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\title{Single Spin Localization and Manipulation \\ in Graphene Open-Shell Nanostructures}
%\title{\tf{Spin localization and spin coupling \\ in  graphene nanostructures}}

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\author
{Jingcheng Li$^{1}$, Sofia Sanz$^{2}$, Martina Corso$^{2,3}$, Deung Jang Choi$^{2,3,5}$,  Diego Pe{\~{n}}a$^{4}$, \\ 
Thomas Frederiksen$^{2,5}$, Jose Ignacio Pascual$^{1,5}$ \\
\\
\normalsize{$^{1}$ CIC nanoGUNE, 20018 Donostia-San Sebasti\'an, Spain}\\
\normalsize{$^{2}$Donostia International Physics Center (DIPC), 20018 Donostia-San Sebasti\'an, Spain}\\
\normalsize{$^{3}$ Centro de F{\'{\i}}sica de Materiales 	CFM/MPC (CSIC-UPV/EHU),  20018 Donostia-San Sebasti\'an, Spain}\\
\normalsize{$^{4}$Centro Singular de Investigaci\'on en Qu\'imica Biol\'oxica e Materiais Moleculares (CiQUS),} \\
\normalsize{and Departamento de Qu\'imica Org\'anica, Universidade de Santiago de Compostela, Spain}\\
\normalsize{$^{5}$Ikerbasque, Basque Foundation for Science, 48013 Bilbao, Spain}
\\
\\
%\normalsize{$^\ast$ To whom correspondence should be addressed; E-mail: }
}

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%\date{\today}



\begin{abstract}
Turning graphene magnetic is a promising challenge to make it an active material for spintronics. Predictions state that graphene structures with specific shapes can spontaneously develop magnetism driven by Coulomb repulsion of $\pi$-electrons, but its experimental verification  is demanding. Here, we report on the observation and manipulation of individual magnetic moments in graphene open-shell nanostructures on a gold surface. Using scanning tunneling spectroscopy, we detect the presence of single electron spins localized around certain zigzag sites of the carbon backbone via the Kondo effect.  We find near-by spins coupled into a singlet ground state and quantify their exchange interaction via singlet-triplet inelastic electron excitations. Theoretical simulations picture how electron correlations result in spin-polarized radical states with the experimentally observed spatial distributions. Extra hydrogen atoms bound to radical sites quench their magnetic moment and switch the spin of the nanostructure in half-integer amounts.  Our work demonstrate the intrinsic  $\pi$-paramagnetism of graphene nanostructures. 


\end{abstract}

\newpage

\section*{Introduction}
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 \cite{Han2014}. 
Generally, magnetism is associated to a large degree of electron localization and strong spin-orbit 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 \cite{Lieb1989}, causes a spin imbalance in the system. This can be done by either inserting defects that remove a single ${p_z}$ orbital \cite{Yazyev2007,Nair2012,McCreary2012,Gonzalez2016} or by shaping graphene with zigzag edges \cite{Fernandez-Rossier2007,Yazyev2010}.
However, magnetism can also emerge  in graphene nanostructures where  Lieb's theorem does not apply \cite{Alexandre2012,Ortiz2016}. For example, in $\pi$-conjugated systems with small band gaps, Coulomb repulsion between valence electrons forces the electronic system to reorganize into open-shell configurations \cite{Morita2011} 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 $\mu_\mathrm{B}$, 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 \cite{Son2006,Tao2011,Ruffieux2016} and chiral \cite{Yazyev2011,Carvalho2014} graphene nanoribbons (chGNRs). 

The  experimental observation of  spontaneous magnetization driven by electron  correlations is still challenging, because, for example, atomic defects and metal impurities in the graphene structures \cite{Sepioni2010,Nair2013,Li2018} hide the weak paramagnetism of radical sites \cite{Cervenka2009}. Scanning probe microscopies can spatially localize the source states of magnetism \cite{Gonzalez2016,Li2018}, 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 \cite{Kondo1964,Ternes2009}, 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.



