Realization of quantum nanomagnets in metal-free porphyrins

*Corresponding Authors: shiyong.wang@sjtu.edu.cn, zhuang@sjtu.edu.cn Quantum nanomagnets exhibit collective quantum behaviors beyond the usual long range ordered states due to the interplay of low dimension, competing interactions and strong quantum fluctuations. Despite numerous theoretical works treating quantum magnetism, the experimental study of individual quantum nanomagnets remains very challenge, greatly hindering the development of this cutting-edge field. Here, we demonstrate an effective strategy to realize individual quantum nanomagnets in metal-free porphyrins by using combined on-surface synthesis and atom manipulation approaches, with the ultimate ability to arrange coupled spins one by one as envisioned by Richard Feynman 60 years ago. A series of metal-free porphyrin nanomagnets have been constructed on Au(111) and their collective magnetic properties have been thoroughly characterized on the atomic scale by scanning probe microscopy together with theoretical calculations. Our results reveal that the constructed S=1/2 antiferromagnets host a gapped excitation in consistent with isotropic Heisenberg antiferromagnets S=1/2 model, while the S=1 antiferromagnets with odd-number units exhibit two zero-mode end states due to quantum fluctuations. Our achieved

Molecular nanomagnets have been proposed as promising candidates for information storage, molecular spintronics, and quantum computing. Amongst, porphyrins and related macrocycles stand out due to their extraordinary stability, remarkable chemical versatility and ability to stabilize different ions inside, hosting engineerable biological, electronic and magnetic properties [1][2][3][4] . Although individual magnetic porphyrins have been widely studied and well understood, little is known about the coupled spins in porphyrin systems. The magnetism of porphyrin macrocycle comes from the center magnetic metal ions, in which the unpaired d/f electrons highly localize at the center, making the spins in assembled porphyrin architectures with negligible magnetic exchange interaction. In the past decade, a series of porphyrin architectures have been achieved on surfaces, such as single porphyrin molecules, covalent porphyrin polymers, self-assembled nanostructures 1,3,[5][6][7][8][9][10][11][12][13][14][15][16][17] . However, none of them exhibits detectable collective magnetic behaviors, hindering the study of their strongly correlated effects.
Recently, delocalized -electron magnetism has been introduced in porphyrins through engineering their  electron topologies [18][19][20] . Such delocalization effect allows for further realization of quantum nanomagnets with coupled spins in covalent porphyrin architectures. However, due to their high reactivity and/or low solubility, it remains challenge to synthesize such porphyrin quantum nanomagnets by traditional 'wet' chemistry. Pioneered by Grill et al. in 2007, on-surface synthesis has become a powerful approach for fabrication of atomically precise covalent nanostructures, with milestones including single molecules, covalent porphyrin polymers, graphene nanoribbons, and two-dimensional covalent molecular frameworks [21][22][23][24][25][26][27][28][29][30][31] . Meanwhile, atom manipulation approach has been used by Hla and Here, we take advantage of both on-surface synthesis and atom manipulation approach to construct complex custom designed molecular nanomagnets in metal-free porphyrins one by one on an Au(111) surface. On-surface synthesis is used to fabricate extended porphyrin chains with two sp 3 carbon sites per porphyrin unit, forming an extended one-dimensional sp 3 carbon lattice. Through STM tip induced atom manipulation, one of the two hydrogens in each sp 3 carbon site can be controllably dissociated at the predefined locations in the sp 3 carbon lattice. Each hydrogen dissociation step transforms an sp 3 carbon into an sp 2 carbon, and thus introduces one delocalized  radical into the aromatic system. The delocalized character of -electron magnetism gives rise to a considerable intramolecular as well as intermolecular magnetic coupling, allowing for the construction of quantum nanomagnets with tunable magnetic exchange interactions. A series of molecular nanomagnets have been constructed and thoroughly characterized by non-contact atomic force microscopy (nc-AFM) and scanning tunneling microscopy (STM) together with density functional theory (DFT) calculations and theoretical modeling.

