Lina Bouzouaid

Barbara Lothenbach

Alejandro Fernandez-Martinez

Christophe Labbez

Gluconate and hexitols effects on C-S-H solubility

This study investigates the effect of gluconate, a carboxylate ion, and three uncharged hexitols, D-sorbitol, D-mannitol and D-galactitol on the solubility of C-S-H. Thermodynamic modeling is used to determine the kind and amount of Ca-organic-silicate-OH complexes that potentially form in the conditions studied. All the organics form complexes with calcium and hydroxide, In addition, heteropolynuclear organics complexes with calcium, hydroxide and silicate are observed at high pH values and high calcium concentrations: Ca 2 Hex 2 (H 3 SiO 4 ) 2 (OH) 2 0 , Ca 2 Hex 2 (H 2 SiO 4 )(OH) 2 -2 and Ca 3 Gluc 2 (H 3 SiO 4 ) 2 (OH) 2 0 , with the exception of mannitol. The strength of complexation with silicate decreases in the order gluconate > sorbitol > galactitol. The adsorption of the selected organics on portlandite and C-S-H systems follows the order gluconate >> sorbitol > mannitol ~ galactitol. For C-S-H, a typical Langmuir isotherm is found only when buffered with Ca(OH) 2 . The adsorption on C-S-H increases with the Ca/Si ratio.

1.

Introduction

Hydration of cement, involving mainly the anhydrous phases Ca 3 SiO 5 (C 3 S) and Ca 2 SiO 4 (belite), is a complex reaction where two main hydrates are formed: calcium silicate hydrates (C-S-H), and portlandite, Ca(OH) 2 [START_REF] Barret | Fundamental hydration kinetic features of the major cement constituents: Ca 3 SiO 5 and Ca 2 SiO 4[END_REF]. It involves the concomitant dissolution of the anhydrate phases and precipitation, from the solution, of the hydrate phases. The passage from solution to these hydrates happens because the ion activity product of the solution (IAP) rapidly exceeds the solubility product (Ksp) of the newly formed solid phases [START_REF] Yoreo | Principles of crystal nucleation and growth[END_REF]. As the concentration and activity of ions build up, the driving force for the nucleation of hydrates (∆µ) increases as does the rate of nucleation, J. The latter is proportional to

J ∝exp (-Δ μ -2 v m 2 γ
3 /kT ) with kB being the Boltzmann constant and T the temperature and where v m and  are the molecular volume and surface tension of the hydrate. The driving force is defined by the change in chemical potential (∆µ) of the crystallizing ions, and measures the free energy response to transferring the ions from the solution to the solid, ∆µ = kBT(ln IAP -ln Ksp). The same reasoning applies to the dissolution of anhydrous phases in a symmetric way. The activity of the dissolving and crystallizing ions is an essential thermodynamic quantity if one wants to quantify and understand the hydration of cement.

However, ion activities are strongly influenced by complex formation, e.g between calcium and organics. In the present study we aim at extending our previous work [START_REF] Bouzouaid | Portlandite solubility and Ca 2+ activity in presence of gluconate and hexitols[END_REF] on the calcium activity in the presence of four cement organic retarders, namely sodium D-gluconate and three hexitols (D-mannitol, D-sorbitol and D-galactitol), to the speciation and activity of calcium and silicate solution species in the presence of the same organics. Superplasticizers, in particular, and organic molecules, in general, often behave as retarders when used in concrete (4) [START_REF] Banfill | The relationship between the sorption of organic compounds on cement and the retardation of hydration[END_REF] [START_REF] Chandra | Interactions of polymers and organic admixtures on portland cement hydration[END_REF]. At low percentage, less than 1% wt of Portland cement, they retard the initial and final setting times of cement [START_REF] Ramachandran | Conduction calorimetric investigation of the effect of retarders on the hydration of Portland cement[END_REF] [START_REF] Diamond | Interactions between cement minerals and hydroxycarboxylic acid -acid retarders: I, 474 apparent adsorption of salicylic acid on cement and hydrated cement compounds[END_REF]. Several studies have been conducted to highlight their influence on the hydration of cements, in order to obtain a better understanding of the mechanisms of retardation and the setting times, but still the physical and chemical mechanisms responsible for this retardation remained elusive [START_REF] Marchon | Molecular and Submolecular Scale Effects of Comb-Copolymers on Tri-Calcium Silicate Reactivity: Toward Molecular Design[END_REF] [START_REF] Singh | Effect of phenols on the hydration of Portland cement[END_REF] [START_REF] Zhang | Effect of saccharide set retarders on the hydration of ordinary portland cement and pure tricalcium silicate[END_REF](12) [START_REF] Pourchez | Changes in C 3 S hydration in the presence of cellulose ethers[END_REF]. Using small organic molecules as a model for the more complex superplasticizers, previous works have been directed to decipher which step (C 3 S dissolution or C-S-H nucleation/growth) of the cement hydration is specifically impacted by organics. These includes the charged molecule gluconate known to behave as a strong retarder and hexitols [START_REF] Singh | Effect of gluconates on the hydration of cement[END_REF] [START_REF] Zhang | Effects of superplasticizers and retarders on the fluidity and strength of sulphoaluminate cement[END_REF] [START_REF] Singh | Influence of calcium gluconate with calcium chloride or glucose on the hydration of cements[END_REF] [START_REF] Lv | The Effect of Sodium Gluconate on Pastes' Performance and Hydration Behavior of Ordinary Portland Cement[END_REF] [START_REF] Ma | Influence of sodium gluconate on the performance and hydration of portland cement[END_REF]. For some hexitols and gluconate, the dissolution rate of Ca 3 SiO 5 was observed to be only marginally affected [START_REF] Nalet | Effects of hexitols on the hydration of tricalcium silicate[END_REF] and they were thus conjecture to act mainly as inhibitors of the nucleation/growth of C-S-H [START_REF] Nalet | Effects of functionality and stereochemistry of small organic molecules on the hydration of tricalcium silicate[END_REF] and portlandite [START_REF] Juilland | Hindered calcium hydroxide nucleation and growth as mechanism responsible for tricalcium silicate retardation in presence of sucrose[END_REF]. The neutral hexitol molecules were observed to retard the hydration of cement much less than the charged gluconate molecule, and their retardation power was found to depend on their stereochemistry [START_REF] Nalet | Effects of hexitols on the hydration of tricalcium silicate[END_REF] [START_REF] Nalet | Effects of functionality and stereochemistry of small organic molecules on the hydration of tricalcium silicate[END_REF] [START_REF] Nalet | Ionic complexation and adsorption of small organic molecules on calcium silicate hydrate: relation with their retarding effect on the hydration of C 3 S[END_REF].

In a recent study, we investigated the effect of gluconate, D-sorbitol, D-galactitol and Dmannitol on calcium speciation at high pH values [START_REF] Bouzouaid | Portlandite solubility and Ca 2+ activity in presence of gluconate and hexitols[END_REF]. It was found that the sorption of organics on portlandite as well as the strength of organics complex formation with Ca decreases in the order gluconate >> sorbitol > mannitol ~ galactitol, similar to the organics tendency to retard the C 3 S hydration [START_REF] Nalet | Effects of hexitols on the hydration of tricalcium silicate[END_REF]: gluconate >> sorbitol > galactitol > mannitol. In the presence of portlandite, polynuclear complexes with calcium and hydroxide such as Ca 3 Gluc 2 (OH) 4 0 dominate the Ca-speciation with gluconate, while ternary CaHexOH + and polynuclear Ca 2 Hex 2 OH 4 0 complexes are dominant in the presence of the hexitols (3).

In the present paper, we investigate the combined speciation of calcium, silicate and organics (gluconate, D-sorbitol, D-galactitol or D-mannitol) at concentrations and pH values relevant for cementitious systems. Complex formation is experimentally studied based on solubility measurements of calcium silicate hydrate (C-S-H) at various Ca/Si, ranging from 0.75 to 1.5, in the presence of increasing amount of organics. The strength and the various types of calcium and silicate complexes with the organic molecules is determined with a speciation model.

2.

Materials and methods

Materials

The sorption and complex formation of organics were studied on pre-synthesized C-S-H. A large stock of C-S-H was synthesized with a Ca/Si of 0.75 by adding 4.2 g of lime and 5.9 g of silicate. The reactants were mixed with boiled and degassed water, within 250 mL PE containers protected from air, using a liquid to solid ratio (L/S) of 25 to obtain a homogeneous suspension. The containers were placed on a shaking Sigma-Aldrich, ≥99% purity). Note that the three hexitols have the same structural units but have a different configuration as illustrated in Figure 1.

Solubility experiments

Four different series of samples were prepared in a glove box for each organic molecule: C-S-H equilibrated with 0 mM, 11 mM and 20 mM calcium, added in the form of CaO, as well as a series with saturated lime solution. For each experiment 400 mg of C-S-H (C/S =0.75)

were used as a solid buffer, enclosed in a dialysis membrane and placed in a 250 mL polypropylene flask filled with 250 mL of CO 2 -free solution with different amounts and type of organic molecule (see Figure 2). Note that in the case of gluconate only 200 mg of C-S-H was used. Based on mass balance calculations [START_REF] Haas | From C-S-H to C-A-S-H: Experimental study and thermodynamic modelling[END_REF] The dialysis membranes (Spectra / Por, MWCO 12-14 kD) were dipped before use in distilled water for 30 minutes to remove any organic residues and dried in a desiccator overnight. The dialysis bags were closed with polyamide clamps (Carl Roth, length 50 mm).

Finally, the samples were stored in plastic barrels filled with N2 gas to guarantee CO2 free conditions, and placed on a shaking table during four weeks at 23°C to equilibrate. In each case, in addition to the samples containing the dialysis bag filled with C-S-H, blank samples containing only the lime and organic molecule solution were prepared and used as reference.

