Yongfeng Tong

Massine Kelai

Kaushik Bairagi

Vincent Repain

Jerome Lagoute

Yann Girard

Sylvie Rousset

Marie-Laure Boillot

Talal Mallah

Cristian Enachescu

Massine Kelaï

Jérôme Lagoute

Amandine Bellec
email: amandine.bellec@u-paris.fr

Voltage-Induced Bistability of Single Spin-Crossover Molecules in a Two-Dimensional Monolayer

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In particular, switchable single molecules [START_REF] Böckmann | Direct Observation of Photoinduced Tautomerization in Single Molecules at a Metal Surface[END_REF][START_REF] Nacci | Reversible Photoswitching and Isomer-Dependent Diffusion of Single Azobenzene Tetramers on a Metal Surface[END_REF][START_REF] Köbke | Reversible coordination-induced spin-state switching in complexes on metal surfaces[END_REF][START_REF] Dri | Spatial periodicity in molecular switching[END_REF][START_REF] Harsh | Controlling Hydrogen-Transfer Rate in Molecules on Graphene by Tunable Molecular Orbital Levels[END_REF][START_REF] Bouatou | Control of Dipolar Switches on Graphene by a Local Electric Field[END_REF] are attracting lot of interest for applications such as memory devices. Spin-crossover (SCO) molecules are prototypes of switchable and bistable components that are presently considered in this area. [START_REF] Kahn | Molecular bistability: An overview[END_REF][START_REF] Kahn | Spin Transition Molecular Materials for displays and data recording[END_REF][START_REF] Kahn | Spin-Transition Polymers: From Molecular Materials Toward Memory Devices[END_REF][START_REF] Frisenda | Stretching-Induced Conductance Increase in a Spin-Crossover Molecule[END_REF][START_REF] Dugay | Phase Transitions in Spin-Crossover Thin Films Probed by Graphene Transport Measurements[END_REF][START_REF] Molnár | Spin Crossover Nanomaterials: From Fundamental Concepts to Devices[END_REF][START_REF] Bellec | Molecular electronics: Scanning tunneling microscopy and single-molecule devices[END_REF] Their two electronic spin states reversibly switch with various stimuli (including temperature, light, electric field) via a transition process involving structural changes (volume and metal-ligand distances). [START_REF] Real | Thermal, pressure and light switchable spincrossover materials[END_REF][START_REF] Nicolazzi | Thermodynamical aspects of the spin crossover phenomenon[END_REF] Accordingly, they present a diagram of potential energy vs internal coordinate with two minima separated by an energy barrier similarly to bistable molecules. However, the occurrence of bistability (hysteretic transition) in spin crossover materials mainly results from cooperative elastic interactions taking place in the assembly of molecules. [START_REF] Ridier | Hysteresis, nucleation and growth phenomena in spin-crossover solids[END_REF] The size decrease, mandatory to incorporate the molecule-based systems in electronic devices, completely modifies the cooperativity as demonstrated for nanoparticles [START_REF] Volatron | Spin-Crossover Coordination Nanoparticles[END_REF][START_REF] Félix | Enhanced Cooperative Interactions at the Nanoscale in Spin-Crossover Materials with a First-Order Phase Transition[END_REF][START_REF] Bertoni | Elastically driven cooperative response of a molecular material impacted by a laser pulse[END_REF] and thin films. [START_REF] Groizard | Enhanced Cooperativity in Supported Spin-Crossover Metal-Organic Frameworks[END_REF][START_REF] Kipgen | Evolution of cooperativity in the spin transition of an iron(II) complex on a graphite surface[END_REF][START_REF] Liu | Collective Spin Manipulation in Antiferroelastic Spin-Crossover Metallo-Supramolecular Chains[END_REF][START_REF] Kelai | Thermal Bistability of an Ultrathin Film of Iron(II) Spin-Crossover Molecules Directly Adsorbed on a Metal Surface[END_REF] The bistability derived from cooperative interactions was still evidenced for patterned SCO dots, [START_REF] Molnár | A Combined Top-Down/Bottom-Up Approach for the Nanoscale Patterning of Spin-Crossover Coordination Polymers[END_REF][START_REF] Bartual-Murgui | Guest Effect on Nanopatterned Spin-Crossover Thin Films[END_REF] or for single nanoparticles using electrical [START_REF] Prins | Room-Temperature Electrical Addressing of a Bistable Spin-Crossover Molecular System[END_REF] or optical read-out. In the context of electronic or spintronic devices, a first fundamental issue is to preserve their switchable properties when molecules are connected to a conducting surface for electrical addressing. [START_REF] Gruber | Spin-Crossover Complexes in Direct Contact with Surfaces[END_REF][START_REF] Kipgen | Spin-Crossover Molecules on Surfaces: From Isolated Molecules to Ultrathin Films[END_REF][START_REF] Kumar | Sublimable Spin-Crossover Complexes: From Spin-State Switching to Molecular Devices[END_REF] The bistability of a very few examples of single SCO molecules was evidenced by scanning tunneling microscopy. A low-temperature memristive behavior governed by the local energy barrier occurs for isolated molecules when decoupled from the metallic substrate. [START_REF] Miyamachi | Robust spin crossover and memristance across a single molecule[END_REF][START_REF] Jasper-Tönnies | Robust and Selective Switching of an Fe III Spin-Crossover Compound on Cu 2 N/Cu(100) with Memristance Behavior[END_REF] And very recently, a similar effect was reported on a tetramer of SCO molecules deposited directly on Ag(111). [START_REF] Johannsen | Electron-Induced Spin-Crossover in Self-Assembled Tetramers[END_REF] Another issue that is especially relevant for high-density storage, is to avoid interference (or interplay) between molecules in self-assembled monolayers. In the case of conformational or volume-dependent process like SCO, the control over this requirement represents an open question and a true bottleneck. As a whole, the switching of single SCO molecules belonging to a well-organized 2D array and importantly, in direct contact with a conducting substrate without affecting neighboring molecules is still a challenge.