\section*{Results}

\textbf{Formation of GNR nanostructures.} The graphene nanostructures studied here are directly created  
on a Au(111) surface  by cross-dehydrogenative coupling of adjacent chiral GNRs (chGNRs)\cite{Dienel2015}. We deposited  the organic molecular precursors  2,2'-dibromo-9,9'-bianthracene (Fig.~1\textbf{a}) on a clean Au(111) surface, 
and  annealed stepwisely to 250~\oC\ (step 1 in Fig.~1\textbf{a}) to produce narrow (3,1)chGNRs, i.e. ribbons that alternate three zig-zag sites with one armchair along the edge \cite{Dimas2016}. They are semiconductors with a band-gap of 0.7 eV  and show two enantiomeric forms on the surface\cite{Merino2017}. 
By further annealing the substrate to 350 
\oC\ (step 2 in Fig.~1\textbf{a}),  chGNRs  fuse together into junctions, as shown in  Fig.~1\textbf{b}.  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.~1\textbf{c}).  The creation of this stable nanostructure implies the reorganization of the carbon atoms around the 
initial contact point\cite{Shiotari2017} into the final structure shown in Fig.~1\textbf{d},   \li{ as described in Supplementary Note~1}.


In  Fig.~1\textbf{b}, 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.~1\textbf{e}), over the terminal zigzag 
(ZZ) site of the junction (Type 2, Fig.~1\textbf{f}), or over both (Type 3, Fig.~1\textbf{g}). Supplementary Note~2 quantifies the probability of finding each type of junction. Despite these 
different LDOS distributions in the three types of junctions,  they all have the same 
carbon lattice  arrangement, shown in Fig.~1\textbf{d}.
Such low-energy LDOS enhancements are absent over bare chGNRs segments due to their semiconductor character, and only the bare hexagonal backbone is resolved. 



\textbf{Spectral features around zero-bias.} 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.~2\textbf{a,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\cite{Kondo1964,Ternes2009}.
Their observation  is a proof of  a localized 
magnetic moment  screened by conduction electrons\cite{Fernandez-Torrente2008,Zhang2013} (see Supplementary Note~3). The relationship between the observed peaks and the Kondo effect is proven by measurements of $dI/dV$ spectra at different temperatures (Fig.~2\textbf{c}) and magnetic fields (Fig.~2\textbf{d}).    
The resonance line width increases with temperature following the characteristic behavior of a Kondo-screened state  with a  Kondo Temperature  $T_K \sim 6$ K\cite{Nagaoka2002,Zhang2013}  (Fig.~2\textbf{c}), and broadens with magnetic field as expected for a spin-\textonehalf\ system (Fig.~2\textbf{d}). Hence, the bright regions are caused by the localization of a single magnetic moment. 



Junctions with two bright regions (Type 3) show   
different low-energy features: two peaked steps in $dI/dV$ spectra at $\sim \pm$10 meV 
(Fig.~2\textbf{e}). The steps \rev{appear always symmetric with respect to zero bias, and at the same energy over the terminal ZZ segment and over the PC region for a given nanostructure, while vanish quickly away from these sites. }
Based on the existence of localized spins on  bright areas of Type 1 and 2 junctions, we attribute such \rev{bias-symmetric 
peaked steps } to the excitation of two exchange coupled spins  localized  at each 
junction site \rev{by  tunneling electrons}. 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 \rev{inelastically} excite a spin reversal in any of them when their energy equals the exchange coupling energy between the spins, i.e., $eV\geq J$.  
Usually, such \rev{singlet-triplet  inelastic excitation} is revealed in $dI/dV$ spectra as   
steps at the onset of spin excitations\cite{Hirjibehedin2006}, from which one can directly determine the strength of the exchange coupling $J$ between the spins.  
Here, the \rev{inelastic  spectra additionally show asymmetric peaks on top of the excitation onsets, with a pronounced logarithmic fall off for biases above. Such peaked steps are characteristic of Kondo-like  fluctuations of the spin once the anisotropy energy has been overcome by tunneling electrons (i.e. out of equilibrium) \cite{Heersche2006,Paaske2006,Ternes2015,Ortiz2017}. The more pronounced signal for either particle tunneling (over ZZ) or for hole tunneling (over PC) indicates the spins system lies out of particle-hole symmetry point, with \Ef closer to the corresponding singly unoccupied or singly occupied state, respectively. }
Hence, the gap between $dI/dV$ peaks in Fig.~2\textbf{e} 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.
In Fig. 2\textbf{f} 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-\textonehalf\ systems\cite{Ternes2015}, one obtains the exchange coupling $J=2.7$ ($9.9$) meV for the upper (lower) spectrum.