The pH values and total elemental concentrations were measured in the solution after removing the dialysis bags. The pH electrode was calibrated using Sigma Aldrich buffer (pH 4, 7, 9 and 12). It should also be mentioned that the pH was not used as a fitting parameter for the complex formation. The reason being the difficulty to get accurate and reliable pH values inherent to the impossibility of measuring the proton activity alone, see e.g. ref [START_REF] Buck | Measurement of PH. Definition, Standards, and Procedures (IUPAC Recommendations[END_REF]. The total concentration of the elements Ca and Si were measured by inductively coupled plasma-optic emission spectroscopy (ICP-OES 5110, Agilent) in diluted solution acidified with HNO3.

Five or six different organic concentrations were studied, with a starting concentrations between 0 mM to 200 mM (detailed values are given in the Supplementary Information). The bulk concentration of organics at equilibrium was measured as total organic content with a TOC VCPN instrument (Shimadzu). This tool is based on the oxidation of organic molecules contained in solution by gaseous oxygen with a platinum-based catalyst in an oven raised to a temperature of 720°C. The CO 2 formed is detected by Infra-Red Non-Dispersive (NDIR).

The detection threshold for this device is very low (4µg/L).

Thermodynamic simulation and complexation constants

The solubility of C-S-H and the activity of calcium, silicate and hydroxide solution species at equilibrium were fitted using a speciation model solved by the geochemical software PHREEQC version 3 (3.6.2-15100) and the WATEQ4f database. The activity of the ion species i, a i , was calculated according to a i = γ i •m i , where γ i is the activity coefficient and m i the molality in mol/kg H 2 O. The activity coefficients were calculated in PHREEQC for major species with the WATEQ Debye Hückel equation:

log γ i = -A z i 2 √I 1+B d i √ I +b i I (1)
where z i denotes the charge of species i, I the molal ionic strength, d i the individual ion-size parameter, and b i is an ion specific parameter. A and B are pressure-and temperaturedependent coefficients. Equation 1 is applicable up to approximately 1 M of ionic strength.

For non tabulated species, the Davies equation is used to calculate the activity coefficients in PHREEQC.

Aqueous species

Ca +2 + OH -= CaOH + 1.22 b 24
H4SiO4 0 = H3SiO4 -+ H + -9.83 25
H4SiO4 0 = H2SiO4 -2 + 2H + -23.10 25
Gluc -+ H + = GlucH 0 3.64 26 c Gluc -+ OH -= GlucOH -2 -0.44 27 c
Ca +2 + Gluc -= CaGluc + 1.56 28 c

Ca +2 + 2Gluc -= CaGluc2 0 2.85 3

Ca +2 + OH -+ Gluc -= CaGlucOH 0 3.95 3 2Ca +2 + 4 OH-+ 2Gluc-= Ca2Gluc2(OH)4 -2 11.25 3 3Ca +2 + 4 OH -+ 2Gluc -= Ca3Gluc2(OH)4 0 16.10 3 3Ca +2 + 2 OH -+ 2Gluc -+ 2H3SiO4 = Ca3Gluc2(H3SiO4)2(OH)2 0 20.45
This study a The standard error on the fitted Log K values is estimated to be less than 0.05. b The potential formation of a Ca(OH)2 0 complex with a log10 K = 1.85 for the reaction Ca 2+ +2OH -= Ca(OH)2 0 (29) was initially considered, but its presence or absence had no significant effect at pH values below 13, such that it was neglected in the final calculations. c Values given in the present table are those reported by the cited references extrapolated to 0 M ionic strength using the WATEQ Debye Hückel equation, see (3) for more details. The fitted complex formation constants between calcium, silicate, hydroxide and the organics used in the present study are listed in Tables 1 and2. The quaternary complexes were determined by simple and systematic variations of the ternary complexes determined in Kutus and Pallagi's works and further confirmed in ref [START_REF] Bouzouaid | Portlandite solubility and Ca 2+ activity in presence of gluconate and hexitols[END_REF] in the CaO-Org-H2O system. This amounted to keep the Ca/Org stoechiometric ratio constant, substituting OH by silicate monomer or adding silicate mononer and varying the ionization degree of the latter. The calculations made to identify the composition of the solution at equilibrium with C-S-H in suspensions with and without organic molecules used the surface complexation model of Haas and Nonat, which takes into account the variation of the solubility and stoichiometry of C-S-H phases [START_REF] Haas | From C-S-H to C-A-S-H: Experimental study and thermodynamic modelling[END_REF]. The values of the solubility constants and surface complexation of the phases ,  and  of C-S-H are listed in Table 3. The raise in silicate and calcium concentration in response to hexitol addition becomes stronger when the C/S of C-S-H is increased, i.e. at high pH and calcium concentrations, while at the lowest C/S studied, C/S = 0.75, the addition of hexitols has no significant impact.

Results and discussion

At C/S 1.5 (Ca(OH) 2 buffered systems) the silicate concentration increases by more than 2 orders of magnitude in presence of ~200 mM of sorbitol, see Figure 4-b. The impact of the different hexitols on the silicate concentration is clearly different and increases in the following order: mannitol < galactitol << sorbitol, i.e. similar to that observed for calcium.

These results indicate the formation of quaternary complexes, involving silicate-calciumhydroxide and hexitols for galactitol and sorbitol, while none or very weak complexes are formed in the case of mannitol. Below, we shall show that such complexes derived from the ternary complex Ca 2 Hex 2 (OH) 4 0 identified in our previous study can give an accurate description of the solubility data of C-S-H presented above.

The measured and calculated silicate and calcium concentrations are compared in Figure 5.

The Ca and Si concentration were calculated using the known Ca-hexitol complexes increase of y and z) with the organic and calcium concentrations. Also, at high calcium and organic concentrations, we experimentally observed that the solutions were extremely difficult to filtrate, which was one of the motivation to separate the solids from the solution with a dialysis membrane. This is another indication of the formation of large complex clusters and of the variation of the size of the complex clusters with the equilibrium conditions. ) are negligibly small (more than ten times smaller than the quaternary complexes). On the other hand, the quaternary complexes has a negligible impact on the total calcium concentration as seen in Figure 6-a and Figure S3. To further illustrate the importance of the quaternary complexes on the C-S-H solubility a comparison of the measured and predicted total equilibrium concentrations of Si and Ca when those complexes are ignored is provided in the supplementary materials, see Figure S5.

In the case of mannitol, a very good fit of the experimental data is also obtained, see Figure 5, without the need of the Ca 2 Man 2 (H 3 SiO 4 ) 2 (OH) 2 0 and Ca 2 Man 2 (H 2 SiO 4 )(OH) 4 -2 complexes (see Table 2), as no significant increase of Si-concentration was observed. This is shown by the simulated speciation data plotted in Figure 6 where no polynuclear calcium organic silicate complexes are found, contrary to the case of sorbitol and galactitol. The H 4 SiO 4 0 , H 3 SiO 4 -, and H 2 SiO 4 -2 species thus dominate the silicate speciation at all Ca/Si. and varying the equilibrium concentration of hexitols.

Similarly to sorbitol, the use of CaGalOH + , Ca 2 Gal(OH) [START_REF] Bouzouaid | Portlandite solubility and Ca 2+ activity in presence of gluconate and hexitols[END_REF]. This is also illustrated in Figure 7, which compares the solubility of C-S-H buffered with portlandite (C/S 1.5) in the presence of sorbitol, galactitol and mannitol.

Compared to sorbitol, a much lower amount of silicate is found in solution for galactitol but clearly more than in the case of mannitol for which no or only very weak polynuclear silicate complexes are formed. Ca 2 Gal 2 (H 3 SiO 4 ) 2 (OH) 2 0 and Ca 2 Gal 2 (H 2 SiO 4 ) 2 (OH) 4 -2 are predicted to dominate the solution speciation of silicates only at high C/S ratio, comparable to sorbitol. performed with the complexes listed in Table 1.

Sodium gluconate

The evolution of calcium and silicate concentration in solution at equilibrium with C-S-H as a function of gluconate concentrations is shown in Figure 8. Compared to the hexitols, the measured total calcium concentration is observed to raise more strongly in the presence of gluconate at all C/S studied, indicating a strong complexation between gluconate and calcium in solution. A four times higher calcium concentration is observed in the presence of 192 mM of gluconate for the lowest C/S studied ([Ca(OH) 2 ] i = 0 mM) than in its absence, while at C/S=1.3 ([Ca(OH) 2 ] i = 11 mM), the calcium concentration doubled. At the highest C/S, calcium concentration increases from 13 mM to 20 mM at 176 mM of gluconate.

The qualitative evolution of the silicate concentration upon addition of gluconate is similar to that of calcium for all C/S studied. At the lowest C/S ratio (0.75), a moderate increase of silicate concentration from 1.1 mM in the absence of gluconate to 3.2 mM in the presence of 192 mM gluconate is observed. At higher C/S (1.1 and 1.3), the relative increase in silicate concentration in response to gluconate is stronger. The equilibrium silicate concentration with C-S-H of C/S ratio 1.3 in the presence of ~200 mM of gluconate is observed to be two orders of magnitude larger than in the absence of gluconate.

In Figure 8, the calculated Ca and Si concentrations using the Ca-gluconate complexes from

(3) as summarized in Table 1 together with the polynuclear Si-complex,

Adsorption of the organics on C-S-H and portlandite.

