Christine Mounaïm-Rousselle

Fabien Halter

Fabrice Foucher

Francesco Contino

Guillaume Dayma

Philippe Dagaut

Fuel Class Valerates

Introduction and Fuel Properties

Origins of Valerate Molecules

Due to the internal structure of lignocellulose (a compound of hemicellulose, cellulose, and lignin), its conversion still remains a real challenge. Lignocellulosic biomass typically contains more than 50 wt% sugars that can be upgraded to valuable platform molecules, such as levulinic acid (LA) and γ-valerolactone (GVL), while the other ligneous parts can be used as solvents. Figure 3.1 indicates one possible roadmap proposed by Azadi et al. [START_REF] Azadi | Catalytic conversion of biomass using solvents derived from lignin[END_REF] for different transformations of these three components and their potential uses.

Geboers et al. [START_REF] Geboers | Chemocatalytic conversion of cellulose: opportunities, advances and pitfalls[END_REF] described the opportunities, advances, and pitfalls in the conversion of cellulose and stressed that while it is generally agreed that cellulose will be the basis for many future technologies, it is important to note that the only way to achieve this is not to produce "chemicals for the chemical industry" but biofuels and fine chemicals.

Valeric acid (VA) esters, called valerates or pentanoates, are derivatives of GVL. As pointed out by Chalid [START_REF] Chalid | Levulinic acid as a renewable source for novel polymers[END_REF], several applications of GVL already exist in the food and perfume industries and drug delivery systems (especially due to its herbal odor) [START_REF] Leonard | Levulinic acid as a basic chemical raw material[END_REF][START_REF] F Á B O S | Integration of homogeneous and heterogeneous catalytic processes for a multi-step conversion of biomass: from sucrose to levulinic acid, γ-valerolactone, 1,4pentanediol, 2-methyl-tetrahydrofuran, and alkanes[END_REF], but GVL can also be used as a green solvent. Potential applications such as an oxygenate in transportation fuels, a comonomer for the preparation of polymers [START_REF] Saiyasombat | Ring strain and polymerizability of cyclic esters[END_REF], or a precursor for long-chain alkanes to be used as hydrocarbon fuels [START_REF] Serrano-Ruiz | Direct conversion of cellulose to levulinic acid and gamma-valerolactone using solid acid catalysts[END_REF] are quite new and have been studied for less than 10 years. Further reinforcing the potential of GVL as a biofuel platform chemical, Bond et al. [START_REF] Bond | Integrated catalytic conversion of γvalerolactone to liquid alkenes for transportation fuels[END_REF] reported its conversion to liquid C 8 alkenes for fuel applications.

Valerates themselves, especially ethyl and methyl pentanoate, are commonly used not only in fragrances, beauty care, soap, and laundry detergents at levels of 0.1-1% but also in food due to their fruit flavor. In a very pure form (greater than

99.5%

), methyl pentanoate is used as a plasticizer in the manufacture of plastics andalsoasaninsecticide.

Valerates as Fuel for Internal Combustion Engines

Since 2004, researchers at Shell have developed this "new" generation of biofuels, valeric biofuels. Lange et al. described in 2010 the process to produce these levulinic acid derivatives from lignocellulose. These fuels are more suitable than GVL itself because they can provide biofuels that have similar properties and that can be either blended with gasoline or diesel or used as fuels themselves. The process developed by Lange et al. at Shell is schematized in Figure 3. [START_REF] Geboers | Chemocatalytic conversion of cellulose: opportunities, advances and pitfalls[END_REF]. It involves the following four steps: the classical production of levulinic acid by the acid hydrolysis of lignocellulosic materials, the hydrogenation of LA (C 5 H 8 O 3 ) to obtain GVL (C 5 H 8 O 2 ) and of GVL to obtain valeric acid (C 5 H 10 O 2 ), and finally the esterification of VA to produce a valerate.

After the final step, that is, esterification, the biofuel may be in the form of biogasoline or biodiesel, depending on the reactants used, and can be mixed with other currently available fuels. The choice of alcohol (ethanol, methanol, propanol, butanol, or pentanol) provides different valerates (respectively, ethyl valerate EV, methyl valerate MV, propyl valerate PRV, butyl valerate BV, and pentyl valerate PV), inducing different properties.

Lange et al. [START_REF] Lange | Valeric biofuels: a platform of cellulosic transportation fuels[END_REF] first identified some properties of the different valerate molecules such as the blending research octane number (BRON) and the boiling point. They also identified properties of some other biofuels such as alcohols and fatty acid methyl esters (FAME) or other levulinic acids (MTHF, methyl tetrahydrofuran, or EL, ethyl levulinate). The lighter esters are more suitable for spark-ignition (SI) engines and the heavier esters for diesel engines.

The properties of the five VA esters are summarized in Table 3.1.

