP) basis set generated with an 0.02 Ry energy shift for the cutoff radii.The molecules, represented with periodic unit cells, were separated by a vacuum of at least 10 Å in any direction.The electronic density was converged to a stringent criterion of 10 5 .The force tolerance was set to 0.002 eV/ Å.
In Fig. 3 in the main text we report the GGA results.

Role of exchange-correlation functional
In Figure S5 we compare the calculated spin polarization for the generic (2,2) graphene nanojunction within both LDA [4] and GGA [5] XC approximations.We also compare the real-space spin density with a Mulliken population analysis.From Figure S5 it is clear that the emerging picture for the radicals is robust among all four approaches.As expected, the intensity of the spin polarization is more pronounced in GGA than in LDA.
Energetically preferred hydrogen passivation sites In the main text we showed the hydrogen passivation on ZZ sites (Type 1 junctions) and PC sites (Type 2 junctions).In Figure S2 we report a higher probability of hydrogen passivation on ZZ sites than PC sites.To quantitatively study this phenomenon, we analysed the energetics of different hydrogen passivations of the edges from DFT simulations.The results are summarized in Figure S6.We find that hydrogen passivation on the ZZ and PC sites are indeed the two most stable configurations, with the former being the energetically most favoured one.This is in agreement with the experimental observations (Figure S2).

Mean-field Hubbard model
To complement the DFT simulations described above we also performed simulations based on the mean-field Hubbard (MFH) model, known to provide a good description for carbon π-electron systems [6-10].We describe the graphene nanostuctures with the following Hamiltonian for the sp 2 carbon atoms: where c iσ (c † iσ ) annihilates (creates) an electron with spin σ in the p z orbital centred at site i.The first three terms describe a tight-binding model with hopping amplitudes t 1 , t 2 , and t 3 for the first, second, and third-nearest neighbour matrix elements (defined in terms of interatomic distances d 1 < 1.6 Å< d 2 < 2.6 Å< d 3 < 3.1 Å).We follow the parameterizations of Ref. [10]   and consider both a simple first-nearest neighbour (1NN) model with t 1 = 2.7 eV and t 2 = t 3 = 0 as well as a more accurate third-nearest neighbour (3NN) model with t 1 = 2.7 eV, t 2 = 0.2 eV, and t 3 = 0.18 eV.
The term proportional to the empirical parameter U accounts for the on-site Coulomb repulsion.By comparison with first-principles simulations it has been established that DFT-GGA (DFT-LDA) are generally best reproduced when U/t ≈ 1.3 (0.9) [8].Consistent with this, we find a good overall agreement with our experimental observations using U ∼ 3.5 eV as analysed below.
The expectation value of the spin-resolved density operator n iσ = c † iσ c iσ is computed from the eigenvectors of H. From the self-consistent solution of the Hamiltonian in Eq. ( 1) we obtain the local spin density from the charge difference Q i↑ − Q i↓ , with Q iσ = e n iσ .In units of µ B the magnetization is We solve the mean-field Hubbard model using a custom-made Python implementation based on SISL [11].In Fig. 3  Indeed this narrow cGNR is intrinsically non-magnetic, consistent with previous works [8,9,12].Singlet-triplet excitations From Figure S9 we have established that U = 3.5 eV yields a good description for these nanostructures as compared with DFT.As an approximation to the true singlet-triplet excitation energy J, we computed the mean-field energy difference ∆E ST between the converged electronic configurations with n ↑ = n ↓ and n ↑ = n ↓ + 2. In Figure S14 we explore the variation of ∆E ST with U for a Type 3 junction.Within the 3NN model a minimum is observed close to ∆E ST ∼ 19 meV at U ∼ 3.5 eV, in reasonable agreement with (albeit larger than) the experimentally observed peak splitting.

Figure 1 :
Figure 1: Formation of graphene junctions by cross-dehydrogenative coupling of adjacent graphene nanoribbons.a, Model structures of the organic precusor 2,2'-dibromo-9,9'bianthracene and of the on-surface synthesized (3,1)chGNR after Ullmann-like C-C coupling reaction and cyclodehydrogenation on Au(111).b, Constant-height current images (V = 2 mV, scale bar: 2 nm) showing joint chGNR nanostructures, with an angle of ∼50 • , obtained after further annealing the sample.A CO-functionalized tip was used to resolve the chGNR ring structure.Dashed boxes indicate the most characteristic chGNR junctions, whose structure is shown in panels c,d.c, Laplace-filtered image of the junction shown in panel g to enhance the backbone structure, and d, model structure of the junction.PC labels the pentagonal cove site and the ZZ the zigzag site.e-g, Constant-height current images (V = 8 mV, scale bar 0.5 nm) of the three types of chGNR junctions with same backbone structures but with different LDOS distribution.