Based on the comparison of the measured organic concentrations with the initial concentrations, adsorption isotherms of the gluconate, sorbitol, mannitol and galactitol on C-S-H and Ca(OH) 2 (portlandite data are reproduced from (3)) could be obtained as summarized in Figure 10. Gluconate adsorbs strongly on portlandite where an uptake of up 0.3 gluconate per Ca(OH) 2 was observed (see Figure 10a), while the sorption of sorbitol, mannitol and galactitol is much weaker. In the case of C-S-H buffered with portlandite (C/S polyelectrolyte and sulfate ions. The calcium mediated adsorption is obvious in the case of gluconate since both the latter and C-S-H are negatively charged and even more so as the pH increases [START_REF] Ioannidoua | A review of coarse grained and mesoscale simulations of C-S-H, Special Issue on molecular modeling of Cement and Concrete Research[END_REF]. As a consequence, adsorption of gluconate (or SO 4 2-) on C-S-H becomes significant only in conditions where the accumulation of calcium ions on the C-S-H surface is high enough to overcompensate the bare charge of C-S-H. That is at high enough pH and bulk calcium concentration, i.e. above 2 mM of Ca(OH) 2 or C/S > 0.95. In the case of the hydrophilic and neutral hexitol molecules, the fact that their binding on C-S-H is most certainly also mediated by calcium ions might seem more surprising at first sight. As we have shown, however, these neutral molecules also form aqueous complexes with calcium ions and their adsorption increases with their complexation strength with calcium. Furthermore, the binding of hexitols on C-S-H is also observed to increase with the calcium content of the solution in the same qualitative manner as that of gluconate (and SO 4 2-). Finally, the surface affinity of the molecules is found to be correlated to their effectiveness to bind calcium ions in solution. This generic behavior was predicted by Monte Carlo simulations in the case of calcium mediated adsorption of anionic molecules on negatively charged surfaces [START_REF] Turesson | Calcium mediated polyelectrolyte adsorption on like-charged surfaces[END_REF][33] [START_REF] Ioannidoua | A review of coarse grained and mesoscale simulations of C-S-H, Special Issue on molecular modeling of Cement and Concrete Research[END_REF]. It was recently confirmed in the recent experimental work of Nalet and co-workers whom observed a clear correlation between the calcium binding effectiveness (calcium complexation) and adsorbed amount on C-S-H particles of a large set of anionic molecules [START_REF] Nalet | Ionic complexation and adsorption of small organic molecules on calcium silicate hydrate: relation with their retarding effect on the hydration of C 3 S[END_REF].

Interestingly also, the adsorption isotherm of organics at C/S = 1.1 is not observed to increase monotonically with the organics concentration as it does in buffered portlandite conditions (C/S = 1.5). Upon progressive addition of organics, it first increases to a maximum and decreases at higher organic additions. Such a behavior is not observed when C-S-H is buffered with portlandite, that is when the calcium hydroxide activity is maintained constant.

Instead, when the solution is buffered with portlandite ( constant calcium hydroxide activity) a typical Langmuir isotherm is recovered. This generic behavior was well described and predicted by Turesson and co-authors [START_REF] Turesson | Calcium mediated polyelectrolyte adsorption on like-charged surfaces[END_REF] studying the adsorption of polyanions on negatively charged surfaces in presence of calcium ions with the help of Monte-Carlo simulations in the framework of the primitive model. It can be explained as follows. At C/S = 1.1, there is no calcium reservoir (no portlandite excess) and the calcium (and hydroxide) activity decreases progressively with increasing the organic concentration, because of the increasing formation of calcium-organics aqueous complexes. This complex formation leads to the progressive desorption of the calcium ion from the C-S-H surface, up to the point where the calcium mediated organic adsorption reaches a maximum and finally drops. In presence of an excess of portlandite, the complex formation upon organics addition leads instead to the progressive dissolution of the portlandite, such as to maintain a constant mean activity of calcium hydroxide in the solution. As a result, the adsorption of both calcium and organics increases continuously until the saturation of the C-S-H surface is reached.

Conclusions

The solubility of C-S-H in the presence of three hexitols (D-sorbitol, D-mannitol, Dgalactitol) and sodium gluconate has been measured. The experimental solubility data could be modeled with a speciation model for the liquid phase, while C-S-H was described based on the surface complexation model of Haas and Nonat (23) for the solid phase using the thermodynamic modelling package PHREEQC.

Sorbitol, mannitol, galactitol and gluconate did not only form aqueous complexes with calcium ions, but also polynuclear complexes with silicates, with the exception of mannitol.

These polynuclear complexes resulted in a significant increase in the silicate concentration of in equilibrium with C-S-H. The increase in silicate concentration in response to organics addition was found to strengthen with the Ca(OH) 2 content in the solution, i.e. with the stoichiometric calcium to silicon ratio (C/S) of C-S-H. In the case of gluconate and sorbitol an increase of up to two orders of magnitude could be observed at the highest organic concentration and C/S ratio studied. With the exception of mannitol, the complexation power of the organic molecules with silicate aqueous species was observed to follow the same order as with calcium ions. That is gluconate > sorbitol >> galactitol > mannitol for the silicate complexation as compared to gluconate >> sorbitol > mannitol > galactitol for the calcium complexation. Interestingly, the complexation strength of the organics with silicates seems to be correlated to their observed retarding effect on C 3 S hydration: gluconate >> sorbitol > galactitol > mannitol. [START_REF] Nalet | Effects of hexitols on the hydration of tricalcium silicate[END_REF], but not with complexation strength of the organics with calcium.

The fact that both high pH and calcium concentration is required for the complexation of silicate by the organics was well captured with the formation of hetero polynuclear complex involving Ca and OH ions, namely Ca 2 Hex 2 (H 3 SiO 4 ) 2 (OH) 2 0 , Ca 2 Hex 2 (H 2 SiO 4 )(OH) 4 -2 and Ca 3 Gluc 2 (H 3 SiO 4 ) 2 (OH) 2 . These Si-complexes when combined with the organic-Ca complexes introduced in our previous work allowed us to describe very satisfactorily the solubility of C-S-H in the presence of the organics.

The adsorption of the organics on C-S-H follows the same trend as on portlandite. The organics affinity with C-S-H was found with the order gluconate >> sorbitol > mannitol galactitol.

A typical Langmuir isotherm was found when C-S-H is buffered with Ca(OH) 2 .

The organics adsorption was observed to drop with decreasing the C/S of C-S-H and at high organic concentrations, strongly suggesting a calcium mediated adsorption.

Figure 1 :

 1 Figure 1: Structure of (from left to right) D-gluconate, D-sorbitol, D-galactitol and Dmannitol. "T" corresponds to the threo diastereoisomer configuration. "E" corresponds to erythro diastereoisomer configuration. Configuration refers here to that of two adjacent stereo-centers (carbons) relative to each others.

  the final Ca/Si in C-S-H corresponded to 0.75 (0 mM Ca), 1.1 (11 mM Ca), 1.3 (20 mM Ca), and to 1.5 (saturated lime solution; initial Ca/Si in solid = 0.75).

Figure 2 :

 2 Figure 2: Schematic representation of the different series of C-S-H with 0 mM, 11 mM, 20 mM and saturated with Ca(OH) 2 , used for the solubility and adsorption experiments. The flask used for the solubility measurement contains a dialysis bag filled with 200mg (Gluconate) or 400 mg (Hexitols) of C-S-H powder, immersed in 250 mL of solution containing the organic molecule. The second flask containing the organic molecule solution only is used as a blank/reference to verify the organic concentration introduced initially. This allows the determination of the organic adsorption on C-S-H by mass balance based on the measured difference. Note that the same stock solution is used for each sample pair.

- 2 =Table 3 . 6  4 *

 2364 Ca2Man2(H2SiO4)(OH)4 -2 NA* This study Ca +2 + Gal 0 = CaGal +2 -0.53 3 Ca +2 + Gal 0 + OH -= CaGalOH + 2.80 3 2Ca +2 + 2Gal 0 + 4OH -= Ca2Gal2(OH)4 0 9.29 3 2Ca +2 + 2Gal 0 + 2OH -+ 2H3SiO4 -= Ca2Gal2(H3SiO4)2(OH)2 0 14.60 This study 2Ca +2 + 2Gal 0 + 4OH -+ H2SiO4 -2 = Ca2Gal2(H2SiO4)(OH)4 -2 13.00 This study a The standard error on the fitted log10 K values is estimated to be less than 0.05. *NA: Not available: no constants could be fitted in this study due to the weak complexation of mannitol with Si. Solubility and surface complexation constants of the C-S-H phases at standard conditions (1 bar, 25°C) and I = 0 (23) log10 K  -C-S-H: Ca4Si5O16H4 0 + 8H + + 4H2O = 4Ca +2 + 5H4SiO4 0 53.5 -C-S-H: Ca2Si2O7H2 0 + 4H + + H2O = 2Ca +2 + 2H4SiO4 0 29.-C-S-H: Ca6Si4O15H2 0 + 12H + + H2O = 6Ca +2 + 4H4SiO4 0 104.5 ≡SiOH 0 = ≡SiO -+ H + -9.8 ≡SiOH 0 + Ca +2 = ≡SiOCa + + H + -7.0 ≡SiOH 0 + Ca +2 + OH -= ≡SiOCaOH 0 -9.0 2≡SiOH 0 + H4SiO4 0 = (≡SiO)2Si(OH)2 0 + 2H2O 5.8* 2≡SiOH 0 + Ca +2 = (≡SiO)2Ca 0 + 2H + -11.The indicated value is for -C-S-H and -C-S-H; log K = 4.4 for -C-S-H

3. 1 Figure 3 :

 13 Figure 3: Measured solution concentrations of calcium in equilibrium with C-S-H and portlandite (red symbols, from (3)) as a function of the equilibrium concentration of hexitols. Sorbitol, mannitol and galactitol are represented by circles, squares and triangles, respectively. The C-S-H (C/S = 0.75) containing dialysis bags were immersed in 250 mL of ultra-pure and degassed water containing initially 0 mM Ca(OH) 2 (blue symbols), 11 mM Ca(OH) 2 (orange symbols), and 20 mM Ca(OH) 2 (grey symbols). The corresponding initial pH are 10.6, 12.1, 12.4, see the sup. info. The black symbols show the results for C-S-H in buffered portlandite conditions 1 , pH 12.7, see also Figure S.1.

Figure 4 :

 4 Figure 4: Measured solution concentrations of a) silicate and b) relative increase of the silicate concentration in the solution, in equilibrium with C-S-H prepared in the same conditions as in Figure 3. The relative increase of silicate is expressed as the ratio of the equilibrium silicate concentration to the equilibrium silicate concentration without hexitols, [Si] 0 . Circle, square and triangle symbols represent sorbitol, mannitol and galactitol, respectively.