Results and Discussion
Synthesis and structural characterization. Figure 1a depicts the scheme to construct coupled spins in porphyrin chains through three sequential steps including precursor synthesis, on-surface synthesis and atom manipulation. The precursor 5,15-bis(4-bromo-2,6-dimethylphenyl)porphyrin is synthesized in solution by traditional 'wet' chemistry (cf. detailed synthesis method in Supplementary figure1). After insolution synthesis, the precursor is thermally deposited on Au(111) held at 180 o C following a subsequent annealing to 290 o C for 10 minutes. Through thermal activation, carbon-carbon coupling and cyclodehydrogenation reactions take place, giving rise to fully aromatic porphyrin chains with different length (cf. Fig. 1b). Bond-resolved nc-AFM imaging was used to characterize the chemical structures of achieved products by functionalizing a CO molecule at tip apex 37 . The nc-AFM image in Fig. 1c reveals that each porphyrin unit compose of two sp 3 carbon sites appeared as a shallow protrusion at opposite outer corners of the porphyrin macrocycle (cf. Fig. 1c). We attribute the high yield of sp 3 carbon sites to the diradical character of each porphyrin unit (cf. Clar non-Kekule structures in Supplementary figure3). During cyclodehydrogenation reactions, the dissociated hydrogen atoms migrate on surface and saturate the radical sites, forming two sp 3 carbon sites per porphyrin unit. For comparison, we studied the 5-(2,6-dimethylphenyl)porphyrin precursor, which results in products with a closed-shell electronic structure after cyclodehydrogenation. As expected, none of the products hosts sp 3 carbon sites (cf. details in Supplementary figure4). Through atom manipulation, we can controllably kick one hydrogen off from an sp 3 carbon site by applying a voltage pulse of 3V (cf. I-V curve in Supplementary figure2), which transforms an sp 3 carbon into sp 2 carbon and thus introduces an unpaired  electron into the aromatic system. Using the above strategy, we constructed two typical examples of porphyrin nanomagnets holding four and eight unpaired spins (cf. Fig. 1a), which can be simplified as a finite S=1/2 and S=1 antiferromagnetic spin chain, respectively (vide infra). As shown in Fig. 1d and e, nc-AFM imaging resolves four sp 3 carbon sites for the S=1/2 nanomagnet and none for the S=1 nanomagnet, confirming such tip-induced dehydrogenation process.

Intra-and intermolecular magnetic exchange interaction. Intramolecular magnetic coupling between
the two spins within a porphyrin monomer has been studied by means of STS measurements, together with DFT calculations and theoretical modelling. As shown in Fig. 2, we dissociated two hydrogens away from the two sp 3 carbon sites one by one and monitored their magnetic ground state change. We refer to the porphyrin monomer with two, one and zero sp 3 carbon site(s) as 2H-Por, 1H-Por and Por, respectively. Both experimental measurements and calculations confirm that the 2H-Por has a closedshell electronic structure (cf. Fig. 2a and d). The 2H-Por transforms into 1H-Por after applying a voltage pulse of 3V by positioning the STM tip above the sp 3 carbon site and retracting 400 pm away from a tunneling setpoint of V=10 mV and I=10 pA. The 1H-Por hosts an odd number of  electrons, with a magnetic ground state of S=1/2 as revealed by DFT calculations (cf. Fig. 2b). Using the same procedure, the 1H-Por is further manipulated into the Por as shown in Fig. 2c, which possesses two unpaired  electrons. DFT calculations suggest that the two spins reside at opposite sides along the long axis of the monomer with a ferromagnetic coupling of 20 meV. Spin-flip spectroscopy measurements confirm such magnetic exchange interaction by showing two symmetric steps above/below fermi level at 20 mV (cf. Fig. 2d), which is due to the presence of a spin-flip tunneling channel induced by inelastic tunneling electrons 38,39 . Additionally, the presence of net spins in Pors has been further confirmed by Kondo resonance effect. The Au(111) surface electrons screen the net spin(s) and result in a many-body Kondo resonance by showing a sharp peak at fermi level. As shown in Fig. 2d, Kondo resonances have been observed in both 1H-Por and Por. However, the Kondo resonance intensity of spin S=1/2 in 1H-Por is significantly stronger than that of spin S=1 in Por. This difference is due to different screening effects, where the quantized spin S=1/2 is completely screened by Au(111) conduction electrons, while the higher spin S=1 is underscreened in consistent with theory predictions and recent experimental observations on magnetic nanographenes 40,41 . Such Kondo screening difference has been further confirmed by dI/dV spectra under a vertical magnetic field. As shown in Fig. 2e-2f, the Kondo resonance of S=1/2 is robust against magnetic field, while the Kondo resonance of S=1 is extremely sensitive to the applied magnetic field due to the high degree of polarizability of a partially screened high spin.