Here, we demonstrate by scanning tunneling microscopy (STM) measurements the bista-bility of single SCO molecules self-assembled in a two-dimensional monolayer on Cu(111). This bistability stems from the delicate balance between intermolecular interactions within the monolayer and the interaction between the molecules and the substrate as evidenced by complementary STM measurements and mechano-elastic simulations. We show that the degree of intermolecular cooperativity within a monolayer of SCO molecules is larger when they are adsorbed on Au(111) than on Cu(111). This information is corroborated by the voltage-induced bistability of single molecules evidenced on Cu(111) and absent on Au(111).

The two dimensional molecular layers grown on metallic substrates are composed of [Fe II ((3, 5-(CH 3 ) 2 Pz) 3 BH) 2 ] (Pz = pyrazolyl) spin-crossover molecules, called FeMPz in the following, which exhibit a hysteretic thermal transition between a diamagnetic low spin (LS) state and a paramagnetic high spin (HS) state at a temperature around 190 K in bulk. [START_REF] Iasco | The disentangling of hysteretic spin transition, polymorphism and metastability in bistable thin films formed by sublimation of bis(scorpionate) Fe(ll) molecules[END_REF] On both Au(111) [START_REF] Bairagi | Molecular-scale dynamics of light-induced spin cross-over in a twodimensional layer[END_REF][START_REF] Fourmental | Importance of Epitaxial Strain at a Spin-Crossover MoleculeMetal Interface[END_REF] and Cu(111) [START_REF] Zhang | Anomalous Light-Induced Spin-State Switching for Iron(II) Spin-Crossover Molecules in Direct Contact with Metal Surfaces[END_REF][START_REF] Kelai | Robust magnetic anisotropy of a monolayer of hexacoordinate Fe(II) complexes assembled on Cu(111)[END_REF] substrates, the molecules FeMPz self-assembled in a molecular 2D network (see Figure S1 in SI). At low temperature, as evidenced by XAS experiments, the molecules coexist in both high spin and low spin states that are imaged by STM at 0.3 V as dark and bright molecules, respectively. [START_REF] Zhang | Anomalous Light-Induced Spin-State Switching for Iron(II) Spin-Crossover Molecules in Direct Contact with Metal Surfaces[END_REF] Unfortunately, no direct signature, such as Kondo peak, can be resolved in tunnelling spectroscopy measurements for a direct assignment of the paramagnetic HS state. [START_REF] Bellec | Molecular electronics: Scanning tunneling microscopy and single-molecule devices[END_REF][START_REF] Bairagi | Molecular-scale dynamics of light-induced spin cross-over in a twodimensional layer[END_REF] Therefore, the assignment of the high/low spin state to the dark/bright molecules is realized by comparing STM and XAS measurements both at low temperature (see SI and Figure S2).

