Mirko Gillet

Suhail Usmani

Mirko Mikolasek

Angélique Gillet

E) b. d José Sanchez Costa

Mathilde Rigoulet

Bruno Chaudret

Azzedine Bousseksou

Benedikt Lassalle Kaiser

Phillipe Demont

Gabor Molnar

Lionel Salmon

Julian Carrey

Simon Tricardf>
email: tricard@insatoulouse.fr

Spin crossover in Fe(triazole}-Pt nanoparticle self-assembly structured at the sub-5 nm scalet

A main goal of molecular electronics is to relate the performance of devices to the structure and electronic state of molecules. Among the variety of possibilities that organic, organometallic and coordination chemistries offer to tune the energy levels of molecular components, spin crossover phenomenon is a perfect candidate for elaboration of molecular switches. The reorganiz ation of the electronic state population of the molecules associ ated to the spin crossover can indeed lead to a significant change in conductivity. However, molecular spin crossover is very sensi tive to the environment and can disappear once the molecules are integrated into devices. Here, we show that the association of ultra-small 1.2 nm platinum nanoparticles with Fe 11 triazole-based spin crossover coordination polymers leads to self-assemblies, extremely well organized at the sub-3 nm scale. The quasi perfect alignment of nanoparticles observed by transmission electron microscopy, in addition to specific signature in infrared spectroscopy, demonstrates the coordination of the long-chain molecules with the nanoparticles. Spin crossover is confirmed in such assemblies by X-ray absorption spectroscopie measure ments and shows unambiguous characteristics both in rnagnetic and charge transport measurements. Coordinating polymers are therefore ideal candidates for the elaboration of robust, well organized, hybrid self-assemblies with metallic nanoparticles, while maintaining sensitive functional properties, such as spin crossover.

Introduction

Arrays of nanoparticles (NPs) have been extensively studied associated with individual molecules. Arnong them NPs have been used as nanoelectrodes to connect molecules. [1][2][3][4][5] In such systems, electrons jump from one NP to another. The limiting elements of the current flow are molecules and equivalent cir cuits are generally assimilated to resistors and capacitors in series. Severa! reports focused on molecular effects in nano particle arrays, as the Jength of the molecule, 6 • 7 its redox state, 8 its charge, 9 its conjugation, 10 etc. Recently, we demon strated that using ultra-small NPs (<2 nm), it was possible to observe Coulomb blockade regime at room temperature in metal NP arrays.11 This finding was particularly interesting as the same transport regime could be observed on a large range of temperature. Charge transport was then determined by the polaàzability of the molecules, as demonstrated with simple thiol functionalized alkyl chains or aromatic cycles. 11 Spin crossover (SCO) molecular compounds show reversible switching between the low spin and high spin states of the central metal ion. The SCO thus corresponds to a reorganiz ation of the electron density of the metal center, which can be modulated by different extemal parameters: temperature, pressure, light irradiation, electric field, etc. 12 - [START_REF] Halcrow | Spin-Crossover Materials: Properties and Applications[END_REF] This elec tronic state population reorganization Jeads to the modifi cation of the charge transport through the molecule, 1 s-1 8 which has been evidenced at different scales: on microcrys tals, 19 nanoparticles, 20 thin layers, 21 and molecules dispersed in a matrix. 22 Severa! attempts have also been reported towards measurements on the single molecule scale, 23 mostly using scanning tunneling microscopy. 24 • 25 Synthesizing hybrid systems combining metallic NPs and SCO molecules is an interesting alternative towards this ultimate size scale, as NPs act as local electrodes at the nanoscale and SCO molecules show at Jeast two electronic states that influence the charge transport between the NPs in the network. A recent study reported the synthesis of core-shell NPs formed by a 12 nm Au SCO, 40 and sometimes to control shaping of objects at the nanoscale. 19,47 Here, we chose a thiophene functionalization, which coordinate to the Pt surface thanks to the strong affinity between S and Pt, but not too strongly to facilitate its relative dissociation, necessary to the SA trial-and-error process. 48,49 We thus synthesized the L ligand (L = (1E)-1-(thiophen-3-yl)-N-(4H-1,2,4-triazol-4-yl)ethan-1-imine) by the condensation of 4-aminotriazole with acetylthiophene. Mixing three equivalent of L with one equivalent of Fe(oTs) 2 •6H 2 O (oTs = tosylate) in THF led to the formation of the FeL 3 (oTs) 2 coordination polymer, called FeL 3 . We first checked that this new compound showed SCO close to room temperature. We indeed confirm that the χ M T product (where χ M is the molar magnetic susceptibility) sharply increased with temperature at 285 K (Fig. 1c). It is important to note that this magnetic behavior corresponds to a light-yellow gel sample with partially evapor- core surrounded by a 4 nm shell of an insulating SCO coordination polymer. Electrical measurements on aggregates of such objects showed a significantly higher conductivity than the corresponding coordination network and a higher current switching ratio between the two spin states. 26 In another attempt, SCO molecules were combined with arrays of gold NPs and the charge transport behavior was correlated with the magnetic properties of the coordination complexes. 27 Generally, authors choose thiols to attach functional molecules to metallic (e.g. Au, Pt, Ag) NPs, in order to stabilize the hybrid systems thanks to the strong interaction between the generated thiolates and the metal surface. [28][29][30] However, the sulfurmetal bond is very energetic and might be too strong to favor the binding-unbinding process, necessary to obtain well-organized molecule-nanoparticle self-assemblies (SA) at large scale. In addition, one can doubt that this strong bond does not affect the SCO in the molecule because of the electronic and steric constraint it imposes. To avoid such drawbacks we chose building blocks in order to obtain stable and robust assemblies: (1) Fe(triazole) based coordination polymer, where three triazole ligands bridge two Fe II centers, geometry which thus increases the stability of the molecular system; (2) ultra-small PtNPs (1.2 ± 0.3 nm), which limit the increase of electronic density in proximity to the Fe II centers; (3) coordination of the molecular polymer to the NP surface by thiophene moieties, which bind Pt less strongly than thiols and thus allows more flexibility and adaptability during the SA process. [START_REF] Rauchfuss | Progress in Inorganic Chemistry[END_REF] By this strategy, we obtained a hybrid system, consisting of lamellae where the NPs aligned with a periodicity of 3 nm. Specific lamellar SA of nanoparticles have already been reported, with liquid crystals, [START_REF] Mitov | [END_REF] diblock copolymers, [33][34][35] or peptidic polymers. 36 But to our knowledge, even if demonstrated for molecular clusters, 37 no work has described organization of ultra-small NPs in quasi perfect linear assemblies with a periodicity lower than 5 nm, so far.

Results and discussion

Synthesis of the hybrid system

The PtNPs were synthesized by decomposition of Pt 2 (dba) 3 (dba = dibenzylideneacetone) under a carbon monoxide (CO) atmosphere in THF, followed by washing of the organic dba ligands with pentane, as previously reported. 11,38 Transmission electron microscopy (TEM) pictures showed well dispersed NPs, with diameters of 1.2 nm ± 0.3 nm (Fig. 1a). Such NPs are particularly interesting as, in addition to their ultra-small sizes, they can be seen as "naked", i.e. free of organic ligand, as they are only stabilized by CO from the synthesis and THF, a coordinating solvent. 39 The other building block of the SA was a triazole based Fe II coordination polymer (Fig. 1b). Such polymers are well referenced in the literature: they are robust, show SCO at temperatures close to room temperature and can easily be processed in nanoparticles, thin films, hybrid materials with polymers, and so forth. [40][41][42][43][44][45][46] An advantage of the triazole moiety is its possibility of functionalization, which has already been extensively used to tune the gated, probably thanks to the bridging aspect of the ligand with triazole on one side and thiophene on the other one, but no alignment was observed (ESI Fig. S2d †).

Fourier-transform infra-red (FT-IR) spectroscopy was performed on the pristine PtNPs, after addition of L only, and on the SA after addition of L and the iron salt (Fig. 2c andd). The spectrum of the pristine NPs showed an intense peak at 2043 cm -1 corresponding to the vibration of terminal CO, and two smaller peaks at 1805 and 1880 cm -1 corresponding to two modes of vibration of bridging CO. Following the vibration position of terminal CO by FT-IR spectroscopy is an efficient tool to probe the electronic density at the NP surface. The significant shift of the vibration from 2043 to 2033 cm -1 is compatible with the coordination of L at the PtNP surface, which turns to be richer in electron. Indeed, higher electronic density at the surface implies stronger back-donation from the NP to the antibonding orbitals of the CO molecule, and a thus vibration at a lower wavenumber. 50 The coordination of the iron salts to the other side of the L ligand in the hybrid SA takes electronic density back, and leads to a CO vibration back to 2042 cm -1 . Such a behavior in FT-IR is in good agreement with the coordination of L at the PtNP surface and the electronic withdrawing effect of the Fe centers linked to the PtNP by coordination through L. This work thus shows for the first ated THF solvent (sic 'gel state'), whereas the pale-white, fully dry powder (sic 'powder state') remains in the high spin state at any temperature (see ESI Fig. S1 †).

