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[Kewei Sun](https://orcid.org/0000-0002-1835-243X), Nan Cao, Orlando J. Silveira, Adolfo O. Fumega, Fiona Hanindita, Shingo Ito, Jose L. Lado, Peter Liljeroth, Adam S. Foster, [Shigeki Kawai](https://orcid.org/0000-0003-2128-0120)

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[On-surface synthesis of Heisenberg spin-1/2 antiferromagnetic molecular chains](https://mdr.nims.go.jp/datasets/ba54e37b-bccc-46db-bfeb-68d1f053d0e1)

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On-surface synthesis of Heisenberg spin-1/2 antiferromagnetic molecular chainsSun et al., Sci. Adv. 11, eads1641 (2025)     28 February 2025S c i e n c e  A d v a n c e s  |  R e s e ar  c h  A r t i c l e1 of 8C H E M I C A L  P H Y S I C SOn-surface synthesis of Heisenberg spin-1/2 antiferromagnetic molecular chainsKewei Sun1,2, Nan Cao3, Orlando J. Silveira3, Adolfo O. Fumega3, Fiona Hanindita4, Shingo Ito4*, Jose L. Lado3, Peter Liljeroth3, Adam S. Foster3,5*, Shigeki Kawai2,6*Magnetic exchange interactions between localized spins in π-electron magnetism of carbon-based nanostruc-tures have attracted tremendous interest due to their great potential for nano spintronics. Unique many-body quantum characteristics, such as gaped excitations, strong spin entanglement, and fractionalized excitations, have been demonstrated, but the spin-1/2 Heisenberg model with a single antiferromagnetic coupling J value remained unexplored. Here, we realized the entangled antiferromagnetic quantum spin-1/2 Heisenberg model with diazahexabenzocoronene oligomers (up to 7 units) on Au(111). Extensive low-temperature scanning tunnel-ing microscopy/spectroscopy measurements and density functional theory and many-body calculations show that even-numbered spin chains host a collective state with gapped excitations, while odd-numbered chains fea-ture a Kondo excitation. We found that a given antiferromagnetic coupling J value between first neighbors in the entangled quantum states is responsible for the quantum phenomena, strongly relating to their parities of the chain. The tunable molecular building blocks act as an ideal platform for the experimental realization of topo-logical spin lattices.INTRODUCTIONAtomically defined carbon nanostructures hosting π-electron mag-netism (1) have great potential as nanoscale magnetic components in spin-electronic devices (2–4). Compared to d/f-electron magne-tism in transition metal elements, π-electrons in the molecules are usually more delocalized, and the weak spin-orbit interaction with long spin coherence time and length (5–9) is expected to exhibit tunable quantum properties. A key development target is the fabri-cation of various atomically defined carbon nanostructures with spin polarization, offering a platform for investigating low-energy excitations. However, since molecules with unpaired electrons are usually highly reactive and short-lived, the synthesis is challenging by solution-based chemical reactions. On-surface synthesis has been developed to fabricate atomically accurate carbon-based nano-structures via activation and conjugation of precursor molecules on metal substrates (10, 11) and has opened an exciting possibility of studying low-energy spin excitations in carbon-based materials. Several nanographene structures and graphene nanoribbons with unpaired π-electrons or zigzag edges have been successfully synthe-sized and characterized on surfaces, and their magnetic properties give rise to a variety of correlated phases (12–24). For example, mag-netic chains have been fabricated by conjugating triangulenes and porphyrin oligomers, and the Coulomb repulsion between the π-electrons in each unit that compose the chains gives rise to an anti-ferromagnetic ordering, bringing the whole chain to a topological Haldane spin chain phase (24–27). Another strategy to achieve different correlated scenarios in a controlled manner is to consider nitrogen doping into the organic oligomers, creating a surplus of π-electrons that populate previously unoccupied energy levels and bringing the whole system to completely different phases (28, 29).Here, we demonstrate the realization of a text-book spin S = 1/2 Heisenberg chain (Fig. 1) (30, 31), within metal-free organic chains through a strategic on-surface synthesis of nitrogen doped chains derived from an aza-coronene building block. We synthesized a unit of the diazahexabenzocoronene (N2HBC) molecule (32) and N2HBC chains that present a perfect alignment of spin