Voltage pulses can be used to trigger the transition of a single molecule from one spin state to the other. [START_REF] Miyamachi | Robust spin crossover and memristance across a single molecule[END_REF][START_REF] Jasper-Tönnies | Robust and Selective Switching of an Fe III Spin-Crossover Compound on Cu 2 N/Cu(100) with Memristance Behavior[END_REF][START_REF] Gopakumar | Electron-Induced Spin Crossover of Single Molecules in a Bilayer on Gold[END_REF] The manipulation with voltage pulses has thus been tested on both metallic substrates. appeared nearby, evidencing a non-local switching process. [START_REF] Gopakumar | Electron-Induced Spin Crossover of Single Molecules in a Bilayer on Gold[END_REF] The 4-bright-molecule defect is stabilized for a few minutes (typically two minutes) before the network recovers its initial superstructure (see Figure S3 in SI). Applying larger voltage pulse can lead to the formation of larger defective area as presented in Figure S3 (see SI), where lines of four or seven bright molecules are observed. Most probably, these 4-bright-molecule and 7-bright-molecule lines can be stabilized because of their commensurability with the thermal state superstructure. [START_REF] Bairagi | Molecular-scale dynamics of light-induced spin cross-over in a twodimensional layer[END_REF] Applying a voltage pulse of 2.2 V in the middle of the image locally induces a phase-shifted domain (Figure 1.b). Within less than fifteen minutes (few scans), the inner domain is healed (Figure S4). Therefore, applying voltage pulses enables the conversion of some molecules from the HS state to the LS one (dark to bright) but single molecule bistability is not achieved within the 2D network on Au(111) as the original electronic state is spontaneously recovered.