\textbf{Theory simulations to uncover the origin of spin polarization.} 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 Hubbard (MFH) models (see Supplementary Notes~6 and 7).
Fig. 3\textbf{a} shows the spin-polarization of a junction of Fig.~1\textbf{d}. The ground state exhibits a net spin localization  at the ZZ and PC regions with opposite sign, which is absent in the bare ribbons. The spin distribution along the edge sites reproduces the  distribution of dI/dV signal measured in Type 3 junctions. This supports that this signal is an intrinsic effect of junction edge sites, rather than caused by defects or other atomic species. 

The origin of the spontaneous magnetization can be rationalized by considering  the effect 
of Coulomb correlations between $\pi$-electrons as described within a tight-binding (TB) model (Fig. 3\textbf{b}).
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 (Fig. 3\textbf{c}).
These are split-off states from the VB of the (3,1)-chGNR, which lies close below \Ef \cite{Merino2017}. 
In the absence of electron-electron correlations, these two states conform the highest occupied (HO) and lowest unoccupied (LU) molecular states of the nanostructure.
Due to the large degree of localization 
(Supplementary Figures~10-11), the Coulomb repulsion energy \UHH\ between two electrons in the HO state becomes comparable  with
the energy difference $\delta$ 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.~3\textbf{b}. 
Similar  conclusions  regarding the emergence  of radical states at PC and ZZ sites can also be reached by applying the empirical Clar's aromatic $\pi$-sextet rule to the close-shell structure of Fig.~\textbf{1}d, as described in the Supplementary Note~4.

According to both DFT (Fig.~3\textbf{a}) and MFH (Supplementary Figure 14) 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.~2\textbf{e}) 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 Note~8) agrees with a weaker exchange interaction due to a larger localization of the spin-polarized states. Alternative scenarios for peaks around \Ef, such as single-particle states or Coulomb-split radical states\cite{Gonzalez2016}, would show the opposite trend with
the system size.


\revbi{The observation of spin localization in only one of the two radical regions in Type 1 and 2 junctions implies that  one of the two edge magnetic moments has  vanished. Foreign atoms bonding to a singly occupied p$_z$ orbital  remove the local spin and suppress the magnetic signal at this site. Metal atoms can bind to C-sites, but the interaction is too weak to bind to $\pi$-radicals over a metal substrate  \cite{Pavlicek2017c}.}
Instead,  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\cite{Talirz2013}. 
DFT simulations show that attaching an extra H atom into  an edge 
carbon in either the ZZ   or PC  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 (Fig.~3\textbf{d}), and leaves the junction 
with a single electron localized at the opposite radical site ((Fig.~3\textbf{e}) and Supplementary Figure~7). 
According to this, a Type 1 junction shows Kondo at the PC site because it has a H atom bonded to the ZZ site that quenches that magnetic moment, and opposite for Type 2.
The computed wave function amplitude  distributions for the two energetically most favourable adsorption sites (Fig.~3\textbf{f}) are also in excellent agreement with the extension of the Kondo resonance mapped in Fig.~2\textbf{a,b}. 