Additionally, we simulated the observed dI/dV spectra by using a perturbative approach established by Ternes 38 , which nicely reproduced the experimental features (cf. Supplementary figure 6).
Intermolecular magnetic coupling has been studied by constructing four spins one by one in a covalent porphyrin dimer (cf. Fig. 3). After the first manipulation step, a  radical was created inside the dimer, which localizes at the dehydrogenated side exhibiting a sharp Kondo resonance in the dI/dV spectrum.
In the second step, we deliberately created a second  radical inside the other unit of the dimer to reveal showing a spin flip feature below and above fermi level at 2.6 mV. In the following step, the third spin was introduced in the system. We refer to the porphyrin unit with two ferromagnetic coupled spins as S=1 considering the ferromagnetic intramolecular coupling strength is drastically larger than that of intermolecular coupling. After positioning the tip over the S=1 unit, two steps are observed at 3 mV and 20 mV due to the presence of inelastic tunneling channels from inter-and intramolecular spin flip process (cf. the #4 spectrum in Fig. 3d). Similar observations have been made on S=1 dimer, confirming the intramolecular ferromagnetic coupling and intramolecular antiferromagnetic coupling. As illustrated in Fig. 3e, we modelled the magnetic exchange interactions among the four spins in the dimer by considering an intra-molecular coupling of 20 meV, and inter-molecular coupling of 4 meV (same side) and 3.2 meV (opposite side). As shown in Fig. 2d, the simulated spectra nicely agree with the STS measurements, confirming the created spins are coupled together.
Spin S=1/2 and S=1 antiferromagnetic quantum nanomagnets. The spin S=1/2 antiferromagnets were constructed one by one in a long porphyrin polymer as shown in Fig. 4. We probed the excitation gap of the S=1/2 antiferromagnets with different length by means of inelastic tunneling spectroscopy.
As shown in Fig. 4d, a dip-like feature has been observed in site-resolved dI/dV spectra, which can be attributed to the presence of the first excitation gap of the spin systems, that is, the energy difference between the ground state and the first excited state as excited by inelastic tunneling electrons. To better determine the excitation energy positions, we took numerical derivation of all dI/dV spectra and found the energy positions are almost the same for all sites with a value around 3 meV as shown in Fig. 4e.
Apparently, our constructed spin S=1/2 antiferromagnets cannot be explained by classic Ising model, where the energy required to flip a spin in the center would be twice larger than that at two termini of a spin chain. The deviation away from Ising model originates from the extremely weak spin orbital coupling of carbons, which results in a negligible magnetic anisotropy energy. In this case, the physics of our constructed molecular nanomagnets is dominated by quantum effects and can be captured by the isotropic Heisenberg antiferromagnets S=1/2 model 42  The spin S=1 antiferromagnets with different length are constructed and thoroughly studied as shown in Fig. 5. The S=1 antiferromagnetic spin chain represents a prototype of fractional and topological phase as proposed by Haldane in 1980s, also known as Haldane chain. According to the Haldane conjecture, the ground state of such a spin chain is a gapped state due to quantum fluctuations, with all spins canceled in the bulk and spin 1/2 edge states at the ends 43 . Here, finite-size S=1 antiferromagnets up to five units were construct to obtain size-dependent magnetic excitations. Figure 5c and d show siteresolved dI/dV and d 2 I/dV 2 spectra taken on each unit of even-numbered and odd-numbered chains. For even-numbered chains, step-like features are observed at all units, where the first excitation gap (d 2 I/dV 2 spectra) decreases from 2.4 meV to 1.1 meV with increased length from two to four units. For odd-length chains, a zero-bias peak together with two steps have been observed at ends, while a dip is observed in the bulk units. A simple isotropic Heisenberg antiferromagnets S=1 model has been used to elucidate our observations. For even-numbered chains, the spectroscopic features can be nicely reproduced by modelling calculations (cf. dashed lines in Fig. 5c). For odd-length chains, however, we notice that the end state feature cannot be captured by this simple Hamiltonian, which gives a U-shape features in simulated dI/dV spectra at both bulk and end sites (cf. Fig. 5d). We can exclude the possibility that our observed zero-energy state is due to Kondo screening of a net spin S=1 of the odd-numbered spin chain.