Figure 5 :

 5 Figure 5: Total experimental (symbols) and simulated (lines) concentrations of aqueous calcium and silicate species at equilibrium with C-S-H immersed in 250 mL of solution containing various initial concentrations of Ca(OH) 2 , [Ca(OH) 2 ] i, and varying the equilibrium concentration of hexitols.

Figure 6 :

 6 Figure 6: Simulated speciation of calcium and silicate species in a 250 mL solution containing 200 mM of hexitols in equilibrium with 200 mg of C-S-H with varying C/S ratio. (a) and (c) provides the results for sorbitol; (b) and (d) those for mannitol. The distribution diagram can be found in the sup. info., see Figure S3 and S4.

Figure 7 :

 7 Figure 7: Total experimental (symbols) and simulated (lines) concentrations of silicate species in the aqueous phase in equilibrium with C-S-H buffered with portlandite (C/S 1.5)

Figure 8 :

 8 Figure 8: Experimental (symbols) and simulated (lines) concentrations of aqueous calcium and silicate species at equilibrium with C-S-H for various initial concentrations of Ca(OH) 2 in the solution, [Ca(OH) 2 ] i , as detailed in materials and methods. The simulations were

Ca 3

 3 Gluc 2 (H 3 SiO 4 ) 2 (OH) 2 0 , were used to describe the increase in the experimental calcium and silicate concentrations at equilibrium with C-S-H as a function of gluconate concentration. At all C/S studied, the thermodynamic modeling describes globally well the increase in the Si and Ca concentrations.

Figure 9 :

 9 Figure 9: Simulated speciation of calcium and silicate species in a 250 mL solution containing 200 mM of sodium gluconate in equilibrium with 200 mg of C-S-H with varying C/S ratio. Note that both Ca 2+ and CaOH + can hardly be seen as there concentration is always lower than 3 mM whatever the C/S. The distribution diagram can be found in the sup. info., see Figure S3 and S4.

Figure 9

 9 Figure9highlights the calculated calcium and silicate speciation as a function of the C/S ratio in C-S-H in solutions in equilibrium with 200 mM of sodium gluconate. The calcium concentration is dominated by Ca-gluconate-hydroxide complexes, while the quaternary Ca 3 Gluc 2 (H 3 SiO 4 ) 2 (OH) 2 0 complex is present at low concentrations only. In contrast, the experimental and calculated data highlight a visible increase of the silicate complex Ca 3 Gluc 2 (H 3 SiO 4 ) 2 (OH) 2 0 in solution, which dominates the silicate speciation at C/S above 0.9, and lower the amount of free silicates species in solution, H 4 SiO 4 0 , H 3 SiO 4 -, and H 2 SiO 4 -, in particular at high pH. To further illustrate the importance of the quaternary Ca 3 Gluc 2 (H 3 SiO 4 ) 2 (OH) 2 0 complex a comparison of the measured and predicted total equilibrium concentrations of Si and Ca when this complex is ignored is provided in the supplementary materials, see FigureS5.

1. 5 )Figure 10 :

 510 Figure 10: Adsorption isotherms of the organics on: a) portlandite, b) C-S-H buffered with an excess of portlandite and c) C-S-H with an initial C/S = 1.12. For the C-S-H systems, the organic adsorption is expressed as the number ratio of adsorbed organics to C-S-H silicon.

Table 1 .

 1 Solubility

	log10 K a References

and complex formation constants of calcium, silicate, hydroxide and gluconate (Gluc -) containing species at standard conditions (1 bar, 25°C) and I = 0 reported in literature and determined in the present study.

Table 2 .

 2 Complex formation constants of calcium, silicate, hydroxide and sorbitol (Sorb), mannitol (Man) and

	galactitol (Gal) containing species at standard conditions (1 bar, 25°C) and I = 0 reported in literature and
	determined in the present study
		log10 K a References
	Ca +2 + Sorb 0 = CaSorb +2	0.10	3
	Ca +2 + Sorb 0 + OH -= CaSorbOH +	2.85	3
	2Ca +2 + 2Sorb 0 + 4OH -= Ca2Sorb2(OH)4 0	9.75	3
	2Ca +2 + 2Sorb 0 + 2OH -+ 2H3SiO4 -= Ca2Sorb2(H3SiO4)2(OH)2 0	16.00 This study
	2Ca +2 + 2Sorb 0 + 4OH -+ H2SiO4 -2 = Ca2Sorb2(H2SiO4)(OH)4 -2	13.60 This study
	Ca +2 + Man 0 = CaMan +2	-0.36 3
	Ca +2 + Man 0 + OH -= CaManOH +	2.65	3
	2Ca +2 + 2Man 0 + 4OH -= Ca2Man2(OH)4 0	9.65	3
	2Ca +2 + 2Man 0 + 2OH -+ 2H3SiO4 -= Ca2Man2(H3SiO4)2(OH)2 0	NA* This study
	2Ca +2 + 2Man 0 + 4OH -+ H2SiO4

Table 2 .

 2 (CaHexOH + and Ca 2 Hex 2 (OH) 4 0 ) as summarized in Table 2 together with two quaternary Sicomplexes, Ca 2 Hex 2 (H 2 SiO 4 )(OH) 4 -2 and Ca 2 Hex 2 (H 3 SiO 4 ) 2 (OH) 2 0 , which were fitted here.It should also be noted that the modeling of the silicate and calcium concentrations using Indeed, preliminary speciation simulations in the framework of the primitive model indicate that the complexes tend to form clusters that grow in size (i.e.

	classical speciation modeling (e.g. PHREEQC or GEMS) is strictly equivalent if one uses
	complexes with different size (stoichiometric coefficient) but same stoichiometry, i.e.
	Ca y Hex y (H 3 SiO 4 ) y (OH) y 0 and Ca z Hex 0.5z (H 2 SiO 4 )0.5 z (OH) 2z -z with y > 2 and z > 2 (provided
	that the formation constants are modified accordingly) or if one defines a different
	deprotonation degree (n) for the silicate and hexitols in the complex providing that the overall
	charge of the complex is maintained constant (i.e. number of OH-groups adapted

The comparison of the calculated with the experimental calcium and silicate concentrations in equilibrium with C-S-H in Figure

5

shows in both cases significant increase of the Ca and silicate concentrations at high C/S and high pH values. The figures for galactitol are presented in the Supplementary Information, see Figure S.2.

As the silicate complexes with organics occur mainly at high Ca-concentrations and pH values, we hypothesized that polynuclear complexes similar to the main Ca-hexitol complexes are present in these conditions, namely Ca 2 Hex 2 (OH) 4 0 : a neutral Ca 2 Hex 2 (H 3 SiO 4 ) 2 (OH) 2 0 and a negatively charged Ca 2 Hex(H 2 SiO 4 )(OH) 4 -2 complex. The use of only one of these complexes was not able to reproduce the experimental data for sorbitol and galactitol adequately, nor the use of simpler complexes, i.e. CaHexH 2 SiO 4 0 or CaHex(H 3 SiO 4 ) 2 0 . For mannitol no Si-containing complexes were found as detailed in accordingly). In other words, the use of Ca y Hex y (H 3-n SiO 4 ) y (OH) y-n 0 and Ca y (Hex - n ) y (H 3 SiO 4 ) y (OH) y-n 0 as well as Ca z (Hex -n ) 0.5z (H 2 SiO 4 ) 0.5z (OH) 2(z-n) -z and Ca z (Hex) 0.5z (H 2- n SiO 4 ) 0.5z (OH) 2(z-n) -z leads exactly to the same modelling results. Again the choice of y=2 and z=2 was guided by previous works by Pallagi et al.

[START_REF] Pallagi | Multinuclear complex formation between Ca(II) and gluconate ions in hyperalkaline solutions[END_REF]

[START_REF] Kutus | Recent advances in the aqueous chemistry of the calcium(II)-gluconate system -Equilibria, structure and composition of the complexes forming in neutral and in alkaline solutions[END_REF]

and ourselves (3), but is somewhat arbitrary.

  The use of CaSorbOH + , Ca 2 Sorb(OH) 4 0 together with Ca 2 Sorb 2 (H 3 SiO 4 ) 2 (OH) 2 0 and Ca 2 Sorb 2 (H 2 SiO 4 )(OH) 4 -2 allows us to reproduce the increase in Ca concentrations at all Ca/Si Ca 2 Sorb 2 (H 2 SiO 4 ) 2 (OH) 4 -2 complex becomes only important at high pH values and Ca concentrations, typically in the buffered portlandite systems, where the concentrations of free silicates (H 3 SiO 4 -, H 2 SiO 4 -2

ratios studied as well as the moderate increase in Si concentrations in the high range of Ca concentrations and pH values. The speciation of Si is dominated by H 3 SiO 4 -at low Ca(OH) 2 concentration (C/S = 0.75) and by Ca 2 Sorb 2 (H 3 SiO 4 ) 2 (OH) 2 0 at C/S of 1 and above, as shown in Figure

6

and Figure

S4

. We can further note that the negatively charged

  4 0 , Ca 2 Gal 2 (H 3 SiO 4 ) 2 (OH) 2 0 and Ca 2 Gal 2 (H 2 SiO 4 )(OH) 4 -2 complexes allows us to fit accurately the measured calcium and silicate concentrations in presence of increasing amount of galactitol. Note that the fitted constants for Ca 2 Gal 2 (H 3 SiO 4 ) 2 (OH) 2 0 and Ca 2 Gal 2 (H 2 SiO 4 )(OH) 4 -2 as given in Table 2 are several log units weaker than those obtained for Ca 2 Sorb 2 (H 3 SiO 4 ) 2 (OH) 2 0 and Ca 2 Sorb 2 (H 2 SiO

4 )(OH) 4 -2 consistent with the much weaker complexation of galactitol with calcium ions (

Acknowledgements

We would like to thank for the financial support from Nanocem (core project 15). We are also very grateful for many helpful discussions with the representatives of the industrial partners L. Pegado, J.H. Cheung, V. Kocaba, P. Juilland and M. Mosquet and their interest. A special thanks to L. Brunetti, S. El Housseini, K. Alloncle and D. Nguyen for their help in the laboratory work.