Description of the self-assembly

SA between the NPs and the SCO compound was carried out in the same solvent: solutions of NPs, L and Fe(oTs) 2 •6H 2 O were mixed together and agitated in THF for two hours. The obtained hybrid SA is called PtNPs-FeL 3 SA. The precursor concentrations were adapted to obtain 0.2 equivalents (eq.) of L and 0.06 eq. of Fe per introduced Pt. The equivalent number (eq.) is defined as the ratio between the quantity of ligands or Fe and the quantity of platinum atoms present in the system. These ratios were chosen to keep the Fe : L ratio equal to 1 : 3 (as in the coordination polymer), and to have a L : Pt ratio equal to 0.2 : 1, as it was previously demonstrated to be the equivalence ratio, when all the ligands are coordinated at the NP surface. 11 TEM images of the PtNPs-FeL 3 SA showed zones were the ultra-small PtNPs were perfectly aligned (Fig. 2a and ESI Fig. S2a,b,c †), forming parallel lines separated by 3.2 nm from each other. A basic geometrical model suggests that a single strand of polymer separates the NP lines (Fig. 2b). We verified that such a structuration was not induced by the presence of L alone: without Fe(oTs) 2 but only L, the NPs aggre-FeL 3 coordination polymer and, in a smaller proportion, in the PtNPs-FeL 3 SA (Fig. 3b andc). In order to estimate the proportion of Fe that underwent SCO in each samples, we compared the shifts between the two curves in low and high spin states to the one of the [Fe(NH 2 Trz) 3 ]Br 2 reference, for which we considered a full SCO. 52,53 SCO was thus estimated to be equal to 89% in the FeL 3 coordination polymer alone, and to 36% in the PtNPs-FeL 3 SA. XAS measurements thus proved that SCO was present, to some extent, in the self-assembled system. In magnetic measurements on the FeL 3 coordination polymer, χ M T value decreased from 3.2 to 0.4 cm -3 K mol -1 while decreasing the temperature from 320 K to 100 K (Fig. 1c), a difference that corresponds to a decrease of 88% of the magnetization, in very good agreement with the spin population conversion of 89% estimated by XANES measurements between these two temperatures.

Magnetic and charge transport measurements

Magnetic measurement on PtNPs-FeL 3 SA showed an incomplete, abrupt and slightly hysteretic transition in the 'gel state' (Fig. 4a). In this sample, the χ M T value decreased from 3.0 to 1.7 cm -3 K mol -1 while decreasing the temperature from 300 K to 250 K. This decrease of 42% of magnetization is in the same order of magnitude as the 36% of SCO determined by XAS. This incomplete and relatively gradual SCO in the PtNPs-FeL 3 SA could arise from three different sources. The first possible reason is intrinsic and can be due to the presence of the platinum NPs, which might block SCO, as they time that an appropriate coordination between coordination polymers and metal NPs can lead to well-organized hybrid system, at a sub-5 nm scale.

Spin crossover in the hybrid system Spectroscopic characterizations are irrefutable proofs of the presence of SCO in a system as complex as our SAs. We thus performed X-Ray near edge absorption spectroscopy (XANES) measurements at the Fe K-edge, as the iron atom is the SCO center. As an element of comparison, we first measured spectra of [Fe(NH 2 Trz) 3 ]Br 2 (NH 2 Trz = 2-amino-1,2,4-triazole), known to show a full SCO between 260 and 310 K. 51 We observed a shift of the Fe K-edge energy towards lower values between 100 K (low spin) and 323 K (high spin), attributed to the SCO signature (Fig. 3a). A similar shift was observed in the state is then the more conducting state, as already observed in hybrid systems made of metal NPs and NCO coordination molecules. 20,27

Conclusion

In summary, we have shown that mixtures of a coordination polymer with ultra-small platinum nanoparticles can afford well-organized SA, where lines of NPs intercalated with single polymer strands. The key aspect of this SA is the coordination of the polymer to the NP surface by the thiophene moiety, sufficiently strong to ensure the system cohesion, but not too strong to facilitate the elements' rearrangement. Such an approach is particularly interesting to build hybrid material structures at the lower than 5 nm scale, for which thermal energy is too high to assemble the building blocks by van der Waals forces only. 59 Besides, the robustness of the triazole based coordination polymer gave the opportunity to maintain its SCO functional properties, even in the hybrid SA, as confirmed by XAS measurements. The consequence of such a SCO implied significant discrepancies in the magnetic and electrical characteristics of the sample.

In the future, to ensure optimal performances, the rational design of hybrid SA including metallic NPs and functional molecules, should consider ultra-small NPs, robust molecular systems such as coordination polymers and a fine tuning of the chemical interaction between the anchoring moiety of the functional molecules and the NP surface, as demonstrated in this work.

Experimental methods

Chemical syntheses

Ligand L. 4-Amino-4H-1,2,4 triazole (2 g, 0.023 M) and 3-acetylthiophene (2.9 g, 0.023 M) were mixed in 50 mL ethanol and the solution was stirred and heated overnight at reflux. The solution was partially evaporated and a white solid was obtained (yield 80%). 1 FeL 3 coordination polymer. 10 mL of a solution of the L ligand (at 6 × 10 -3 mol L -1 in THF) and 10 mL of a solution of Fe(oTs) 2 •6H 2 0 (at 2 × 10 -3 mol L -1 in THF-oTs = paratoluene sulfonate) were mixed under vigorous stirring. The precursor concentrations were adapted to obtain 3 equivalent of the L ligand per Fe. The solution was agitated for 2 hours. The remaining solution was partially evaporated to a light yellowgel called 'gel state'. Evaporation was stopped when an equivalent of 50% in mass of solvent remained in the system. A particular care to avoid evaporation has to be taken for characterization as the THF is particularly volatile. Further evaporation to dryness led to a pale white powder called 'powder state'. TEM images of the pristine FeL 3 coordination polymer do not show any presence of nanostructure objects.

bring high electronic density in the vicinity of the Fe II center. A second reason can come from the inhomogeneity of the SA: some parts of it, well-organized, would switch, whereas the other ones would not. The third reason is more experimental and could come from a quantity of remaining solvent not sufficiently high. Indeed, as for the coordination polymer, no SCO was observed anymore on PtNPs-FeL 3 SA in the dry 'powder state', where the system remained at the high spin state (ESI Fig. S3 †).

Transport measurements were performed on SA deposited on interdigitated electrodes by drop casting. During the measurements, the temperature was swept at the rate of 1 K min -1 . Below 250 K, the current slope decreased gradually towards low temperatures (Fig. 4b). Decrease in current at low temperature is a typical characteristic of arrays of NPs separated by molecules and can arise due to the less thermal energy available to overcome the charging energy. [54][55][56][57] However, this description does not explain the sharp decrease (increase) in current during cooling (heating) cycle observed between 250 K and 300 K. Charge transport in hybrid compounds with ultrasmall nanoparticles is governed by Coulomb blockade, even at room temperature, 11 as observed in the PtNPs-FeL 3 SA (ESI Fig. S4 †). Coulomb blockade is directly linked to the polarizability of the compounds surrounding the nanoparticles, 11 i.e. the coordination polymer here. During the SCO from the low to the high spin state, the antibonding orbitals of the iron center are populated, increasing the Fe-N bound distance and thus the polarizability of the coordination compound. As a result, the dielectric constant is (in general) higher in the high spin state, as already demonstrated. 58 As a direct consequence, the conductivity of the high spin state is higher than that of the low spin state in the hybrid system.

Resistance of the hybrid assemblies varied in the range of 10-10 3 MΩ for different assemblies, and voltages ranging between few tenths of a volt up to 2 V (ESI Fig. S5 †). The current values were observed in the range of few nA to few hundred nA. In other experiments, a cycle opening was observed in the current-temperature curve when the temperature was swept at 3 K min -1 (ESI Fig. S6 †). Faster sweeping rate thus results in a temperature lag, which gives rise to a hysteresis-like curve in the current-temperature cycles.

Magnetic measurement and charge transport measurements on the PtNPs-FeL 3 SA show similar behaviors. While the χ M T rapidly decreases from 300 K to 250 K in magnetic measurements, current also shows a relatively sharp decrease in roughly the same temperature regime. Such changes in conductivity can arise due to several factors. Different charge transport mechanism such as sequential tunneling and cotunneling could result in changes in current-temperature slope. 57 However, we unlikely believe this hypothesis because such a transport mechanism change typically takes place at lower temperatures. In our case, we have observed a sharp change in the current near 250 K. So far, the most likely explanation of the observed transport behavior comes from the SCO process where the current follows the same behavior as the magnetic moment in magnetic measurements. The high spin 500 mA. The energy was monochromatized thanks to a Si(311) double crystal monochromator and the data were collected as fluorescence excitation spectra using a silicon drift detector (Bruker). The energy of the beamline was calibrated to the first inflection point of a metallic iron foil (7112.0 eV). All data were normalized using the Athena software of the IFEFFIT package. The reference sample [Fe(NH 2 Trz) 3 ]Br 2 was measured as a diluted powder in a graphite pellet. To maintain the PtNPs-FeL 3 and PtNPs-FeL 3 samples in a 'gel state' and avoid THF evaporation during measurement, we used a home-made liquid sample holder where the gel was placed and sealed with a Kapton window. The difference of shifts of the Fe K absorption edge between the low and high spin curves was determined to quantify SCO. Even if some differences can be observed between HS and LS states in the pre-edge structure, differences are significantly higher comparing the absorption edges. 60,61 Comparison of such shift were calculated by determining the area delimited by the two curves in the low and high spin states, between xµ(E) values equal to 0.4 and 1. We then calculated the ratios between the areas of interest and the one of the reference [Fe(NH 2 Trz) 3 ]Br 2 compound, in which a 100% SCO was assumed. SCO was thus estimated to be equal to 89% in the FeL 3 coordination polymer alone, and to 36% in the PtNPs-FeL 3 SA. The estimation of SCO can vary from ±10%; that is why we integrated the area of interest on a range of xµ (E) values as large as possible.

