Benjamin Burcher

Kevin J Sanders

Ladislav Benda

Guido Pintacuda

Erwann Jeanneau

Andreas A Danopoulos

Pierre Braunstein

Hélène Olivier-Bourbigou

Pierre-Alain R Breuil

A Straightforward Access to Stable, 16 Valence-electron Phosphine-Stabilized Fe 0 Olefin Complexes and their Reactivity

), and [Fe 0 (L) 2 (dvtms)], L = PMe 3 , (3), by a mild reductive route using AlEt 2 (OEt) as reducing agent. In contrast, by the same methodology, the 18 valence-electron complexes [Fe 0 (L-L) 2 (ethylene)], (L-L) = dppm (1,2-bis(diphenylphosphino)methane), 6, (L-L) = dppa (1,2bis(diphenylphosphino)amine) 7 or (L-L)=dppe, 8, were obtained, which do not contain dvtms. In addition, a combined DFT and solid-state paramagnetic NMR methodology is introduced for the structure determination of 5. A comparative study of the reactivity of 1,2,4-6 and 8 with 3-hexyne highlights emerging mechanistic implications for C-C coupling reactions using these complexes as catalysts.

INTRODUCTION

The catalytic chemistry of iron complexes is being intensively revisited with the objective to develop surrogates for noble metals in homogeneous catalysis. 1 Recent progress has led to Fe complexes in various oxidation states with unprecedented reactivities. 2 In particular, over the last decade, low-valent iron chemistry has enjoyed a renaissance thanks to well-defined complexes, which are catalytically competent in numerous transformations. 3 Indeed, the synthesis of well-defined low-valent Fe complexes is crucial for a better understanding of the mechanisms operating in Fe-catalyzed reactions. Among low-valent Fe complexes, nitrogen-donor ligand-based Fe complexes currently constitute the mainstream of the ongoing research efforts, 4,[START_REF] Stoian | Selected examples of low-oxidation state iron complexes stabilized by nitrogen-based ligands: a)[END_REF] although the possible non-innocent character of certain N-ligands often casts doubt on the metal oxidation state in these coordination compounds. [START_REF] Blanchard | For reviews treating of non-innocent ligands see: a)[END_REF] An alternative approach employs phosphorus donor ligands, since their easily-tunable electronic and steric properties are advantageous to stabilize low oxidation state metal complexes. Indeed, numerous examples have been described, where low-oxidation state iron complexes are stabilized by phosphorus based ligands. [START_REF] Muetterties | Selected references of P-based iron(0) complexes: a) Rathke[END_REF] However, they almost invariably feature 18 valence-electron (ve) metal centers, with limited reactivity due to their coordinatively and electronically saturated nature. For this reason we focused our effort on accessing well-defined, coordinatively unsaturated, thus more reactive, P-based species, typically 16 ve Fe 0 complexes. Isolated and well-characterized examples of the latter are scarce, 8,9,10,11 a fortiori low-coordinate 16 ve Fe 0 centers with alkene and mono-or bidentate P-donor ligands. The only reported examples of the latter with alkyl phosphines have to be handled at temperatures below 0°C to avoid decomposition, which limits the study of their reactivity. 9 Very recently, [Fe 0 (dipp)(C 2 H 4 ) 2 ], dipp = bis(diisopropylphosphino)propane was described by Fürstner et al.. 10 Remarkably, while most reported 16 ve Fe 0 complexes bearing P-donor ligands were accessed via conventional reducing routes based on the use of sodium, potassium or magnesium, [Fe 0 (dipp)(C 2 H 4 ) 2 ], as well as the complexes described in the present work were obtained by the uncommon "reductive alkylation" methodology. Furthermore, it has to be emphasized that Deng and coworkers introduced the use of chelating functionalized organosilicons associated to bulky monodentate aminocarbenes to ensure the synthesis and isolation at ambient temperature of well-defined 14-and 16 ve Fe 0 species. 11 Prior this work, the use of such organosilicon derivatives were scarcely reported on ironcarbonyl complexes 12 and other transition metals such as nickel or palladium. 13 Herein, we report the straightforward synthesis and characterization of various stable 16 valence-electron Fe 0 alkene complexes bearing mono-and/or bidentate donor ligands and illustrate their potential in terms of reactivity in the oxidative coupling of alkynes. 10,14,15 Moreover, while the 3D structure of complex 5 could not be determined by X-ray crystallography, we obtained the coordinates de novo by density functional theory (DFT) calculations and utilized solid-state paramagnetic NMR (PNMR) spectroscopy to validate the resulting model.

RESULTS AND DISCUSSION

Synthesis and Characterization of the 16 ve Complexes 1-5. In the search for a mild reductive methodology to access reactive 16 ve complexes comprising [Fe 0 (L-L)] and [Fe 0 (L) 2 ] fragments, L being a 2-electron P-or N-donor, we carefully investigated the reductive/alkylating reactivity of the commercial AlEt 2 (OEt), previously employed for the synthesis of the 18 ve [Fe(dppe) 2 (C 2 H 4 )], dppe = Ph 2 P(CH 2 ) 2 PPh 2 . 16 Addition of one equivalent of dppe at room temperature to a mixture of divinyltetramethyldisiloxane (dvtms), [Fe(acac) 3 ] and AlEt 2 (OEt) in an optimized ratio (see below), afforded the new 16 ve dialkene complex [Fe 0 (dppe)(dvtms)] (1) as a green solid (81% yield). This method was then applied similarly, except substituting dppe with Ph 2 P(CH 2 ) 3 PPh 2 (dppp) affording the analogous green complex [Fe 0 (dppp)(dvtms)] (2) in 71% yield (Scheme 1). Encouraged by the versatility of this straightforward approach, we employed PMe 3 in place of (L-L) and isolated at low temperature (-80 °C) the highly air-sensitive blue solid [Fe 0 (PMe 3 ) 2 (dvtms)] (3), but in low yield (19%), arguably because of its high solubility in all common solvents, including pentane. Furthermore, mixed bidentate P,N ligands also appeared to be suitable for this methodology, since under similar conditions the use of pyNMeP i Pr 2 led to the brown complex [Fe 0 (pyNMeP i Pr 2 )(dvtms)] ( 4) in 48% yield (Scheme 1). With stronger σ-donor bidentate phosphines, such as i Pr 2 P(CH 2 ) 2 P i Pr 2 (dipe), the corresponding [Fe 0 (dipe)(dvtms)] ( 5) was readily isolated as a blue solid (up to 81% yield) (Scheme 1).

Scheme 1. Synthesis of complexes 1-5.

Single-crystal X-ray diffraction studies established the structures of the [Fe 0 (L-L)(dvtms)] and [Fe 0 (L) 2 (dvtms)] complexes 1-4 and revealed the η 2 :η 2 coordination mode of the dvtms (Figure 1). The metal coordination geometry in 1 can be considered as distorted tetrahedral; the C-C bond distances in the vinyl moiety of 1.409(5) Å and 1.419(5) Å are indicative of dàπ* back donation. 11 Similarly, the structures of 2 and 3 exhibit distorted tetrahedral coordination geometries; the molecule of 3 exhibits C 2v symmetry (relative to the Fe-O axis). Significant structural differences are observed in 4, where the two vinyl moieties are coplanar (torsion angle of 4.22°) and perpendicular to the plane of the ligand containing the P, N and N py atoms. The P and Fe atoms lie almost in the plane formed by the vinyl fragments so that the coordination geometry of 4 is best described as trigonal pyramidal. NMR-Validated de novo DFT Structure of 5. Because no single crystals suitable for X-ray diffraction could be obtained for 5, we constructed a putative structural model by de novo DFT optimization (Figure 2, (b), see Experimental) and confirmed the dipe ligand binding to Fe 0 by using PNMR calculations 17 and PNMR spectroscopy of a precipitated powder sample which was also characterized by elemental analysis. Previous reports described that DFT may provide high-quality structures of high-spin open-shell transition metal complexes, in excellent agreement with those obtained by experimental structural determination with X-ray diffraction. 18 Reliable DFT methodology requires a proper functional, a sufficiently large atomic basis, and a dispersion correction properly accounting for van der Walls forces. The method chosen here (see Computational Details) meets all these demands. The energy minimum found by the DFT structure optimization for complex 5 indeed very closely resembles the X-ray structure of related complex 1, as shown in Figure 2.