Qidong Xie

Weinan Lin

Jinghua Liang

Hengan Zhou

Moaz Waqar

Hao Chen

Xiufang Lu

Xinyu Shu

Liang Liu

Shaohai Chen

Chenghang Zhou

Jianwei Chai

Ping Yang

Kian Ping Loh

John Wang

Wanjun Jiang

Aurelien Manchon
email: aurelien.manchon@univ-amu.fr

Hongxin Yang
email: hongxin.yang@nimte.ac.cn

Jingsheng Chen

Prof Jingsheng Chen

Prof Hongxin Yang

Prof Aurelien Manchon

Rashba-Edelstein effect in the h-BN van der Waals interface for magnetization switching

Current induced spin-orbit torque (SOT) offers an electrical way to control the magnetic state [START_REF] Liu | Currentinduced switching of perpendicularly magnetized magnetic layers using spin torque from the spin hall effect[END_REF][START_REF] Miron | Perpendicular switching of a single ferromagnetic layer induced by in-plane current injection[END_REF] , which is promising for future low-power spintronics. In general, the SOT originates from spin Hall effect (SHE) in heavy metals [START_REF] Sinova | Spin Hall effects[END_REF] , and/or Rashba-Edelstein effect (REE) in interfaces or structures without inversion symmetry [START_REF] Manchon | New perspectives for Rashba spin-orbit coupling[END_REF] . The REE-induced SOT relies on the Rashba spin-orbit coupling (SOC) in the studied structure, which enables the electric-field tunability on spin-orbit effective fields and thus attracts great interests [START_REF] Noël | Non-volatile electric control of spin-charge conversion in a SrTiO3 Rashba system[END_REF][START_REF] Lesne | Highly efficient and tunable spin-to-charge conversion through Rashba coupling at oxide interfaces[END_REF][START_REF] Chen | Electric-field control of interfacial spin-orbit fields[END_REF] . However, the unambiguous demonstration of the REE-SOT induced magnetization switching and its electric-field tunability is still lacking. Here, we demonstrate the REE-SOT induced magnetization switching in a h-BN/SrRuO3 bilayer structure. The insulating h-BN unexpectedly induces a giant Rashba effect at the van der Waals interface with a perpendicular magnetized SrRuO3 (110)pc thin film, which is supported by our first-principles calculations. In addition, a simplified tight-binding model is built to explain the origin of the SOT. Furthermore, modulation of the currentinduced SOT and magnetization switching by an electric field have been successfully achieved via ionic-liquid gating experiment. Our study paves the way for exploring the current-induced SOT and magnetization switching by integrating van der Waals materials with the functional ferromagnets.

The electric field tunability on the current-induced SOT not only gives rise to an extra degree of freedom for electrically manipulating the magnetizations for devices application, but also provide a powerful method for fundamental studies. In a conventional heavy metal (HM)/ferromagnetic metal (FM)/oxide tri-layers structure, the current-induced SOTs are considered to be mainly due to the SHE from the bulk HM, which has a very small screening length and thus makes the directly electrostatic effect trivial [START_REF] Liu | Control of current-induced spin-orbit effects in a ferromagnetic heterostructure by electric field[END_REF] . Consequently, a sizable modulation of the SOTs can only be achieved via electric-field driven motion of oxygen at the interface between the oxide layer and ferromagnetic metal (FM) [START_REF] Mishra | Electric-field control of spin accumulation direction for spin-orbit torques[END_REF] , which strongly influences the magnetic anisotropy of FM simultaneously. Compared to the SHE-induced SOT, the modulation of REE-induced SOT is more straightforward and desirable, thanks to the essential role of the Rashba effect, whose strength is related to the potential difference that the involving charge electrons experience. Indeed, there are a few works reporting the tunable REE-induced spin-orbit effective field in structures like SrTiO3-based heterostructures [START_REF] Noël | Non-volatile electric control of spin-charge conversion in a SrTiO3 Rashba system[END_REF][START_REF] Lesne | Highly efficient and tunable spin-to-charge conversion through Rashba coupling at oxide interfaces[END_REF] , ferroelectric/metal interface [START_REF] Lin | Tuning of current-induced effective magnetic field through Rashba effect engineering in hybrid multiferroic structures[END_REF][START_REF] Fang | Tuning the interfacial spin-orbit coupling with ferroelectricity[END_REF] and Fe/GaAs interface [START_REF] Chen | Electric-field control of interfacial spin-orbit fields[END_REF] . However, the REE in these structures has not been demonstrated to have the ability to drive magnetization switch by applying a charge current. Furthermore, whether the electric field effect on the REE-induced SOT can be transferred to the tuning capability on the current-induced magnetization switching remains unexplored.

These might be achieved by searching appropriate material systems which host significant REE and FM layer with perpendicular magnetic anisotropy (PMA) simultaneously.

On the other hand, to date, SOTs have been mostly demonstrated in transition metals [START_REF] Liu | Currentinduced switching of perpendicularly magnetized magnetic layers using spin torque from the spin hall effect[END_REF][START_REF] Miron | Perpendicular switching of a single ferromagnetic layer induced by in-plane current injection[END_REF][START_REF] Liu | Spin-torque switching with the giant spin hall effect of tantalum[END_REF][START_REF] Pai | Spin transfer torque devices utilizing the giant spin Hall effect of tungsten[END_REF] and van der Waals materials [START_REF] Macneill | Control of spin-orbit torques through crystal symmetry in WTe2/ferromagnet bilayers[END_REF][START_REF] Xie | Giant Enhancements of Perpendicular Magnetic Anisotropy and Spin-Orbit Torque by a MoS2 Layer[END_REF][START_REF] Song | Coexistence of large conventional and planar spin Hall effect with long spin diffusion length in a low-symmetry semimetal at room temperature[END_REF] which possess strong SOC and act as a source of spin current and torques. In order to boost the torque efficiency, one strategy is to exploit a topological insulator as a spin source layer, rather than a heavy metal. In this situation, the current is expected to mostly flow at the interface with the ferromagnet and generate extremely efficient torques. However, the difficulty to grow truly insulating topological insulator limits the applicability of this approach and strategies exploiting sputtered topological compounds are currently being explored [START_REF] Dc | Room-temperature high spin-orbit torque due to quantum confinement in sputtered BixSe(1-x)films[END_REF] . Alternatively, it has been proposed to use light elements such as graphene to enhance the interfacial potential drop [START_REF] Yang | at grapheneferromagnet interfaces due to the Rashba effect[END_REF] . The cooperation between the enhanced interfacial electric field and the atomic SOC of the ferromagnetic layer results in large Rashba SOC [START_REF] Yang | at grapheneferromagnet interfaces due to the Rashba effect[END_REF] and generates a SOT [START_REF] Manchon | New perspectives for Rashba spin-orbit coupling[END_REF] . The hurdle posed by this approach is that graphene shunts a substantial portion of the flowing current and therefore limits the torque efficiency. Therefore, an ideal solution would be to utilize an insulating material whose hybridization with the ferromagnetic orbitals would result in enhanced interfacial potential drop. Nonetheless, these two criteria, insulating bulk with strong interfacial hybridization, seem contradicting each other.

In this work, we demonstrate that an ideal compromise is realized by transferring h-BN onto SrRuO3 (SRO), resulting in giant Rashba SOC and gate-controlled current-driven magnetization switching, the schematic illustration of which is shown in Fig. 1a. This result is surprising as insulating van der Waals materials such as h-BN are regarded as inert with respect to transport measurement and are also not expected to strongly hybridize with adjacent metals.

In fact, our first principles calculations demonstrate that at the h-BN/SRO interface metalinduced gap states emerge close to Fermi level upon hybridization between pz orbitals of h-BN and t2g orbitals of SRO. The presence of these mid-gap states at the h-BN/SRO interface unlocks the gate voltage control of the REE splitting. The exotic role of the interface between h-BN and SRO is also distinguished by our control experiments on SRO single layer and the amorphous LaAlO3 (LAO) inserted h-BN/LAO/SRO structure.

For the structure investigated in this report, an epitaxial SRO (6nm) was deposited onto the SrTiO3 (STO) substrate with (110) crystallographic orientation by pulsed laser deposition (PLD). Then an exfoliated h-BN was transferred to the surface of the grown SRO thin film, whose optical image is shown in the insert of Fig. 1b. The Raman peak of the h-BN onto SRO is located at 1366 cm -1 , as shown in Fig. 1b, which is the same as the one exfoliated onto SiO2.

The Raman peak located at 1300 cm -1 for the h-BN/SRO structure is from the STO substrate.

In order to get SRO films with perfect PMA property for the SOT device, the (110)-oriented STO is chosen for the growth such that the magnetic easy axis of SRO (in the [010] lattice direction of the orthorhombic structure) will be aligned exactly along the out-of-plane (OOP) direction [START_REF] Liu | Current-induced magnetization switching in all-oxide heterostructures[END_REF] , which is verified by the X-ray diffraction (XRD) (see Fig. S1). The cross-sectional scanning transmission electron microscopy (STEM) was utilized to further characterize the quality of the h-BN/SRO structure (Fig. 1c). Good crystallinity of the epitaxial SRO thin film and a sharp SRO/STO interface can be confirmed from the high magnification high angle annular dark field (DF) and bright field (BF) images as shown in Fig. 1c(2) and Fig. 1c(3), respectively. Besides, the thickness of SRO (6 nm) is confirmed, and the layer structure of h-BN with a distance of 0.34 nm in the direction of c axis is clearly seen (Fig. 1c(4)). Finally, the magnetic measurements were performed to characterize the easy axis of the grown SRO (110)pc film, where pc subscript refers to pseudo-cubic. The temperature dependent magnetization of the SRO thin film along in-plane (IP) and OOP directions are shown in Fig. 1d. The negligible IP component of magnetization indicates the perfect PMA of the grown SRO thin film. This is further confirmed by the magnetic hysteresis loops under OOP and IP directions for SRO at 60 K (Fig. 1e), where the remnant magnetic moments at zero field are almost zero for both IP loops. For each M-T curve, the sample was cooled first from 300 K to 10 K under an external magnetic field of 40000 Oe, and then the magnetization was measured under zero magnetic field with the increasing temperature. Inset is the anomalous Hall effect (AHE) loop of h-BN/SRO at 60 K. e, Magnetic hysteresis loops of SRO at 60 K.

