Ekaterina M Titova

S M Wahidur Rahaman

Elena V Shubina

Rinaldo Poli

Natalia V Belkova
email: nataliabelk@ineos.ac.ru.

Eric Manoury
email: eric.manoury@lcc-toulouse.fr.

S M Wahidur

Elena S Shubina

Catalytic redox isomerization of allylic alcohols with rhodium and iridium complexes with ferrocene phosphine-thioether ligands

Keywords: Allylic alcohols, Redox isomerization, Hydrogenation, Transfer hydrogenation, Rhodium, Iridium, Hydrogen-free activation

come

product was the saturated alcohol 1-phenyl-1-propanol (9a) when working under a 30 bar H 2 pressure, but activation for only 1 min under H 2 pressure and then continuation under 1 bar of H 2 or Ar led to increasing amounts of the allylic isomerization product propiophenone (8a).

Continued reaction under H 2 converted (8a) into (9a). The Rh precatalysts were more active than the Ir analogues. For the rhodium precatalysts (3) and ( 4), the redox isomerization reaction could be carried out after precatalyst activation in iPrOH/MeONa under Ar at 82°C (without H 2 ) with complete conversion in 1 h (1% catalyst loading). However, longer reaction times resulted in slow transfer hydrogenation of (8a) leading to (9a) with low enantiomeric excess. Extension of the H 2free activation of the Rh precatalysts in iPrOH to other allylic alcohol substrates (7b-d) yielded the corresponding ketones with good to excellent yields and excellent chemoselectivities under appropriate conditions.

Introduction

The isomerization of primary and secondary allylic alcohols into the corresponding aldehydes and ketones is of a great interest, especially because it is an atom economical reaction and provides valuable synthetic intermediates [1][2][3][4][5][6][START_REF] Shul | pin, Organic Reactions Catalyzed by Metal Complexes[END_REF]. Great effort has been devoted to the development of this reaction leading to significant achievements. Efficient asymmetric catalytic systems have been developed [START_REF] Cahard | [END_REF][9][10][11][12][13][14][15][16][17][18][19][20][21][22] as well as catalytic systems in green solvents [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37] such as water or supported versions [38][39][40]. An additional interest of this reaction is the possibility to couple it with other transformations by taking advantage of the high reactivity of the enolate-intermediates with various electrophiles [41]. Thus, tandem reactions were used for the preparation of αhalogenoketones [42][43][44], β-hydroxy and β-amino ketones [45][46][47][48], cyclopentenones [49], etc [18,21]. Allylic isomerization has also been coupled with hydrogenation or transfer hydrogenation to yield saturated alcohols [17,20,31,54]. Although various metals such as iron, copper, nickel or palladium [46,55] have been used, most of the catalysts used so far are based on ruthenium [56][57][58][59][60][61][62][63][64][65], rhodium and iridium [66][67][68][69][70], mainly with phosphorus and nitrogen-donor ligands [1][2][3][4][5][6]. In this article, we wish to present our results on the first use of chiral P,S ligands [71][72][73][START_REF] Malacea | Phosphorus-Sulfur Ligands in[END_REF][START_REF] Lam | [END_REF] in the redox allylic isomerization reaction. Our group has contributed to the development of chiral ligands based on P and S donor atoms with the synthesis of the 1,2-substituted ferrocenes (P,SR)

shown in Figure 1 [START_REF] Manoury | Phosphine-Containing Planar Chiral Ferrocenes: Synthesis, Coordination Chemistry and Applications to Asymmetric Catalysis[END_REF]. These ligands can be efficiently obtained in enantiomerically pure form or as a racemic mixture [START_REF] Manoury | Phosphine-Containing Planar Chiral Ferrocenes: Synthesis, Coordination Chemistry and Applications to Asymmetric Catalysis[END_REF]. The use of these ligands in complexes of different metals has led to a number of catalytic applications in asymmetric allylic substitution [START_REF] Routaboul | [END_REF]78], asymmetric methoxycarbonylation of alkenes [79] and hydrogenation of alkynes, alkenes, imines and ketones [80][81][82][83][84]. Here we report the application of the rhodium and iridium complexes [M(P,SR)(diene)X] (M = Ir, Rh; diene = cyclooctadiene, norbornadiene; X = BF 4 , Cl, see Figure 2) [80,81,86] in the isomerization of allylic alcohols.