Magnetic measurements

PPMS-VSM from Quantm design was used to perform the magnetic measurements during which the magnetic moment from the sample was measured at a constant magnetic field of 1.5 T while varying the temperature at 1 K min -1 . The sample was carefully placed in a closed cylindrical sample holder of known mass which is placed in VSM such that it experiences the field in the direction perpendicular to its cross-section. For sample in the gel state, temperature was never set above 300 K, in order to avoid solvent evaporation. Evaluation of susceptibility from magnetic moment requires the mass of the measured sample inside the sample holder. This was calculated by weighing the measured sample and subtracting the mass of empty sample holder from it. For the samples measured in gel state, an additional mass of the solvent present in the sample could result in inaccurate values of susceptibility. In order to avoid this, the sample was left to dry after the measurement until there was no reduction in mass due to solvent evaporation. The mass of the dried sample was then carefully recorded for further calculation of susceptibility. The pristine PtNPs did not give any magnetic signal as they are diamagnetic.

Charge transport measurements

The electrodes for transport measurements consisted of eight pairs of interdigitated combs elaborated by photolithography. 62,63 They were composed of 20 interpenetrated fingers with a height of 30 nm, a length of 200 μm, and separated by a gap of 5 μm. Integration of the particles Platinum nanoparticles. The PtNPs have been synthesized as previously described. 11,38 All operations were carried out using Fischer-Porter bottle techniques under argon. A solution of Pt 2 (dba) 3 (90 mg; 0.165 mmol of Pt) in 20 mL of freshly distilled and deoxygenated THF was pressurized in a Fischer-Porter bottle with 1 bar of CO during 30 minutes at room temperature under vigorous stirring. During this time, the solution color changed from violet to brown (attesting the formation of the NPs). The mixture was evaporated and washed with pentane to eliminate the dba (3 × 20 mL), and to obtain native NPs. The colloid was then redissolved in 20 mL of THF. The size of the NPs was found to be equal to 1.2 ± 0.3 nm. For each series of measurements, the sizes were determined by TEM imaging.

Self-assembly. 1 mL of a solution of the L ligand (at 6×10 -3 mol L -1 in THF) and 1 mL of a solution of Fe(oTs) 2 •6H 2 0(at2×10 -3 mol L -1 in THF) were simultaneously added to 4 mL of the native NP mixture under vigorous mixing. The precursor concentrations were adapted to obtain 0.2 eq. of L and 0.06 eq. of Fe per introduced Pt. The brown solution was agitated for 2 hours. Drops of the crude solution were deposited on specific substrates for each characterization (see below). The remaining solution was partially evaporated to a viscous liquid called 'gel state'. Evaporation was stopped when an equivalent of 50% in mass of solvent remained in the system. A particular care to avoid evaporation has to be taken for characterization as the THF is particularly volatile. Further evaporation to dryness led to a dark-brown powder called 'powder state'. The selfassembly experiments have been repeated several times and led to reproducible results. The systems presented here come from optimization of the experimental conditions, in the scope of a larger study where different parameters have been tested (varying the equivalent numbers, the nature of the counter-ions, the order of addition of the building blocks, etc.).

Structural characterization of the assemblies

Samples for TEM were prepared by deposition of one drop of the crude solution on a carbon covered holey copper grid. TEM analyses were performed at the "centre de microcaractérisation Raimond Castaing" using a JEOL JEM 1400 electron microscope operating at 120 kV. The mean size of the particles was determined by image analysis on a large number of particles (∼300) using the ImageJ software. Scanning transmission electron microscopy with energy dispersive X-ray spectroscopy (STEM-HAADF/EDS) analysis was performed on a JEOL JEM-ARM200F Cold FEG operated at 200 kV.

FT-IR spectra were recorded on a Thermo Scientific Nicolet 6700 FT-IR spectrometer in the range 4000-700 cm -1 , using a Smart Orbit ATR platform. The sample deposition was performed by drop casting of the crude solution on the germanium crystal of the platform; the measurement was acquired after evaporation of the THF solvent.

XAS measurements

X-ray absorption spectra were collected on the LUCIA beamline of SOLEIL at a ring energy of 2.75 GeV and a ring current of

Fig. 1

 1 Fig. 1 Building blocks. (a) TEM image of pristine ultra small (1.2 ± 0.3 nm) platinum nanoparticles. (b) Schematic illustration of the FeL 3 coordination polymer L = (1E) 1 (thiophen 3 yl) N (4H 1,2,4 triazol 4 yl)ethan 1 imine. Fe triazole networks form unidimensional struc tures, where two Fe II centers are linked to each other by three bridging triazole ligands. (c) Magnetic measurement on the FeL 3 coordination polymer in the 'gel state', showing an abrupt SCO at 285 K. The curve is normalized per mole of Fe.

Fig. 2

 2 Fig. 2 Hybrid self assembly made of Pt nanoparticles (NPs) and FeL 3 coordination polymers. (a) TEM image of the self assembly. (b) Structural model of the self assembly, showing the intercalation of coordination polymers and aligned NPs. Infrared spectra of the pristine PtNPs, after addition of L, and after addition of L and the iron salt Fe(oTs) 2 •6H 2 O: (c) full spectra (the baselines are shifted for clarity) and (d) zoom on the terminal CO region. The shift of the CO bond vibration from 2043 to 2033 cm 1 is a signature of the L coordination at the PtNP surface, which turns to be richer in electron; the coordination of the iron salts to the other side of the L ligand takes electronic density back, and leads to a shift of the CO bond vibration back to 2042 cm 1 .

Fig. 4

 4 Fig. 4 Magnetic and electrical measurements on the PtNPs FeL 3 self assembly. (a) Magnetic measurement. The curve is normalized per mole of Fe. (b) Electrical measurement. The slope break around 280 K in the current characteristics can be attributed to the spin crossover observed in magnetic measurements and demonstrated by XAS measurements (Fig. 3).

Fig. 3

 3 Fig. 3 Spin crossover. XAS measurements at 100 K and 323 K at the Fe K edge on (a) [Fe(NH 2 Trz) 3 ]Br 2 (NH 2 Trz = 4 amino 1,2,4 triazole). (b) FeL 3 coordination polymer. (c) PtNPs FeL 3 self assembly. By comparison with the [Fe(NH 2 Trz) 3 ]Br 2 reference, known to show a full spin crossover at 310 K, the spin crossover was estimated to be equal to 89% in the FeL 3 coordination polymer, and to 36% in the PtNPs FeL 3 self assembly.

Acknowledgements

We thank Marc Respaud and Sébastien Pinaud for their significant help in magnetic measurements. We also thank Sébastien Cher for experimental support, Thomas Blon for gold evaporation on substrates and Gautier Félix for insightful discussions. We acknowledge SOLEIL for provision of synchrotron radiation facilities on the LUCIA beamline. Financial support from Agence Nationale de la Recherche (PhoCatSA grant ANR-10-LABX-0037-NEXT, MOSC grant ANR-18-CE09-0007 and Nanohybrid grant ANR-13-BS07-0020-01), from the Marie-Curie research program (NanoSCOpe 328078) and from the Indo-French Centre for the Promotion of Advanced Research -CEFIPRA is acknowledged. This study has been partially supported through the EUR grant NanoX n° ANR-17-EURE-0009 in the framework of the Programme des Investissements d'Avenir. JSC is grateful to the Spanish MINECO through National Research Project (CTQ2016-80635-P) and the Ramon y Cajal Research program (RYC-2014-16866).

Conflicts of interest

There are no conflicts to declare. Electronic Supplementary Material (ESI) for Nanoscale. This journal is © The Royal Society of Chemistry 2020

Supporting information

Spin crossover in


Yacine Meslem
email: yacinemeslem@hotmail.fr

Abeldjalil Aïssa-El-Bey

Mustapha Djeddou

A Simple ADMM Solution to Sparse-Modeling-Based Detectors for Massive MIMO Systems

Keywords: Alternating Direction Method of Multipliers(ADMM), Detection, Massive MIMO, Optimization, Sparse-modeling

 for massive MIMO systems. Our solution relies on a special reformulation of the associated optimization problem by describing the constraints as a Cartesian power of the probability simplex. Simulation results show that the proposed algorithm is as accurate as the best known solvers (interior point methods), while its complexity remains linear with respect to the size of the system.