One of the main results in this study is that the current-induced magnetization switching is un-expectedly achieved in the h-BN/SRO(110)pc bilayer considering the insulating property of h-BN, whose set-up is shown in Fig. 2a. Here, the Hall resistance is utilized as an indicator for the magnetization of the SRO layer and the measurement is performed at 60 K. Fig. 2b shows the current-induced magnetization switching (red curves) under a sweeping pulsed DC current and various external magnetic fields applied parallel to the DC current. One can see that a deterministic magnetization switching can be achieved with an external magnetic field applied, and the polarity of the switching loops changes when reversing the magnetic field from Hx=-1000 Oe to Hx=1000 Oe. Furthermore, the critical current for switching is found to decrease with increasing of the external magnetic field, as shown in Fig. 2c (the switching loops can be found in Fig. S2a). All these observations are consistent with the features of the SOT-induced magnetization switching 1,2 . Nevertheless, there are no conventional SOT sources in the h-BN/SRO bilayer structure. In order to distinguish the role of the h-BN in this structure, we fabricated two control devices, one is from the SRO single layer and the other from a structure with a LAO layer inserted between the h-BN and SRO layers. The LAO layer here is an insulator with a thickness of 2 nm and in-situ grew onto SRO. Both control devices show similar (AHE) loops at 60 K to that of h-BN/SRO bilayer (Fig. S2). However, neither of them presents the current-induced magnetization switching as the one from the h-BN/SRO device.

The blue curves in Fig. 2b shows the result from the device based on h-BN/LAO/SRO, where no switching loops are observed whether there is an IP magnetic field or not. The switching result for the device of SRO single layer is shown in Fig. S3. Therefore, it can be inferred that the current-induced magnetization switching in h-BN/SRO device is strongly related to the interface between h-BN and SRO. It is noted that the switching ratio, defined as currentinduced resistance change divided by AHE resistance, is below one hundred percent. The possible factors responsible for the partial magnetization switching is discussed in the section 4 of the Supplementary Material.

Next, we quantify the current-induced spin-orbit effective field in the h-BN/SRO bilayer by measuring the current-induced shift of the OOP hysteresis loop as functions of the IP bias magnetic field. Here, the quantified current-induced spin-orbit field refers to the damping-like spin orbit field, which is the driving source for the magnetization switching [START_REF] Lin | Tuning of current-induced effective magnetic field through Rashba effect engineering in hybrid multiferroic structures[END_REF] .

We do not use the conventional second harmonic Hall voltage method because it mixes with the signal from the thermoelectric effect (section 5 in the supplementary), which can be ruled out by the method used here [START_REF] Pai | Determination of spin torque efficiencies in heterostructures with perpendicular magnetic anisotropy[END_REF] . Fig. 2d shows the AHE loops at ±1.5mA under a bias IP magnetic field of 8.5 kOe. One can see that the AHE loops shift towards opposite directions under opposite DC current, indicating the existence of a current-induced effective field due to the SOT. The effective field 𝐻 𝑒𝑓𝑓 can be extracted from the horizontal shift of the AHE loop under the DC current. Fig. 2e shows the summarized 𝐻 𝑒𝑓𝑓 /Jc as a function of the bias IP magnetic field along x direction, where Jc is the current density. 𝐻 𝑒𝑓𝑓 /Jc increases linearly with Hx at first and saturates around 10 Oe/(10 7 A/cm 2 ) when Hx is larger than 5000 Oe. These observations also suggest that the magnetization switching in the h-BN/SRO layers occurs through magnetic domain nucleation and expansion [START_REF] Baumgartner | Spatially and time-resolved magnetization dynamics driven by spin-orbit torques[END_REF] , which implies the presence of the Dzyaloshinskii-Moriya interaction (DMI) in the structure. In such a scenario, the IP field is to suppress the DMI effective field to achieve the domain expansion, i.e. assisting the magnetization to switch in SRO, as shown in Fig. 2b. Accordingly, the IP bias field, which corresponds to the saturated position of the 𝐻 𝑒𝑓𝑓 /Jc, equals to the DMI field in the structure, i.e. DMI field in h-BN/SRO is about 5000 Oe. Furthermore, one can obtain that the damping-like spin-orbit effective field is the saturated value of 10 Oe/(10 7 A/cm 2 ), which is comparable with the damping-like spin-orbit effective field observed in TmIG/Pt [START_REF] Avci | Current-induced switching in a magnetic insulator[END_REF] .

Consequently, we can evaluate the DMI exchange constant D, which is obtained from D=𝜇 0 𝑀 𝑠 𝛥𝐻 𝐷𝑀𝐼 . Here 𝛥 is domain wall width [START_REF] Avci | Current-induced switching in a magnetic insulator[END_REF] and can be obtained from 𝛥 = √ 𝐴/𝐾 𝑢,𝑒𝑓𝑓 , where A is the exchange stiffness constant, 𝐾 𝑢,𝑒𝑓𝑓 is the effective magnetic anisotropy energy. H loop. Exchange stiffness constant A is assumed to be 2 pJ/m for SRO [START_REF] Ziese | Inverted hysteresis and giant exchange bias in La0.7 Sr 0.3 MnO3/SrRuO3 superlattices[END_REF] Next, we would like to discuss the possible SOT origin in the h-BN/SRO bilayer.

Generally, in the scenario of SOT-induced magnetization switching, SHE and REE are recognized as the main mechanisms to generate the spin current to exert a torque onto magnetization. While SHE originates from the bulk SOC, the REE comes from the interfacial SOC. In the case of SHE, a spin current with transverse spin polarization is generated when a charge current passes through a heavy metal with strong SOC. In the h-BN/SRO structure, no current passes through the insulating h-BN layer. Therefore, SHE from the non-magnetic layer shall not exist in the h-BN/SRO bilayer due to the electric-insulating nature and weak SOC in h-BN. Thus, one may think that the spin Hall current arises from SRO itself. Recently, anomalous spin current sources have been reported to emerge in a magnetic single layer, for example, the SHE and AHE-induced spin currents [START_REF] Wang | Anomalous spin-orbit torques in magnetic single-layer films[END_REF] . However, the SHE-induced spin current would have opposite components in opposite directions that would cancel each other, while the AHE-induced spin current will have the same spin polarization direction as the magnetic moment of SRO, which cannot execute a torque on itself. These are further supported by the disappearance of the current-induced magnetization switching in the two control devices (one is with the SRO single layer, and the other with the h-BN/LAO/SRO structure). Therefore, it is reasonable to ascribe the origin of the SOT in the h-BN/SRO bilayer to the interface between h-BN and SRO layers.

The first-principles density functional theory (DFT) calculations were implemented to reveal the role of the h-BN/SRO interface in determining the current-induced SOT. Extended data Fig. 1a and1b show the side and top views of the structure models of h-BN/SRO (110)pc for the calculations. In order to see the structure-contributed spin splitting (not Zeeman-type), the electronic band structures of h-BN/SRO (110)pc are calculated with the magnetization aligned along [100]o and [1 ̅ 00]o directions (subscript o refers to orthorhombic), respectively, as shown by the black and red curves in Fig. 3a. One can see that the band structure of the h-BN/SRO (110)pc heterostructure presents characteristic Rashba-type splitting, and the splitting magnitude strongly depends on the position of the band. For example, considering the two bands that intersect the Fermi level and have the lowest energy in Γ point, as shown in the zoom-in plot in Fig. 3a, one can see that a larger band splitting exists in the upper bands. To quantify the Rashba effect, Rashba coefficients of the two bands are extracted as α 1 = 2𝐸 1 /𝑘 1 and α 2 = 2𝐸 2 /𝑘 2 with 𝐸 1 = 0.001 meV and 𝐸 2 = 7.693 meV being the Rashba splittings at the wave vectors 𝑘 1 = 0.001 Å -1 and 𝑘 2 = 0.028 Å -1 for the two bands, respectively. 𝐸 1 and 𝑘 1 are not shown in Fig. 3a due to their small values. We find that although Rashba coefficient α1 of the band nearest to the Fermi level is only 2 meV Å, the Rashba coefficient α2 of the other band is as large as 550 meV Å, which is comparable to that of Au (111) (330 meV Å) [START_REF] Lashell | Spin splitting of an Au(111) surface state band observed with angle resolved photoelectron spectroscopy[END_REF] and Bi(111) (550 meV Å) [START_REF] Koroteev | Strong spin-orbit splitting on Bi surfaces[END_REF] surfaces. In order to further shed light on the origin of the Rashba splitting at the h-BN/SRO interface, we calculated the density of states (DOS) of h-BN/SRO. From Fig. 3b, it can be identified that, for the h-BN, there are in-gap states at about -0.8 eV below the Fermi level (indicated by green arrow) due to the hybridization of Ru-3d and (B+N)-2p states.

Those in-gap states are mostly contributed by the pz orbitals of N atoms for both spin channels as shown in the top panel of Fig. 3c. It is noted that the in-gap states are strongly coupled to all the five Ru-3d orbitals for the spin-up channel, while it is only coupled to the dz 2 , dxz, and dx 2y 2 orbitals for the spin-down channel from the bottom panel of Fig. 3c.

With the band structure information of the h-BN/SRO interface, we develop an effective tight-binding model to qualitatively describe how the interfacial hybridization induced in-gap state modify the SOT properties of h-BN/SRO. In such a model, which is described in detail in the method, the hybridization between the two layers is tuned by modifying the onsite energy detuning (𝜀 0 ) between h-BN and SRO. It is found that there is a strong resonance state around the Fermi level when 𝜀 0 is in the range between 2.5t1 and 3t1, where t1 is the in-plane orbital hopping matrix element in SRO. Three experimentally relevant quantities, the field-like torque, the damping-like torque and the DMI, are calculated under different onsite energy detuning. All these three quantities emerge from the combination of magnetism, spin-orbit coupling and inversion symmetry breaking. Concretely, tuning 𝜀 0 modifies the hybridization between the insulating and magnetic layers and thereby changes the interfacial potential gradient between them. Consequently, the two interfaces of the ferromagnetic layer become inequivalent, resulting in non-vanishing torques and DMI.