Experimental

General Considerations.

All reactions were carried out under an argon atmosphere using standard Schlenk techniques. Solvents were carefully dried by conventional methods and distilled under argon before use. The iridium and rhodium complexes [M(P,SR)(diene)X] (M = Ir, Rh; R = tBu, Bz; diene = NBD, COD; X = BF 4 -, Cl) were prepared according to a published procedure from (R/S)-2-diphenylphosphanyl-(R-thiomethyl)ferrocene ligands (R = tBu, Bz) and [Ir(COD)Cl] 2 [80,81], [86]. Optical purities and the yields for the hydrogenation experiments were determined by NMR spectoscopy and GC: Supelco BETADEX™ 225 (reactions of 6a, isotherm at 105°C), Supelco SPB-20 (reactions of 6e, 30°C for 7 minutes then heating 15°C/min up to new isotherm at 120°C), NMR yield determination (reactions of 6b-d).

[Rh(COD)Cl] 2 , [Rh(NBD)Cl] 2 or [Rh(COD) 2 ]BF 4

General procedure for the 1-phenyl-2-propene-1-ol allylic isomerization in THF.

A solution containing 6.4•10 -3 mmol of precatalyst and 0.13 mmol of substrate (20 equiv.) in 2 mL of THF was transferred into a 5 mL glass vial which was then placed under argon into a stainless steel autoclave equipped with a magnetic stirring bar. The reaction vessel was pressurized with H 2 to 30 bars and stirred for the desired time at room temperature. Then pressure was released and the reaction vessel was stirred for the desired time at controlled temperature under a dihydrogen atmosphere at 1 bar. Alternatively, after venting the H 2 pressure used for the catalyst activation, the residual H 2 was purged with argon by continuous flushing before continuing the reaction. The pure products were obtained by chromatography of the reaction mixture on silica gel using dichloromethane as eluent and then analyzed by NMR spectrosopy and chiral GC for the determination of the yields and enantiomeric excesses.

General procedure for the 1-phenyl-2-propene-1-ol allylic isomerization in iPrOH 2.3.1. Precatalyst activation by H 2 .

A solution containing 6.4•10 -3 mmol of precatalyst, 3.2•10 -2 mmol of CH 3 ONa (5 equiv.) and 0.64 mmol of substrate (100 equiv.) in 2 mL of isopropanol was transferred into a 5 mL glass vial which was then placed under argon into a stainless steel autoclave equipped with a magnetic stirring bar. The reaction vessel was pressurized with H 2 to 30 bars and stirred for the desired time at controlled temperature. The reaction was stopped by venting the H 2 atmosphere. The pure products were obtained by chromatography of the reaction mixture on silica gel using dichloromethane as eluent and analyzed by NMR spectroscopy and chiral GC for the determination of the yields and enantiomeric excesses.

Precatalyst activation by iPrOH.

A solution containing 6.4•10 -3 mmol of precatalyst, 3.2•10 -2 mmol of CH 3 ONa (5 equiv.) and 0.64 mmol of substrate (100 equiv.) in 2 mL of isopropanol was prepared in a Schlenk tube under an argon atmosphere and stirred for the desired time at the reflux temperature. The pure products were obtained by chromatography of the reaction mixture on silica gel using dichloromethane as eluent and analyzed by NMR spectroscopy and chiral GC for the determination of the yields and enantiomeric excesses.