Such Kondo screening effect has been included in the perturbative calculation, where a shallow zerobias peak appears at all units of the trimer and becomes invisible for the longer pentamer (cf. details in Fig. 5d). We attribute the zero-energy peaks at end sites in dI/dV spectra to the presence of a S=1/2 end spin. This end spin S=1/2 is screened by Au(111) electrons, and thus give a sharp zero-energy Kondo resonance in dI/dV spectra. This presence of end states in S=1 spin chain with odd-number units suggests that quantum fluctuations transform the antiferromagnetic S=1 spin chain into a topological phase with spin canceled in the bulk and the emergence of end states as proposed by Haldane (cf. Fig.   5e). It is still unclear why quantum fluctuations play a dominate role in short odd-numbered but not in even-numbered S=1 spin chain, awaiting further many-body theoretical investigations.

Conclusions
We have demonstrated an effective approach to build molecular quantum nanomagnets in metal-free porphyrins on Au(111), with the ultimate ability to arrange coupled spins one by one at the predefined locations. The quantum magnetism behaviors of the constructed nanomagnets have been revealed by scanning probe techniques together with theory calculations. Due to the delocalized character of  radicals, a significant intra-and intermolecular magnetic exchange interaction has been observed with values up to 20 meV and 3 meV, respectively. Using our established strategy, we construct a series of S=1/2 and S=1 antiferromagnetic nanomagnets one by one, and monitored their magnetic properties change. A finite excitation gap has been observed for S=1/2 nanomagnets, in consistent with the isotropic Heisenberg antiferromagnets S=1/2 model. Interestingly, we observed an end state for S=1 nanomagnets with odd-number units, which cannot capture by simple Heisenberg model. We attribute the presence of end-state to quantum fluctuations, which induce a topological phase transition as proposed by Haldane in 1980s. Our work provides a widely engineerable platform to further explore the exotic phases of quantum magnetism in real space, such as magnetic plateaux, spin liquid states or spin-Peierls states, to name a few. Additionally, complex custom-designed spin devices can be constructed on surfaces using our established strategy, allowing for the realization of quantum computation taking advantage of recent developed electron spin resonance based STM 44 .

Methods
On-Surface synthesis and characterization. Under ultra-high vacuum (3x10 -10 mbar) conditions, a commercially available low-temperature Unisoku Joule-Thomson scanning probe microscope was used for sample preparation and characterization. The Au(111) single-crystal was cleaned cyclically by argon ion sputtering, and then annealed to 800K to obtain an atomically flat terraces. The molecular precursor of 5,15-bis(4-bromo-2,6-dimethylphenyl)porphyrin/5-(2,6-dimethylphenyl)porphyrin was thermally deposited on the clean Au(111) surface at a temperature of 180 ℃, and subsequently annealed to 290 ℃ for 10 minutes. After that, the sample was transferred to a cryogenic scanner at 4.9K (1.36K) for characterization. Carbon monoxide molecules are dosed onto the cold sample around 12 K (1.5x10 -8 mbar,1 minutes). In order to improve the resolution of scanning tunneling microscope (STM) and atomic force microscope (AFM) imaging, CO molecule is picked up from Au surface to the apex of the tungsten tip. In nc-AFM imaging, a quartz tuning fork with a resonance frequency of 28 KHz was used. A lock-in amplifier (531 Hz, 1-10 mV modulation) has been used to obtain dI/dV spectra. The spectra were taken at 1.36K unless otherwise stated. The STM and nc-AFM images were processed with the WSxM software.
DFT calculations and theoretical modeling. Spin-polarized DFT calculations were performed using the Gaussian 16 package. The PBE0-D3 (BJ) 45 functional was applied to reveal the electronic structure of all gas-phase molecular nanomagnets, and using def2-SVP basis set 46 for geometry optimization which was extended to a def2-TZVP basis set 46 for the single point energy calculation. The electronic structures of molecules were calculated using the restricted and unrestricted methods for spins with different coupling strengths, respectively. Molecular orbitals and electron spin density were analyzed by Multiwfn 47 . Images of the structures and isosurfaces were plotted using VESTA 48 . To understand the scattering and screening effects in STM junction, we fitted our dI/dV spectra using the perturbation approach up to third order developed by Ternes 38,49 . We calculated the finite Heisenberg spin chain using exact diagonalization methods to investigate the excitation features in our dI/dV experiments. The Hamiltonian of Heisenberg model is ̂= − ∑ ⃗ • ⃗ < , > , where the J is magnetic coupling strength between two spin ⃗ and ⃗ , which are ferromagnetic coupling for J>0 and anti-ferromagnetic coupling for J<0.