To improve our knowledge of these fuels' properties, new experiments have been performed in a homogeneous combustion engine to determine some "optimum" regions where each fuel can autoignite and where 50% of fuel has burned between 1 and 5 crank angle degrees (CAD), as performed by Masurier et al. [START_REF] Masurier | Homogeneous charge compression ignition combustion of primary reference fuels influenced by ozone addition[END_REF] for other specificities. Experiments were performed, for each fuel, at different intake temperatures and by varying the intake pressure. For each experiment, the CA50 was determined and only the data points with a CA50 ranging from 1 to 5 CAD were conserved to draw the map. The modified PSA engine used for the experiments is fully described in Refs. [START_REF] Dubreuil | Analysis of flame and OH natural emissions of n-heptane combustion in a homogeneous charge compression ignition HCCI engine effect of burnt gas dilution[END_REF] and [START_REF] Masurier | Homogeneous charge compression ignition combustion of primary reference fuels influenced by ozone addition[END_REF]. For the experiments, six primary reference fuels (PRFs) (mixtures of iso-octane and n-heptane) were used: PRF0, 20, 40, 60, 80, 100, with, respectively, 0, 20, 40, 60, 80, 100 vol% of iso-octane.

The results are plotted in Figure 3.3, where the upper limit of each fuel is an iso-CAD50 for 1 CAD and the lower limit is for 5 CAD. As expected, the fuels are classified according to the BRON: the highest BRON (PR100) requires high intake pressure and temperature to ignite. So for this presentation of fuel properties regarding homogeneous ignition, valerates can be divided into two categories: fuels for SI engines (EV, MV) and fuels for compression-ignition (CI) engines (BV and PenV). These results are in good agreement with the properties presented by Lange et al. [START_REF] Lange | Valeric biofuels: a platform of cellulosic transportation fuels[END_REF].

Kinetic Properties of Valerate Fuels

From a chemical kinetic point of view, alkyl esters have been shown to behave similarly to alkanes [START_REF]Experimental and kinetic modeling study of the oxidation of methyl hexanoate[END_REF][START_REF] Dayma | Detailed kinetic mechanism for the oxidation of vegetable oil methyl esters: new evidence from methyl heptanoate[END_REF][START_REF] Hadj-Ali | A study of the low temperature autoignition of methyl esters[END_REF], with potentially a cool flame, a negative temperature coefficient (NTC), and high-temperature reactivity, depending on the length of the carbon chain. Methyl esters (from C 2 up to C 19 ) have been extensively studied over the past decade, and the only difference with alkanes as far as reactivity is concerned lies in the influence of the carbonyl group on the neighboring carbon (carbon #2). Indeed, El-Nahas et al. [START_REF] El-Nahas | Enthalpies of formation, bond dissociation energies and reaction paths for the decomposition of model biofuels: ethyl propanoate and methyl butanoate[END_REF] calculated the bond dissociation energies in the case of methyl butanoate and ethyl propanoate and demonstrated the relative weakness of the C-H and C-C bonds neighboring the carbonyl group. In addition, it is well accepted that the shorter the carbon chain is, the greater the impact this weakness has on the reactivity. In the particular case of valerates, the carbon chain on the acid side involves five carbon atoms. Thus, the peculiarity of carbon #2 cannot be neglected and alkyl propenoates are expected to be important intermediates. In addition, from ethyl valerate to pentyl valerate, a molecular reaction yielding valeric acid (pentanoic acid) and an olefin (from ethylene to 1pentene) was also shown to be of primary importance at high temperature (above 800 K) [START_REF]Experimental and kinetic modeling study of the oxidation of methyl hexanoate[END_REF]. Moreover, Hayes and Burgess [START_REF] Hayes | Exploring the oxidative decompositions of methyl esters: methyl butanoate and methyl pentanoate as model compounds for biodiesel[END_REF] investigated theoretically the early CO 2 production observed during methyl ester combustion. These three elements make the oxidation of valerates important when studying the use of these compounds as fuels.

In the literature, ignition delays were only measured in a rapid compression machine for methyl valerate/air mixtures by Hadj-Ali et al. [START_REF] Hadj-Ali | A study of the low temperature autoignition of methyl esters[END_REF]. In their study, the authors compared the ignition characteristics of different methyl esters and n-alkanes over the low and intermediate temperature ranges (650-850 K) and for pressures between 4 and 20 bar. Under these conditions, methyl valerate exhibits a two-stage autoignition, with a clearly identified cool flame event. No kinetic mechanism was proposed for methyl valerate autoignition in the study. Moreover, no ignition delays measured in shock tubes are reported in the literature for alkyl valerates and detailed kinetic modeling suffers from this lack of experimental data.

As far as spark ignition is concerned, laminar burning velocities, S L ∘ ,weremeasured for ethyl and methyl valerate/air mixtures by Contino et al. [START_REF] Contino | Engine Performances and Emissions of Second-Generation Biofuels in Spark Ignition Engines: The Case of Methyl and Ethyl Valerates[END_REF] in a spherical combustion chamber at T u = 423 K (the fresh gas temperature), at two initial pressures (p = 1 and 3 bar), and for equivalence ratios (𝜑)r a n g i n gf r o m0 . 7t o1 . [START_REF] Leonard | Levulinic acid as a basic chemical raw material[END_REF] .