Results and discussion

Catalytic studies carried out in THF

The substrate chosen for our initial studies was racemic 1-phenyl-2-propene-1-ol (7a). We first attempted the thermal activation of the ( 1)-( 6) precatalysts to carry out the redox isomerization of allylic alcohol (7a), but no rearrangement was observed in refluxing THF overnight. This lack of reactivity may be related to the need to activate the precatalyst by diene ligand removal, as discussed previously [80,83,85]. We therefore decided to use a hydrogen source to reduce the diene ligand in order to open the metal coordination sphere [14,15,19]. When the reaction was carried out under pressure (30 bar of H 2 ) and at room temperature, allylic alcohol was converted to 1-phenyl-1-propanol (9a) (see Table 1). Interestingly, the rhodium catalysts were more efficient than the iridium one in this process and, as already documented in the literature for other hydrogenation reactions [87], the complexes bearing the nbd ligand are more active than the corresponding complexes bearing the cod ligand. Although this phenomenon may be interpreted as an effect of the diene nature on the catalytic activity, implying that the diene remains coordinated to the metal in the active species, it is also consistent with the well known faster removal of nbd by hydrogenation relative to cod and thus to a shorter induction time for the nbd system in catalysis [87]. Alcohol (9a) can result from the direct hydrogenation of the C=C bond of (7a) or from the hydrogenation of the C=O double bond of the product of redox isomerization, propiophenone (8a) (see scheme 1) [START_REF] Shilov | Shul'pin, Activation and Catalytic Reactions of Saturated Hydrocarbons in the Presence of Metal Complexes[END_REF]. No ketone (8a) has been observed during these experiments, even after incomplete conversions showing that if any (8a) produced, it must be quickly hydrogenated to (9a) under these experimental conditions. In addition, 1-phenyl-1propanol (9a) was found to be racemic indicating that either the ketone hydrogenation has very low enantioselectivity or that (9a) results from the direct C=C double bond hydrogenation of racemic (7a) without any chiral resolution, leaving the asymmetric carbon already present in (7a) untouched.

Scheme 1.

Possible pathways leading from [START_REF] Shul | pin, Organic Reactions Catalyzed by Metal Complexes[END_REF] to [START_REF] Cahard | [END_REF] and (9).

Table 1

Hydrogenation of 1-phenyl-2-propene-1-ol (7a) in THF. а

Entry

Catalyst Conversion, % Yield of (8a), % Yield of (9a), % In order to avoid full substrate hydrogenation and to observe any possible isomerization to the ketone intermediate, the autoclave was pressurized with H 2 at 30 bar for only 1 min at room temperature, then the pressure was released and the reaction vessel was stirred for the desired time at reflux under a dihydrogen atmosphere of 1 bar. Under these conditions, the alcohol (9a) was still the main reaction product but the redox isomerization product (8a) was also observed (see Table 2, entries 1-3). By replacing dihydrogen by argon after the 1 minute activation time, it was possible to obtain more ketone (Table 2, runs 4-9). The comparison of the results obtained after 2 h and 16 h suggests a fast C=C bond hydrogenation during the minute under dihydrogen and a slower allylic alcohol isomerization at longer reaction times under argon. Ketone (8a) could even be obtained with good selectivity (93%, Table 2, entry 9).

Table 2

Results of the isomerization/hydrogenation reaction of 1-phenyl-2-propene-1-ol (7a) in THF under various reaction conditions. а Entry Catalyst Conversion, % Time, h Yield of (8a), % Yield of (9a), % (8a)/(9a) а Reaction conditions: catalyst (6.4•10 -3 mmol), 1-phenyl-2-propene-1-ol (7a) (0.13 mmol), solvent = THF (2 mL). The conversions were determined by GC. b P H2 = 30 bar, 25 °C, 1 min, then P H2 = 1 bar, 70 °C. c P H2 = 30 bar, 25 °C, 1 min, then Ar, 70 °C.

1 (R)-(2)

Catalytic studies carried out in isopropanol with dihydrogen activation

The reaction was also carried out in iPrOH instead of THF, in the presence of NaOMe (5 equiv relative to the catalyst) under 30 bar of hydrogen, using only the more active rhodium precatalysts.

Excellent conversions were obtained like in THF (cf. Table 3 andTable 1) but again only racemic 1-phenyl-1-propanol (9a) was obtained and no ketone isomerization product was observed.