To support the DFT-optimized structure, we measured and calculated 13 C PNMR shifts of 5. NMR spectra of paramagnetic complexes contain a wealth of structural information since the unpaired electrons induce large perturbations in the chemical shifts and the NMR relaxation properties of the surrounding nuclei. These PNMR effects depend on the distribution of unpaired electron density ("spin density") on the ligands, which in turn is highly sensitive to the metal binding and the conformation of the ligands. 19 The spin density provides a qualitative insight into this phenomenon (Figure 2, (c)). Notably, negative unpaired electron density and large negative contact shifts are predicted for the 13 C nuclei of the -(CH 2 ) 2 -bridge. The corresponding experimental 13 C NMR spectrum was acquired under magic-angle spinning conditions on a powdered sample of 5 (Figure 2, (d)). The magnitude of the experimental 13 C shifts is often overestimated in the DFT calculations (see below), but a few assignments can be reliably established in the less crowded regions of the spectrum. This is the case around -1000 ppm, where only two very broad 13 C signals are observed, and directly assigned to the -(CH 2 ) 2 -bridge of the dipe ligand coordinated to Fe 0 . We note in passing that without extensive further modeling such a clear assignment could not be made for any other resonances in the PNMR spectra of 5 (see Discussion of the computational protocol below). Nevertheless, the agreement between the experimental and predicted shifts for the -(CH 2 ) 2 -bridge confirms the dipe binding to Fe 0 and, by extension, the putative structure of complex 5. Discussion of the PNMR Computational Protocol. The main accuracy limiting factors of our modeling approach were: (1) the method for calculating the spin-orbit coupling (SOC)-dependent electron paramagnetic resonance (EPR) property tensors g and D,

(2) the method for hyperfine coupling (HFC) calculations, and (3) the quality and relevance of the molecular structure for which the PNMR calculations were performed to the experimental conditions in the molecular crystal.

(1) Reliable g-and D-tensor calculations in 3d transition metal complexes require the use of correlated multi-reference ab initio methods. Performing such calculations for systems as large as ∼80 atoms is currently at the very limit of standard computational capabilities. Comparing PNMR shifts calculated without and with DFT-based SOC property tensors g and D (Table 1), we see that upon inclusion of the SOC-dependent property tensors the PNMR shifts decrease by several tens of ppm. Comparable or perhaps even slightly larger effects might be expected when using ab initio g-and D-tensors.

(2) To the best of our knowledge, there is currently no benchmark ab initio method for reliable HFC calculations. Pure (generalized gradient approximation Kohn-Sham) DFT is known to over-delocalize spin density from the metal center, 20 leading to overestimation of the Fermi-contact HFCs and shifts on the metal ligand atoms, which in this case dominate the total HFC and PNMR shifts. Adding exact exchange admixture in hybrid DFT usually improves the results 21 but this improvement can be nonsystematic and non-uniform across the NMR-active atoms of the molecule. Only qualitative accuracy of the calculated Fermi-contact HFCs and shifts may be expected from our PBE0 HFC calculations.

(3) Even though there is an overall agreement between DFToptimized structure of 5 and the X-ray structure of the closely related complex 1, only a qualitative agreement between the PNMR calculations and the experiment can be expected in view of the high sensitivity of the PNMR shifts to the metal coordination geometry. The influence of a strong structural dependence of the PNMR shifts becomes important when internal dynamics at the metal center takes place. Modeling the dynamical effects on PNMR shifts, albeit potentially worthwhile and relevant for molecular crystals with flexible groups, goes beyond the scope of this article. Exp.

-800, -890 a PBE0-D3 optimized structure. b The level of PNMR theory employed, "no SOC" denoting the doublet-like theory and "full" Vaara's 2015 theory. 17

Synthesis and Characterization of the 18 ve Complexes 6-8. Strikingly, we observed considerable differences when the synthetic methodology used to access 1-5 was applied to the small bite angle bidentate ligands bis(diphenylphosphino)methane (dppm) or bis(diphenylphosphino)amine) (dppa). In these cases, the added dvtms did not enter the coordination sphere, which now comprises two bidentate phosphines and one ethylene ligand in the 18 ve complexes [Fe 0 (dppm) 2 (C 2 H 4 )] ( 6) and [Fe 0 (dppa) 2 (C 2 H 4 )] ( 7), respectively. The origin of the ethylene ligand is presumably due to β-H elimination from a FeEt 2 moiety formed in situ, from which also ethane (detected by GC) can arise, via reductive elimination from the transient Fe(H)Et moiety. 22 Optimized yield of the orange complex 6 (83%) was obtained by adjusting the mole ratio diphosphine/Fe to 2, without addition of dvtms (Scheme 2). The use of dppa led to complex 7 in a priori high yield (87%), however important inconsistencies were observed in elemental analyses (see Experimental). Suitable single crystals of X-ray diffraction quality could however be grown for structure determination. The previously characterized (by elemental analysis and IR spectroscopy) red complex [Fe 0 (dppe) 2 (C 2 H 4 )] ( 8) was also obtained by this method in 85% yield. 16 The diamagnetic complexes 6 and 8 were characterized by elemental analyses and 1 H and 31 P NMR spectroscopic methods. The 31 P NMR spectrum of 8 (20°C in C 6 D 6 ) contains a pair of triplets at δ 78.8 and 95.5 ppm, assignable to the two groups of non-equivalent P-atoms of the dppe ligands (A 2 X 2 spin system). In contrast, in the 31 P NMR spectrum of 6, (20°C, C 6 D 6 ) the four equivalent phosphorus nuclei of the dppm ligands appear as a broad singlet at δ 23.9 ppm, as reported previously. 23 In the 1 H NMR spectrum of 8, the coordinated ethylene gives rise to two broad signals at δ 0.93 and 1.13 ppm, the latter overlapping with two protons of the ligand backbone.

Scheme 2. Synthetic route to complexes 6-8.

The structures of 7 and 8, determined crystallographically, exhibit trigonal bipyramidal coordination geometries (calculated values of τ: 0.96 for 7 and almost 1 for 8, Figure 3 and Figure 4). The Fe-C ethylene (2.082 (8) and 2.099(7) Å) bond distances in 8 are larger than those in complex 7 (2.069(2) and 2.050(2) Å), consistent with a greater back donation from the Fe(dppe) 2 moiety to the ethylene, compared to Fe(dppa) 2 . Noteworthy, the PNHP atom in 7, localized in the difference Fourier map of the crystal structure determination, did not react with the excess of AlEt 2 (OEt) used in the synthesis, opening future possibilities of ligand proton responsiveness during catalysis. Cyclotrimerization of Alkynes. We then considered the cyclotrimerization of 3-hexyne as a model reaction to compare the reactivity of the 16 and 18 ve complexes (see Table 2). Up to 35% conversion was obtained with 1 leading to exclusive formation of hexaethylbenzene (HEB). Increasing the bite angle of the ligand from dppe to dppp (as in 1 and 2, respectively) disfavors 3-hexyne conversion (12%); in addition, the mixed donor ligand in 4 does not lead to an efficient catalyst (11% conversion to HEB). The conversion of 3-hexyne was higher with 5 than with 1 (49% vs. 35%, respectively), however, cyclic and linear C12 products accompanied HEB formation. Postulating the involvement of a metallacyclic reaction mechanism, the lower selectivity with 5 could be rationalized by the steric hindrance brought about by the isopropyl P-substituents that hampers coordination of a third molecule of 3-hexyne to the 16 ve intermediate C and thus the formation of the metallacycle D precursor to HEB (see Scheme 3).

The catalytic results with the 18 ve complexes 6 and 8 clearly highlight the reduced accessibility of the metal by the 3-hexyne substrate: 6 and 8 gave no conversion; catalytic results obtained with 7

were not explored because of concerns about the purity of the sample. Mechanistically, it is reasonable to assume that the reaction initiation involves displacement of the coordinated ethylene by an alkyne. However, propagation by metallacycle formation requires coordination of one additional alkyne, which is prevented by a disfavored dissociation of at least one P-donor.

Synthesis and Characterization of 9.