Introduction

Large-scale Multiple-Input Multiple-Output, more commonly known as massive MIMO are attractive wireless communication systems that utilizes tens to hundreds antennas for transmission and reception. This powerful technology has emerged as an effective solution to the growing tremendous demand on high quality wireless communication in a limited radio spectrum. This is because it can provide high data transmission rates, when applied in a spatial multiplexing mode (V-BLAST), without needing additional bandwidth allocation. For that, massive MIMO systems are one of the key enablers for deploying the next generation cellular systems [START_REF] Larsson | Massive MIMO for Next Generation Wireless Systems[END_REF]. However, as a result of requiring a large number of antennas, the detection task becomes very challenging. Thought the maximum likelihood (ML) is the optimal detector in the sense that it leads to the smallest probability of error, it is equivalent to solve an integer least square minimization, and thus it is extremely expensive from a complexity perspective. Sphere decoding can effectively resolve this problem for small size MIMO systems but not for large scale ones [START_REF] Hassibi | On the Sphere-Decoding Algorithm I. Expected Eomplexity[END_REF]. As an alternative to the ML optimal approach, many suboptimal detectors have been proposed and studied in the literature. Those techniques range from the simple linear detectors such as zero forcing (ZF) and minimum mean square error (MMSE) to the more sophisticated semidefinite relaxation (SDR) based detectors. All these detectors have their floors. The decoders which rely on SDR still not so tolerable in terms of complexity while the performances (in terms of BER) of linear decoders are so poor. On another front, an emerging detection strategy relying on sparse and redundant representations theory has recently shown promising results [START_REF] Fadlallah | New Iterative Detector of MIMO Transmission Using Sparse Decomposition[END_REF][START_REF] Hajji | Low-Complexity Half-Sparse Decomposition-Based Detection for Massive MIMO Transmission[END_REF] and [START_REF] Elgabli | Two-Stage LASSO ADMM Signal Detection Algorithm for Large Scale MIMO[END_REF]. Sparse and redundant representations theory is a powerful and emerging paradigm that is at the core of compressive sensing and it has been successfully applied to a wide range of signal and image processing problems [START_REF] Elad | On the Role of Sparse and Redundant Representations in Image Processing[END_REF]. As we will briefly show in section 3, the references above have all adopted the sparse decomposition approach introduced in [START_REF] Aïssa-El-Bey | Sparsity-Based Recovery of Finite Alphabet Solutions to Underdetermined Linear Systems[END_REF]. Subsequently, their proposed detectors are the same from an optimization point of view. On the side of numerical solutions, the first two papers have suggested interior point (IP) methods while the last one have employed ADMM after converting the optimization model to Least Absolute Shrinkage and Selection Operator (LASSO) problem. The ADMM technique [START_REF] Boyd | Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers[END_REF] is a first order optimization method. It has been extensively applied in a variety of fields thanks to its ability to break down a hard minimization to easier sub-problems, and separately solves them. Let us return to [START_REF] Elgabli | Two-Stage LASSO ADMM Signal Detection Algorithm for Large Scale MIMO[END_REF]. It is well known that the penalized LASSO form requires an additional regularization parameter, which is, in general, very difficult to determine in advance. In this work, we propose simple way to solve all those detectors using ADMM. In order to do that, we describe the constraints set in terms of the standard (probability) simplex. Based on this new formulation of the detection problem, our algorithm is derived. The rest of this paper proceeds as follows. In section 2, we give the system model. We shortly review sparse-modeling-based detectors in section 3. Our proposed ADMM-based solution is presented in section 4. Section 5 is devoted to simulation results. Finally, we conclude this paper in section 6

Definitions and Notation. The proximity operator of a scaled function as λf (•) is defined as

prox λf (v) = argmin x∈D f (x) + 1 2λ x -v 2 2 . The orthogonal projec- tion of a vector v onto a convex closed set D is Π D (v) = argmin x∈D 1 2 x -v 2
2 . As a widely adopted convention, we use uppercase boldface letters for matrices and lowercase boldface letters for vectors. The i th standard unit vector of an Euclidean space R n is denoted as e i . We denote the d × d identiy matrix by I d and the all ones vector of length d by 1 d . The symbols (•) T and (•) H stand for the transpose and the Hermitian of a matrix respectively. As usual, we denote the set of reals by R and the set of complexes by C. (•) and (•) are used for the real part and the imaginary part of a complex number (resp. vector). By the symbol ⊗, we denote the Kronecker product. For an integer n, 1, n denotes the set {1, 2, . . . , n}. We write, (•) (•) to emphasize that the first object is greater or equal to the second one component-wise. The indicator function of closed convex set D is defined as

I D (z) = 0 z ∈ D +∞ z / ∈ D

System Model

We assume that our large-scale MIMO system is constituted of N t transmit and N r receive antennas (uplink scenario). The transmission of the data symbols x ∈ M Nt , where M is the signaling set, is made through a flat fading channel modeled as a matrix H ∈ C Nr×Nt . The entries of H are assumed to be i.i.d CSGS random variables of zero mean and unit variance. The received vector y ∈ C Nr is then given by

y = Hx + ν, (1)
where, y ∈ C Nr is the received vector and ν represent the AGWN noise at the receiver, which is their entries are also i.i.d CSGS random variable of zero mean and a variance equal to σ 2 . Furthermore, we assume that the receiver knows perfectly the CSI (Channel Information state) but the emitter does not. The ML detector requires the solution of the following least square problem under discrete constraints, minimize

1 2 y -Hx 2 2 subject to x ∈ M Nt . (2)
Some detection approaches work on the real equivalent model to (1) which is

ỹ = Hx + ν, (3)
where

, ỹ = [ (y) (y)] T , x = [ (x) (x)] T and

H = (H) -(H) (H) (H) .

Note that x ∈ P 2Nt , where, P is the equivalent PAM to the original (generally) QAM constellation.

Review on sparse-modeling-based massive MIMO detection

For the sake of completeness, we present in this section a brief review on the sparse-modeling-based massive MIMO detection strategy. The sparse decomposition in [START_REF] Aïssa-El-Bey | Sparsity-Based Recovery of Finite Alphabet Solutions to Underdetermined Linear Systems[END_REF][START_REF] Fadlallah | New Iterative Detector of MIMO Transmission Using Sparse Decomposition[END_REF] exploits the finteness propriety of the modulation set in the way that we shortly explain hereafter. Let m = [m 1 , . . . , m L ] T , then any symbol m i ∈ M can be written as

m i = m T e i ,
Clearly, e i is sparse since it has only one nonzero entry. Extending this to the transmitted signal x gives

x = (I Nt ⊗ m T D )s, (4)
where, s ∈ R LNt and D ∈ C Nt×LNt is the dictionary.

One drawback of this transform is its ultimate dependency on the modulation being used and thus, its dimension may be burden for higher order alphabets [START_REF] Hajji | Low-Complexity Half-Sparse Decomposition-Based Detection for Massive MIMO Transmission[END_REF]. A solution to this issue has been given in [START_REF] Hajji | Low-Complexity Half-Sparse Decomposition-Based Detection for Massive MIMO Transmission[END_REF], where it has been proposed to apply the previous transform after converting rectangular L-QAM to BPSK constellation using the technique of [START_REF] Choi | Iterative Receivers with Bit-Level Cancellation and Detection for MIMO-BICM Systems[END_REF]. Leveraging these representations for (2) and relaxing the hard constraint give the following minimization problem [START_REF] Fadlallah | New Iterative Detector of MIMO Transmission Using Sparse Decomposition[END_REF][START_REF] Hajji | Low-Complexity Half-Sparse Decomposition-Based Detection for Massive MIMO Transmission[END_REF] minimize 1 2 y -Φs 2 2 subject to Bs = 1 s 0.

(

) 5
The minimization ( 5) represents what we refer to as sparse-modeling-based detectors. Here, Φ = DH or Φ = WD H depending of the transform being used. The matrix W mapping L-QAM symbols to BPSK ones [START_REF] Choi | Iterative Receivers with Bit-Level Cancellation and Detection for MIMO-BICM Systems[END_REF], where

D = I ⊗ [-1, +1]. The matrix B = I ⊗ 1 T
, where, again, the dimensions are determined with respect to the chosen decomposition. Therefore, to keep our derivations general, we assume, in the rest of this paper, that our sparse representation vector s ∈ R pN , where N is the size of the equivalent data vector to be sparsely represented and p is the dimension of the associated standard unit vector. For the sparse decomposition used in [START_REF] Elgabli | Two-Stage LASSO ADMM Signal Detection Algorithm for Large Scale MIMO[END_REF], it is exactly that of [START_REF] Aïssa-El-Bey | Sparsity-Based Recovery of Finite Alphabet Solutions to Underdetermined Linear Systems[END_REF][START_REF] Fadlallah | New Iterative Detector of MIMO Transmission Using Sparse Decomposition[END_REF] applied to the PAM equivalent constellation (to QAM) when the real model ( 3) is used, and its LASSO formulation has been demonstrated to be equivalent to (5) [START_REF] Fadlallah | New Iterative Detector of MIMO Transmission Using Sparse Decomposition[END_REF][START_REF] Hajji | Low-Complexity Half-Sparse Decomposition-Based Detection for Massive MIMO Transmission[END_REF]. At the end of this section, we want to mention that the minimization in ( 5) is convex and straightforward separable (in objective and constraints), and hence many ADMM solutions are possible and they are guaranteed to converge.