S = 1/2 units repre-sented by the simple Heisenberg Hamiltonian with exchange cou-pling J between neighboring unitswhere �⃗S i denotes the spin half operator at site i. We were able to theo-retically and experimentally establish the behavior of the Heisenberg chains and correlate the number of units that each chain is formed (even or odd) with their collective quantum spin excitations in low-bias scanning tunneling spectroscopy (STS) experiments. These mo-lecular chains offer a flexible platform for the design and experimental realization of spin lattices.RESULTSOn-surface synthesis of N2HBC molecule and respective chainsThe precursor molecule 1 was prepared according to the same pro-cedure as in the literature (see the Supplementary Materials for the details) (33). The corresponding reaction processes were shown in Fig. 1. Annealing the precursor molecules on Au(111) at 300°C led to the formation of the hexagonal monomer (dashed circles in Fig. 2A) and its oligomers with different lengths (yellow arrows in Fig. 2A), as well as nanoribbons (blue arrows in Fig. 2A). The synthesis of the nanoribbons indicates that the precursor molecule was initially split (molecule 2) and subsequently connected to each other (see the �H =∑iJ �⃗S i ⋅�⃗S i+1 (1)1International Center for Young Scientists, National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan. 2Center for Basic Research on Mate-rials, National Institute for Materials Sciences, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan. 3Department of Applied Physics, Aalto University, Espoo, Finland. 4School of Chemistry, Chemical Engineering and Biotechnology, Nanyang Techno-logical University, 21 Nanyang Link, Singapore 637371, Singapore. 5WPI Nano Life Science Institute (WPI-NanoLSI), Kanazawa University, Kakuma-machi, Japan. 6Grad-uate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba, 305-8571, Japan.*Corresponding author. Email: kawai.​Shigeki@​nims.​go.​jp (S.K.); adam.​foster@​aalto.​fi (A.S.F.); sgito@​ntu.​edu.​sg (S.I.)Copyright © 2025 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. Distributed under a Creative Commons Attribution NonCommercial License 4.0 (CC BY-NC). Downloaded from https://www.science.org at National Institute for Materials Science on March 04, 2025mailto:kawai.​Shigeki@​nims.​go.​jpmailto:adam.​foster@​aalto.​fimailto:adam.​foster@​aalto.​fimailto:sgito@​ntu.​edu.​sghttp://crossmark.crossref.org/dialog/?doi=10.1126%2Fsciadv.ads1641&domain=pdf&date_stamp=2025-02-28Sun et al., Sci. Adv. 11, eads1641 (2025)     28 February 2025S c i e n c e  A d v a n c e s  |  R e s e ar  c h  A r t i c l e2 of 8Supplementary Materials, inset III of Fig. 2A and figs. S1 to S4). The complicated reaction pathways and the presence of coexisting na-noribbons limited the length the oligomer with the hexagonal unit up to heptamer (fig. S5). Since we are interested in the exploration of possible molecular spin structures, we focus on the hexagonal mono-mer and its oligomers and do not discuss the nanoribbons further. To investigate the chemical structures of the products, the scanning tunneling microscopy (STM) tip apex was terminated with a carbon monoxide (CO) molecule (34, 35). Inset I of Fig. 2A shows the close-up view of the monomer, whose inner structure was clearly observed in the constant height dI/dV map (Fig. 2B) and the corresponding Laplace filtered image (Fig. 2C). We found that the synthesis of the Fig. 1. Scheme of the reaction processes and resulting structures. (A) Reaction processes to form an S = 1/2 unit and the oligomers (N2HBC chains) as well as graphene nanoribbon. (B) N2HBC single molecule donates one electron to the surface, achieving an S = 1/2 spin state. (C) Schematic drawing of Heisenberg S = 1/2 antiferromag-netic molecular chains composed of odd and even numbers of molecular units and the corresponding magnetic couplings.Fig. 2. Synthesis of N2HBC molecule and respective chains 3. (A) STM topography of a Au(111) surface after annealing at 300°C for 5 min. Insets I, II, and III show close-up views of three different products. (B) Constant height dI/dV map of individual 3 and (C) the corresponding Laplace filtered image and (D) the chemical struc-ture. (E) The simulation of constant height dI/dV map is performed using a relaxed CO tip. Constant height dI/dV simulations were acquired with a mixture of s and pxy wave tips considering different ratios. The comparison of simulated images with different tips is presented in note S1 and figs. S6 and S7. (F) dI/dV curves