With the aim to observe or trap suggested reaction intermediates such as the bis(alkyne) iron species A or the iron-cyclopentadiene-like moiety B ensuing from the oxidative coupling of two alkynes (Scheme 3), we exposed 1 to 3-hexyne. This resulted in an immediate color change from green to brown; however, no complex could be isolated. Addition of few equivalents of PMe 3 , in order to trap the reactive species as a stable 18 ve species, unexpectedly led to the clean isolation in moderate yields (28%) of the air-sensitive, green diamagnetic complex [Fe(dppe)(PMe 3 )(3-hexyne)] (9), which was characterized by 1 H, 31 P and 13 C NMR spectroscopy and crystallographically (Figure 5). The XRD study confirmed that this unprecedented complex features one alkyne, one bidentate dppe and one PMe 3 ligands. The coordination geometry at Fe can be described as tetrahedral or distorted square pyramidal, depending on whether the unsaturated ligand is considered as an ɳ 2 -alkyne or a κC,κC-metallacyclopropene. The much elongated C-C bond distance in the hexyne ligand (1.303(6) Å) compared to that in free 3-hexyne (1.210 Å), falls in the range associated with C=C double bonds and implies substantial back donation from the metal to the π*-orbital(s) of the alkyne, thus supporting the description of the coordinated 3-hexyne as metallacyclopropene. 13 C NMR spectrum analysis supports this hypothesis as a downfield-shifted chemical shift at 189 ppm is measured, corresponding 4-electron donor acetylene ligand (see Experimental). Although a plausible precursor to 9 could be the bis(3hexyne) species A, it may also be considered as arising by cleavage of the postulated iron-cyclopentadiene B after the addition of PMe 3 (Scheme 3). In this case A and B should be in equilibrium. 5); Fe1-C35 1.860( 5); C34-C35 1.303 (6).

CONCLUSIONS

In conclusion, we described a convenient reductive path to 16 valence-electron Fe 0 reactive species. The successful synthesis of a range of olefin complexes bearing monodentate and bidentate phosphines or P,N hybrid ligands demonstrates its versatility and scope. The nature of the P-donor ligand determines the coordination of the final product, as demonstrated by the selective isolation of the 18 ve complexes with small bite angle diphosphines. The dvtms-stabilized 16 ve species showed a better propensity to yield hexaethylbenzene as a cyclo-trimerization product of 3-hexyne, than their 18 ve counterparts. This direct access to valuable [Fe 0 (L) 2 ] fragments opens perspectives for mechanistic investigations of reactions involving oxidative addition and coupling as elementary steps. Finally, because X-ray crystallography could not be used to determine the structure of 5, we established a putative structural model de novo using DFT optimization and used paramagnetic solid-state NMR spectroscopy to validate this model.

EXPERIMENTAL

General Considerations Unless stated otherwise, all reactions were carried out under atmosphere of argon using standard Schlenk techniques. All reagents were purchased from commercial suppliers and used without further purification. All yields refer to isolated products. Anhydrous common solvents were purified by solvent purification system (SPS-M-Braun). NMR spectra were recorded on a Bruker AV 300 MHz. Deuterated solvents were purchased from Sigma-Aldrich or Eurisotop. GC-MS analyses were carried out with an Agilent 6890 N apparatus equipped with a PONA or HP-MS column and an Agilent 5975B inert XL EI/CI MSD mass spectrometer. FT-IR spectra were recorded in the solid state by ATR Golden Gate (Specac) on a Perkin-Elmer spectrum one spectrometer. Elemental analyses were determined at London Metropolitan University. Abbreviations used in the experimental section are as follows: dvtms

= divinyltetramethyldisiloxane, dipe = 1,2-bis(diisopropylphosphino)ethane, dppe = 1,2- bis(diphenylphosphino)ethane, dppp = 1,2- bis(diphenylphosphino)propane, pyNMeP( i Pr) 2 = N- (diisopropylphosphino)-N-methylpyridin-2-amine, dppm = 1,2- bis(diphenylphosphino)methane, dppa = 1,2- bis(diphenylphosphino)amine.
[Fe(dppe)(dvtms)] (1). 1,2-Bis(diphenylphosphino)ethane (0.60 g, 1.51 mmol, 1.03 eq.), [Fe(acac) 3 ] (0.50 g, 1.46 mmol, 1.00 eq) and dvtms (0.79 g, 4.25 mmol, 2.90 eq.) were suspended in diethyleth-er (40 mL). Diethylaluminum ethoxide (1.50 mL, 10.0 mmol, 6.85 eq) was added dropwise. After it was stirred for 30 min, the solution became dark green. The reaction mixture was further stirred for 5 h. Diethylether was evaporated under reduced pressure leaving a green oil which was triturated with pentane to form a green solid that was washed 3 times with pentane (3x5 mL). The solid was dried under reduced pressure affording 0.77 g (81%) of a green solid. X-ray quality crystals were obtained by cooling a saturated toluene solution of the title complex to -20 °C. Anal. found (calcd.) for C 34 H 42 FeOP 2 Si 2 : C, 58.12 (63.74); H, 6.17 (6.61). Inconsistencies observed in the elemental analysis might be due to partial sample decomposition during work up.

[Fe(dppp)(dvtms)] (2). 1,2-Bis(diphenylphosphino)propane (1. 30 g, 3.15 mmol, 1.07 eq.), [Fe(acac) 3 ] (1.04 g, 2.94 mmol, 1.00 eq) and dvtms (1.17 g, 6.28 mmol, 2.14 eq.) were suspended in diethylether (30 mL). Diethylaluminum ethoxide (3.10 mL, 20.7 mmol, 7.04 eq) was added dropwise. The reaction mixture was stirred overnight. Diethylether was evaporated under reduced pressure leaving a dark green oil which was dissolved in pentane (10 mL) and the solution was cooled to -80 °C for 2 h. The solid formed was isolated by decantation and dried under reduced pressure at -80 °C affording 1.15 g of a green powder. A second crop was obtained after cooling the pentane filtrate to -20 °C overnight. Combined crops yielded 1.37 g (71%) of product. X-ray quality crystals were obtained by cooling down to room temperature a filtered saturated diethylether solution of the title product. Selected IR data (cm -1 ): 3057(w), 3016(w), 2950(w), 2905(w), 2859(w), 1481(m), 1431(s), 1290(s), 1242(s), 1180(m), 964(s), 820(s), 771(s), 739(vs), 693(vs), 499(vs). Elemental analyses (C, H) of this compound were attempted 4 times on 4 different crystalline samples. The closest agreement between experimental and theoretical values was: Anal. found (calcd.) for C 35 H 44 FeOP 2 Si 2 : C, 62. 31 (64.21); H, 6.86 (6.77).

[Fe(PMe 3 ) 2 (dvtms)] (3). PMe 3 (4.40 mL, 4.40 mmol, 3.10 eq.), [Fe(acac) 3 ] (0.50 g, 1.42 mmol, 1.00 eq.) and dvtms (0.29 g, 1.56 mmol, 1.10 eq.) were suspended in diethylether (20 mL). Diethylaluminum ethoxide (1.50 mL, 9.94 mmol, 7.00 eq.) was added dropwise and the reaction mixture was stirred for 1 h. Diethylether was evaporated under reduced pressure leaving a blue oil which was dissolved in the minimum of pentane (approx. 3 mL). The blue solution was filtered with a filter cannula and the extract was cooled to -80 °C for 24 h. A small amount of blue solid formed that was filtered off from the blue solution. The blue extract was cooled to -80 °C for 2 days giving blue crystals which were isolated and dried under vacuum (0.11 g, 19% yield). X-ray quality crystals were obtained by storing a pentane solution of the title product at -34 °C for 3 days. Reliable elemental analysis could not be performed owing to the oily nature of the product at ambient temperature. 1 H NMR (300 MHz, C 6 D 6 , 300 K) δ(ppm) -7.44 (br. s), 0.0355 (br. s), 1.74 (m), 9.25 (s), 33.3 (s).

[Fe(pyNMeP( i Pr) 2 )(dvtms)] (4).