The dependence of the three spin-orbit properties as a function of 𝜀 0 are reported on Fig. 3d, where the vertical dashed lines indicate selected remarkable situations. Away from the resonance range ( 𝜀 0 < 2.5𝑡 1 and 𝜀 0 > 3𝑡 1 ), the calculated torques and DMI are small due to weak coupling between h-BN and SRO. Between these two detuning values, the three quantities display quite different behavior, illustrating their different microscopic physical origin: The field-like torque only involves intra-band transitions, whereas both the dampinglike torque and DMI arise from inter-band transitions. The field-like torque reaches a maximum in the resonance region, which is reasonable since hybridization between the h-BN and SRO is maximized in this range and therefore the dissimilarity between the two ferromagnetic interfaces is optimized. The behavior of the damping-like torque and DMI is more intriguing and displays two main features: away from resonance (for 𝜀 0 < 2.5𝑡 1 and 𝜀 0 > 2.9𝑡 1 ), they both increase when tuning 𝜀 0 towards resonance. In the resonance region through, these two quantities exhibit opposite behavior, that is DMI reaches a maximum while the damping-like torque vanishes (markers (1) and ( 3)) and vice-versa (marker (2)). This opposite behavior is likely to be related to the different energy dependence of the two physical properties, as displayed by the equations in method.

Although this effective model would not quantitatively describe the experimental observations, it does suggest that the measured spin-orbit field and DMI arise from the hybridization effect between SRO and h-BN, which thus results in the current-induced magnetization switching in SRO. Based on our DFT calculations, the mid-gap states of h-BN that drives the inversion symmetry breaking are located a few hundreds of meV away from Fermi level so that the hybridization at h-BN/SRO interface is off-resonance, which will give rise to small but finite torques and DMI. As a result, it is expected that the spin-orbit field and DMI in the h-BN/SRO structure will be either enhanced or quenched with the change of the hybridization state via, for example, gating voltages in this off-resonance regime. So does the current-induced magnetization switching efficiency. Consequently, we employed an ionic-liquid gating experiment to investigate the electrostatic effect on the current-induced SOT and thus the magnetization switching. Fig. 4a shows the schematic set-up for the gating experiment. In this experiment, the transverse effective magnetic field (HT) measured by the second harmonic Hall measurement is extracted to indicate the current-induced SOT, since the Hall voltage related to the longitudinal damping-like field contributing to the magnetization switching mixes strongly with the signal from the thermal effect (section 5 in the supplementary), and the currentinduced shift of the OOP hysteresis loop as a function of the IP bias magnetic field is not able to be conducted in this set-up. During the measurement, a small AC current with a frequency of 13.7 Hz and an IP sweeping magnetic field within a small range are applied to the Hall bar device, and the resulted first harmonic voltage and second harmonic voltage are simultaneously probed by two lock-in amplifiers. Fig. S8 shows the second harmonic voltages V2ω as a function of the transverse magnetic field under gating voltages ranging from -1 V to +2.5 V at 60 K , where "M+" and "M-" represent moment up and down in SRO, respectively. One can see that the slope of the second harmonic Hall voltage changes sign upon reversing the magnetic moment direction, consistent with the feature of the transverse field due to the odd SOT [START_REF] Manchon | Current-induced spin-orbit torques in ferromagnetic and antiferromagnetic systems[END_REF] . The transverse effective magnetic field HT is obtained by

{ ∂𝑉 2𝑤 ∂H / ∂ 2 𝑉 𝑤 ∂H 2 }H‖T.
It is estimated to be 198 Oe/(10 7 A/cm 2 ) when the gate voltage is 0V, which is far larger than that extracted from the current-induced AHE shift as function of the IP bias magnetic field. Since the effective field from the latter method reflects the magnitude of the damping-like effective field for the magnetization switching while the former one for the field-like effective field, the large difference between these two fields is consistent with the feature of the current-induced SOT from REE [START_REF] Manchon | New perspectives for Rashba spin-orbit coupling[END_REF] . Fig. 4b summarizes the extracted transverse effective magnetic field under various gate-voltages. One can see that the HT increase as the gate-voltage increases, indicating a significant electrostatic effect. Fig. 4c shows the current-induced magnetization switching loops under -1 V, 0 V and +2.5 V of the gate-voltage, where the critical switching current and the switching loops are modulated obviously. Fig. 4d and Fig. 4e plot the extracted magnetization switching ratios and critical currents as functions of gate-voltages, respectively. One can see that the switching ratio increases upon the gate-voltage varying from -1 V to +2.5 V, while the critical current decreases upon the gate-voltages. These observations indicate that the gate-voltage can undeniably enhance the current-induced switching efficiency in h-BN/SRO structures. Such a trend, as well as that of the extracted field-like effective field, is consistent with the offresonance scenario inferred from the tight-binding model, i.e. the gate-voltage modulates the torques and DMI induced by the hybridization state at the h-BN/SRO interface. Furthermore, we also calculate the electric field dependence of the Rashba coefficients as shown in the Fig. 4f, which are extracted from the calculated band structures (Fig. 3a) from first-principles calculations (Methods). It is found that the Rashba coefficient can be effectively tuned by the electric field. In particular, the electric field of 0.2 V/nm can further enhance the Rashba coefficients α1 and α2 up to 33 and 616 meV Å, respectively. The modulation of the Rashba effect by the gate-voltage is consistent with the enhanced hybridization effect at the h-BN/SRO, which results in inequivalent interfaces on two sides of SRO. During the gating experiment, the AHEs under different gate-voltages were measured too (Fig. S9). They show almost the same shape under different gate-voltages, which hints that the trivial gating effect on the magnetic property of SRO does not contribute to the tuning effect on the current-induced SOT and magnetization switching.

In conclusion, current-induced REE-SOT and magnetization switching are demonstrated in a bilayer structure with vdW interface between the insulating h-BN and lock-in-amplifiers were employed for the switching and harmonic Hall measurement. The current-induced shifts of the OOP hysteresis loop as function of the IP bias magnetic field were measured by a SOT magnetometry method via accessing a Cryogenic triple-axis superconducting magnet (5T-2T-2T).

Rashba splitting and DOS calculations:

The first-principles calculation were performed within the framework of density functional theory (DFT) as implemented in the Vienna abinitio simulation package (VASP) [START_REF] Kresse | Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set[END_REF] . The electron-core interactions are described by the projector augmented wave method [START_REF] Kresse | Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set[END_REF] and the exchange correlation energy are calculated within the generalized gradient approximation of the Perdew-Burke-Ernzerhof (PBE) form [START_REF] Perdew | Generalized gradient approximation made simple[END_REF] . In addition, we include on-site Coulomb interaction with U = 1.4 and J = 0.4 eV for the Ru d states. To reduce the lattice mismatch between SRO (110)pc and h-BN, we have considered a large h-BN/SRO(110)pc heterostructure consisting of 4√3⨯3 unit cell of h-BN monolayer and 3⨯2 SRO(110)pc surface unit cell with three Sr-Ru-O layers. We use an energy cutoff of 500 eV and k-point sampling on a Γ-centered 2×1×1 k-point mesh for the system. Extended data figure 1a and 1b show the side and top views of relaxed crystal structure of h-BN/SRO(110)pc heterostructure with the forces on each atom are smaller than 0.001 eV/Å. We find that average distance between h-BN and SRO(110)pc surface is 3 Å, and, more importantly, both the structures of h-BN and SRO(110)pc are distorted due to their interlayer interaction. Next, to extract the Rashba coefficient, we solve the Kohn-Sham equations with no SOC taken into consideration to determine the charge distribution and the DOS for ground state of the relaxed structure. Then SOC is included and the electronic band structures of system are determined when the magnetization points along the opposite [100]o and [1 ̅ 00]o directions, respectively.

The dipole moment correction is considered in the calculations of the electric field dependence of the band structure.

Tight-binding model of SOT and DMI:

We develop an effective tight-binding model that qualitatively describes the modification of the spin-orbit properties of h-BN/SRO upon modifying the interfacial hybridization between the two layers. In fact, the large lattice mismatch between h-BN and SRO and the resulting large supercell required to model the band structure of the bilayer impedes the use of Wannier interpolation procedure. Therefore, we opt for an effective tight-binding model that comprises the following key ingredients: (i) the SRO magnetic layer modeled by an undistorted cubic structure with t2g orbitals and possessing atomic spin-orbit coupling; (ii) the insulating h-BN is modeled by a cubic bipartite lattice whose lattice parameter matches that of the magnetic layer; (iii) the hybridization between the two layers is tuned by modifying the onsite energy detuning between the two layers. Notice that because of the perfect lattice matching in our model, no mid-gap states emerge upon interfacial hybridization. To uncover the relation between interfacial potential drop and spinorbit properties, we focus on the region of parameters where the Fermi level is close to the valence band, a situation that features qualitatively similar physics.

The magnetic layer is modeled based on the effective undistorted cubic SRO structure proposed in Reference 31 [START_REF] Chen | Weyl fermions and the anomalous Hall effect in metallic ferromagnets[END_REF] Here 𝑡 𝑧 is the 𝜋-hopping integral between pz orbitals, and 𝜀 𝐴,𝐵 are the onsite energies of the two sublattices. In our model, we take 𝑡 𝑧 = 0.5 and 𝜀 𝐴,𝐵 = 𝜀 0 ± 𝜀 𝑔

2

, where 𝜀 𝑔 = 5 is the insulating gap and 𝜀 0 is the energy detuning of the insulating states with respect to the ferromagnetic ones.