Proposed ADMM solution

We denote by A + the feasible set (5), i.e.,

A + = s ∈ R pN | Bs = 1 N , s 0 pN .
Since the vector s is a concatenation of N unit vectors i of length p, we can regard the set A + as the N -Cartesian power of the unit simplex ∆ p of dimension p. So, we can write

A + = ∆ N p , (6)
where,

∆ p = s ∈ R p | 1 T s = 1, s 0 p .
For the simplicity of notation, we omit hereafter the subscript p. Using (6), we can rewrite (5) as follows

minimize 1 2 y -Φs 2 2 subject to s i ∈ ∆, ∀i ∈ 1, N . (7)
In order to apply ADMM for solving [START_REF] Fadlallah | New Iterative Detector of MIMO Transmission Using Sparse Decomposition[END_REF], we need first to write it in a split form as follows

minimize 1 2 y -Φs 2 2 + Nt i=1 I ∆ (z i ) subject to s = z, (8)
where, z = z T 1 , . . . , z T N T ∈ R pN is a slack variable. The ADMM method solves a convex optimization problem such as (8) in three steps. The first two steps are an alternated minimization of the augmented Lagrangian associated with the problem of interest with respect to the primal variables s then z (respectively z then s ). The last step is an updating of the dual variable w. For our problem (8), its augmented Lagrangian reads

L ρ (s, z, w) = 1 2 y -Φs 2 2 + Nt i=1 I ∆ (z i ) + w T (s -z) + ρ 2 s -z 2 2 (9)
By simple algebraic manipulations, we can put (9) in the so-called scaled form as follows

L ρ (s, z, u) = 1 2 y -Φs 2 2 + Nt i=1 I ∆ (z i ) + ρ 2 s -z + u 2 2 - ρ 2 u 2 2 , (10)
where, u = w ρ . Note that the last term in [START_REF] Hassibi | On the Sphere-Decoding Algorithm I. Expected Eomplexity[END_REF] does not affect the optimization with respect to both s and z and thus it will be omitted. s-update. Updating s requires the optimization of the following problem

s k+1 = argmin s 1 2 y -Φs 2 2 + ρ 2 s -z k + u k 2 2 . (11)
This is a smooth quadratic convex problem and it solution can be easily obtained by seeking the value of s for which the gradient vanishes. Subsequently, the solution is given by

s k+1 = 1 2 Φ H Φ + Φ H Φ T + ρI -1 Φ H y + ρ z k -u k . ( 12
)
It worth mentioning that, for the derivation of the gradient, we have used the fact that our optimization variable s is real. That is to say, that for a complex-valued function h of a real variable α, we simply define its derivative as

dh(α) dα = d (h(α)) dα +  d (h(α)) dα .
Note that the matrix to be inverted is constant in throughout all the process. So, its inverse is needed to be determined only once.

z-update. The problem to solve in this step is given by

z k+1 = argmin z1,...,z N N i=1 I ∆ (z i ) + ρ 2 s k + u k -z 2 2 ( 13
)
Algorithm 1 Proposed ADMM based algorithm

Input: s0 ∈ R N , z0 ∈ R N , u0 ∈ R N , ρ > 0 1: preprocessig: 2: Ψ ← 1 2 Φ H Φ + Φ H Φ T + ρI -1
%% save matrix inverse 3: ỹ ← Φ H y %% save matrix multiplication 4: k ← 0 5: repeat 6:

s k+1 ← Ψ ỹ + ρ z k -u k 7:
for i ← 1, N do 8:

z k+1 i ← Π∆ u k i + s k+1 i 9:
end for 10:

u k+1 = u k + s k+1 -z k+1 11:
k ← k + 1 12: until a halting criterion is met 13: x ← Ds K %% back to the x domain 14: x ← Ω(x) %% hard slicing Output:

x

Since the minimization ( 13) defines the proximity operator of a separable function, we can use the separability property of the proximity operator [12, p. 129] to write

z k+1 =    prox I ∆ (s 1 + u 1 ) . . . prox I ∆ (s N + u N )    . (14)
Furthermore, the proximity of an indicator function of any set is nothing but the orthogonal projection on the same set. Therefore, (14) becomes

z k+1 =    Π ∆ (s 1 + u 1 ) . . . Π ∆ (s N + u N )    . ( 15
)
All we need now, is to determine how to perform the orthogonal projection onto the standard simplex. Clearly, the Euclidean projection onto a simplex is a convex optimization problem as any orthogonal projection onto any convex set. Although, there is no closed-form solution to this problem, one can still get it in different simple ways. One well known iterative method is presented in [12, p. 182]. A simpler, reasonably fast and easy-to-implement algorithm is derived in [START_REF] Chen | Projection Onto A Simplex[END_REF]. This algorithm is our choice to perform the z-update step.

u-update For the completeness of the algorithm, we recall that the scaled dual variable u updates as follows

u k+1 = u k + s k+1 -z k+1 . (16)
We summarize our proposed solution in algorithm 1. The derived algorithm is simple and it alternates between an updating of a regularized least square solution (s-update) and a series of projections onto the standard probability simplex (z-update).

Computer Experiments

In this section, we assess the performances of our algorithm, in terms of i) the quality of solution that it provides, ii) the BER, specially for the underdetermined scenario when the number of receive antennas is less than the number transmitters and iii) the runtime needed for the algorithm to execute. We Fellow the system model described in (2). The simulations have been conducted using a workstation with Xeon(R) E5 -2630 v3 CPU and 8 GB of RAM. All the algorithms are implemented using Matlab. We should mention that due to space limitation, we only present the results corresponding to the flat fading channel mode. The extension to the selective channel environment is not difficult [START_REF] Fadlallah | New Iterative Detector of MIMO Transmission Using Sparse Decomposition[END_REF]. First, we evaluate the proposed algorithm in terms of the reconstruction quality.

To do that, we compare the solution of our algorithm with that of the highly precise interior point (IP) method, for two instances of (5), i.e., for a QPSK 64 × 64 MIMO system and a 16-QAM 32 × 32 one. We employed cvx [START_REF] Grant | CVX: Matlab Software for Disciplined Convex Programming[END_REF], a Matlab toolbox for modeling and solving convex optimization problems relying on IP methods. The same hard slicing techique is used to round the solutions of both algorithms to the signaling set. The obtained results are depicted in Fig. 1, where we can see that our algorithm produces exactly the same quality of solutions as the IP method for the two MIMO settings that we have considered and this remains true for the whole SNR range.

In order to get some insight about the performances of the sparse-modelingbased detectors and in particular our proposed algorithm, we compare it to one of the high-performance SDR based detectors, (SDR-rbr), for QPSK and BPSK constellations [START_REF] Wai | Cheap Semidefinite Relaxation MIMO Detection Using Row-by-Row Block Coordinate Descent[END_REF]. We use the code provided by the authors, available at http://www.ee.cuhk.edu.hk/~wkma/mimo/rbr.html. The comparison is made for two under-determined (overloaded) massive MIMO systems scenarios using QPSK signaling. The results of this comparison are given in Fig. 2. It is clear that the SDR-rbr decoder outperforms our detector for both configurations 64 × 58 and 64 × 48. One important thing to notice here, is that the gap of performances between the two algorithms decreases (64 × 48 case) as the system becomes more overloaded. This confirms that the sparse-modeling-based detection approach is more suitable for the under-determined case [START_REF] Fadlallah | New Iterative Detector of MIMO Transmission Using Sparse Decomposition[END_REF][START_REF] Hajji | Low-Complexity Half-Sparse Decomposition-Based Detection for Massive MIMO Transmission[END_REF]. Finally, we compare the run time of our algorithm with respect to one of the most low-complexity detectors, MMSE, and one of the cheapest SDR based detectors, SDR-br. THe results are shown in Fig. 3 We have used QPSK modulation for a variety of antennas number. The average runtime was obtained for 250 independent simulations at 15 dB. We notice that the complexity of our algorithm is in between the complexity of MMSE and that of the SDR-rbr. The ratio between our algorithm and the SDR-rbr one is roughly 10 in the favor of our method, and so it is when compared to the MMSE decoder in the favor of the latter. Furthermore, as an interesting remark, the proposed algorithm scales linearly with the dimension of the system. We should point out that, for all the results presented above, we have used a standard stopping criterion [START_REF] Boyd | Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers[END_REF] for our algorithm without any acceleration technique. We believe, however, that a modification of the halting criterion of the proposed algorithm such as an early termination, i.e., running the algorithm for a prefixed number of iterations and / or an incorporation of an acceleration scheme like using a variable step (ρ) [START_REF] Boyd | Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers[END_REF], will help in further reducing the runtime of the proposed algorithm.