Table 3

Results of the reaction of 1-phenyl-2-propene-1-ol (7a) in Pr i OH. а

Entry

Catalyst Conversion, % Yield of (8a), % Yield of (9a), % 6) 100 0 100

1 (R)-(3) 95 0 95
2 (R)-(4) 100 0 100
3 (R)-(
a Reaction conditions: catalyst (6.4•10 -3 mmol), NaOMe (3.2•10 -2 mmol), 1-phenyl-2-propene-1-ol (7a) (0.64 mmol), T = 25 °C and P H2 = 30 bar, reaction time 2 h, solvent = Pr i OH (2 mL). The conversions were determined by GC.

Catalytic studies carried out in isopropanol without dihydrogen activation

Finally, again in order to avoid the hydrogenation reaction and increase the selectivity in favor of the ketone, we checked whether the precatalyst could be activated by isopropanol itself under transfer hydrogenation reaction conditions, in the absence of dihydrogen. It is in fact known from literature that [MCl(COD)L] compounds (M = Rh, Ir) react with β-H containing alkoxides at room temperature to yield COD-containing hydride products by ketone elimination and these species were shown to be active in transfer hydrogenation catalysis [START_REF] Yamazaki | [END_REF][90][91][92][93]. The reaction was carried out in iPrOH in the presence of a base (NaOMe) under an argon atmosphere at reflux. After 1 h (Table 4, entries 1-2), (7a) was selectively converted to the allylic isomerization product (8a) in good to excellent yields, proving the efficient activation of the precatalyst under these conditions. When the reaction time was increased to 6 h, however, significant amounts of alcohol (9a) resulting from the transfer hydrogenation of (8a) could also be observed (Table 4, entries 3-4). The transfer hydrogenation was slow and only slightly enantioselective (ee up to 17%). With this information in hands, we decided to check whether this dihydrogen-free procedure could be used for catalytic redox isomerization of other allylic alcohols with good selectivity in favor of the carbonyl compounds (see table 4). Indeed, the expected ketones [START_REF] Cahard | [END_REF] were obtained in good to excellent yields and very high chemoselectivities for all investigated substrates (see table 4), although the reaction was very slow for (7e) with both racemic rhodium complexes 3 and 4. Only for substrate (7a) was a subsequent slow and poorly enantioselective transfer hydrogenation observed over 6 h (entries 3-4), whereas for substrates (7b-d) no evidence of transfer hydrogenation was observed over as many as 45 h.

Table 4

Results of the reaction of allylic alcohols (7) a in the absence of H 2 .

a Reaction condition: catalyst (6.4•10 -3 mmol), NaOMe (3.2•10 -2 mmol), allylic alcohol (0.64 mmol), T = 82 °C. The conversion and ee were determined by GC. b The ee is reported with respect to the R-configuration. c: Reaction run at RT. The nature of the active catalyst remains for the moment unknown. As stated above, hydridediene species should be formed upon interaction of methoxide or isopropoxide at room temperature, but how these species evolve upon reflux is a question that has not been addressed in detail in previous investigations. We are now carrying out studies in this direction and will report the corresponding results in due course.

Conclusions

In conclusion, the rhodium and iridium complexes of ferrocene phosphine-thioether ligands described in this paper are efficient catalysts for the hydrogenation of the allylic alcohol (7a) to racemic (9a), probably by direct hydrogenation of the C=C double bond. However, competitive alcohol isomerization to the saturated ketone (8a) occurs upon replacing dihydrogen with argon Entry Catalyst Substrate t, h Conversion, % Yield of (8), % Yield of ( 9 after a short activation step (1 minute under 30 bar of dihydrogen). Perhaps the most interesting new discovery of our study is that the rhodium precatalysts can be activated in basic isopropanol without using any hydrogen, yielding the allylic isomerization products in good to excellent yields and very high chemoselectivities, comparing well with some other catalytic systems [1][2][3][4][5][6]. This procedure does not require pressure reactor and then could be more practical on laboratory scale.