A sc a nb es e e nf r o mF i g u r e3 . 4 a ,S L ∘ reaches a maximum around 𝜑 = 1.1 and the laminar burning velocities for EV are slightly higher than those of MV and iso-octane. For ethyl valerate at stoichiometric ratio, a negative dependence on pressure was observed (Figure 3.4b). A detailed kinetic mechanism able to reproduce these experimental data was proposed, and these laminar burning velocities were shown to depend mainly on reactions belonging to the C 0 -C 1 submechanism andinvolvingHatoms.

The flame structures of methyl and ethyl valerate were also investigated by Shmakov et al. [START_REF] Shmakov | Experimental and modeling study of premixed methyl pentanoate flames stabilized at atmospheric and low-pressure conditions[END_REF] and Knyazkov et al. [START_REF] Knyazkov | Structure of a low pressure ethyl pentanoate (ethyl valerate) flame studied by flame sampling molecular beam mass spectrometry with VUV photoionization and numerical simulation[END_REF], respectively. In both of these studies, the authors probed the flames at different heights above the burner and reported mole fractions of several species (fuel, intermediates, etc.) as a function of this height. Shmakov et al. [START_REF] Shmakov | Experimental and modeling study of premixed methyl pentanoate flames stabilized at atmospheric and low-pressure conditions[END_REF] studied stoichiometric and rich methyl valerate/O 2 /Ar flames at low and atmospheric pressures using molecular beam mass spectrometry with tunable synchrotron vacuum ultraviolet photoionization for low-pressure flames and soft electron impact ionization for atmospheric flames. A kinetic mechanism was validated using these experimental results. Knyazkov et al. [START_REF] Knyazkov | Structure of a low pressure ethyl pentanoate (ethyl valerate) flame studied by flame sampling molecular beam mass spectrometry with VUV photoionization and numerical simulation[END_REF] focused on low-pressure ethyl valerate/O 2 /Ar flames using molecular beam mass spectrometry with vacuum ultraviolet photoionization and found that the calculations performed using the kinetic mechanism developed by Dayma et al. [START_REF]Experimental and kinetic modeling study of the oxidation of methyl hexanoate[END_REF] were in good agreement with their experimental data.

Mbuyi Katshiatshia et al. [START_REF] Mbuyi Katshiatshia | Experimental study of rich ethyl valerate flame at low temperature[END_REF] also provided new data on a rich premixed flat flame of ethyl valerate/O 2 /Ar at low pressure in order to validate and improve the mechanism proposed by Dayma et al. [START_REF] Dayma | Experimental and detailed kinetic modeling study of ethyl pentanoate (ethyl valerate) oxidation in a jet stirred reactor and laminar burning velocities in a spherical combustion chamber[END_REF].

Lastly, ethyl valerate oxidation was also studied in a jet-stirred reactor (JSR) at a high pressure (10 atm), for three different equivalence ratios (0.6, 1, and 2), and over a wide range of temperatures (560-1160 K) by Dayma et al. [START_REF]Experimental and kinetic modeling study of the oxidation of methyl hexanoate[END_REF]. Mole fraction profiles were reported as a function of the temperature for several stable compounds, among which are pentanoic acid and ethyl propenoate. A cool flame and an NTC were observed and the detailed kinetic mechanism developed was well able to reproduce the experimental data, as shown in Figure 3. [START_REF] F Á B O S | Integration of homogeneous and heterogeneous catalytic processes for a multi-step conversion of biomass: from sucrose to levulinic acid, γ-valerolactone, 1,4pentanediol, 2-methyl-tetrahydrofuran, and alkanes[END_REF].

Preliminary results on extensive road tests [START_REF] Lange | Valeric biofuels: a platform of cellulosic transportation fuels[END_REF] for gasoline mixed with 15% by volume of ethyl valerate showed no negative impacts on engine running, fuel tank, and fuel lines after a total distance of 250 000 km.

The following sections first present the performance of methyl and ethyl valerate in a spark-ignition engine and then the performance of butyl and pentyl valerate in a compression-ignition engine.

Performance in Spark-Ignition Engines

Lange et al. [START_REF] Lange | Valeric biofuels: a platform of cellulosic transportation fuels[END_REF] mention tests of engines operated with valeric biofuels. In their study, 10 current types of vehicle, representative of the current market technologies, were fueled exclusively with a mixture of normal gasoline mixed with 15% by volume of ethyl valerate and were sent out on the road to cover 500 km/day. Compared to methyl valerate, ethyl valerate benefits of a higher volumetric energy content. To further investigate the potential of valeric biofuels, we first tested pure and blends fuels in two different single-cylinder SI engines but with different and complementary evaluation of their performances as fuels.