N-(diisopropylphosphino)-Nmethylpyridin-2-amine (0.97 g, 1.95 mmol, 1.05 eq.), [Fe(acac) 3 ] (0.66 g, 1.86 mmol, 1.00 eq) and dvtms (1.09 g, 5.84 mmol, 3.14 eq.) were suspended in diethylether (30 mL). Diethylaluminum ethoxide (2.00 mL, 13.0 mmol, 7.00 eq) was added dropwise and the reaction mixture was stirred overnight. The solution was filtered with a filter cannula and the solvent was evaporated under reduced pressure. Pentane was added and the solid formed was washed twice with pentane then dissolved in the minimum of diethylether and the solution was filtered and placed at -20 °C overnight giving a first crop of brown crystals (0.39 g). A second crop was obtained after cooling the diethylether filtrate to -20 °C overnight. By combining the two crops a total of 0.44 g (48%) of product was isolated. X-ray quality crystals were obtained by cooling a pentane/toluene solution of the title complex to -34°C. Anal. found (calcd.) for C 20 H 39 FeN 2 OPSi 2 : C, 51. 36 (51.49); H, 8.55 (8.43); N, 5.95 (6.00). Selected IR data (cm -1 ): 3037 (m), 2952 (m), 2923 (m), 2876(m), 1598(s), 1565 (m), 1473(s), 1330(m), 1299 (s), 1242(s), 1188(s), 967(vs), 858(vs), 825(vs), 776(vs), 569(s), 472(vs).

[Fe(dipe)(dvtms)] ( 5). 1,2-Bis(diisopropylphosphino)ethane (0.82 g, 2.97 mmol, 1.05 eq.), [Fe(acac) 3 ] (1.00 g, 2.82 mmol, 1.00 eq.) and dvtms (1.58 g, 8.49 mmol, 3.01 eq.) were suspended in diethylether (30 mL). Diethylaluminum ethoxide (3.00 mL, 20.0 mmol, 7.09 eq.) was added dropwise and the reaction mixture was stirred overnight. Diethylether was evaporated under reduced pressure leaving a blue oil which was triturated with pentane to form a blue solid that was washed twice (2x5 mL) with pentane and dried under vacuum affording 0.80 g of product. The combined blue extracts were cooled to -20 °C and the solid formed was isolated and dissolved in the minimum amount of ether. The solution was cooled to -20 °C giving 0.35 g of blue crystals. A total of 1.15 g (81%) of product was isolated. Anal. found (calcd.) for C 22 H 50 FeOP 2 Si 2 : C, 52.14 (52.37); H, 9.93 (9.99). Selected IR data (cm -1 ): 2953(s), 2894 (m), 2870 (m), 1601(w), 1532(w), 1458(m), 1287(s), 1238(s), 1186(s), 964(s), 859(s), 824(vs), 769(vs), 718(s), 707(s), 686(s), 667(s), 642(s), 621(s), 600(s), 578(s).

[Fe(dppm) 2 (C 2 H 4 )] ( 6). 1,2-Bis(diphenylphosphino)methane (4.00 g, 10.4 mmol, 2.04 eq) and [Fe(acac) 3 ] (1.77 g, 5.01 mmol, 1.00 eq) were suspended in toluene (50 mL). The suspension was chilled to 0 °C and diethylaluminum ethoxide (5.10 mL, 34.0 mmol, 6.78 eq.) was added dropwise and the reaction mixture was stirred for 1 h at 0 °C and 2 h at ambient temperature. The solid formed was collected by filtration and washed several times with diethylether (3 times 10 mL) and pentane (2 times 10 mL). The solid was dried under vacuum affording 3.56 g (83%) of an orange powder. Selected IR data (cm -1 ): 3053 (w), 2997(w), 2952(w), 2932(w), 2896(w), 1584(w), 1571(w), 1479(m), 1432(s), 1146(s), 1077 (m), 1053 (m), 1025(m), 767(s), 732(vs), 688(vs), 502(vs), 483(vs). 1 H NMR (300 MHz, C 6 D 6 , 300 K) δ(ppm) 2.22 (br. s, CH 2 dppm , 4H), 3.86 (m, CH 2 ethylene , 2H), 4.35 (m, CH 2 ethylene , 2H), 6.87-7.38 (H aromatics , 20H). 31 P{ 1 H} NMR (121 MHz, C 6 D 6 , 300 K) δ(ppm) 23.9 (br.s). Anal. found (calcd.) for C 54 H 48 FeP 4 : C, 73.32 (73.25); H, 5.69 (5.67).

[Fe(dppa) 2 (C 2 H 4 )] ( 7). 1,2-Bis(diphenylphosphino)amine (0.45 g, 1.17 mmol, 2.06 eq) and [Fe(acac) 3 ] (0.20 g, 0.57 mmol, 1.00 eq) were suspended in diethylether (10 mL). Diethylaluminum ethoxide (0.60 mL, 3.90 mmol, 6.85 eq) was added dropwise and the reaction mixture was stirred overnight. The volatiles were evaporated under reduced pressure and the orange solid was washed three times with pentane and dried under vacuum, affording 0.44 g (87%) of a light brown powder. X-ray quality crystals of 7 were obtained by cooling a saturated toluene solution of the title complex to -20 °C. Anal. found (calcd.) for C 50 H 46 FeN 2 P 4 : C, 37.59 (70.27); H, 2.94 (5.43); N, 2.06 (3.28). These considerable deviations regarding carbon and hydrogen microanalyses might be due to decomposition of the complex during work up resulting in the presence of inorganic materials in the sample. Selected IR data (cm - 1 ): 3054(w), 1591(w), 1526(w), 1483(w), 1436(s), 1383(w), 1123(s), 1096 (m), 1064 (m), 1027 (m), 998(w), 827 (m), 747 (m), 724(s), 691(vs), 554(vs), 508(vs).

[Fe(dppe) 2 (C 2 H 4 )] (8). 1,2-Bis(diphenylphosphino)ethane (6.87 g, 17.2 mmol, 2.03 eq) and [Fe(acac) 3 ] (3.00 g, 8.49 mmol, 1.00 eq) were suspended in diethylether (100 mL). Diethylaluminum ethoxide (8.90 mL, 59.4 mmol, 7.00 eq.) was added dropwise. The initially red solution turned yellow, then brown until a red solid precipitated. After the suspension was stirred for 2 h, the solid formed was collected by filtration with a filter cannula and washed several times with diethylether (5x10 mL). The solid was dried under reduced pressure, affording 6.37 g (85%) of a deep red powder. X-ray quality crystals were obtained by vapor diffusion of pentane into a concentrated toluene solution of the title complex. Selected IR data (cm -1 ): 3048(w), 3016(w), 2906(w), 1601 (w), 1531 (m), 1478 (m), 1431(s), 1160(m), 1151 (m), 1094 (m), 1065 (m), 1051 (m), 1027 (m), 872 (m), 818 (m), 793 (m), 738(s), 692(vs), 655(s), 515(vs), 502(vs). 1 H NMR (300 MHz, C 6 D 6 , 300 K) δ(ppm) 0.93 (m, CH 2 ethylene , 2H), 1.13 (m, CH 2 ethylene , 2H), 1.13 (m, CH 2 dppe , 2H), 2.10 (m, CH 2 dppe , 4H), 2.44 (m, CH 2 dppe , 2H), 6.35-7.87 (H aromatics , 20H). 31 P{ 1 H} NMR (121 MHz, C 6 D 6 , 300 K) δ(ppm) 78.9 (2P, t, J PP = 39.19 and 39.58 Hz), 95.5 (2P, t, J PP = 39.13 and 39.64 Hz). 13 C NMR (75 MHz, C 6 D 6 , 300K) δ(ppm) 25.97 (s, CH 2 ethylene , 2C), 29.27 (m, CH 2 dppe , 2C), 35.45 (m, CH 2 dppe , 2C), 126.86, 128.38, 131.8, 133.5, 142.8, 143.9, 145.6. Anal. found (calcd.) for C 54 H 52 FeP 4 : C, 73.68 (73.64); H, 6.05 (5.95).