recorded at three different sites on the molecule and one site on Au(111) as a reference, as indicated by colored dots in the left inset. The right inset shows the spatial distribution of the Kondo resonance state. (G to I) Constant height dI/dV map of individual trimer-N2HBC3+ (G) and the corresponding Laplace filtered image (H) and the chemical structure (I). Measurement parameters: Sample bias voltage V = 200 mV and tunneling current I = 5 pA in (A). V = 200 mV and I = 5 pA in inset I of (A), V = 200 mV and I = 3 pA in inset II of (A), and V = 200 mV and I = 10 pA in inset III of (A). V = 1 mV and Vac = 10 mV in (B) and (G).Downloaded from https://www.science.org at National Institute for Materials Science on March 04, 2025Sun et al., Sci. Adv. 11, eads1641 (2025)     28 February 2025S c i e n c e  A d v a n c e s  |  R e s e ar  c h  A r t i c l e3 of 8N2HBC molecule (Fig. 2D) resulted from the C─C recoupling, de-chlorination, and dehydrogenation of two 2. The constant height dI/dV map taken near the Fermi level has a higher intensity at the cen-ter, suggesting that the net spin arises from a pair of N atoms in the monomer. Density functional theory (DFT) calculations indicate that the gas-phase N2HBC molecule is in a closed-shell singlet state in its neutral form but assumes a cationic state when deposited on Au(111) due to misalignment of their Fermi levels, thus bringing the system to the open-shell S = 1/2 state. It was found that each N2HBC unit approximately donates one electron until the Fermi level of the chains matches that of the underlying substrate (see the work func-tion calculations in table S1). A simulated constant-height dI/dV map of the positively charged N2HBC+ at 0 mV (Fig. 2E) captures all the main features of the experiment. Therefore, the central high-intensity signal is attributed to the Kondo resonance, which can be seen in the low bias dI/dV spectrum (Fig. 2F). Inset II in Fig. 2A was a trimer-N2HBC3+, in which each unit is connected by a C─C bond (Fig. 2, G and H). Such coordinated fusion leads to the structure seen in Fig. 2I having all nitrogen atoms along the longitudinal direction of the chain. The unit in the center of the trimer-N2HBC3+ chain shows a darker contrast than the other peripheral two units in the dI/dV map (Fig. 2G).Electronic structure characterization of the N2HBC chainsWe conducted STS measurements over a pentamer of N2HBC (inset of Fig. 3A) and performed DFT and mean-field (MF)–Hubbard cal-culations of a periodic chain made of N2HBC+ units. The dI/dV spectra, along with that on a bare Au(111) substrate (gray curve) as a reference, exhibits several characteristic peaks (Fig. 3A). We iden-tified −0.7 V as the singly occupied molecular orbital (SOMO in Fig. 3B) and 0.5 V as the singly unoccupied molecular orbital (SUMO in Fig. 3C), leading to an SOMO-SUMO gap of 1.2 eV (see fig. S8 for the electronic properties of the pentamer). The electronic properties of the N2HBC molecule and chains from dimer to tetramer were also measured by STS (figs. S9 to S12), exhibiting similar SOMO-SUMO gaps and unoccupied states as compared to penta-N2HBC5+. Substantial spectroscopic signatures observed around the Fermi level as indicated by the dashed rectangle in Fig. 3A suggest the presence of low-energy spin excitations in the penta-N2HBC5+. Both DFT and MF-Hubbard calculations of free-standing periodic chain consisting of dimer-N2HBC2+ in its unit-cell indicate that its ground state is antiferromagnetic. MF-Hubbard calculations with U = 1.5t (t is the nearest neighbors hopping parameter, we use t = 2.7 eV) leads to the total energy difference between antiferromagnetic and ferromagnetic states of about 10 meV. This value depends on U, Fig. 3. Electronic properties of pentamer-N2HBC5+ 3. (A) dI/dV curves collected at different sites of the pentamer-N2HBC5+, as indicated by colored dots in its STM to-pography (inset). (B to G) Constant current dI/dV maps measured at sample bias voltages of −0.7, 0.5, 1.3, 1.5, 1.7, and 1.9 V, respectively. (H) Band structure and spin polar-ized density of states (DOS) of a periodic antiferromagnetic chain. The inset shows the DOS map of the valence band (bottom) and conduction band (top) resolved by spin. (I to N) Constant height dI/dV maps were calculated at bias voltages corresponding to the simulated DOS. The simulations were carried out with a flexible CO tip (a com-bination of 13% of s and 87% of pxy waves), which is comparable to the experimental ones. Measurement parameters: V = −700 mV, I = 160 pA, and Vac = 10 mV in (B). For STS measurement, the tip-sample distance was adjusted at the corresponding bias voltages and I = 160 pA and Vac = 10 mV in (C) to (G). PDOS, projected density of states.Downloaded from https://www.science.org at National Institute for Materials Science on March 04, 2025Sun et al., Sci. Adv. 11, eads1641 (2025)     28 February 2025S c i e n c e  A d v a n c e s  |  R e s e ar  c h  A r t i c l e4 of 8reaching up to 21 meV for U = 2.0t. Following the same trend, DFT-B3LYP total energies indicate that the antiferromagnetic periodic chain is 97 meV more stable than its ferromagnetic counterpart. The stability of the chains through their total energies can be used to estimate the exchange coupling J, since the spin excitations will bring the periodic chains to a ferromagnetic excited state from an antiferromagnetic ground state. The fact that the DFT-B3LYP and MF-Hubbard modeling predict antiferromagnetic coupling between the units of the dimer-N2HBC2+ chains in the absence of a substrate suggests that the role of any Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction mediated by the metallic surface is negligible. The mag-nitude and nature of the coupling within the chains are more char-acteristic of the superexchange interaction seen in previous molecular systems (36–38). In the next section, we will discuss in more detail the comparison with the experimental data.Figure 3H shows the DFT-B3LYP band structures and density of states (DOS) of the dimer-N2HBC2+ periodic chain, revealing a bandgap of 1.1 eV, very close to the measured SOMO-SUMO gap of 1.2 eV (also see note S2 and figs. S13 to S15). The calculated local DOS maps obtained for the valence and conductance bands (see in-sets in Fig. 3H) highlight the antiferromagnetic behavior of the dimer-N2HBC2+ chain: Both valence and conduction bands have alternating spin contributions in the central hexagon of the subse-quent N2HBC+ units. Figure 3 (D to G) shows the constant current dI/dV maps at corresponding sample bias demonstrating the evolu-tion of spatial distribution for these unoccupied states, and the same trend of the inner N2HBC+ units is observed in the simulated dI/dV maps in Fig. 3 (I to N). We note here that in the comparison between experimental (Fig. 3, B to G) and simulated maps (Fig. 3, I to N), the simulations are periodic and do not demonstrate the chain end ef-fects seen in experiments.Low-bias measurements and an effective model for N2HBC chainsNext, we investigated the magnetic properties of the N2HBC+ chains up to maximum observed experimentally, the heptamer, by low-bias constant height STS measurements around the Fermi level, in which we collected dI/dV curves on the N2HBC+ units of each chain and dI/dV maps on selected bias values (Fig. 4). Local spin excitations that influence the inelastic tunneling spectroscopy of each chain were treated by the dynamical spin correlator (DSC) A(ω, n)which takes the many-body ground state ∣GS⟩ and energies EGS ob-tained by solving Eq. 1 (39–41). The frequency of the excitation ω corresponds to the applied bias voltage in the experiment, n indi-cates which unit is treated within the chain and S±n= Sxn± iSyn. As the spin spectral weight of the magnetic units is related to the dI/dV line shape (42) and consequently its spatial distribution, we cou-pled the DSC to both DFT dI/dV simulated maps and MF-Hubbard spin densities by modulating their spatial distribution with A(ω, n), allowing us to emulate the conduction maps and estab-lish their behavior with the size and parity of the chains and to their spin polarization.We observed a systematic behavior of the dI/dV curves and the DSC relative to the number of N2HBC+ units, in which we assigned as even (Fig. 4, A to H, and fig. S16) or odd (Fig. 4, I to T, and fig. S17) Heisenberg chains according to their parity. For the dimer-N2HBC2+ in Fig. 4A, there is no prominent Kondo peak at the Fermi level, and we find symmetric conduction peaks around the Fermi level in the dI/dV curves acquired above each unit of the dimer. The constant height dI/dV map of dimer-N2HBC2+ collected at 1 mV reveals that the signal is quite uniform over all the structure (fig. S18) while still resembling the signal from a single N2HBC+ molecule at 0 V. The tunneling conduction peaks of the dimer-N2HBC2+ are consistent with the peaks of the DSC calculated with J = 30 meV (Fig. 4B), in agreement with the experimental value (fig. S16) and within the range of our MF-Hubbard estimated exchange coupling (between 20 and 40 mV) and DFT (see the Supplementary Materials for more details of the calculations, note S3, and figs. S14, S15, and S19 to 21). The two spin-1/2 subunits in the dimer are antiferromagnetically coupled, and the low-energy spectroscopic features correspond to an inelastic singlet-triplet excitation (S = 0 to S = 1). Both N2HBC+ units display equal intensity as simulated in the energy-normalized conductance maps, and both DFT and MF-Hubbard spin densities are concentrated over the central part of each molecule-unit where the N pair is located (fig. S18). The same behavior as for the dimer is observed in the dI/dV curves of the tetramer-N2HBC4+ (Fig. 4E), with no prominent Kondo peak and symmetric conduction peaks around the Fermi level, and the assignment of the phenomenology is similar. No strong feature is observed at 0 V in the dI/dV curves, and the dI/dV map taken at 1 mV has a slightly brighter signal at the peripheral N2HBC+ units (fig. S18). We then extended our dimer-N2HBC2+ model to a four spin-1/2 system in the tetramer-N2HBC4+, keeping the same exchange coupling J = 30 mV. The DSC gives several peaks around the Fermi level, consistent with the conduc-tion peaks in the dI/dV curves (Fig. 4H). Unexpectedly, the DSC-modulated conductance map simulations in (fig. S18) correctly display the slightly stronger intensity over both peripheral units in the tetramer-N2HBC4+ as observed in the experimental map. The MF-Hubbard spin density of the tetramer-N2HBC4+ shows that the spin distributes at center of each unit, similar to the one obtained for the dimer-N2HBC2+ (fig. S18). Constant height conduction maps for both dimer and tetramer at higher energies display comparable spin intensity with the simulated ones (Fig. 4, C, D, G, and H), which also correlate to DSC-modulated simulations. The hexamer also ex-hibits similar dI/dV curves to those of the tetramer (fig. S16) al-though the excitation gap is smaller. To investigate the relationship between chain length and spin excitation energy, d2I/dV2 spectra were measured on the chains with different lengths. We found that the lowest spin excitation energies of the dimer, tetramer, and hex-amer were 30, 14, and 6 meV, respectively (fig. S16), generally con-sistent with the calculated values of 30, 19, and 14 meV. As the chain length increases, the energy values decrease (Fig. 4U). However, the number of the units was not large enough to demonstrate gapless spinon excitations.The spectroscopy features of the odd Heisenberg chains (Fig. 4, I and O, and fig. S17) seem to contrast to the features observed in the even cases, as several peaks with different intensities and broad-enings are observed in the tunneling conductance curves at the Fermi level. However, we demonstrate that they are still characteristic of a chain with only exchange coupling between spin-1/2 N2HBC+ units. In Fig. 4 (I and O), the dI/dV curves of both trimer- N2HBC3+ and pentamer-N2HBC5+ chains reveal zero-bias reso-nance peaks at the peripheral N2HBC+ units, with extra symmetric peaks in the dI/dV curves at higher bias voltages. While the dI/dV curves taken at the central N2HBC+ unit of the trimer-N2HBC3+ A(ω, n) = ⟨GS ∣S−nδ�ω+EGS−Ĥ�S+n∣GS⟩ (2)Downloaded from https://www.science.org at National Institute for Materials Science on March 04, 2025Sun et al., Sci. Adv. 11, eads1641 (2025)     28 February 2025S c i e n c e  A d v a n c e s  |  R e s e ar  c h  A r t i c l e5 of 8are apparently featureless at the Fermi level (Fig. 4I), the central N2HBC+ unit in the pentamer-N2HBC5+ has the same zero-bias features as the peripheral ones, with stronger intensity (Fig. 4O). In contrast, the N2HBC+ units next to the central one have no features at the Fermi level (see more details in the two-dimensional dI/dV map composed of 121 dI/dV curves taken along the pentamer-N2HBC5+ chain in fig. S22). The relative contrast of the molecular units inverts at higher bias—this is particularly visible in the dI/dV maps: The constant height dI/dV maps of the trimer-N2HBC3+ taken at 1 mV (Fig. 4K) corroborate to the strong intensity of the zero-bias peak at the peripheral N2HBC+ units, while at −30 mV, (Fig. 4M) the signal from the central N2HBC+ unit becomes more intense relative to the peripheral units. The DSC calculated at the peripheral units of the trimer-N2HBC3+ (Fig. 4J) reveals a sharp peak at the Fermi level, consistent with the zero-bias resonances observed in the experiment, which is attributed to an emergent collective twofold degenerate