Conclusion

We have proposed a simple and fairly fast algorithm for solving the sparsemodeling-based detectors. We have shown, by simulations, that the proposed algorithm achieves the accuracy level as the IP methods with a lower complexity. Our solution is based on the ADMM framework after reformulating (in terms of the probability simplex) the optimization problem modeling the underlined detection strategy. Future work includes a further detailed study on the different parameters of ADMM (step size, stopping criterion), and a comparison with other possible ADMM implementations. As another interesting directions, we will evaluate the robustness of our solution to multi-cell interference and the multiple access scenarios.

Fig. 1 .

 1 Fig. 1. BER performance comparison between the proposed ADMM and interior point solution for two different massive MIMO transmissions scenarios

Fig. 2 .

 2 Fig. 2. BER performance comparison of the proposed ADMM solution versus MMSE and SDR-rbr for two overloaded mssive MIMO systems using QPSK signaling

Fig. 3 .

 3 Fig. 3. Runtime of the proposed ADMM algorithm, SDR-rbr and MMSE for a variety of antennas number at SNR = 15 dB


Can Xiao

Huawei Sun

Luming Cheng

Xavier Devaux

Anthony Ferri

Weichuan Huang

Rachel Desfeux

Xiao-Guang Li

Sylvie Migot

Mairbek Chshiev

Sajid Rauf

Yajun Qi

Ruilong Wang

Tianjin Zhang

Changping Yang

Shiheng Liang
email: shihengliang@hubu.edu.cn

Yuan Lu
email: yuan.lu@univ-lorraine.fr

Temperature dependence of transport mechanisms in organic multiferroic tunnel junctions

Keywords: multiferroic tunnel junctions, tunneling electroresistance, tunneling magnetoresistance, temperature dependence, ferroelectric domain

Organic multiferroic tunnel junctions (OMFTJs) with multi-resistance states have been proposed and drawn intensive interests due to their potential applications, for examples of memristor and spintronics based synapse devices. The ferroelectric control of spin-polarization at ferromagnet (FM)/ferroelectric organic (FE-Org) interface by electrically switching the ferroelectric polarization of the FE-Org has been recently realized. However, there is still a lack of understanding of the transport properties in OMFTJs, especially the interplay between the ferroelectric domain structure in the organic barrier and the spin-polarized electron tunneling through the barrier. Here, we report on a systematic study of the temperature dependent transport behavior in La0.6Sr0.4MnO3/PVDF/Co OMFTJs. It is found that the thermal fluctuation of the ferroelectric domains plays an important role on the transport properties. When T>120K, the opposite temperature dependence of resistance for in up and down ferroelectric polarization states results in a rapid diminishing of tunneling electroresistance (TER). These results contribute to the understanding of the transport properties for designing high performance OMFTJs for memristor and spintronics applications.

Introduction

The organic multiferroic tunnel junctions (OMFTJs) [1 ,2 ,3 ,4 ] have recently attracted much attention due to their synergetic advantages of spintronics, organic electronics, and ferroelectric electronics. In comparison to inorganic based devices, organic materials are appealing because of the long spin lifetime of charge carriers [5], low cost and chemical diversity [6,7]. In an OMFTJ, the core structure comprises a ferroelectric organic (FE-Org) tunnel barrier layer sandwiched between two ferromagnetic (FM) electrodes. Owing to the combined tunneling magnetoresistance (TMR) and tunneling electro-resistance (TER) effects [8 ,9 ,10 ], it shows a performance of a multi-resistance switching behavior. Therefore the magnetic and ferroelectric dependent nonvolatile multi-states properties can be utilized to develop spintronics-based artificial intelligence devices, such as synapse [10,11]. More interestingly, it has been demonstrated that the spin-polarization at the FM/FE-Org interface, such as "spinterface" can be inverted by electrical switching of the ferroelectric polarization of the FE-Org [1]. This discovery emphasizes the critical role of "spinterface" [12 ,13 ] on the determination of the spin polarization at the organic/ferromagnetic interface and opens up new functionality in controlling the injection of spin polarization into organic materials via modulating the ferroelectric polarization of the barrier.

In the inorganic all-perovskite multiferroic tunnel junction (MFTJ), the temperature dependence of transport properties and mechanisms have been studied [14,15]. The structural defects such as oxygen vacancies in the oxide ferroelectric barriers were found to lead to a thermally activated inelastic hopping through chains of localized states in thicker barriers and at higher temperatures. This conduction channel is not sensitive to the ferroelectric orientation and cannot carry spin polarization information, which reduces the TMR and TER effects significantly at higher temperatures [16]. For OMFTJ, the replacement of inorganic ferroelectric barrier by organic polymer material should introduce different mechanisms to influence the temperature dependent transport behavior. However, up to now, there is still a lack of illumination on this issue. In this work, we have measured temperature dependence of transport behavior in OMFTJs, which shows different mechanisms dominate the transport properties at different temperature ranges. The understanding of the transport properties is essential for designing advanced OMFTJs for memristor and spintronics applications.

Experimental methods

In our experiments, OMFTJ samples based on La0.6Sr0.4MnO3 (LSMO)/Polyvinylidene fluoride (PVDF)/Co/Au structure were fabricated. The sample structure is shown in Figure 1(a). LSMO film with thickness of ∼85 nm was firstly epitaxial grown on <100> oriented SrTiO3 (STO) substrates at 750°C using DC magnetron sputtering. The film was subsequently annealed at 800°C for two hours in O2 atmosphere before being slowly cooled down to the room temperature. For the devices prepared for transport measurement, the LSMO layer was etched by using hydrogen chloride (37%) to pattern 200μm width bars as the bottom electrodes. The PVDF film was prepared by spin-coating method.

The solution was obtained by dissolving PVDF powders (purchased from Sigma-Aldrich) into N,Ndimethylformamide (DMF) (purchased from Sigma-Aldrich). The solution was then spin-coated onto the LSMO/STO(001) substrate with a speed of 3000 RPM for 1min. Subsequently, the as-coated film was annealed at 150°C in air for two hours to improve the crystallinity of the ferroelectric β-phase.

The thickness of the PVDF film was controlled by adjusting the concentration of the DMF:PVDF solution. With the concentration of 20mg/mL, the thickness of PVDF is estimated to be about 20 nm.

After spin-coating of PVDF layer, the 10nm Co/10nm Au was deposited by molecular beam epitaxy (MBE) with a shadow mask to form the top electrode. In the purpose of minimizing the metal diffusion into organic material, the temperature during the growth of the top electrode was maintained at ~80K by cooling the substrate with liquid nitrogen. The final junction, that is schematically shown in Figure 1(a), has a typical size of about 200×200 µm 2 . HR-STEM was performed by using a probe-corrected microscope JEOL ARM200F (cold FEG) equipped with a GATAN GIF Quantum energy filter to reveal the structure and element distribution in the FM/FE-Org interface. Thin lamella were prepared by conventional focused ion beam milling with FEI Helios Nanolab dual beam microscope. Pt-C deposit was used as capping layer. Due to the strong sensitivity of polymers to electron-beam damages, the microscope was operated at 80kV and the temperature of the sample was held at 103K using a Gatan double-tilt liquid nitrogen cooling sample holder. Electron energy loss spectroscopy spectrum images (EELS-SI) were denoised using a principal component analysis before to be processed. Before observation the lamella were plasmacleaned under Ar-O2 atmosphere during 2 minutes.

Piezoresponse force microscopy (PFM) was used to check the ferroelectric properties of the PVDF film. For this study, the PVDF film was spin-coated on a thermal oxidized SiO2/n-Si substrate covered with 100nm Au. The surface morphology was studied using an atomic force microscopy (AFM) (Asylum Research/Oxford Instruments, MFP-3D, USA) working in contact mode under environmental conditions. Local electrical experiments were performed by using dual AC resonance tracking (DART) PFM.

The magneto-transport measurement was performed in a closed cycle cryostat by varying temperature from 10K to 300K in the presence of magnetic field up to 4 kOe. I-V measurements were performed using Keithley-2400 as a voltage source and a Keithley-6487 picoammeter to measure the current. Since junction resistance is much larger than electrode resistance, two terminal configuration has been used for I-V characterization. To polarize PVDF barrier, different amplitude of voltage pulses with a ramp of 0.1V/s and a duration of 1s was applied to the junction. It was verified with conductive AFM that the polarizing voltage around ±3V range does not induce damages to organic barrier with the formation of pinholes inducing leakage currents.

Results and discussion

The surface morphology of PVDF barrier layer has been investigated by AFM observation. It reveals a smooth surface with root mean square (RMS) roughness <3.5 nm in 1×1 μm 2 scanning range, as shown in Figure 1(b). The surface morphology exhibits a feature of grains composed by needlelike crystallites with a width of ~30 nm and length of ~100 nm, which is characteristic of the ferroelectric β-phase of PVDF [17 ]. The ferroelectric properties of the PVDF barrier have been characterized by PFM to check the homogeneity in ferroelectric polarization switching. The PFM phase map was recorded over 10×10 μm 2 PVDF surface area, as shown in Figure 1(c). The film was initially polarized with a biased tip at positive voltage (+3V), then an opposite poling bias (-3V) over an inside area of 5×5 μm 2 . As observed, the clear switching of the polarization is obtained by applying positive and negative bias voltages, suggesting a homogeneous polarization switching. The spacer layer PVDF appears homogenous without pinholes with a thickness of ~20 nm. This also validates the homogeneous ferroelectric switching measured by PFM phase mapping (Figure 1(c)).