[Fe(dppe)(PMe 3 )(3-hexyne)] (9). Complex 2 (0.21 g, 0.32 mmol, 1.00 eq.) was dissolved in diethylether (10 mL) and PMe 3 (0.96 mL, 0.960 mmol, 2.99 eq.) was added. The solution was cooled to -40 °C and 3-hexyne (0.26 g, 3.21 mmol, 10.0 eq.) was added. The reaction mixture was allowed to warm to room temperature and was stirred overnight. Then the diethylether was evaporated, the residue was extracted with pentane (5x3 mL) and filtered; the green filtrate was concentrated to approx. one third of its original volume and stored at -20 °C overnight. A solid formed that was isolated and dried under vacuum affording 0.05 g (28 %) of a green crystalline material. 1 H NMR (300 MHz, C 6 D 6 , 300 K) δ(ppm) 0.557 (br. s, CH 3 PMe3 , 9H), 1.49 (br. s, CH 3 3-hexyne , 6H), 2.10 (br. s, CH 2 3-hexyne , 4H), 3.24 (br. s, CH 2 dppe , 4H), 7.03 (s, CH PPh2 meta + para , 12H), 7.50 (d, CH PPh2 ortho , 8H). 31 P{ 1 H} NMR (121 MHz, C 6 D 6 , 300 K) δ(ppm) 30.09 (1P, t, J PP = 24.08 Hz), 106.3 (2P, t, J PP = 24.10 Hz). 13 C NMR (75 MHz, C 6 D 6 , 300K) δ(ppm) 14. 66, 22.85, 27.99, 31.70, 32.14, 131.17, 132.81, 141.23, 144.48, 189.44. Elemental analyses (C, H) of this compound were attempted 3 times on 3 crystalline samples. The closest agreement between experimental and theoretical values was: Anal. found (calcd.) for C 35 H 43 FeP 3 : C, 54. 16 (68.63); H, 3.76 (7.08). These considerable deviations regarding carbon and hydrogen microanalyses might be explained by the presence of inorganic material. Selected IR data (cm -1 ): 3044(w), 2954(w), 2898(m), 1431(s), 1267(s), 1092(s), 933(s), 741(s), 694(vs), 656(vs), 630(s), 517(vs), 497(vs), 482(vs).

Procedure for the cyclotrimerization of 3-hexyne The complex catalyst (typically 0.2 mmol) was charged in a Schlenk flask in the glovebox and dissolved in THF (5 mL). The substrate (typically 2.0 mmol of 3-hexyne) was then added to the solution. The reaction mixture was stirred at ambient temperature for 48 h under argon atmosphere. After 48 h the reaction was quenched with approx. 5 mL aqueous H 2 SO 4 (10 wt%). The solution was transferred into a separating funnel and the organic phase was collected. The aqueous phase was extracted twice with diethylether. The combined organic phases were analyzed by GC-MS.

Solid state NMR.

The natural abundance solid-state 13 C NMR spectrum of complex 5 was acquired on a Bruker Avance III spectrometer operating at an external magnetic field strength of 11.7 T (corresponding to a 13 C Larmor frequency of 125.7 MHz) using a Bruker HX 2.5 mm wide-bore MAS probe. The powdered sample was packed in a standard 2.5 mm ZnO 2 rotor in an Argon-filled glovebox, then placed in a sealed glass tube before removal from the glovebox in order to protect the sample from oxygen. Immediately before measurement, the sealed tube was opened and the rotor was quickly inserted into the MAS probe, and simultaneously spun to a rate of 31.25 kHz (corresponding to a 32 µs rotor period) while cooling the stator to a sample temperature of approximately 300 K using a Bruker BCU XTreme cooling unit. Nitrogen gas dried to a dew point of -80 °C was used for sample rotation.

The π/2 excitation pulse length was 2.1 µs (corresponding to an RF field strength of 119 kHz) at an offset of 270 ppm. Due to the broad span of 13 C resonances we employed short, high-powered adiabatic Tanh/Tan pulses (SHAPs) 24 to refocus the chemical shift evolution. 25 The pulses were 32 µs in length, and swept through 5 MHz with an RF field strength of 119 kHz. No 1 H decoupling was used during acquisition. Using a recovery time of 30 ms, 2M scans were acquired resulting in a total experiment time of 19.2 hours. DFT calculations. Complex 5 and the NMR reference compound tetramethylsilane (TMS) were fully optimized with DFT, employing the hybrid PBE0 functional, 26 Grimme's D3 dispersion correction with Becke-Johnson damping, 27 and a locally dense Gaussian basis set using def2-TZVP for Fe and def2-SVP for main group elements 28 as implemented in the Turbomole code. 29 All calculations for the Fe 0 complex 5 were done in vacuo for a triplet ground state. The initial model for the structure of 5 was built from the coordinates of the framework atoms of the closely related complex 1 obtained crystallographically, and substituting the Ph groups of the dppe ligand of 1 with i Pr moieties. A frequency calculation confirmed that the optimized structure is a true minimum, finding that all eigenvalues of the mass-weighted Hessian are positive.

The total PNMR shielding tensor is a sum of hyperfine and orbital shielding terms. The hyperfine shielding calculations were performed with two approaches, allowing to assess the importance of spin-orbit coupling. The results according to the recent formulation of Kurland-McGarvey PNMR theory 30 in terms of EPR property tensors by Vaara et al. 17 were compared to the "doublet-like" approximation neglecting all SOC effects (see Supporting Information). The temperature 300 K was used in all PNMR calculations.

The EPR g-tensor, zero-field-splitting (ZFS, D-) tensor, and hyperfine coupling tensors were calculated in Orca 31 using the PBE0 functional. For both g-and D-tensors the spin-orbit meanfield approximation 32 was applied to the spin-orbit matrix elements in the Breit-Pauli form. The basis used in the DFT structure optimizations was enhanced with diffuse functions optimized for molecular property calculations, 33 thus employing def2-TZVPD and def2-SVPD bases for Fe and main group elements, respectively. Van Wüllen's pre-factors for ZFS contributions from different spin channels were utilized. 34 Fermi-contact and spin-dipolar terms of HFC were calculated using def2-TZVPD and IGLO-III [START_REF] Kutzelnigg | NMR -Basic Principles and Progress[END_REF] basis sets for Fe and main group elements, respectively.

The 13 C orbital shielding tensors of TMS and complex 5 were calculated with gauge-including atomic orbitals 36 using Gaussian package. 37 The PBE0 functional and the above defined HFC basis were employed. The calculated 13 C isotropic reference shielding, 𝜎 $ 𝐫𝐞𝐟 , was 185.7 ppm and the resulting 13 C isotropic shift 𝛿 $ was obtained from the total isotropic PNMR shielding 𝜎 $ as 𝛿 $ = 𝜎 𝐫𝐞𝐟 -𝜎 $ .

(1)

ASSOCIATED CONTENT Supporting Information

Text, figures, tables, CIF files giving detailed experimental, analytical and spectral data for all new compounds, crystallographic data for 1-4 and 6, 8 and 9 and solid state NMR and computational details for the determination of the structure of 5. The Supporting Information is available free of charge on the ACS Publications website. CIF files have also been deposited with the CCDC and can be obtained on request free of charge, by quoting the deposi-tion numbers 1489026-1489029, 1497593-1497594 and 1510841.

Figure 1 .

 1 Figure 1. Thermal ellipsoid representation (at 50% probability) of complexes (from top to bottom) 1, 2, 3 and 4; H atoms are not shown for clarity. Selected bond lengths (Å) and angles (°): For 1: P1-Fe1-P2 84.75(3); P1-Fe1 2.302(10); P2-Fe1 2.316(10); C3-C4 1.419(5); C1-C2 1.409(5); for 2: P1-Fe1-P2 91.37(2); P1-Fe1 2.291(6); P2-Fe1 2.335(6); C3-C4 1.418(3); C1-C2 1.415(3); for 3: P1-Fe1-P1

Figure 2 .

 2 Figure 2. (a) X-ray structure of 1 (H atoms not shown for clarity). (b) DFToptimized structure of 5. (c) Visualization of positive (blue) and negative (red) isosurfaces of spin density distribution in 5 (for ±0.0002 a.u. isovalues). (d) 13 C PNMR spectrum of 5. The two CH2 carbons and their signals are labeled with a circle and a square in panels (c-d).

Figure 3 .

 3 Figure 3.Thermal ellipsoid representation (at 50% probability) of complex 7. H atoms are not shown for clarity. Selected bond length (Å) and angles (°): P2-Fe1-P4 71.70(2); P29-Fe1-P31 71.78(2); C57-C56 1.423(3); C56-Fe1 2.069(2); C57-Fe1 2.050(2); P4-Fe1 2.189(6); P2-Fe1 2.209(6); P31-Fe1 2.198(6); P29-Fe1 2.175(6).

Figure 4 .

 4 Figure 4. Thermal ellipsoid representation (at 50% probability) of complex 8 (50% probability displacement ellipsoids). H atoms are not shown for clarity. Selected bond length (Å) and angles (°): P2-Fe1-P5 84.35(8); P33-Fe-P30 83.72(8); C59-C58 1.441(11); C59-Fe1 2.082(8); C58-Fe1 2.099(7); P5-Fe1 2.229(2); P2-Fe1 2.238(2); P33-Fe1 2.214(2); P30-Fe1 2.210(2).