The coupling between the {𝑑 𝑦𝑧 , 𝑑 𝑥𝑧 , 𝑑 𝑥𝑦 } orbitals of the ferromagnetic layer and the 𝑝 𝑧 of the insulating layer is parameterized using Slater-Koster scheme [START_REF] Slater | Simplified LCAO method for the periodic potential problem[END_REF] . The interlayer coupling reads: Our intention is to understand how the spin-orbit coupling properties are modified when tuning the hybridization between the ferromagnet and the insulating substrate. We will particularly focus on the longitudinal conductivity, 𝜎 𝐿 , the field-like and damping-like SOT, 𝑻 𝐹𝐿 and 𝑻 𝐷𝐿 , and the DMI. These quantities are computing using Kubo linear response [START_REF] Bonbien | Symmetrized decomposition of the Kubo-Bastin formula[END_REF][START_REF] Hajr | Semirealistic tightbinding model for Dzyaloshinskii-Moriya interaction[END_REF] : Here, 𝐺 𝑅,𝐴 = (𝜀 -𝐻 ± 𝑖Γ) -1 are the retarded and advanced Green functions, 𝒗 ̂= 𝜕 ℏ𝒌 𝐻 is the velocity operator and 𝑻 ̂= Δ𝐳 × 𝛔 ̂ is the torque operator [START_REF] Bonbien | Symmetrized decomposition of the Kubo-Bastin formula[END_REF][START_REF] Hajr | Semirealistic tightbinding model for Dzyaloshinskii-Moriya interaction[END_REF] 𝜎 𝐿 is expressed in Ω -1 ⋅ 𝑚 -1 , 𝑻 𝐹𝐿 and 𝑻 𝐷𝐿 are normalized to the electric field and expressed in ( ℏ 2𝑒

𝐻
𝜎 𝐿 =
) Ω -1 ⋅ 𝑚 -1

and the DM tensor element, 𝐷 𝑖𝑗 , defined as 𝑫 ⋅ (𝒎 × 𝜕 𝑗 𝒎) is expressed in meV ⋅ Å per unit cell. In the calculations, we apply the electric field along x and take N=3.

The density of states of our bilayer is reported on extended data figure 3 projected on the magnetic layer (blue) and on the insulator orbitals (red). In this configuration, we set 𝜀 0 = 0, so that the peaks of the valence and conduction bands of the insulator are symmetrically positioned with respect to the center of the ferromagnetic band width.

We first compute the longitudinal conductivity as a function of the parameter 𝜀 0 at 𝜀 𝐹 = 0. The results are displayed in extended data figure 3. The bottom panel shows the conductivity as a function of 𝜀 0 . As a reference, we also report the layer-projected density of states for three selected detuning. It is clear that the resonance occurs around 𝜀 0 ≈ 2.5𝑡 1 , which corresponds to a sharp modification of the conductivity.

Figure1|

  Figure1| Basic characterizations of the h-BN/SrRuO3 structure. a, Schematic illustration

  . Then we obtain the DMI exchange constant D=0.21 mJ/m 2 , which is comparable with the DMI exchange constant of Ta/CoFeB/MgO 20 .

Figure 2 |

 2 Figure 2 | Current-induced magnetization switching in h-BN/SRO bilayer. a, Schematic

Figure

  Figure 3|Microscopic origin of SOT at the h-BN/SRO interface. a, The calculated band

Figure

  Figure 4| Gate-voltage tunable effective magnetic field and current-induced

2 𝑉

 2 𝛾 𝛼 represents the hopping integral between the 𝑝 𝑧 orbital of sublattice 𝛼 and the 𝑑 𝛾 orbital of the magnetic lattice. Explicitly, 𝜎 and 𝑉 𝜋 are the p-d Slater-Koster parameters that we fix to 𝑉 𝜎 = 0.1 and 𝑉 𝜋 = -0.05.

  . In the {𝑑 𝑦𝑧 , 𝑑 𝑥𝑧 , 𝑑 𝑥𝑦 } basis, it reads: 2𝑡 1 (cos 𝑘 𝑦 + cos 𝑘 𝑧 ) -2𝑡 2 cos 𝑘 𝑥 𝜀 𝑥𝑧 = -2𝑡 1 (cos 𝑘 𝑥 + cos 𝑘 𝑧 ) -2𝑡 2 cos 𝑘 𝑦 𝜀 𝑥𝑦 = -2𝑡 1 (cos 𝑘 𝑥 + cos 𝑘 𝑦 ) -2𝑡 2 cos 𝑘 𝑧 𝑓 𝑎𝑏 = -4𝑓 sin 𝑘 𝑎 sin 𝑘 𝑏 Since we do not intend to quantitatively describe the actual band structure of SRO, we simply adopt the parameters of Reference 31[START_REF] Chen | Weyl fermions and the anomalous Hall effect in metallic ferromagnets[END_REF] , given in the table below. In the following, 𝐻 SRO is discretized along z in order to build a N-layer slab, as depicted on extended data, where 𝐻 𝐿 is the Hamiltonian of the square lattice in the (x,y) plane and 𝐻 𝑇 is the hopping matrix along z.

				𝐻 𝐿 𝐻 𝑇 0
		𝐻 SRO → 𝐻 𝑠𝑙𝑎𝑏 = (	𝐻 𝑇 †	⋱ 𝐻 𝑇	)
				0 𝐻 𝑇 †	𝐻 𝐿
	SrRuO3 parameters (a=3.93A in the undistorted cubic structure)
	𝒕 𝟏	𝑡 2	𝑓			∆	𝜆
	1	-0.2	0.2		1	0.4
	Based on the density functional theory calculations, h-BN hybridizes with SRO through
	its pz orbitals. In our model, we consider a (checkerboard) bipartite square lattice with pz
	orbitals only. In the sublattice representation, the Hamiltonian reads:
	𝐻 I = ( 𝑡 𝑧 (cos 𝑘 𝑥 + cos 𝑘 𝑦 ) 𝜀 𝐴	𝑡 𝑧 (cos 𝑘 𝑥 + cos 𝑘 𝑦 ) 𝜀 𝐵	)
		𝜀 𝑦𝑧 -∆𝜎 𝑧	𝑓 𝑦𝑧,𝑥𝑧		𝑓 𝑦𝑧,𝑥𝑦
	𝐻 SRO = (	𝑓 𝑦𝑧,𝑥𝑧	𝜀 𝑥𝑧 -∆𝜎 𝑧	𝑓 𝑥𝑧,𝑥𝑦	) + 𝑖𝜆𝜖 𝑎𝑏𝑐 𝜎 𝑐
		𝑓 𝑦𝑧,𝑥𝑦	𝑓 𝑥𝑧,𝑥𝑦		𝜀 𝑥𝑦 -∆𝜎 𝑧
	𝜀 𝑦𝑧 = -figure 2:

  𝑒ℏ 4𝜋𝑎 ∫ 𝑑𝜀𝜕 𝜀 𝑓(𝜀)Tr[(𝐺 𝑅 -𝐺 𝐴 )𝑣 ̂𝑥(𝐺 𝑅 -𝐺 𝐴 )𝑣 ̂𝑥] 𝑻 𝐹𝐿 = ℏ 4𝜋 ∫ 𝑑𝜀𝜕 𝜀 𝑓(𝜀)Tr[(𝐺 𝑅 -𝐺 𝐴 )(𝑒𝑬 ⋅ 𝒗 ̂)(𝐺 𝑅 -𝐺 𝐴 )𝑻 ̂] 𝜀)Tr[(𝐺 𝑅 -𝐺 𝐴 )(𝑒𝑬 ⋅ 𝒗 ̂)(𝜕 𝜀 𝐺 𝑅 + 𝜕 𝜀 𝐺 𝐴 )𝑻 ̂] 𝜀 -𝜀 𝐹 )𝑓(𝜀)Tr[(𝜕 𝜀 𝐺 𝑅 𝑣 ̂𝑗𝐺 𝑅 -𝐺 𝑅 𝑣 ̂𝑗𝜕 𝜀 𝐺 𝑅 )𝑇 ̂𝑖]

	𝑻 𝐷𝐿 = ∫ 𝑑𝜀𝑓(𝐷 𝑖𝑗 = ℏ 4𝜋 ℏ 2𝜋 Re∫ 𝑑𝜀(

Acknowledgment:

The research is supported by the Singapore National Research Foundation under CRP Award No. NRF-CRP10-2012-02 and the Singapore Ministry of Education MOE2018-T2-1-019, MOE2018-T2-2-043, MOE2019-T2-2-075, A*STAR Grant No. A1983C0036, A*STAR IAF-ICP 11801E0036, MOE Tier1 R-284-000-195-114.

perpendicularly magnetized SRO (110)pc. These observed phenomena are ascribed to the Rashba effect induced at the interface between h-BN and SRO, which is confirmed by the firstprinciples calculations. A simplified tight-binding model is employed to explain how the SOTs and DMI are generated in such an asymmetric h-BN/SRO bilayer, which is further supported by the evident electrostatic effect on the current-induced SOT and magnetization switching.

The exotic properties induced by the insulating h-BN reported here also remind the 2D materials community to be careful with the hidden role the h-BN may play in studies of the novel properties of the van der Waals materials, where the h-BN is widely used as an inert protection layer.

Methods:

Sample preparation: SRO thin films were deposited by PLD with laser wavelength of 248 nm. The base pressure of the chamber for growth SRO was 5×10 -7 torr. The growth parameters were optimized as following: the energy density of laser was 1.5 J/cm 2 , the substrate was heated up to 750 o C and oxygen pressure was set to 20 mtorr during growth. After the SRO thin films were prepared well, h-BN was exfoliated from single crystals and then transferred onto SRO.

Characterizations: Raman spectrum was measured by a Thermo Scientific DXR Raman microscope with a 514 nm excitation and a 100X objective. Magnetic properties were measured by SQUID (Quantum design MPMS3). Cross-sectional STEM was carried out in a JEOL ARM200F atomic resolution electron microscope equipped with cold field emission gun, an ASCOR 5 th order aberration corrector.

Device fabrication and transport measurement:

Competing financial interests' statement

The authors declare no competing financial interests.