In addition, we have performed the chemical analysis by using EELS to check the Co diffusion in the organic barrier. It is found the resistance increases at small bias, which can be understood due to the deformation of barrier height at larger bias. It is interesting to find that the temperature dependent behavior is different for small and large bias. Figure 3(c) displays the differential resistance as a function of temperature for zero bias and +0.5V bias. At zero bias, the resistance varies in three temperature regions: firstly decreases from 15K to 40K, and then increases with the increase of temperature to 120K following by a decrease up to 300K. However, the resistance at +0.5V bias shows a monotonous increase with the temperature. This could be due to the influence of large bias on the ferroelectric domain in PVDF barriers, and this effect could be more pronounced at high temperature [18]. In the following part, we will discuss more details for the temperature dependent resistance. acts as a final spin-filter for electrons tunneling through the PVDF barrier by considering Jullière's model [19]. We have verified the stability of ferroelectric repetition and the reproductivity of TMR sign change with another device with a thinner PVDF thickness (15mg/mL) (see Supplementary S2).

Figure 5(a) shows the magneto-response loops at different temperature for both polarization states. We have firstly polarized PVDF in both polarization states at 10K and then increased the temperature separately in each polarization state. It is found that the TMR values in both polarization states decrease monotonously when increasing the temperature (Figure 5(b)). The positive TMR completely vanishes at temperature higher than 150K while the negative TMR can persist even at 250K. This behavior generally occurs for the organic tunneling junction using the LSMO electrode [1,13,20]. The reduction of MR at a high temperature can be understood by the reduction of LSMO interface spin-polarization in addition with the decrease of PVDF spin diffusion length [4]. Figure 5(c) shows the variation of TER with temperature. It is found that the TER reveals a much complicated temperature dependent behavior. It firstly increases from 65% at 10K to a maximum of 80% at 100K, then following with a rapid decrease to 5% up to 300K.

To understand the temperature dependent TER and transport mechanisms, we have studied the temperature dependent resistances in both polarization states, as shown in Figure 6(a). To avoid the influence of large bias on the ferroelectricity of PVDF, all resistances are measured with a small bias of +10mV without performing I-V measurement. It can be observed that after positive polarization at 10K, the resistance firstly decreases slightly with temperature from 10K to 60K (green region) and then increases with the increase of temperature to 120K (yellow region), followed by a decrease up to 290K (grey region). This behavior is quite similar as the tendency of dV/dI measured at zero bias shown in Figure 3(c). For the case after negative polarization at 10K, the resistance firstly decreases to a minimum at 60K and then increases monotonously with temperature until to 290K. Below 120K, the resistance in both polarization states varies in the same tendency with the temperature and there is small variation in TER. However above 120K, the opposite change tendency of resistance in both polarizations induces a rapid decrease of TER for the OMFTJ device.

To explain this temperature dependence of transport behavior, we have defined three temperature ranges. For the first range from 10K to 60K (green region), the decrease of resistance with increasing temperature could be due to the activation of the hopping process due to the inelastic tunneling which reduces the effective tunneling resistance [21]. Since the thickness of PVDF organic barrier is about 20 nm, it is not possible for electrons to directly tunnel through the barrier. Hopping process through the defect states close to Fermi level inside the barrier is indispensable. Thermal activated phonon can help electron hopping through the defect sites and effective reduce the tunneling resistance [21,22]. Kondo effect due to the magnetic impurity scattering can also effectively increase the junction resistance at low temperature [23]. However, this mechanism can be excluded in our case because that this effect will also manifest zero-bias anomaly (ZBA) in the I-V curves at low temperature, but we do not observe this ZBA in our measurements shown in Figure 3(b).

From 60K to 120K (yellow region), the increase of resistance with temperature for both polarization states can be due to several mechanisms. First of all, the metallic behavior induced by pinholes inside the barrier can result in such behavior [24]. However, as observed in our TEM, the barrier is almost homogenous and no pinhole is observed. To definitively confirm this point, we have performed conductive AFM characterization. No conducting path is obtained for an applied bias of +5V, as demonstrated by the uniform contrast associated to insignificant background current (~30pA) as shown in Supplementary Figure S3. The second possibility is that PVDF has a semi-crystalline nature which is known for the ubiquitous presence of amorphous phase in addition to the ferroelectric crystalline phase [25]. When temperature increases, thermal energy can result in a structural disorder in PVDF film, as already demonstrated that in some organic superconductors the structure transition exists around 80K [26]. The thermal activation of structural disorder could induce an increase of electron scattering and result in the increase of resistance. However, this hypothesis can be also excluded because the structure disorder will also induce a disorder in ferromagnetic domains, which should manifest a decrease of resistance in the positive polarization state with the increase of temperature. The third possibility could be due to the thermal strain effect. Supplementary Figure S4 displays the saturation magnetization (Ms) as a function of temperature for the PVDF/Co bilayers and pure Co. We have observed an increase of magnetization about 10% from 10K to 300K for the Co on PVDF. This behavior is completely different from the normal decrease of MS with temperature for the pure Co due to the magnetization disorder generated by the limited Curie temperature. In fact, the increase of Co Ms is related to the magnetostriction effect of Co because PVDF has an anisotropic thermal expansion, which can generate a uniaxial strain on Co when changing the temperature. The thermal strain can then effectively influence on the junction resistance [ 27 ], as discussed in Supplementary S4.

From 120K to room temperature (grey region), the temperature dependence can be explained by the thermal fluctuation of ferroelectric domains, as schematic shown in Figure 6(b). In fact, every needle-like PVDF crystallite can act as an individual ferroelectric domain [4]. When the thermal energy is high enough to overcome the energy barrier (Eb) between the two polarization states [28],

the chain of molecular starts to rotate to another polarization state. With the increase of temperature, more or more domains with opposite polarization nucleate in both polarization states, which results in a reduce of resistance for the positive polarization state while an increase of resistance for the negative polarization state. Since negligible electric field was applied during the increase the temperature, the evolution of ferrielectric domain of PVDF could be described by the Kolmogorov-Avrami-Ishibashi (KAI) model [18,29,30], which assumes the statistical formation of a large number of nucleation sites and homogeneous domain growth. The transition temperature (TTr) at 120K can allow us to roughly estimate the energy barrier between the two polarization states to be about

Eb=kBTTr=10meV. This value is one order smaller than the reported nucleation energy barrier for P(VDF-TrFE) thin film (0.4eV) grown by Langmuir-Blodgett method [31 ]. The smaller energy barrier could be related to the crystal inhomogeneities, lattice defects, interface defects or small residual nuclei [32 ,33 ,34 ]. With the increase of temperature, the opposite change tendency of resistance in both polarizations results in the disappearing of the contrast of the two polarization states, thus vanishing the TER effect. In addition, we have measured the temperature dependent magnetotransport behavior for another thin device of LSMO/PVDF(13nm)/Co (see Supplementary S5), which has been polarized by two different methods during the increase of temperature: 1) states only polarized at 20K and 2) states polarized at each measuring temperature. As shown in Supplementary Figure S5, the second polarizing method can indeed achieve better polarization states at higher temperature. The TER can be much enhanced at RT compared to the first polarizing method. This validates that the polarization relaxation by the thermal fluctuation dominates the transport properties in the range T>120K in the first polarizing method. In comparison, the influence of thermal activation of domain switching plays a negligible role in the temperature dependent behavior in inorganic MFTJ based on BaTiO3 [14] due to the high nucleation barrier energy (40kBT) [35].

Conclusions:

In summary, we have studied the temperature dependent transport behavior in La0.6Sr0.4MnO3/PVDF/Co OMFTJs. We have found that different mechanisms can dominate the transport properties in different temperature ranges. Below 60K, the transport is dominated by electron hopping through the thick organic barrier, which shows a decrease of resistance with the increase of temperature in both polarization states. Between 60K and 120K, the thermal strain could induce an increase of resistance in both polarization states when increasing the temperature. When T>120K, it is found that the thermal fluctuation of the ferroelectric domains plays an important role on the transport properties. The opposite temperature dependence of resistance for both ferroelectric polarization states results in a rapid diminishing of tunneling electroresistance. However, polarizing the junction at high temperature can recover better polarization degree to enhance TER at room temperature. These results pave the ways to develop high performance OMFTJs for memristor and spintronics applications.

Materials for a Sustainable Growth" is acknowledged for funding of MFP-3D microscope.

Experiments were performed using equipment from the platform TUBE-DAUM funded by FEDER (EU), ANR, the Region Lorraine and Grand Nancy.