Global Performance of SI Engine Fueled with Valerate Blend and Pure Valerates

To improve the results obtained by Lange et al., both blended fuels and pure fuels of MEV and EV were tested, and to compare the performance, gasoline was not used but a mixture of iso-octane/n-heptane, a PRF (PRF95), with 95% of iso-octane as SP95.

Experimental Setup

The experiments were carried out in a four-cylinder SI engine (PSA EP6) converted into single-cylinder operation. This engine has a four-valve pent-roof chamber with a displacement volume of 399.5 cm 3 /cylinder and a compression ratio of 10.5. The bore, stroke, and connecting rod lengths are 77, 85.8, and 138.5 mm respectively. The engine, driven by an electric motor, was kept at a fixed engine speed: 1500 and 2500 rpm. The intake air, supplied by an air compressor, was dehumidified to a dew point of 4 ∘ C and electrically heated to keep the temperature in the range 45-50 ∘ C. This air flow was metered and controlled by a Brooks flow meter to obtain an intake pressure ranging from 0.4 to 1 bar. The fuel flow from a pressurized tank was metered and controlled by a 0-8 kg/h Bronkhorst Coriolis flow sensor with a maximum combined standard uncertainty of ±1% for the minimum flow rate considered in the present work. The fuel was fully premixed with the intake air by supplying a fuel/air mixture from a heated fuel-vaporization chamber upstream of the intake plenum (see Figure 3.6). The mixture was ignited by a conventional spark plug with an electrode space of 1 mm, and the spark timing was optimized to maintain a crank angle of maximum pressure around 12 ± 0.5 Degree after top dead center (TDC) for the various loads (from 2 to 9 bar indicated mean effective pressure (IMEP)) and speeds.

Cylinder pressure was recorded with a water-cooled AVL quartz pressure transducer connected to a charge amplifier. The acquisition was performed every 0.1 CAD through an optical encoder mounted on the main shaft. A timer card ensured synchronization of the various trigger signals and data acquisition systems. The average values presented result from 100 consecutive cycles and were analyzed following the method described in Refs. [START_REF] Contino | Combustion characteristics of tri-component fuel blends of ethyl acetate, ethyl propionate, and ethyl butyrate in homogeneous charge compression ignition (HCCI)[END_REF][START_REF] Contino | Coupling of in situ adaptive tabulation and dynamic adaptive chemistry: an effective method for solving combustion in engine simulations[END_REF].

The exhaust emissions of nitric oxides (NO x ), unburned hydrocarbon (UHC), methane (CH 4 ), carbon monoxide (CO), carbon dioxide (CO 2 ), and oxygen (O 2 ) were measured by an Environnement S. A. emission 1% of full scale (HC: 10 000 ppm, CH 4 : 1000 ppm, CO: 5000 ppm and 10%, CO 2 : 20%, and O 2 : 25%).

Main Results

The thermal efficiencies obtained from the experimental results for all mixtures and speeds are shown in Figure 3. [START_REF] Serrano-Ruiz | Direct conversion of cellulose to levulinic acid and gamma-valerolactone using solid acid catalysts[END_REF]. As expected, thermal efficiency increases with load as the inlet pressure increases and the pumping losses decrease. There is no significant difference between the reference fuel PRF95 and the mixture of valeric esters with PRF95, at 1500 rpm (empty symbols) and 2500 rpm (filled symbols).

Only the error bars for PRF95 are presented but are similar to all other fuels at the same load. The CO 2 emissions are linked to the efficiency evolution. However, the mass of carbon per unit energy in the fuel should be considered to explain the higher CO 2 emission for the valeric esters compared to PRF95 (67.7 g c /kW h fuel ): 77.6 and 76.8 g c /kW h fuel forMVandEV ,respectively. For the following results, only the experiments at 1500 rpm and for pure PRF95, MV, and EV are presented for the sake of clarity, as the effect of 20% of valerate blend is not distinguishable.

The exhaust emissions of nitric oxides (NO x )a n dU H C sa r ep r e s e n t e di n Figure 3.8. The differences in NO x concentration are within the error bars, but a slight decrease can be observed when using valeric esters. On the other hand, the HC emissions are slightly higher at high loads and lower at low loads. The small variability observed throughout the different loads might explain this tendency. The CO emissions for the various fuels are similar and no specific trend was observed [START_REF] Contino | Combustion and emissions characteristics of valeric biofuels in a compression ignition engine[END_REF].

An example of pressure traces and corresponding heat release rates (HRRs)at mid-load (IMEP = 4.5 bar) are presented in Figure 3.9. The HRRs of the valeric esters are slightly above that of PRF95 due to the slightly higher amount of energy injected in the combustion chamber under stoichiometric conditions. The spark timing (indicated in the figure) was adjusted to keep the crank angle of maximum pressure at 12 ± 0.5 CAD due to the difference in laminar burning speed as shown in Figure 3.4a.