ground state that is only possible due to the odd number of spin-1/2 units, allowing the development of a Kondo resonance when in contact with the conduction elec-trons in the substrate. For higher energies, other steps consistent with higher-order inelastic spin excitations are also observed. On the other hand, the DSC calculated at the central unit of the trimer-N2HBC3+ reveals a quenched zero-bias peak and a single sharp peak for higher and lower energies. Given the simplicity of the trimer-N2HBC3+ case, we were able to describe in more detail the zero-bias spin excitations by analytically solving the Hamiltonian in Eq. 1. The twofold degenerate many-body states that result in Sz = ±1∕2 are ∣ α⟩ = 1√6(∣↑↑↓⟩ − 2 ∣↑↓↑⟩ + ∣↓↑↑⟩) and ∣ β⟩ = 1√6( ∣↓↓↑⟩−2 ∣↓↑↓⟩+∣↑↓↓⟩) (see note S4 for the details). Note that the units at the edges of the chain are equivalent as given by mirror symmetry, whereas the central unit is different. This stems Fig. 4. Magnetic properties of even and odd Heisenberg chains on Au(111). Experimental dI/dV curves and constant height maps and simulations for dimer (A to D), tet-ramer (E to H), trimer (I to N), and pentamer (O to T). The insets in (A), (E), (I), and (O) correspond to the STM topography of each chain, with the colored dots indicating the STS measurement positions [gray color is the signal from the Au(111) substrate for reference]. The colored hexagons in (B), (F), (J), and (P) indicate in which unit of the chains the DSC was projected. The simulated DSC of spin excitations for chains, where we adopted a small broadening factor (δ = 5), allows a better identification of the spin excitations (fig. S26). [(D), (H), (L), (N), (R), and (T)] Simulations were obtained by modulating the DFT calculated constant-height dI/dV maps at 0 meV with the DSC at respective energies in the left and were acquired by modulating the spin densities calculated by MF-Hubbard with the DSC in the right panel. (U and V) The relationship between the lowest spin excitation energy and the chain length summarized from the STS measurement and calculations. Measurement parameters: V = −30 mV and Vac = 3 mV in (C) and (M). V = −15 mV and Vac = 2 mV in (G). V = −20 mV and Vac = 2 mV in (S). V = 1 mV and Vac = 10 mV in (K). V = 0 mV and Vac = 1 mV in (Q). a.u., arbitrary units.Downloaded from https://www.science.org at National Institute for Materials Science on March 04, 2025Sun et al., Sci. Adv. 11, eads1641 (2025)     28 February 2025S c i e n c e  A d v a n c e s  |  R e s e ar  c h  A r t i c l e6 of 8from the open boundary conditions of the chain. At zero frequency (or zero bias), the DSC is proportional to the ⟨α ∣S+n∣ β⟩2 matrix ele-ment of the ladder operator (42) that will flip a single spin in the unit n of the trimer where the excitation occurs. The matrix element calculated flipping the spin in the peripheral units is four times larger than the one calculated at the central unit, giving rise to more intense zero-bias peak as seen in the DSC curve Fig 4J (see the Sup-plementary Materials for a short summary of the calculation). The DSC-modulated conductance map shown in Fig. 4L correctly dis-plays the contrast obtained in the experiment, demonstrating that the zero-bias contrast is related to the development of a Kondo resonance when in contact with the conduction electrons in the substrate. The inverted behavior of the tunneling conductance at −30 mV is also captured in the simulated maps, which agrees well with the experi-mental one, shown in Fig. 4 (M and N).Extending our analysis from the trimer-N2HBC3+ to the pentamer- N2HBC5+ becomes then straightforward with our model, reproducing especially all the zero-bias resonances and their respective intensi-ties [see Fig. 4 (O to T)], which are also related to elastic spin excita-tions and some inelastic excitations. To verify our experimental and theoretical findings, the heptamer was also investigated by STS measurements (fig. S17). We found the similar electronic behavior as the zero-energy peaks exist only in units with an odd number, while units with an even number primarily exhibit extra symmetric peaks. Furthermore, the d2I/dV2 spectra revealed that the lowest spin excitation energies for the trimer, pentamer, and heptamer are 29, 21, and 12 meV, respectively (fig. S17), in good agreement with the theoretical calculations of 30, 21, and 16 meV. The energy exhibits a decreasing trend with increasing chain length (Fig. 4V). Figure S23 shows a schematic visualization of the DSC calculated at several