The catalytic reactions were carried out with rather good catalytic activities (only 1 mol% at temperature ranging from RT to 82°C) . Indeed, we have so far only tested a limited number of substrates. To compare more accurately the performance of the catalytic systems described in this article with other catalytic systems, an extension of this catalytic transformation to a broader substrate scope will be necessary. Further work is in progress in our laboratories.

Figure 1 .

 1 Figure 1. Structure of P,SR ligands used in this study.

Figure 2 .

 2 Figure 2. Structure of the iridium and rhodium complexes used in this study.

а

  Reaction conditions: catalyst (6.4•10 -3 mmol), 1-phenyl-2-propene-1-ol (7a) (0.13 mmol), T = 25 °C and P H2 = 30 bar, reaction time 1 h, solvent = THF (2 mL). The conversions were determined by GC.

Acknowledgments

We are grateful to the European Commission, Contract No. 654198 (Marie Curie action IIF) for a post-doctoral Fellowship to SMWR, the CNRS (Centre National de la Recherche Scientifique) and the RFBR (Russian Foundation for Basic Research) for support through the GDRI (Groupe de Recherche Internationale) "Homogeneous Catalysis for Sustainable Development", and the IUF (Institut Universitaire de France) for additional funding. EMT thanks the Embassy of France in Moscow for a Ph.D. grant.


F Mazaleyrat
email: mazaleyrat@satie.ens-cachan.fr

Zs Gercsi

M Lécrivain

L K Varga

A novel method determining longitudinally induced magnetic anisotropy in amorphous and nanocrystalline soft materials

In ferromagnetic amorphous and nanocrystalline soft magnetic alloys the induced magnetic anisotropy plays a fundamental role in the hysteresis behavior but , due to the elongated shape, it can be measured only if K U is perpandicular to the sample long axis. In order to measure the longitudinal induced anisotropy, an original method derive from known thin layers measurement techniques was used. Hysteresis loops shifted by perpendicular bias field were recorded for this purpose. Direct measurement of the longitudinal induced anisotropy in amorphous and nanocrystalline ribbons or wire without needing sample preparation is reported for the first time. Evidence of self-induced anisotropy is brought in a Fe-Co based nanocrystalline alloy.

In the early years after the discovery of Finemet, various experiment have been conducted in the aim of inducing uniaxial anisotropy (K U ) in nanocrystalline alloys. As it was expected from previous experiments with amorphous materials, uniaxial magnetic anisotropy were successfully induced in the direction of the field applied during nanocrystallization [1].

Herzer has shown that this phenomenon is related to the Fe-Si pair ordering during the crystallization stage [2]. The possibility of inducing anisotropy in Finemet by stress annealing was first attested by Glaser [3] and was proved to be transversal and strikingly strong. This last method can yield both transversal (positive) or longitudinal (negative) depending of magnetic and mechanical properties of both phases [4]. However a more general method consisting in the computation of the second derivative of the return branch of the hysteresis loop was proposed in [5] and multiplying by the field yields the distribution of anisotropy fields [6] (see Fig. 1 top right box). The same result can be obtained in amore accurate way by a second harmonic detection induced by a small ac field superimposed to the dc field [7]. In the case of longitudinal induced anisotropy, the square hysteresis loop is clearly unsuitable for these evaluations because the magnetization reversal The torque method as well as bi-axial magnetic measurement can be applied but both requires circular samples which are difficult to cut from brittle ribbons. In addition, these methods are very sensitive to the shape of the sample. For this purpose, a method originally proposed by Weber et al. [8] have been adapted to long samples without needing sample preparation. The sweeping field (H) is applied along the easy axis which is longitudinal in this case. The hysteresis loop is obtained by integration of the pick-up coil voltage within the same axis. If a transversal bias field H B larger than the anisotropy field H K is applied, the hysteresis loop is flattened and pratically anhysteretic until a critical value of H is reached at which the magnetization switch is shifted at H S ± H C (see Fig. 1).