Finally, in addition to the BRON (Table 3.1), we performed ignition delay simu-lationsofmethylandethylvaleratecomparedtoPRF95.ThemechanismofCurran et al. [START_REF] Curran | A comprehensive modeling study of iso-octane oxidation[END_REF] was used for PRF95, the mechanism developed by Dayma et al. [START_REF] Dayma | Experimental and detailed kinetic modeling study of ethyl pentanoate (ethyl valerate) oxidation in a jet stirred reactor and laminar burning velocities in a spherical combustion chamber[END_REF] was used for ethyl valerate, and a currently developed mechanism was used for methyl valerate. The simulations were performed with the TDAC method [START_REF] Contino | Engine Performances and Emissions of Second-Generation Biofuels in Spark Ignition Engines: The Case of Methyl and Ethyl Valerates[END_REF][START_REF] Contino | Combustion characteristics of tri-component fuel blends of ethyl acetate, ethyl propionate, and ethyl butyrate in homogeneous charge compression ignition (HCCI)[END_REF][START_REF] Contino | CFD simulations using the TDAC method to model iso-octane combustion for a large range of ozone seeding and temperature conditions in a single cylinder HCCI engine[END_REF] at 40 bar and Φ=1 for a range of temperatures between 800 and 1200 K. The ignition delay was defined as the maximum pressure rise rate in an adiabatic vessel. As expected from the BRON values, MV and EV are significantly more resistant to autoignition compared to PRF95 (see Figure 3.10). An inversion is observed between EV and MV around 990 K, which needs to be investigated with future experimental results.

A second series of experiments was performed in another single-cylinder port-fuel-injection SI engine with pure fuels (MV, EV), compared to isooctane. The main interest of this study was to measure nonregulated pollutant emissions.

Specific Consumptions and Nonregulated Pollutant Emissions for Pure Valerates

The setup was fully described in Ref. [START_REF] Broustail | Experimental determination of laminar burning velocity for butanol and ethanol iso-octane blends[END_REF]. The global characteristics are summarized here. The four-valve pent-roof combustion chamber of the single cylinder is characterized by a displacement volume of 499 cm 3 and a compression ratio of 9.5. The bore, stroke, and connecting rode lengths were, respectively, 88, 82, and 137 mm. The oil and coolant temperatures were fixed at 80 ∘ Candtheintake temperature at 23 ∘ C. A common spark plug, with an electrode space of 1 mm, equipped the engine. The engine was fed by pressurized air through a volume flow meter with an accuracy of ±0.7% on the instantaneous flow. Before the intake pipe, all the gases passed through a plenum volume, to avoid pressure oscillations inside the intake port. The liquid fuel was measured by using a 0-8 kg/h Brooks Quantim (QMBM) Coriolis mass flow meter with a maximum combined standard uncertainty of ±1% for the minimum flow rate considered in the present work. An optical encoder mounted on the crankshaft, giving a 0.1 CAD as resolution, was used with a water-cooled AVL quartz pressure transducer connected to a charge amplifier to record in-cylinder pressure. An Environnement S.A. 5 gas emission tester was used to measure the regulated emissions, with an accuracy <2% of the measured value and 1% of full scale. For the nonregulated emissions, an Environnement S.A. Fourier transform infrared spectroscopy (FTIR) was used to measure in particular CH 4 (methane), C 2 H 2 (ethylene), C 6 H 6 (benzene), HCOH (formaldehyde), and CH 3 HCO (acetaldehyde), with an accuracy <2% of full scale (Table 3.

2).

Only two operating points were selected for this study to represent middle and low engine operating conditions, the three different fuels are studied, and the spark timing is adjusted to maximize IMEP.

Use of valeric biofuels induced a small diminution of the timing advance due to higher reactivity for valeric biofuels, confirmed by laminar burning velocity measurements (Figure 3.4a). The specific consumptions (g/kW h) are plotted in Figure 3.11 versus the low heating values (LHV). As the IMEP is kept constant for each condition, the specific consumption is directly sensitive to the fuel consumption in mass. The specific consumption is observed to decrease linearly with the LHV, with a notable low value in the case of iso-octane.

By considering the specific consumption in volume and not in mass, the biofuels partly catch up. Indeed, the density of the biofuels is higher than that of iso-octane (0.692 kg/l for iso-octane, 0.875 kg/l for MV, and 0.875 kg/l for EV).

The molecular structure of valeric biofuels, which contain oxygen atoms, slightly counterbalances the higher consumption. UHC emissions are mainly generated by incomplete combustion. UHC emissions divided by the specific consumption are reported in Figure 3. 12. iso-Octane exhibits the largest UHC emissions, twice higher than the other two, for both cases. Methyl and ethyl valerates have almost the same level of emissions. UHC emissions are dependent on the (H/C) ratio, which is 2 for the valeric biofuels and2.25foriso-octane. This could slightly reduce the differences. No noticeable differences were observed concerning NO x emissions, mainly due to burnt gases' temperature and the chemical residence time. Concerning CO, the presence of oxygen atoms in the valerates does not induce large modifications in CO emissions as it was previously demonstrated with alcoholic fuels [START_REF] Broustail | Experimental determination of laminar burning velocity for butanol and ethanol iso-octane blends[END_REF].