On the contrary, on Cu(111), we demonstrated the bistability of single molecules in the 2D network. We then investigated in more details the tunneling conditions to switch the molecules from one spin state to the other on Cu(111). The first observation was realized by scanning at 0.7 V an area with a high proportion of LS molecules. We observed by zooming out that in the area scanned at 0.7 V all the molecules are now appearing black at 0.3 V with clear-cut edges (see Figure S6 in SI). Thus, for this voltage bias the molecular switching from the LS state to the HS state is favored. The reverse switching can also be induced by 2.f and SI). When surrounded by molecules in the HS state, both switching events (from HS to LS and LS to HS) are equally probable with equivalent yield values of Y HS→LS = 5.5 10 -8 and Y LS→HS = 3.9 10 -8 . In this environment, for a bias voltage of 0.5 V, the potential energies of both spin states are thus equivalent as schematized in Figure 2.g. On the contrary, when surrounded by molecules in the LS state, the switching yield from HSto-LS (Y HS→LS = 18.6 10 -8 ) is one order of magnitude larger than the switching yield from LS-to-HS (Y LS→HS = 1. 3 10 -8 ). At the same bias voltage of 0.5 V, the HS state is therefore destabilized compared to the LS one (Figure 2.h) probably due to the internal pressure in the molecular monolayer. [START_REF] Bertoni | Elastically driven cooperative response of a molecular material impacted by a laser pulse[END_REF] Often, the final state imaged after the voltage pulse reveals that some of the bright neighbors are switched to the dark state. This clearly underlines that if the molecules can be addressed individually, the neighborhood is still influencing the from room temperature (tip approach and scanning at 0.3 V and 50 pA to avoid any switching of the molecules). The main difference, with the Au substrate, is the organization of the LS molecules observed at 0.3 V. Indeed, on Au(111) an order lattice of LS and HS molecules is developed over a large area (up to 100 × 100 nm 2 ) 37 indicating strong interactions between the molecular spin states. On Cu(111), the distribution of the bright (LS) molecules seems more random (compare Figure 3 In order to rationalize the experimental results and get insight into the influence of the substrate nature on the single molecule bistability behavior, we performed mechanoelastic simulations. [START_REF] Enachescu | Model for Elastic Relaxation Phenomena in Finite 2D Hexagonal Molecular Lattices[END_REF][START_REF] Enachescu | Monte Carlo Metropolis study of cluster evolution in spin-crossover solids within the framework of a mechanoelastic model[END_REF][START_REF] Enachescu | Study of switching in spin transition compounds within the mechanoelastic model with realistic parameters[END_REF] We investigated the influence of the molecule-substrate interaction on the local correlations. For this purpose, we fixed a value for the intermolecular interaction (k mol ) to 4 N.m -1 and calculated the thermal state for two different molecule-substrate interactions (k sub = 0.2 and 1 N.m -1 ), which are represented in Figure 3.c. The first effect of varying k sub is the change in the proportion of the HS/LS molecules within the thermal state as previously reported. [START_REF] Kelai | Thermal Bistability of an Ultrathin Film of Iron(II) Spin-Crossover Molecules Directly Adsorbed on a Metal Surface[END_REF][START_REF] Fourmental | Importance of Epitaxial Strain at a Spin-Crossover MoleculeMetal Interface[END_REF] We obtained proportions of molecules in low spin state (p LS ) of 0.46 and 0.34 for k sub values of 0.2 and 1 N.m -1 , respectively. As presented in Figure 3.d, we then determined in the thermal state the probability to have n consecutive LS molecules along the three equivalent directions of the triangular lattice. For a k sub value of 1 N.m -1 the probability to have n consecutive LS molecules follows a random distribution (lines in Figure 3.d). On the contrary, for a reduced value of k sub (0.2 N.m -1 ), the measured probability is away from the random distribution. Correlation between the molecules can also be quantified through the Moran index which decreases while the interaction to the substrate increases (see Figure S8 in SI). Thus, increasing the interaction between the molecules and the substrate leads to the decrease of the correlations inside the molecular layer. This also suggests that the molecules interact more with the Cu(111) substrate than with the Au(111). The different experiments and simulations described here highlight the role of the substrate nature on the local correlation in the molecular layers and the possibility to stabilize at will a molecule in a given spin state. The molecular layer on Au(111) presents a strong cooperativity as evidenced by the long range correlation in the superstructure and the impossibility to control or stabilize any specific feature. On Cu(111), the long range correlation is weaker leading to a relatively larger molecule-substrate interaction responsible of the bistability of the single molecules within the 2D monolayer. This work opens the way for ultrahigh-density memory devices that can be electrically addressed and read-out using spin crossover molecules.

Number of molecules in HS state

Methods

Experimental methods

Prior to the molecular deposition, the metallic Cu(111) and Au(111) single crystals are cleaned under ultra high vacuum (UHV, base pressure of 10

Mechanoelastic simulations

For the mechanoelastic simulations, spin-crossover molecules are represented as balls arranged in a triangular configuration and linked to their first neighbors situated in the same layer by springs with an elastic constant k mol . The ball radii code for the molecular spin states by taking a value of 0.22 nm and 0.2 nm for the HS and the LS states, respectively.

The distance between two LS molecule centres is 1 nm. The interaction to the substrate is taken into account by linking each spin-crossover molecule to three surface molecules in a face centred cubic configuration by springs with an elastic constant k sub . The intrinsic parameters of the system are ∆H = 1500 × 10 -23 J and ∆S = 9.7 × 10 -23 J.K -1 , thus giving a thermal transition temperature around 155 K.