S3. Possibility of pinhole

Conductive AFM (c-AFM) measurement is the most direct way to identify the existence of pinholes. Nanoscale conductivity variations were probed through current mapping experiments using the c-AFM technique. A Ti/Ir-coated silicon tip and cantilever with a stiffness of 3Nm -1 were used.

DC bias voltages ranging from -10 and +10V between the grounded AFM tip and the bottom electrode were applied during the scan. The electrical conductivity was locally probed over the surface of the PVDF layer. The current map recorded over 20×20 µm² large area is displayed in Figure S3 for samples with PVDF thicknesses of 20nm. No conducting path was obtained (here for an applied bias of +5V), as demonstrated by the uniform contrast associated to insignificant current (~30pA). Such absence of conduction signal was confirmed in all places measured regardless the applied bias voltage when varying between -10 and +10V. It confirms that the contribution of pinhole on transport is very limited. This also proves that the polarizing voltage in the 3V range does not induce damages to the organic barrier with the formation of pinholes.

S5. Temperature dependence of transport behavior with two polarization methods

We have measured the temperature dependence of resistance and magneto-transport behavior for a thin device of LSMO/PVDF(13nm)/Co with two polarizing setting methods: 1) states polarized only at 20K and 2) states polarized at each measuring temperature. In the first polarizing setting method, we have firstly ferroelectrically polarized PVDF in the negative polarization state at 20K, and then heated the sample to measure the magneto-response loops at different temperature. After reaching 300K, the sample is again cooled down to 20K and was polarized in the positive polarization state to perform temperature dependent measurement. In the second polarizing setting method, the PVDF is polarized at each measuring temperature in both states before measuring the magnetoresponse loops.

For both polarization methods, all MR curves decrease with the increase of temperature (Figure S5(a)). This validates that the diminishing of MR is mainly due to the loss of surface spin-polarization of LSMO electrodes but not due to the polarizing states of PVDF. For the temperature dependent resistance, as shown in Figure S5(b), it is found that the difference between resistances in both polarization states decreases with temperature for the first method, but the difference is enlarged for the second method. This means that the second method can achieve better polarization states at higher temperature. Thermal activation of the fluctuation of ferroelectric domain should happen for the first method. The more evidence change can be observed in the negative polarization state, which means that positive polarization state is more stable with temperature. As a consequence, we have observed an increase of TER with increasing temperature for the second method (Figure S5(c)). The TER is much enhanced and reaches about 200% at RT with the second polarization method. This study gives a strong argument that the decreasing of TER for the temperature range higher than 120K is mainly due to the thermal fluctuation on the ferroelectric domains.

Figure 2 (

 2 Figure 2(a) shows a bright-field STEM image of the sample. The bottom LSMO magnetic

Figure 2 (

 2 b) shows an high angle annular dark-field (HAADF) STEM image where EELS spectrum image was recorded. For the three regions marked with orange, red and blue squares on the STEM image, EELS spectra are collected and presented in Figure 2(c). Although the Co signal is well distinguished in the region close to Co/PVDF interface (orange zone), we cannot find any Co signal in the middle of PVDF barrier (red zone). There are also no La and Mn signals in PVDF barrier compared to the strong signals from the region close to PVDF/LSMO interface (blue zone). The chemical EELS maps of Co/PVDF/LSMO interface is presented in Figure 2(d). The maps of chemical elements Co (yellow), F (red) and La (sky-blue) are extracted from the EELS spectrum images by using signals of CoL3(779eV), FK(685eV) and LaM5(820eV) edges, respectively. It also appears that there is very small Co diffusion inside the organic barrier and the interface PVDF/LSMO is quite sharp. All these results prove that there is very limited Co diffusion into the PVDF organic barrier when Au/Co electrode is deposited at low temperature, which agrees well with our previous report in P(VDF-TrFE) based OMFTJ[4].

Figure 3 (

 3 Figure 3(a) shows the I-V characteristic of the device measured at different temperature under

Figure 4 Figure 4 ,

 44 Figure4shows the magneto-response loops measured at 10K after different polarizations (+1.2V

Figure 1 :

 1 Figure 1: (a) Schematics of the LSMO/PVDF/Co device. (b) AFM topography measurement of the PVDF barrier surface over 1×1 μm 2 area. (c) PFM phase image recorded on the PVDF surface. Contrasts showing the ferroelectric switching are obtained after application of +3 V DC bias on the tip over 10×10 μm 2 and subsequently -3 V over inside 5×5 μm 2 area. (d-e) schematics of spin-filter for electron tunneling through PVDF barrier in polarized-up and polarized-down states.

Figure 2 :

 2 Figure 2: (a) Large scale bright-field STEM image of the LSMO/PVDF/Co device. The PtC layer deposited during the lamella preparation appears on the top of the image. (b) HAADF STEM image of the sample. The red frame indicates where an EELS-SI was recorded. The colored squares shows the area where EELS spectra in (c) were extracted. (c) Typical EELS spectra of the Co/PVDF interface, the PVDF layer and the PVDF/LSMO interface. (d) Elemental map drawn from quantitative analysis of EELS-SI.

Figure 3 :

 3 Figure 3: (a) Temperature dependence of I-V characteristics under the range between -0.5V to +0.5V. (b) Differential resistance as a function of bias at different temperatures. (c) Temperature dependence of differential resistance at zero bias and +0.5V.

Figure 4 :

 4 Figure 4: Magneto-response curves measured under a bias of +10 mV at 10 K after +1.2 V and -

Figure 5 :

 5 Figure 5: (a) Magneto-resistance loops measured at different temperatures for positive and negative polarization states. (b) Temperature dependence of MR in both polarization states. (c) Temperature dependence of TER.

Figure 6 :

 6 Figure 6: (a) Temperature dependence of RP in both polarization states. The resistance is measured with small bias of 10mV. (b) Schematics of polarized states in the PVDF barrier at temperature range between 120K and 300K (grey zone). The schematic of energy barrier between two ferroelectric polarization states under thermal fluctuation is also shown.

Figure S2 :

 S2 Figure S2: Tunneling magnetoresistance curves measured under 10mV at 10K after (a) +1V and (b) -1V polarizing of the 15mg/mL PVDF device. Repetition cycles after successive switching with ±1V voltage pulses for (c) parallel resistance and (d) TMR.

Figure S3 :

 S3 Figure S3: C-AFM scanning of barrier conductivity under an applied bias of +5V for 20nm thick PVDF layer.

Figure S4 :

 S4 Figure S4: Saturation magnetization as a function of temperature for PVDF/Co composite and pure Co.

Figure S5 :

 S5 Figure S5: (a) Temperature dependence of MR after positive(black) and negative(red) polarization. The solid circles show the MR measured after being polarized at each temperature, the opened circles show those after being polarized only at 20K. (b) Temperature dependence of RP after positive(black) and negative(red) polarization. The solid circles show the RP measured after being polarized at each temperature, the opened circles show those after being polarized only at 20K. (c) Temperature dependence of TER after being polarized at each temperature (black) and at 20K (red).

Acknowledgements

The authors thank Dr. A. Da Costa for technical support on AFM experiments. We thank also Prof. Zhi-Gang Yu for fruitful discussions. We acknowledge the support from the French National Research Agency (ANR) FEOrgSpin project (Grant No. ANR-18-CE24-0017-01) and SIZMO2D project (Grant No. ANR-19-CE24-0005-02). This work is supported by the National Natural Science Foundation of China (No. 11674086, 11904088), Natural Science Foundation of Hubei Province (No. 2019CFB183), Scientific Research Project of Education Department of Hubei Province (No. Q20191010) and Research Project of Wuhan Science and Technology Bureau (No.

2019010701011394). The "Région Hauts-de-France" and the "Fonds Européen de Développement Régional (FEDER)" under the "Contrat de Plan État-Région (CPER)" project "Chemistry and

Supplementary Information S1. Anisotropic magnetoresistance in the ferromagnetic electrodes

To validate that the measured TMR is not due to the AMR of FM electrodes, we have checked the AMR of LSMO and Co electrodes. As shown in Figure S1, the AMR of LSMO and Co shows a much smaller value lower than 0.4%. However, the MR in our device can be as large as 15%, which is much larger than that of AMR.

S2. Stability of ferroelectric repetition

We have prepared another device with a thinner PVDF thickness (15mg/mL) to check the stability of ferroelectric switching. Compared to the thick PVDF sample (20mg/mL) presented in the main text, a smaller switching voltage of ±1V is enough to saturate the two polarization states due to the thinner thickness. As shown in Figure S2(a) and S2(b), the TMR changes from +1.64% to -1.81% when the PVDF is switched from positive polarization state to negative polarization state. At the same time, a clear difference between the two parallel resistances for the two polarizations allows to reach a TER of about 14.3%. Although the amplitude of TMR and TER is smaller than that presented in the main text, the phenomena of ferroelectric modulation of spin-polarization can be reproduced in our OMFTJs with different PVDF thickness. Successive alternative voltages of ±1V are applied on the device to test the repetition stability. We have collected magnetoresistance curve after each polarizing pulse. As shown in Figure S2(c) and S2(d), the parallel resistance and TMR can be robustly