different energies from 1 to 45 meV, depicting the expected relative behavior of the contrasts in each unit for all chains. Together with that, it also shows that scaling from the numbers of mole-cules will allow us to explore the development of 1/2 Heisenberg spin structure according to the number of molecular components and the transition from expected Kondo resonances for odd chains to quenching in longer chains. The fine tuning of the spin excitation, together with the full control of the number of mole-cules, is a key step to engineering of spin coherence times and realizable spintronics.Additional supporting measurements using an AuSix intercala-tion layer between the N2HBC chains and the Au(111) substrate are shown in the Supplementary Materials (note S5 and fig. S24). The spin excitation energy for the dimer on AuSix/Au(111) is larger than that on Au(111). This is due to the decoupling effect of the AuSix layer, which reduces the polarization effect of the substrate, thereby increasing the excitation energy value (43, 44). Furthermore, even when located on the AuSix layer, the dimers can exhibit different values of spin excitation energy (fig. S25). This variation in excita-tion energy may result from the differing adsorption sites of the di-mers on the AuSix surface.DISCUSSIONWe successfully fabricated spin-1/2 Heisenberg chains with a single antiferromagnetic coupling J by covalently connecting diazahexaben-zocoronene molecules. These molecular spin chains depict different collective features depending on their parity of the chains: gapped excitations for an even number of repeating units and Kondo excitations for those with an odd number. A combination of STM/STS experiments and DFT simulations were used to fully deter-mine their chemical structures, as well as their electronic and magnetic properties, and the complex excitations observed in the low-energy spectra were correctly addressed by the spin-1/2 Heisenberg Hamiltonian with a single antiferromagnetic cou-pling between first neighbors. Our results show that the experi-mental construction of molecular spin units provides a feasible way to realize the quantum Heisenberg spin-1/2 model, allowing direct imaging of the spatial distribution of its quantum many-body excitations. In particular, a molecular system with antiferro-magnetic Heisenberg couplings presents a platform for the realization of topological spin models with fractionalized excitations (e.g., dimer chains and lattices) and frustrated spin systems.MATERIALS AND METHODSSTM experimentsAll experiments were performed in a low-temperature STM system (home-made) at 4.3 K under ultrahigh vacuum condition (<2 × 10−10 mbar). A clean single crystal Au(111) substrate was prepared through cyclic sputtering (Ar+, 10 min) and annealing (720 K, 15 min). The temperature of sample was measured by a thermocouple and a pyrometer. 2,13-Dichloro-7b,7c,18b,18c-tetrahydro-3a2,7c1-diazahexabenzo[a,cd,f,j,lm,o]perylene (1) was deposited from Knudsen cells (Kentax GmbH). A STM tip was made from the chemi-cally etched tungsten. For constant height dI/dV imaging, the tip apex was functionalized by a CO molecule picked up from the surface. The bias voltage was set close to zero voltage. The modulation ampli-tude was 10 mV0-peak, and the frequency was 510 Hz for the wide energy range STS measurements and bond resolved imaging. The modulation amplitude ranged from 1 to 5 mV0-peak, and the fre-quency was 510 Hz for the small energy range STS measurements.Synthesis of compound 1A solution of 2-chloro-8H-isoquinolino[4,3,2-de]phenanthridin-9-ium chloride (10 mg, 0.030 mmol) dissolved in dimethylsulfoxide (2.0 ml) was preheated to 190°C for 30 s. Subsequently, tributyl-amine (0.17 ml, 0.71 mmol) was added and further stirred for 5 min. After cooling down to room temperature, the reaction mixture was extracted with dichloromethane. The combined organic phases were washed with water, dried under sodium sulfate, filtered, and evaporated in vacuo. The crude product was purified by silica gel column chromatography (hexane/dichloromethane = 8/1) to afford 2,13-dichloro-7b,7c,18b,18c-tetrahydro-3a2,7c1-diazahexabenzo[a,cd,f,j,lm,o]perylene (1) as a yellow solid (1.3 mg, 0.002 mmol, 7%). (See the Supplementary Materials for the details).Theoretical calculationsSpin-polarized DFT calculations were performed using the FHI-AIMS code (45). Geometry optimizations were carried out twice, using two different exchange-correlation functionals: initial optimi-zation with PBE (46) and then