As a precursor of several species such as formaldehyde, methane, and acetylene, the impact of ethylene involves its determination (Figure 3

.13).

A large increase in ethylene emissions is observed when valeric fuels are used, and almost no ethylene is emitted when running the engine with iso-octane. With methyl valerate, the value reaches around 1.4 and 2.0 kg/kW h with ethyl valerate.

Methane has an impact both on global warming and on air pollution. A large decrease in methane emissions is observed when using valeric biofuels (Figure 3.13b). This diminution is more pronounced with ethyl valerate. These trends are directly opposed to those of ethylene. The main precursors of methane formation are CH 3 ,C 2 H 4 ,andC 8 H 18 . As a result, it is evident that the production of methane is enhanced by the use of iso-octane as fuel. Then, using fuels containing oxygen atoms favors the transformation of CH 3 in CH 3 O and not in methane. Finally, the path via C 2 H 4 seems to be inhibited when burning methyl valerate and especially ethyl valerate.

Benzene (C 6 H 6 ) is known to be carcinogenic and a soot precursor. A strong reduction in benzene emissions was observed when fueling the engine with alkyl valerates (Figure 3.13c) and equal to zero with ethyl valerate.

Formaldehyde has already been regulated in California due to its carcinogenic specificity (low emission vehicle (LEV II) standards, http://transportpolicy.net). Methyl valerate exhibits larger values of formaldehyde emissions, whereas ethyl valerate presents values only slightly higher than that of iso-octane. As said previously, fuels containing oxygen atoms favor the transformation of CH 3 in CH 3 O. These results have demonstrated the ability of both these fuels to be directly used in a spark-ignition engine, but the limitation is due to their higher consumption.

The new results in single-cylinder engines confirm the previous results of Lange et al. [START_REF] Lange | Valeric biofuels: a platform of cellulosic transportation fuels[END_REF]: no significant differences were observed for emissions and performances when running the engine with pure esters compared with PRF95. As valerates have a higher laminar burning speed, spark timing needs to be adjusted to keep the crank angle of maximum pressure constant and to reach the optimal working point. Moreover, according to the Research Octane Number and numerical simulations of ignition delay, the esters are more resistant to autoignition. Accordingly, methyl and ethyl valerates are very interesting fuel additives or alternatives to gasoline.

Performance in Compression-Ignition Engines

Similar experiments were performed for a CI engine with blends of 20 vol% BV and PenV in diesel fuel, compared with pure diesel fuel [START_REF] Contino | Engine Performances and Emissions of Second-Generation Biofuels in Spark Ignition Engines: The Case of Methyl and Ethyl Valerates[END_REF][START_REF] Contino | Combustion characteristics of tri-component fuel blends of ethyl acetate, ethyl propionate, and ethyl butyrate in homogeneous charge compression ignition (HCCI)[END_REF]. A single-cylinder CI engine, based on a four-cylinder PSA DW10 engine (see Figure 3.14) was used (a displacement volume of 499 cm 3 /cylinder, the bore, stroke, and connecting rod lengths are 85, 88, and 145 mm, respectively, and the compression ratio is 16.7. Air from a compressor is filtered, dehumidified, and preheated before the intake plenum. The fuel is injected in the combustion chamber using a seven-hole Bosch CRI 3.1 injector. A valve located after the exhaust plenum regulates the back pressure at the same value as the inlet pressure. Temperature (type K thermocouple) and absolute pressure (Kistler 4075A piezoresistive absolute pressure sensor) are measured in the intake and exhaust ports. The cylinder pressure is measured by a Kistler 6043A piezoelectric transducer at 0.1 CAD increments. The composition of the exhaust gas is measured with the Environnement S.A. emission analyzer. The smoke content is measured with an AVL 415 smoke meter.

For all experiments, the engine speed, driven by an electric motor, was set at 1200 rpm. The inlet pressure and temperature were kept constant at 1.1 bar and 40 ∘ C, respectively. The engine was preheated by lube oil and cooling water at 88 and 94 ∘ C, respectively, during the whole experiment. The fuel injection was split in two parts: approximately one-third of the fuel was injected as a pilot injection at 8 CAD before TDC and the remaining at 4 CAD after TDC. The injection pressure was set to 1000 bar, and the injection duration was adapted to cover a range of IMEP from 2 to 7. To compare the different fuels, the injection timing was not optimized for each load or fuel blend but was kept constant so that the fuels could be compared under the same thermodynamic conditions. More details about the experimental setup and uncertainty analysis are provided in Ref. [START_REF] Contino | Combustion and emissions characteristics of valeric biofuels in a compression ignition engine[END_REF]. For all results, only average values are presented and error bars are plotted for the BV blend only.