Figure 1 .Figure 1 :

 11 Figure 1: Induced switching by voltage pulses. a) 15×15 nm 2 STM topographic image acquired after the application of four voltage pulses at 0.6 V on the different application points marked by the black dots (V = 0.3 V, I = 20 pA, z varies from 0 to 1.7 Å). b) 20×20 nm 2 STM current image after a voltage pulse at 2.2 V (10 ms) applied at the location of the black dot (V = 0.3 V, < I >= 10 pA, I varies from 0 to 250 pA). The white lines are aligned along the dense direction of the outer superstructure to highlight the phase shift in the inner domain. c) 10 × 10 nm 2 and d) 10 × 12.5 nm 2 topographic images where "LS" and "HS" have been written by voltage pulses (V = 0.3 V, I = 3 pA, z varies from 0 to 2.63 Å).

Figure 2 :

 2 Figure 2: Voltage pulses on Cu(111). a) 3.5 × 3.5 nm 2 STM topographic image of the initial state with dark (HS) neighbors (V = 0.3 V, I = 5 pA) and b) 4.8 × 4.8 nm 2 STM topographic image of the initial state with bright (LS) neighbors (V = 0.3 V, I = 5 pA). The black dots indicate the position of the voltage pulses in both environments. c), d) Typical I(t)-traces recorded during voltage pulses of 0.5 V for dark (HS) and bright (LS) neighbors, respectively. e), f) Distribution of current times duration (I × ∆t) of each plateau of the I(t)-traces for dark (HS) and bright (LS) neighbors, respectively. The red circles (blue squares) correspond to the experimental distribution of events from bright (LS) to dark (HS) (dark (HS) to bright (LS)) molecules. The dotted lines correspond to mono-exponential fits of each distribution. g),h) Schematics of the relative potential energies of the LS and HS states at 0.5 V depending in both environments.

  Figures 2.e and 2.f and SI). When surrounded by molecules in the HS state, both switching

  Figures 2.e and 2.f and SI). When surrounded by molecules in the HS state, both switching

  .a and Figure S2). To have a better understanding of the bright molecule distribution, we measured the probability of observing n consecutive bright molecules along A (green triangles) and along B (orange dots) as reported in Figure 3.b. The measured probabilities are compared to the probability to have n consecutive bright molecules for a random distribution of bright molecules which is given by p n b (1 -p b ) 2 with p n being the measured proportion of bright molecules (p b = 0.25 ± 0.03). The measured probabilities are larger than what is expected for a random distribution especially along the direction B. This indicates that, when adsorbed on Cu(111), correlations exist between the molecules even though they are weaker than on Au(111).

Figure 4 :

 4 Figure 4: Relaxation of a cluster of molecules in HS state in an environment of molecules in LS state as a function of time (in Monte Carlo steps) for different ratio of k sub /k mol with k mol = 4 N.m -1 .

  -10 mbar) by sputtering (Ar + ions at 600 eV or 900 eV for Cu(111) or Au(111) respectively) and annealing (450 • C for both substrates) cycles. Molecules FeMPz are then sublimated under UHV at a temperature of 85 • C from a home-made Knudsen-cell-like evaporator on the metallic substrate. During the molecular sublimation the single crystals are kept at low temperature (around 5 K). The samples are then annealed at room temperature to enable the formation of the molecular islands. All the measurements have been carried out on a low temperature scanning tunneling microscope (STM, Omicron) operating at 4.6 K. The STM images have been processed using Wsxm software.[START_REF] Horcas | A software for scanning probe microscopy and a tool for nanotechnology[END_REF]

Acknowledgement

The authors thank the European Union's Horizon 2020 research and innovation program under grant agreement n • 766726 for support. C.E. thanks UEFISCDI Romania (grant number PN-III-P4-ID-PCE-2020-1946).

switching properties. For higher bias voltage values, the current traces are more noisy and the HS state is favored as evidenced by the possibility to create 'dark' area.