The total magnetic energy depends on the angle ϕ between the magnetization and the measurement direction for a given angle θ between the easy axis and the measurement direction. When two perpendicular fields are applied and the easy axis is parallel to the measurement direction (θ=0) , we have:

E (ϕ) = K U sin 2 ϕ -µ 0 M S H cos ϕ -µ 0 M S H ⊥ sin ϕ (1)
In this case, there is 3 stable positions of the magnetization ϕ = 0 and ϕ = ±π/2 and the magnetization switches from one position to another (at H = H S ) when :

E (0) = -µ 0 M S H = E (π/2) = K U -µ 0 M S H ⊥ For a constant H ⊥ , E (0) = E (π/2) so the anisotropy constant is: K U = µ 0 M S (H S -H ⊥ )
and the anisotropy field is:

H K = 2(H S -H ⊥ ) (2)
For circular samples with in-plane applied fields, K U is deduced from a single split hysteresis loop because the demagnetizing factors are equal in both direction (N = N ⊥ ), so H K comes from eq. ( 2). In the case of long samples the longitudinal field is the applied one because of the negligible demagnetizing effect, but the perpendicular inner field is much smaller than the applied biasing field:

H ⊥ = H B -N ⊥ M ⊥ .
The magnetization can be substituted if the field is smaller or equal to the switching field: as there is no domain, permeability is basically due to a rotational magnetization process and thus depends linearly on the field:

M ⊥ = χH B , so
H K = 2[H S -(1 -N ⊥ χ) H B ] = 2(H S -αH B ) (3)
Of course the parameter α is highly dependent on the the demagnetizing factor which cannot be determined for most of samples with sufficient accuracy. This difficulty is evaded by using a plotting strategy: several hysteresis loops are recorded with various values of the biasing field. The linear plot of H S as a function of H B allows the determination of H K by extrapolation at

H B = 0 ⇒ H K = 2H S (0).
The experimental set-up, is composed of a 0.52 m long solenoid generating the longitudinal sweeping field in the homogeneous part of which the 7 cm long pick up coil and the sample are positioned and a perpendicular 0.3 m in diameter Helmholtz coils set. In our case this coils set is about 35 kg and H B (20 kAm -1 ) is sufficient only for the amorphous wire sample. Another set-up can pass through the deficient field problem, using an arrangement composed of two perpendicular iron cores. This device was already used for magnetostriction measurements by small angle magnetization rotation method [9]. The longitudinal field is known from Ampère's theorem, because N is strictly zero. In the other hand, the perpendicular field depends strongly on the position of the ribbon in the gap. This field is in a given position is The anisotropy associated to the single longitudinal core domain of amorphous Fe 77.5 B 15 Si 7.5 was measured with the present method. The result is a quite low value compared to the perpendicular anisotropy associated with the shell suggesting a quite small quenched-in tensile stress in the core (∼2 MPa). The stress annealed Nanoperm alloy (N S ) exhibits a -150 J/m³ anisotropy only which is very low compared to Finemet (∼+1000 J/m³) annealed in the same conditions. This result suggest a weaker back-stress effect and open new investigation fields on stress induce anisotropy. Concerning the field annealed materials, the F L sample exhibits a slightly higher value of K U compared to transversal field annealing (10-20 J/m³) [10], which can be explained by a shape contribution. In contrast, relatively large K U were induced in the Co doped alloy (C L &C T ) as previously reported [11]. The fact that, in the longitudinal (C L ) and transversal (C T ) field annealed samples have not the same value of K U (by opposite sign) may be explained partly by shape effect but also by the insufficient inner transversal field during annealing of C T sample due to the demagnetizing factor (N ⊥ ≫ N ). A surprising effect is the splitting of the hysteresis loop of Co-doped sample annealed without field showing a notable long range uniaxial anisotropy comparable to that of F L sample. This "self-induced" anisotropy is of great importance in the theory of random anisotropy model proposed by Suzuki et al. [12]. Indeed the change from the classical D 6 dependence of the coercive field to a D 3 law for some alloys (e.g. Nanoperm)

H ⊥ = σnI B /d,
was explained by the introduction of a long range K U in the model which existence was never experimentally demonstrated. The origin of this self-induced anisotropy is not clear at all but two explanations are possible. A first one would involve the magneto-elastic origin linked to the different thermal dilatation coefficients of both amorphous and crystalline phases but it should be a priori a short range contribution subject to averaging out. Another explanations should be the formation of a domain structure during annealing yielding high internal field and finally a long range field induced magnetic anisotropy [13]. It is worth noticing that this effect is not observed with Finemet which is not contradictory. Indeed, the Fe-Si crystallites are in the superparamagnetic phase during annealing [14] whereas it is probably not the case for Co-doped alloy due to the high Curie point of Fe-Co-Si phase [15].