\textbf{Manipulation of the spin state of the nanostructures.} The presence of extra H atoms in Type 1 and 2 junctions \li{was confirmed by  electron induced H-atom removal experiments. Figure~4\textbf{a} shows a structure formed by three chGNRs connected via Type 1 and 2 junctions.} Accordingly, their $dI/dV$ spectra (black curves in Figs.~4\textbf{b,c}) 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.~4\textbf{b}). The resulting junction appeared with double bright regions in 
low-bias images (Fig.~4\textbf{d}), and the PC$_1$ and ZZ$_2$ spectra turned into  dI/dV steps characteristic of Type 3  junctions (blue curves in Figs.~4\textbf{b,c}). 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, \np{and switching the total spin of the junction from spin   \textonehalf\ to zero.}


\textbf{Contacting the junctions with the STM tip.} The magnetic state of the junction was also changed by creating a contact between the STM tip apex and a radical site. \revbi{$\Pi-$radicals show some weak reactivity to bond  metallic atoms, that allows their manipulation with an STM tip \cite{Koch2012}.} In  the experiments shown in  Fig.~5\textbf{a}, the STM tip was approached to the  ZZ sites of a Type 3 junction. A  step in the conductance-distance plot (Fig.~5\textbf{b}) indicated the formation of a contact. The created tip-chGNR contact could be stretched up to 3 \AA\ before breaking (retraction step  in Fig.~5\textbf{b}), signalling  that a chemical bond was formed. \revbi{Such contacts only succeeded over bright PC and ZZ sites, revealing their $\pi-$radical character, while  over passivated sites failed.}

A reference $dI/dV$ spectrum recorded before the bond formation (black point in Fig.~5\textbf{c}) shows the split-peak feature of Type 3 junctions (black spectrum  in Fig.~5\textbf{c}). After the bond 
formation (blue and red points in Fig.~5\textbf{b}), the spectra changed to  show Kondo resonances  (blue and red spectra  in Fig.~5\textbf{c}),  persisting during contact retraction until the bond-breaking step, where double-peak features are recovered (green spectrum  in Fig.~5\textbf{c}). 
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 of a Type 2 junction (shown in Supplementary Note~5) the initial Kondo resonance  disappears from the spectra, signaling the complete demagnetization of the junction. The width of the Kondo resonance in the contacted  junctions  (blue and red plots in Fig.~5\textbf{c}) is significantly larger than in Type 1 and 2 cases, probably because it incorporates scattering with tip states\cite{Jasper-Tonnies2017,Choi2017}, and monotonously narrows as the contact is pulled apart (Fig.~5\textbf{d}). The survival of the Kondo effect in the contacted Type 3 junctions is a remarkable outcome of our experiments, which demonstrate the addressability of such localized magnetic moments in graphene nanostructure devices.

\rev{\section*{Discussion}
Open shell configurations of extended $\pi$ systems can be stabilized on-top of insulating layers~\cite{Wang2016,Pavlicek2017c}. The results presented here prove that the intrinsic  open-shell character of a graphene nanostructure can survive  on the surface of a metal.  This is remarkable because proves that key electron-electron correlations needed for the stabilization of magnetic ground states persist on the metal, in spite of the ubiquitous charge screening by the underlying  substrate \cite{Li2013a}. In addition, the adsorption on the Au(111) substrate has the general trend of hole-doping GNRs \cite{Ruffieux2012,Merino2017b}, which in some systems caused depopulation of the mid-gap states \cite{Koch2012}. The band structure of the (3,1) chGNR and, in particular, the proximity of the VB to \Ef, is a crucial aspect to stabilize the electron population of the GNR junction on the surface and hence, for the survival of their magnetic ground state.  }

 