Figure 5 .

 5 Figure 5. Thermal ellipsoid representation (at 50% probability) of complex 9. H atoms are not shown for clarity. Selected bond length (Å) and angles (°): P11-Fe1-P2 86.76(5); P11-Fe1 2.1501(14); P2-Fe1 2.136(14); P30-Fe1 2.150(14); Fe1-C34 1.874(5); Fe1-C35 1.860(5); C34-C35 1.303(6).

Table 1 .

 1 Experimental and calculated 13 C NMR shifts (in ppm, relative to TMS) of the -(CH2)2-bridge of the bidendate dipe ligand.

	Structure	g, D	PNMR b	δ C
	DFT a	-	no SOC	-1017, -1052
	DFT a	DFT	full	-1047, -1085

Table 2 .

 2 Catalyzed cyclo-trimerization of 3-hexyne.

	Catalyst	Conversion (Selectivity HEB) (wt %) a
	1	35 (100)
	2	12 (100)
	4	11 (100)
	5	49 (48.2)
	6	0 (-)
	8	0 (-)
	Conditions: catalyst (0.20 mmol), 3-hexyne (2.0 mmol), r.t., THF
	(5 mL), 48 h.

a determined by GC-MS. Scheme 3. Suggested mechanism for alkyne cyclo-trimerization.

ACKNOWLEDGMENTS

We gratefully acknowledge IFP Energies nouvelles, the TGIR-RMN-THC Fr3050 CNRS, the European Research Council under the European Union's Horizon 2020 Research and Innovation Programme (Grant 648974 "P-MEM-NMR") and the European Union's Seventh Framework Programme (FP7-PEOPLE-2012-ITN 317127 "pNMR") for the support.

AUTHOR INFORMATION

Corresponding Author * E-mail for P.-A. B: pierre-alain.breuil@ifpen.fr

The authors declare no competing financial interest.


Philippe Jonnard

Meiyi Wu

Jean-Michel André

Karine Le Guen

Franz Schäfers

Andrey Sokolov

Elena O Filatova

Adriano Verna

Zhanshan Wang

Qiushi Huang

Dichroism of x-ray fluorescence under standing waves regime in magnetic periodic multilayers

Keywords: dichroism, standing waves, interface, x-ray emission, fluorescence, multilayer, cobalt

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

The x-ray standing waves (XSW) technique consists in measuring the intensity of a secondary emission (photoelectrons, Auger electrons or fluorescence photons) as a function of the glancing angle of the incident x-ray beam on the sample surface [1,[START_REF] Zegenhagen | The X-Ray Standing Wave Technique: Principles and Applications[END_REF]. This is done with a sample presenting a periodic structure, a crystal or a multilayer, and under the Bragg condition, i.e. when the glancing angle is varying around the Bragg angle set by the incident photon of a given energy and the period of the structure. Owing to the strong standing wave developing into the sample in this condition, a depth selectivity of the excitations and ionizations can be obtained [START_REF] Watanabe | [END_REF][4][5][6][7]. This makes the XSW technique particularly useful for the study of periodic structures and their interfaces.

Following the pioneering theoretical study by Strange et al. [8] and experimental work by Hague et al. [9], it is now well established that the x-ray fluorescence emitted by magnetic materials presents an x-ray magnetic circular dichroism (XMCD). Consequently, it can be conjectured that the fluorescence (that is secondary x-ray emission generated by a primary xray source) should present a XMCD signal modulated by standing waves in periodic magnetic multilayers. In the present study, we give an experimental proof of this phenomenon.

Until this present work, XMCD has been frequently exploited in conjunction with multilayer systems through resonant scattering (that is in the vicinity of an absorption edge) in transmission or reflection mode to deduce optical constants [10], magnetic moments [11] or for quantitative polarization analysis [12] to be non-exhaustive [13,14]. XMCD was extensively used in SW regime detecting the photoelectron current in order to analyze the magnetic properties of buried interfaces [15,16]. But XMCD in x-ray emission (XE) and in the SW regime, referred hereafter as XSW-XE-XMCD has never been reported to our knowledge.

To perform this study, we have chosen to use the Co/Mg multilayer system that has been widely investigated and well characterized by means of a large variety of methods [6,17,18]. It has been shown that the Co/Mg interfaces are rather abrupt with no significant interdiffusion. It is the purpose of this paper to establish the validity and to evidence the interest of the XSW-XE-XMCD. The idea is to combine the depth selectivity of the XSW technique, which has been successfully employed to determine the interfaces of Bragg multilayers [6] to both the chemical and magnetic selectivity of XE-XMCD in order to achieve a sub-nanometer chemically selective characterization of a magnetic profile. Indeed x-ray emission spectroscopy gives local information since it is a core level spectroscopy. It has also the advantage over Auger or photoelectron spectroscopies to probe the bulk properties. In addition, XE-XMCD provides information about the spin-resolved density of occupied states. Let us note that x-ray absorption XA-MCD is not compatible with the XSW technique since in the absorption mode the incident energy is varied while the standard XSW method requires a fixed energy. Let us mention that an important feature of emission spectroscopy is that owing to detection of photons and not of charged particles, strong magnetic fields can be applied to the sample without risk of measurement artifacts.

SIMULATIONS

The simulation model is presented in [19] and we only recall here its main characteristics. The intensity of the characteristic emission is proportional to the quantity 2 , where C(z) is the concentration of the emitting element at a depth z under the surface of the multilayer, |E ex (i,z)| 2 the intensity of the exciting electric field at a depth z and under a given glancing incidence angle i, and |E fluo (d,z)| 2 the fluorescence intensity arriving at the detector under a detection angle d from a source located at depth z. The depth distribution of the incident electric field is calculated using the recurrent formalism widespread to evaluate the optical properties of a stack from the optical constants and thicknesses of its various layers [START_REF] Berning | Theory and calculations of optical thin films[END_REF][START_REF] Bedzyk | X-ray standing wave in multilayers[END_REF]. The emitted intensity is calculated by applying the reciprocity theorem. Owing to the large distance between the detector and the source with respect to the layer thickness, E fluo is calculated by using the same formalism as the one used to calculate E ex , assuming a fictive source located at infinity in the detection direction.

C(z) |E ex (i,z)| 2 |E fluo (d,z)|
To emphasize the potential of the proposed methodology, we make XSW-XE-XMCD simulations for stacks presenting different kinds of defects. For these simulations, the optical constant of cobalt is taken from the literature [START_REF] Zhu | Lensless Holography Methods for Soft Xray Resonant Coherent Imaging[END_REF], owing to its fine structure in the vicinity of the Co L 3 (2p 3/2 ) and L 2 (2p 1/2 ) edges and is given for left and right helicities (labelled "L" and "R" respectively) of the incident radiation. We consider three stacks having the same period but different structural and magnetic characteristics at the interfaces between the constituent layers, as shown in Fig. 1 As suggested from previous works [6], this structure is expected to best represent the multilayer we have measured in our experiment; 2) Addition of Co dead (non-magnetic, noted Co_DL) layers being thick of two atomic planes at all the interfaces; the optical constant of the dead layer is the average of the Co optical constants for left and right helicities [START_REF] Zhu | Lensless Holography Methods for Soft Xray Resonant Coherent Imaging[END_REF]: 3) Addition of MgCo interphases (index calculated from CXRO [START_REF]CXRO X-Ray Interactions With Matter at <http[END_REF] with a density of 6 g/cm3, same for R and L polarizations) having 0.5 nm thickness at all interfaces (0.25 nm in Mg and Co layers): For each polarization, the XSW curve, i.e. the angular distribution of the intensity of the Co Lα characteristic emission is calculated when the incident photon energy is set just above the Co L3 edge, where absorption is maximum. Then the XSW-XE-XMCD curve is obtained by calculating the dichroic signal, i.e. making the difference between the XSW curve obtained with R and L polarizations respectively and then normalizing with respect to the sum of these two XSW curves. They are labeled (R-L)/(R+L) and shown in Figure 1(b) for the three considered stacks. First, it can be seen in the vicinity of the Bragg angle that a strong modulation of the dichroic signal exists. Then, depending on the kind of defect present at the interfaces of the stack, the maximum is shifted either to low (interphase formation) or high (dead layer) angles with respect to the stack without interface defect. This shifts are small, less than 0.1°, but should be observed in an optimized experiment. Finally, let us also note that the shape, width and background of these curves also depend on the kind of defects present in the stack. We show in Figure 2 the real and imaginary parts of the cobalt index extracted from Ref. [START_REF] Zhu | Lensless Holography Methods for Soft Xray Resonant Coherent Imaging[END_REF] as a function of the energy of the incident photons in the Co L 2,3 range (~ 770 -800 eV) and of the helicity of the radiation. The anomalous behaviour of the optical index is clearly seen in the vicinity of the cobalt edges. However, let us note that the optical indices being sensitive the chemical state of the cobalt atoms, it could be that there is still a large difference between the indices of the Co layers of our sample and the ones of Ref. [START_REF] Zhu | Lensless Holography Methods for Soft Xray Resonant Coherent Imaging[END_REF]. Thus results of the simulations should be used with caution. For the other elements present in the multilayer, indices from the databases, such as CXRO [START_REF]CXRO X-Ray Interactions With Matter at <http[END_REF], can be used as they present no absorption edge in the Co L range. Finally, let us note that the CXRO database does not reproduce correctly the optical constant of cobalt, see Figure 2, as at Co L 3 only an absorption edge is present rather than a peak and the amplitude of the real part is underestimated, and no feature exists at the Co L 2 edge.