followed by B3LYP (47), both with the standard “light” basis set. For the gas phase modeled monomer, dimer, trimer, and the infinite chain, structural relaxations were only allowed in xy plane (see the comparison of constrained and unconstrained relaxations in fig. S19). For all the dI/dV simulations of monomer, the adsorption of monomer was first modeled on Au(111) with three atomic layers, and two bottom layers were fully Downloaded from https://www.science.org at National Institute for Materials Science on March 04, 2025Sun et al., Sci. Adv. 11, eads1641 (2025)     28 February 2025S c i e n c e  A d v a n c e s  |  R e s e ar  c h  A r t i c l e7 of 8constrained. All free atoms were allowed to relax until the residual atomic forces reached less than 5e−3 eV/Å. For the periodic chain, we used a distance of 15 Å to avoid interactions between the nonpe-riodic images, and the geometry was relaxed using only the Γ-point. We used eight times denser k-grid in the periodic direction to calcu-late band structures and DOSs. The MF-Hubbard calculations were realized with the PYQULA library (48), while the DSCs were calcu-lated using the DMRGPY library (41).Theoretical constant height dI/dV maps were simulated using ei-ther fixed or relaxed CO tips, as specified in the relevant text. Simu-lations with fixed tips were computed by means of PPSTM code (49), using a mixture of s and pxy waves—different ratios of these waves were considered (see the Supplementary Materials) (50, 51). For the simulations using relaxed tips, the PPAFM code was initially used to model the positions of the CO tips (52). The lateral stiffness for the CO tip was set to 0.25 N/m, and an oscillation amplitude of 1.0 Å was used. Subsequently, the dI/dV maps were generated by PPSTM with a mixed sp-wave tip in a ratio that best reproduces the experiments. We used a broadening parameter of 0.1 eV for all sim-ulations to get a good simulation performance.Supplementary MaterialsThis PDF file includes:Synthesis of 1Supplementary Notes S1 to S5Figs. S1 to S26Table S1ReferencesREFERENCES AND NOTES  1.  J. Fernández-Rossier, J. J. Palacios, Magnetism in graphene nanoislands. Phys. Rev. Lett. 99, 177204 (2007).  2.  A. R. Rocha, V. M. García-suárez, S. W. Bailey, C. J. Lambert, J. Ferrer, S. Sanvitoet, Towards molecular spintronics. Nat. Mater. 4, 335–339 (2005).  3.  O. V. Yazyev, Emergence of magnetism in graphene materials and nanostructures. Rep. Prog. Phys. 73, 056501 (2010).  4. D . Pesin, A. H. MacDonald, Spintronics and pseudospintronics in graphene and topological insulators. Nat. Mater. 11, 409–416 (2012).  5. H . Min, J. E. Hill, N. A. Sinitsyn, B. R. Sahu, L. Kleinman, A. H. MacDonald, Intrinsic and Rashba spin-orbit interactions in graphene sheets. Phys. Rev. B. 74, 165310 (2007).  6.  O. V. Yazyev, M. I. 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Funding: This work was supported in part by Japan Society for the Promotion of Science (JSPS) KAKENHI grant numbers 22H00285 and 24K21721 for S.K., the Ministry of Education, Singapore, under its Academic Research Fund Tier 1 (RG2/23) for S.I., and the Academy of Finland (projects no. 346824 for N.C., O.S., and A.S.F., projects nos. 331342 and 358088 for A.O.F. and J.L., and projects nos. 336243 and 349696 for P.L.). Author contributions: S.K. conceived of the project. K.S. and S.K. performed the measurement and analyzed the data together with P.L. N.C., O.J.S., A.O.F., J.L.L., and A.S.F. performed the theoretical calculations. F.H. and S.I. synthesized the precursor molecules. K.S., O.S., A.O.F., and S.K. wrote the paper with input from all authors. Competing interests: The authors declare that they have no competing interests. Data and materials availability: All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Materials.Submitted 1 August 2024 Accepted 28 January 2025 Published 28 February 2025 10.1126/sciadv.ads1641Downloaded from https://www.science.org at National Institute for Materials Science on March 04, 2025http://github.com/joselado/dmrgpyhttps://github.com/joselado/pyqula On-surface synthesis of Heisenberg spin-1/2 antiferromagnetic molecular chains INTRODUCTION RESULTS On-surface synthesis of N2HBC molecule and respective chains Electronic structure characterization of the N2HBC chains Low-bias measurements and an effective model for N2HBC chains DISCUSSION MATERIALS AND METHODS STM experiments Synthesis of compound 1 Theoretical calculations Supplementary Materials This PDF file includes: REFERENCES AND NOTES Acknowledgments