\begin{methods}
	
	
	\subsection{Sample preparation and experimental details.}
	The experiments were performed on two different scanning tunneling microscopes
	(STM) operating in ultra-high vacuum. A commercial JT STM (from specs) operated
	at 1.2 K with a magnetic field up to 3 Tesla was used to measure the temperature
	and magnetic field dependence of the Kondo resonance, while other experiments
	were done with a home made STM operating at 5 K. Both setups allow in situ
	sample preparation and transfer into the STM. The Au(111)
	substrate was cleaned in UHV by repeated cycles of Ne$^{+}$ ion sputtering and
	subsequent annealing to 730 K. The molecular
	precursor (2,2'-dibromo-9,9'-bianthracene) was sublimated at 170 $^{\circ}$C
	from a Knudsen cell onto the clean Au(111) substrate kept at room temperature.
	Then the sample was first annealed at 200 $^{\circ}$C for 15 minutes in order to
	induce the polymerization of the molecular precursors by Ullmann coupling, then
	the sample was annealed at 250 $^{\circ}$C for 5 minutes to trigger the
	cyclodehydrogenation to form chiral graphene nanoribbons (chGNRs). A last step
	annealing at 350 $^{\circ}$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 M$\Omega$. The $dI/dV$
		signal was recorded using a lock-in amplifier with a bias modulation of $V_\mathrm{rms}=0.1$ mV (Fig. 2d and 2e) and $V_\mathrm{rms}=0.4$  mV at 760 Hz.\\
	
	\subsection{Simulations.}
	We performed calculations with the SIESTA implementation\cite{SIESTA} of density functional theory (DFT). Exchange and correlation (XC) were included within either 
	the local (spin) density approximation (LDA)\cite{LDA} or the generalized gradient approximation (GGA)\cite{PBE}. 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 {\AA} in any direction. The electronic density was converged to a stringent criterion of $10^5$.
	The force tolerance was set to 0.002 eV/{\AA}. 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 $\pi$-electron systems\cite{Fernandez-Rossier2007,Yazyev2010,Yazyev2011,Carvalho2014,Hancock2010,SISL}. 
	\subsection{Data availability} The data that support the findings of this study are available from the corresponding author upon reasonable request.
	
	
\end{methods}





\begin{addendum}
 \item We thank Manuel Vilas-Varela for the synthesis of the chGNR molecular precursor. We are indebted to Carmen Rubio, Dimas G. de Oteyza, Nestor Merino, Nicol\'as Lorente, Aran Garc\'{\i}a Lekue, and Daniel S\'anchez Portal for fruitful discussions. \\
We acknowledge financial support from Spanish AEI 
(MAT2016-78293-C6, FIS2017-83780-P, and the Maria de Maeztu Units of Excellence Programme 
MDM-2016-0618),  the Basque Government (Dep.~Industry, Grant PI-2015-1-42), the EU project 
PAMS (610446), the Xunta de Galicia (Centro singular de investigaci\'on de Galicia 
accreditation 2016-2019, ED431G/09),   and the European Regional Development Fund (ERDF).\\ 
 \item[Author Contributions] J.L,  and J.I.P. devised the experiment.  D.P. designed the  
organic synthesis of the chGNR molecular precursor. J.L. realized the experiments. M.C. and D.J.C. assisted J.L. in part of 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. \\
 \item[Competing Interests] The authors declare no competing interests.

\end{addendum}








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\newpage
\begin{figure}
%\includegraphics[width=\textwidth]{fig1.pdf}
\caption{\textbf{Formation of GNR junctions}. \textbf{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). 
\textbf{b}, Constant-height current images  ($V=2$ mV, scale bar: 2 nm) showing joint chGNR nanostructures,  \ with an angle of $\sim$50$^\circ$, 
obtained  after further annealing the sample.   A CO-functionalized tip was used to resolve the chGNR ring structure. Dashed boxes indicate  the most characteristic chGNR junctions, whose structure is shown in panels \textbf{c,d}.  
\textbf{c},  Laplace-filtered image of the junction shown in panel g to enhance the backbone structure, and \textbf{d}, model structure of the junction. PC labels the pentagonal cove site and the ZZ the zigzag site. 
\textbf{e-g}, Constant-height current images ($V=8$ mV, scale bar 0.5 nm) of the three types of chGNR junctions with same backbone structures but  with different LDOS distribution. 
}
\end{figure}