Figure 2: Real and imaginary parts of the refraction index of cobalt in the L 2,3 range extracted from Ref. [START_REF] Zhu | Lensless Holography Methods for Soft Xray Resonant Coherent Imaging[END_REF], for L and R polarized radiations and comparison with the values of the CXRO database [START_REF]CXRO X-Ray Interactions With Matter at <http[END_REF].

EXPERIMENTAL DETAILS

The sample was prepared by magnetron sputtering and had the following designed structure: vacuum / B 4 C (3.0 nm) / [Co (2.6 nm) / Mg (5.2 nm)]x30 / Si substrate. The boron carbide capping layer is to prevent the oxidation of the stack. From x-ray reflectivity measurements at 8.05 keV performed just after the preparation of the sample, the actual thicknesses of the Co and Mg layers are 2.6 and 5. 4 The measurements were performed at the BESSY-II synchrotron facility using the reflectometer at the Optics beamline [START_REF] Schäfers | [END_REF]25]. The beamline is equipped with a plane-grating monochromator in collimated light (c-PGM) and can be tuned to linearly (in-plane) or elliptically polarised (off-plane) bending magnet radiation. The multilayer was first magnetized outside the experimental chamber and then measurements were taken for reversed R and L helicities of the incident radiation. Let us note that:

-magnetization was applied with a permanent magnet so that the direction of magnetization is in the plane of the sample and parallel to the scattering plane; -changing the polarization leads to a strong variation of the incoming intensity and to a shift of the photon energy requiring a careful calibration and normalization procedure.

We measured Co L emission spectrum of the magnetized Mg/Co periodic multilayer mirror. An incident monochromatic x-ray beam was used, with both left and right circular polarizations. Some measurements have also been done with linear polarization. The characteristic emission of the cobalt atoms generated upon the x-ray irradiation, i.e. the fluorescence, was measured with a silicon drift detector (SDD, from Ketek). The SDD was installed a few centimeters above the sample and perpendicular to the incident x-ray beam as depicted in Figure 3. Its spectral resolution is around 70 eV in the Co L range. All emission spectra were obtained with at least 20000 counts at their maximum, in order to obtain a statistical uncertainty lower than 1%. They were corrected for the dead time of the detector, which was about 1%. By rotating the sample, the glancing angle of the incident beam on the sample surface was changed. In this way it is possible to shift along the depth direction the x-ray standing wave field inside the multilayer to obtain a variation of the fluorescence intensity. Such an angular variation is hereafter called a XSW curve. The precision of the incidence angle is 0.02°, and the positioning accuracy of the sample surface is approximately 0.02 mm. The focal size is 0.36 x 0.2 mm, and the energy resolution was set to 500 meV.

In Figure 4 the x-ray absorption spectra in the Co L 2,3 range clearly evidence the dependence of the absorbed intensity on the helicity of the incident radiation. These spectra are obtained at a glancing angle of 20°, in the total electron yield mode monitored from the measurement of the drain current of the sample. All spectra are normalized with respect to both their acquisition time and the intensity of the incoming beam. The absorption in the Co L 3 range is larger with R polarization while the absorption in the Co L 2 range is larger with L polarization. Measurement in linear polarization gives an intermediate behaviour. The TEY measurements validate the normalization process and so the same normalization procedure was applied on emission spectra. Moreover, they confirm that the magnetization of the sample was applied in the correct direction but show that the amplitude of the dichroic effect is not so strong as expected [START_REF] Zhu | Lensless Holography Methods for Soft Xray Resonant Coherent Imaging[END_REF], probably due to a too weak magnetization that did not reach its saturation value.

To generate the fluorescence of the cobalt atoms, three different incident photon energies were chosen from the absorption spectrum: at the maximum of the L 3 absorption, at the maximum of the L 2 absorption and about 15-20 eV above the L 2 edge.

RESULTS AND DISCUSSION

An example of the measured and decomposed fluorescence spectra is shown in Figure 5. In the main peak of the experimental spectrum are present the unresolved Co Lα (3d -2p 3/2 electron transition) and Lβ (3d -2p 1/2 transition) characteristic emissions [26]. Indeed, owing to the spectral resolution of the SDD, the energy difference between the Lα and Lβ emissions represents around two channels. The shoulder toward the low photon energies (small channel numbers) is mainly caused by incomplete charge collection with a small contribution of the Co Ll (3s -2p 3/2 transition) and Lη (3s -2p 1/2 transition) emissions [26]. Let us note that the intensity of this structure strongly depends on the count rate. Since its tail is of significant intensity in the range of the Co Lαβ emission, this introduces an uncertainty on the intensity values obtained from the fitting process.

To extract the contribution of Co Lαβ emissions alone, we first fit the sum of all the obtained spectra with three Gaussians, regardless the energy or polarization of the incident beam. Figure 5 also shows the fitting result with a main contribution due to Co Lαβ emissions (shadowed area) as well as the secondary peak in the lower channel part. A tiny contribution located at higher channel (around 120) is also found. It should be the Co Lβ 3,4 (870 eV, 3d 3/2 -2s 1/2 transition [26]) emission. A linear background is subtracted. Then in the following, to fit each spectrum obtained under a given polarization and a given angle, both the position and width of these three Gaussian functions are fixed and only their intensity is fitted. Finally, for a given polarization, the intensity of the Co Lαβ component is extracted for all angles to obtain the corresponding XSW curve. In Figure 6 are presented the XSW curves of the extracted Co Lαβ intensities for the three considered incident energies (at the maximum of the L 3 (a) and L 2 (b) absorption and above the L 2 edge (c)), with either left or right circularly polarized lights. The 3 -9° angular range spans the range first diffraction order of the multilayer. The value of the Bragg angle is determined by x-ray reflectivity using the same incident photon energy as for the fluorescence measurement. The error bars represent the counting statistics uncertainty with three standard deviations. However, the observed fluctuations are larger and probably come from the fitting process. When measurements are done at the L 3 maximum of the absorption, curves are almost parallel but the L one is about 10% more intense than the R one. At the L 2 maximum, curves are quite parallel but the L one is about 5% more intense than the R one. These intensity differences are due to the dichroism in the emission of the cobalt atoms. Above the L 2 edge, curves are almost superimposed, within the experimental uncertainty, except toward the lower angles. As we know from our previous studies that the interfaces between the Mg and Co layers are sharp [17,18], we expect that Co atoms are in their standard magnetic state (as in bulk Co) in the whole layer and that only the Co interfacial atoms in contact with the Mg atoms change their magnetic property. Indeed, the magnetic moments and interactions at an interface (or a surface) can be different from the bulk, both for extrinsic (roughness, interdiffusion, strain) and intrinsic (different magnetic and chemical environments) effects experienced by the interfacial atoms [27][28][29]. Consequently, at the angles corresponding to the positions of the From Figure 6 we calculate the dichroic XSW-XE-XMCD curves calculated as (L-R)/(L+R) presented in Figure 7 at the L 3 and L 2 maxima and above the L 2 edge. We see when the incident energy is on the L 3 edge (Fig. 7(a)) and on a particular angular range from 5 to 6.5° that the dichroic effect has significantly changed. However, the change spans a large angular range and not the narrow one expected when crossing a sharp interface. The simulation presented in Figure 1(b) can only reproduce the main feature of the experimental curve at the Co L 3 edge, a wide peak whose maximum is located around 5.8°. The variations at the L 2 edge (Fig. 7(b)) are in the opposite of the ones at the L 3 edge, with a minimum around 5.8°, but are at the limit of the uncertainty. Above L 2 (Fig. 7(c)) we can consider that there is no dichroism within the experimental uncertainty. The simulation of the depth distribution of the intensity of the electric field in the perfect Mg/Co multilayer (without interface defect) is presented in Figure 8(a), with the incident photon energy set at the Co L 3 absorption maximum and under the Bragg condition (grazing angle set to 5.6°). Further simulations in the 4 -7° angular range, see an example in Figure 8(b) with the grazing angle set at -0.5° from the Bragg condition, show that the maximum of the electric field always stands in the Mg layers whatever the helicity, resulting that on XSW curve of Co Lα emission (see Fig. 6) we observe only "valley" and no "peak" (generally the observed fluorescence XSW feature is a valley followed by a peak or a peak followed by a valley). For the incident photon energy at the Co L 2 edge or above, the maximum of the electric field is always varying within the Mg layer while rotating the grazing angle around the corresponding Bragg angle. Let us note that with the CXRO values of the optical indices, it would be possible to put the maxima of the electric field at the Co-on-Mg interfaces. If it was possible to set the maxima electric field at interfaces, where a reduced magnetic moment for the interfacial Co atoms is expected due to a reduced number of exchange interactions with first neighbours, then the dichroism should decrease and we should observe a dichroic signal going toward zero. Let us note that in the case of sharp interfaces an alignment of the magnetic moments can occur and, in this case, would reinforce the dichroism. The impossibility to put the maxima of the electric field at the interfaces comes from the large dispersive effect occurring taking place in the Co L range. We noted that this also induced a behaviour of the reflectivity curves quite different from the Bragg law. We show in Figure 9 the angular position, measured on reflectivity curves, of the first diffraction order Bragg peak as a function of the incident energy of the photons. For comparison, the position of the Bragg peak, calculated applying the Bragg law for a structure of period 7.8 nm is also plotted. This illustrates that the measured Bragg angle values deviate from the Bragg law in the region of the L 3 and L 2 edges and demonstrates the existence of anomalies owing to the presence of the Co L 3 and L 2 edges.