Figure 2 :
Figure 2: Spatial distribution of Kondo resonances and singlet-triplet excitations in chGNR junctions.a,b, Kondo resonances over the bright regions of Type 1 and Type 2 junctions, respectively.The zero-bias peaks are mostly detected over four PC rings of Type 1 junctions and over three ZZ rings of Type 2 junctions.c, Double-peak features around zero bias over Type 3 junctions.d, Temperature dependence of the Kondo resonance.All spectra were measured over the same PC site.The full width at half maximum (FWHM) at each temperature is extracted by fitting a Frota function (red dashed lines)29 , and corrected for the thermal broadening of the tip27 .The temperature dependence of FWHM was fit by the empirical expression (αk B T ) 2 + (2k B T K ) 228 , resulting in a Kondo temperature T K ∼ 6 K and α = 9.5.e, Magnetic field dependence of a Kondo resonance (over the same PC site) at the field strengths indicated in the figure.f, Split-peak dI/dV features for nanostructures with different sizes, determined by the number of precursor units in each chGNR, labeled L and R in panel c.The gap width increases with the length of the ribbons (Supplementary Section 7).The red dashed lines are fits to our spectra using a model for two coupled spin-½ systems30 .The spectra in d and e were acquired with a metal tip, while the others with a CO-terminated tip.

Figure 3 :
Figure 3: Calculated electronic states of chGNR junctions.a,b, Spin polarization obtained from DFT simulations in a Mulliken population analysis.The standard junction shown in a(all peripheral carbons bonded to H) shows spontaneous spin localization in both PC and ZZ regions, revealing the apparition of radical states.Adding a H atom to an external carbon in either the ZZ (Type 1) or PC (Type 2) removes the corresponding radical state and, hence, its spin-polarization.c, Schema of the spontaneous spin polarization when one of the two electrons in the HO level gets promoted to the LU level to form two separated, exchange coupled spin-½ systems (Type 3 junction).This process is energetically favored when the reduction in Coulomb energy U HH − U HL plus exchange energy J exceeds the level separation δ, i.e., δ + U HL − J < U HH .d, Sketch of the spin-½ Kondo state generated with a single radical (Type 1 and 2 junctions).e, Single-particle TB wave functions (HO/LU) for Type 3 junction.f, Single-particle TB wave functions (SO) for Type 1 and Type 2 junctions.Red-green colors represent the positive-negative phase.

Figure 4 :
Figure 4: Spin manipulation by electron-induced removal of extra H-atoms.a, Constantheight current image of two junctions with extra H atoms (V = 8 mV).b, Image with same conditions as in a after the removal of the extra H-atoms induced by tunneling electrons.The dehydrogenation processes were done over the ZZ 1 and PC 2 sites.c,d, dI/dV spectra taken over PC 1 and ZZ 2 regions (indicated in a and b respectively) before (black) and after (blue) the dehydrogenation processes.Inset in c shows the current during the process of dehydrogenation.

Figure 5 :
Figure5: Kondo effect from the spin embedded in a lifted chGNR junction.a, Schematics of the process where the tip of the STM is first approached to the ZZ site of a Type 3 junction (gray dashed arrow) and then retracted to lift the junction away from the substrate (red arrow), resulting in a suspended junction between tip and substrate.b, Simultaneously recorded conductance curve (V = −50 mV) during the approach, jump to contact and lift processes.c, dI/dV spectra recorded at the specific heights indicated with colored points on the curves in b. d, Full widths at half maximum (FWHM) of spectra acquired in the retraction process (points in c), extracted from a fit using the Frota function29 .

Figure S2 .
Figure S2.Statistics of different types of junctions.a, Bar plot of the number of three types of junctions studied in the main text.b, Constant-height current image (V = 2 mV, scale bar 0.5 nm) shows another type of junctions with both radicals are passivated by H atoms, which is classified as Type 4 junction.

Figure
Figure S3 shows two possible resonance structures for the GNR junction: the closed shell structure a, with 8 Clar sextets, and the open shell structure b, with 11 Clar sextets and two radicals at the PC and ZZ sites.The dominance of resonance structure b in our experiments means that the energy required to create the two unpaired electrons (radicals) in structure b is compensated by the stabilization provided by the presence of three additional Clar sextets.In fact, the radical sites can delocalize towards the two second neighbor edge carbon atoms, agreeing with the carbon sites with high density of states shown in Fig. 1e in the main text.Hence, this phenomenological model can qualitatively explain the spontaneous appearance of spin in the nanostructures.

Figure S4 .
Figure S4.Transport properties of the lifted junctions without radical.a, Schema illustrating the process, when the STM tip was approached to the ZZ radical of a Type 2 junction (gray dashed arrow) to form a contact.b, Simultaneously recorded conductance curve (V = −50 mV) during the process in a. Red and black dots indicate the vertical positions at whcih dI/dV spectra in c were taken.

Figure S6 .
Figure S5.Spin polarization in the (2,2)-junction from DFT simulations.a, Real-space spin density calculated within LDA. b, Mulliken population analysis of the spin density calculated within LDA. c,d Same as a,b but for GGA.Panel d corresponds to Fig. 3a in the main text.
in the main text we report the non-interacting single-particle wave functions in the 3NN model (U = 0) as a basis to understand the open-shell electronic configurations obtained in DFT and MFH.Band structure of infinite (3,1)cGNRs As shown in Figures.S7 and S8, both the first-neighbour and third-neighbour MFH models (red bands) provide a good description for the 1D band structure of the (3,1) chiral graphene nanoribbon (cGNR) as compared to DFT calculations (black bands) obtained with SIESTA [3].Unlike DFT and the 3NN model, the simple 1NN model implies electron-hole symmetry of the bands.The low-energy part of the DFT band structure is generally very well reproduced with MFH using an on-site Coulomb repulsion of U ≤ 3.5 eV.