As can be seen in Figure 3.15, where only average values are presented, the indicated efficiency increases with the IMEP up to around 4.5 bar and then decreases. While there is a slight increase in the carbon content when adding 20 vol% of valeric esters, the CO 2 emissions were found to be linked to the efficiency evolution (carbon content was 72.8 and 73.0 g/kW h fuel for the blend with butyl and pentyl valerate, respectively, compared to 72.7 g/kW h fuel for diesel fuel).

As shown in Table 3.1, the cetane number of valerates is less than that of diesel fuel. To determine the ignition delay of the valerates, the difference between the crank angle corresponding to when 5% of fresh gases (CA5) have been burned and the crank angle corresponding to the injection timing (SI) was plotted (Figure 3.16). The ignition delay of the blend with pentyl valerate is slightly shorter than that with butyl valerate, but overall at 1200 rpm, there is a difference of 0.8 CAD for CA5-SI 1 betweenthedieselfuelandtheblends.

In Figure 3.17a, the CO emissions significantly decrease until 5 bar and increase 6 bar, indicating a lower combustion efficiency. The emissions for blends are higher than those for pure diesel fuel. The same trends can be observed for unburnt hydrocarbons (Figure 3.17b). However, in this case, the emissions of the blends are below those of pure diesel fuel even if they fall within the error bar. The NO emissions (Figure 3.17c) are similar for the blends and the pure diesel fuel.

They increase with IMEP due to the increased thermal load and, around 5 bar, decrease. As NO emissions are generally considered as roughly proportional to the mass of fuel injected; this unexpected trend might be explained by the nonoptimal injection timing. The two properties of fuels that can increase the NO emissions are the cetane number, which slightly increases the pressure and temperature, and the oxygenated molecules, which have higher oxygen availability. Since there was no significant difference between the blends and pure diesel fuel, the small differences in these key factors compensate each other.

For the first time, the impact of using valerate blends for diesel combustion is evaluated in terms of particulate emissions by measuring soot FSN. Up to 5 bar, FSN values are very small for both the diesel fuel and the blends. But at a higher load, better combustion efficiency is achieved for the blends (see Figure 3.18). This behavior might be explained by the shorter ignition delay of diesel fuel for which the onset of combustion is in a slightly richer region, in particular when a larger amount of fuel is injected. The effect of valerates on the size distribution or composition of the particulate matter could not be assessed with this setup.

As a first evaluation of the potential of blending valerates in diesel fuel, these results show that there are no significant differences in terms of pollutant emissions and performances when adding 20 vol% of esters to diesel fuel, even if the cetane number and the autoignition are different. Although these experiments were performed without optimizing the process, as the injection timing was kept constant, the differences observed between the blends and the reference diesel All studies about the use of valerates as fuel are referenced in Table 3.3.

Production Pathways

As mentioned in Section 3.1, the generation of valerates from lignocellulose involves different processing steps. As underlined by Geboers et al. [START_REF] Geboers | Chemocatalytic conversion of cellulose: opportunities, advances and pitfalls[END_REF], the hydrolysis of cellulose remains a challenge. The method most commonly used in the industry is hydrolysis by concentrated or diluted mineral acids, mainly sulfuric acid. Typically, 1% of sulfuric acid is used at elevated pressure (2.0 MPa) and temperature (493 K), with residence times of the order of several seconds. However, large-scale application of this method is complicated due to the recycling cost of the acid, reactor corrosion, and the formation of large amounts of neutralization waste. While new processes have emerged, such as solid acid catalytic systems for cellulose hydrolysis, drawbacks still remain due to the problem of adsorbed products and the rapid deactivation of the active sites of the catalysis.

Lange et al. [START_REF] Lange | Valeric biofuels: a platform of cellulosic transportation fuels[END_REF] performed the conversion of LA to valerate in a flow reactor, using different catalysts to increase the conversion efficiency and the selectivity, as summarized in Table 3. [START_REF] Leonard | Levulinic acid as a basic chemical raw material[END_REF].

Assessing the global yield is therefore not straightforward, and each step can be improved by developing new processes, as recently underlined by Kon et al. [START_REF] Kon | Selective hydrogenation of levulinic acid to valeric acid and valeric biofuels by a Pt/HMFI catalyst[END_REF].

For example, Lange et al. [START_REF] Lange | Valeric biofuels: a platform of cellulosic transportation fuels[END_REF] also developed another process where LA is converted to EV in a single step. Cofeeding ethanol with LA as a physical or chemical mixture (in the form of ethyl levulinate) over a zeolite-based catalyst led to the coproduction of VA and EV in a single step. However, no conversion and selectivity ratios were indicated: a mixture of valerate and valeric acid was obtained. Moreover, some conditions such as temperature range, H 2 pressure range, and residence time need to be improved to develop an industrial green concept. Another test was the single-step conversion of GVL into PV ("diesel" valerate), which yielded 20-50% of selectivity.