\begin{figure}
%\includegraphics[width=0.95\textwidth]{fig2.pdf}
\caption{\textbf{Zero bias spectral features}. \textbf{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.
\textbf{c}, 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)\cite{Frota1992}, and corrected for the thermal broadening of the tip\cite{Zhang2013}. The temperature dependence of FWHM was fit by the empirical expression  $\sqrt{(\alpha k_BT)^2+(2k_BT_K)^2}$\cite{Nagaoka2002}, resulting in a Kondo temperature $T_K \sim$ 6 K and $\alpha=9.5$ (Supplementary Note~3). . 
\textbf{d}, Magnetic field dependence of a  Kondo resonance (over the same PC site) at the field strengths indicated in the figure. 
\textbf{e},  Double-peak features around zero bias over Type 3 junctions. 
\textbf{f},  Split-peak $dI/dV$ features for nanostructures  with different sizes, determined by the number of precursor units in each chGNR, labeled \textsf{L} and \textsf{R} in panel \textbf{e}. 
The gap width 
increases with the length of the ribbons (see Supplementary Figure 16a in Supplementary Note~8). The red dashed lines are fits to our spectra  using a model for two coupled spin-\textonehalf\ systems\cite{Ternes2015}. The spectra in \textbf{c} and \textbf{d} were acquired with a metal tip, while the others with a CO-terminated tip. }
\end{figure}

\begin{figure} 
	%\includegraphics[width=\textwidth]{fig3.pdf}
	\caption{\textbf{Calculated electronic states and spin polarization}. \textbf{a}, Spin polarization obtained from DFT simulations in a Mulliken population analysis. 
    The standard junction (all peripheral carbons bonded to H) shows 
    spontaneous spin localization in both PC and ZZ regions, revealing the apparition of 
    radical states. 
    \textbf{b}, 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-\textonehalf\ systems (Type 3 junction). This process is energetically favoured when the reduction in Coulomb energy $U_\mathrm{HH}-U_\mathrm{HL}$ plus exchange energy $J$ exceeds the level separation $\delta$, i.e., $\delta+U_\mathrm{HL}-J<U_\mathrm{HH}$.
	\textbf{c}, Single-particle TB wave functions (HO/LU) for Type 3 junction.
	\textbf{d}, Same as in \textbf{a} but now adding a H atom to an external carbon in either the ZZ (Type 1) or PC 
	(Type 2). The passivation with H removes the corresponding radical state and, hence, its  spin-polarization.
	\textbf{e}, Sketch of the spin-\textonehalf\ Kondo state generated with a single radical (Type 1 and 2 junctions).
    \textbf{f}, Single-particle TB wave functions (SO) for Type 1 and Type 2 junctions.
    Red-green colors represent the positive-negative phase. 
    }
\end{figure}

\begin{figure}[!htb]
\begin{center}
	\centering
	%\includegraphics[width=0.75\columnwidth]{fig4.pdf}
	\caption{\textbf{Spin manipulation by electron-induced removal of extra H-atoms}. 
    \textbf{a}, Constant-height current image of two junctions with extra H atoms ($V=8$ mV). (scale bar 1 nm).
    \textbf{b,c}, $dI/dV$ spectra taken over PC$_1$ and ZZ$_2$ regions (indicated in  \textbf{a}) before (black) and after (blue) the dehydrogenation processes.  Inset in  \textbf{b} shows the current during the process of dehydrogenation.
    \textbf{d}, Image with same conditions as in \textbf{a} after the electron-induced removal of the extra H-atoms.  
    The dehydrogenation processes were done over the ZZ$_1$ and PC$_2$ sites.}
\end{center}
\end{figure}

\begin{figure}
\begin{center}
	\centering
	%\includegraphics[width=\columnwidth]{fig5.pdf}
	\caption{\textbf{Kondo effect from the spin embedded in a lifted chGNR junction}.
    \textbf{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.
    \textbf{b}, Simultaneously recorded conductance curve ($V=-50$ mV) during the approach, jump to contact and lift processes.
    \textbf{c}, $dI/dV$ spectra recorded at the specific heights indicated with  colored points on the curves in \textbf{b}. 
    \textbf{d}, Full widths at half maximum (FWHM) of spectra acquired in the retraction process (points in \textbf{c}), extracted from a fit using the Frota function\cite{Frota1992}. }
\end{center}
\end{figure}


\end{document}