The coercive fields are also reported in Table I. It is to notice that there are no clear relationship between the magnitude of the anisotropy fields and the coercivity of different materials. For instance, the results obtained with Fe-Co based nanocrystalline alloys suggest that the coercivity is basically linked to the magnetization process (rotation or domain wall displacement) and weekly to the magnitude of induced anisotropy. In conclusion, the approach of Weber [8] have been adapted to the determination of uniaxial magnetic anisotropy in anisotropic samples: the plot of H S = f (H B ) overcome the demagnetizing effect. This method allows for the first time to measure directly the longitudinal induced anisotropy in amorphous or nanocrystalline ribbons and wires. To the authors' knowledge, evidence of self-induced anisotropy in nanocrystalline samples is also reported for the first time.

Figure 1 :

 1 Figure 1: Various methods to determine uniaxial induced anisotropy

Figure 2 :

 2 Figure 2: The shape of the hysteresis cycle as a function of increasing bias field

Figure 3 :

 3 Figure 3: The switching fields plotted as a function of bias field. Extrapolation to H B =0 yields H K /2.

Table I :

 I Anisotropy fields measured by the present technique (except for K U > 0) Co 10 ) 73.5 Si 13.5 B 9 Nb 3 Cu 1 C L Co 10 ) 73.5 Si 13.5 B 9 Nb 3 Cu 1 C

	Material	Sample	Annealing	H k (A/m) µ 0 M s (T) K u (J/m 3 ) H c (A/m)
	Fe 77.5 B 15 Si 7.5	A	As-cast	-44±3	1.57	-35±2	19
	Fe 73.5 Si 13.5 B 9 Nb 3 Cu 1	F L	Long. H-550°C/1 h -66±5	1.24	-41±3	5.5
	(Fe 90 Co 10 ) 73.5 Si 13.5 B 9 Nb 3 Cu 1	C	550°C/1 h	-68±3	1.16	-40±2	8.4
	(Fe 90 Long. H-550°C/1 h -158±2	1.16	-92±1	8
	(Fe 90 T Trans. H-550°C/1 h +86±3	1.16	+50±2	5.8
	Fe 90 Zr 7 B 3	N S	Stress-600°C/1 h	-154±6	1.63	-126±5	36.5
	takes place by a single large Barkhausen jump at ±H C . The coercive force in this case
	corresponds to the domain wall nucleation energy which is indirectly linked to K U through
	the domain wall energy. However many other parameters are involved and finally K

U cannot be deduced from H C .

  where σ is Hopkinson's leakage coefficient, if the yoke is far from saturation. Equation 3 becomes H K = 2(H S -α ′ I B ), where α ′ is eliminated by the I. A first important point is to verify the independence of H S upon the maximum sweeping field H max in particular is the sample is not fully saturated. For this purpose, several loops were recorded with a constant H B and varying H max . H S was proved to be independent of H max if the latter is sufficient to occur the switching of the magnetization. The relevance of this is illustrated in Fig.2where it is visible that the samples are not saturated for the largest bias fields. From these split loops, the values of H S are extracted and plotted as a function of H B in Fig.3. The perfect alignment of points allows an accurate extrapolation to zero which give the values of H K by a least means square linear fit with a remarkably low standard deviation. TableIsummarizes the H k and K u values of selected materials.

	plotting strategy.
	Different type of nanocrystalline alloys were produced and annealed with or without

longitudinal (800 A.m -1 ) and/or transverse (10 kA.m -1 ) fields or under a 100 MPa stress according to Table