CONCLUSION

Owing to the complexity of the phenomena taking place at the interfaces of magnetic hetero-structures, such as electronic, orbital, and structural effects, spin transport, spin texture [27], it becomes critically important to progress towards a better understanding in the magnetic properties and the mechanism of formation of interfaces of magnetic thin film structures. As a consequence, it is extremely necessary to develop new approaches to the study such systems in order to develop future performing devices.

In this context, we presented a first test to determine the magnetic state of cobalt atoms in Co/Mg hetero-structures by using an original combination of dichroism of fluorescence (XE-XMCD) and x-ray standing waves (XSW). The present work must be considered as a test of feasibility. From the experimental point of view the operating conditions were not optimal since the sample was not fully magnetized and so the dichroic effect was limited. The counting statistics has also to be improved in order to reduce the uncertainty of the measurements. Moreover, when taking into account realistic optical indices, it is not possible to put the maxima of the electric field at the Co-on-Mg or Mg-on-Co interfaces, so that it was not possible to obtain the Co Lαβ emission selectively excited at these locations. As the interfaces in the Mg/Co system are sharp and present no interdiffusion, limited information about the physicochemical state of an interdiffused layer can be determined from our experiments with this sample. Nevertheless it turns out from this work that XE-XMCD in XSW regime can be observed and should provide interesting data about buried interface in terms of chemical and magnetic profile as suggested by our simulations and by previous works using a standing wave generator to provide in depth-selectivity to study magnetic buried interfaces [15,16,30].

To improve the next experiments, the perspectives are: first, use a new generation SDD in order to get rid of, or at least minimize its sensitivity to the count rate, the peak due incomplete charge collection and to be able to work with higher counting rates to minimize the acquisition time; use a crystal spectrometer to resolve Co Lα and Lβ emissions and do not observe a dichroic effect which is the mean of the dichroic effect occurring for each of these emissions and that can have opposite behaviours. Moreover, it has been recently demonstrated a large dichroism in the Fe Kα emission on a iron single crystal [31]. Thus, it could be envisaged to apply the proposed methodology to the study of single crystals provided the wavelength of the incident radiation is consistent with the inter-reticular distance, i.e. if working in the hard x-ray range.

  (a). The three stacks are the following. 1) Structure without interface defects: B 4 C (4 nm) / [Co (2.60 nm) / Mg (5.41 nm)]x30 / Si substrate;

B 4 C

 4 (4 nm) / [Co_DL (0.44 nm) / Co (1.72 nm) / Co_DL (0.44 nm) / Mg (5.41 nm)]x30 / Si substrate;

B 4 C

 4 (4 nm) / [CoMg (0.5 nm) / Co (2.10 nm) / CoMg (0.5 nm) / Mg (4.91 nm)]x30 / Si substrate.

Figure 1 :

 1 Figure 1: (a) Scheme of one period of the considered Co/Mg multilayer: (1) without interface defects; (2) with the presence Co dead layers at the interfaces; (3) with CoMg interphases at

Fig. 3 :

 3 Fig. 3: Scheme of the instrumental setup and geometry of the experiment. The sample is rotated in an angular range around the Bragg angle defined by the period of the multilayer and the wavelength of the incident radiation.

Fig. 4 :

 4 Fig. 4: Dichroism of the Co L 2,3 absorption spectrum of the magnetized Co/Mg multilayer measured with L (red line) and R (blue line) circularly polarized radiations. The three vertical bars show the three incident photon energies chosen to perform the fluorescence measurements. The insets show an enlargement of the regions of the Co L 3 and L 2 maxima.For comparison, the measurement obtained with linear radiation (green line) is also shown.

Fig. 5 :

 5 Fig. 5: Fluorescence spectrum and extraction of the different components from the sum of all fluorescence spectra. In the shadowed area are the Co Lαβ emissions, whose intensity is taken into account to establish the XSW curves.

Fig. 6 :

 6 Fig. 6: XSW curves of Co Lαβ intensity from the magnetized Mg/Co multilayer measured with three different incident photon energies: at the L 3 maximum (a), at the L 2 maximum (b) and above the L 2 edge (c) and with two opposite helicities (L, red line; R blue line). The vertical bar marks the position of the Bragg angle. The error bars represent the counting statistics.

  ) of the electric field at the interfaces between the Mg and Co layers, expect a modification of the dichroism.

Fig. 7 :

 7 Fig. 7: XE-XSW-XMCD curves, dots and thin dashed line, i.e. dichroism of the XSW curves of the Co Lαβ intensity from the Co/Mg magnetized multilayer, at the three considered incident photon energies: at the L 3 maximum (a), at the L 2 maximum (b) and above the L 2 edge (c). The thick line is obtained from the original experimental points through a decimation procedure of neighbouring values. The error bars represent the standard deviation of the averaged neighbouring values.

Fig. 8 :

 8 Fig. 8: Simulation of the depth distribution of the intensity of the electric field within the Mg/Co multilayer (a) under the Bragg condition, grazing angle set to 5.6°, and (b) at 5.1°, with the incident photon energy set at the Co L 3 maximum and using L (solid curve) and R (dotted curve) helicities of the radiation. Only the region of the B 4 C capping layer and the two first Co/Mg periods is depicted.

Fig. 9 :

 9 Fig.9: Angular position of the Bragg peak as a function of the energy of the incoming photons in the Co L range (dots), compared to the Bragg law calculated with a structure of 7.8 nm period (solid line).

  Photon energy (eV)

  nm respectively.

		0.010
						imaginary part / R
		0.008				imaginary part / L real part / R
						real part / L
		0.006				imaginary part / CXRO real part / CXRO
	Refractive index	0.000 0.002 0.004
		-0.002
		-0.004
		-0.006
		770	775	780	785	790	795	800
					Energy (eV)

Acknowledgments

Dr. R. Delaunay from LCPMR is thanked for is help regarding the magnetization of the sample. Dr. Y. Ménesguen from CEA-LNHB is thanked for his advices regarding the SDD. A.V. is thankful to Regione Lazio and CRUL for financial support.