Therefore, since Lange's paper in 2010, several researchers have been trying to develop new processes for one or several conversion steps in order to optimize conversion and selectivity.

Recently, Kon et al. [START_REF] Kon | Selective hydrogenation of levulinic acid to valeric acid and valeric biofuels by a Pt/HMFI catalyst[END_REF] made a complete study of the effect of various catalyst parameters (such as the metal used) in the catalytic activity to convert LA into VA at 200 ∘ Cwith8barH 2 during 6 h. The best couple, which provided 100% of conversion, was Pt/HFMI. An interesting point is that the test was conducted not with 1 mmol but with 10 mmol. Conversion took 24 h, but as underlined by the authors, this could be due to the small amount of H 2 . They also studied the synthesis of EV and MV from LA and alcohols under an H 2 flow. After 3 h ethyl levulinate, one of the intermediates was totally consumed to produce EV. Only small quantities of VA and MTHF still remained. Therefore, complete conversion was achieved after 6 h with the catalyst Pt/HMFI at 200 ∘ Ca n d8b a rH 2 with 78% of VA and 15% of GVL. Moreover, under solvent-free conditions, LA was converted to VA while in the presence of alcohols, the selectivity varied to form different valerates. The authors concluded that it could be a cost-effective method, thanks to the use of commercial materials such as Pt/HFMI.

A new kind of process, studied by Dong et al. [START_REF] Dong | High yield of ethyl valerate from the esterification of renewable valeric acid catalyzed by amino acid ionic liquids[END_REF], is based on the use of Brønsted acidic amino-acid ionic liquids to convert valeric acid into valerate. The idea is that these liquids allow a biphase esterification without any additional dehydrating agent. They tested many different configurations: three different liquid catalysts (proline bisulfate (ProHSO 4 ), glycine bisulfate, and alanine bisulfate), a temperature range from 25 to 80 ∘ C, concentration of liquid catalyst ranging from 2% to 50% (based on mol of VA), and the VA/ethanol ratio. The highest conversion of VA to EV, more than 99.9%, was achieved with 50% of ProHSO 4 , at a temperature of 80 ∘ C, with an equal molar quantity of VA/ethanol mixture. The reaction was carried out for 7 h, and with this VA/ethanol ratio (1 : 1), due to the obtention of two-phase mixture, it is possible to select the VA easily. Therefore, ProHSO 4 can easily be isolated from the EV. After five cycles, the catalyst liquid appeared to maintain its ability to esterify VA. The authors also determined the properties of EV obtained and compared them with other fuels. The results are very promising: the energy density is higher than those of methanol, ethanol, GVL, and valeric acid. This confirms that EV is a promising biofuel candidate. This new process seems to be highly attractive and needs to be evaluated to produce other valerates.

A recent study conducted by Chan-Thaw et al. [START_REF] Chan-Thaw | New generation biofuels: γ-valerolactone into valeric esters in one pot[END_REF] is based on the use of a nonnoble metal, namely Cu, as an alternative catalyst and non Pt-zeolite one. The authors are the first to develop a one pot-one step process to obtain valerates (EV or PV) from conversion GVL to EV without the intermediate step of VA production. Different catalysts with the same Cu loading (8%) but different supports (SiZr, SiAl, and ZSM) were tested at 250 ∘ C, with 10 bar of H 2. The highest conversion rate of 77% was obtained with Cu/SiZr after a 20 h runandyieldedamixtureof37%EV+ 56%PV .T estswerealsoconductedwith pentanol to increase the quantity of PV, and the conversion ratio reached 93% with more than 80% of PV. This could be a new way to generate biofuels from lignocellulose.

The valeric biofuels introduced by Lange et al. [START_REF] Lange | Towards 'bio-based' nylon: conversion of gamma-valerolactone to methyl pentenoate under catalytic distillation conditions[END_REF] are relatively new in the biofuel world. Very few studies have focused on the origin of the biomass; this is to say that the plant or the feedstock can be optimized for valerate production. Most of the processes focus on the production of LA and then GVL. For instance, Lange et al. [START_REF] Lange | Valeric biofuels: a platform of cellulosic transportation fuels[END_REF] achieved a conversion efficiency of less than 5% for the conversion of the plant by hydrolysis to LA by using H 2 SO 4 as catalyst. Rackemann and Doherty [START_REF] Rackemann | The conversion of lignocellulosics to levulinic acid[END_REF] did an interesting review of all the processes developed to provide LA from lignocellulose. They pointed out that the production of LA from lignocellulose using mineral acids or metal catalysts suffers from several limitations: low yield, poor selectivity, the need for high temperature to convert the feedstocks, and high operating costs. They concluded that the "development of production methods has progressed from batch processes able to achieve <50% of the theoretical yield of levulinic acid to continuous processes incorporating recycling and utilizing multi-stages to optimize processing conditions to improve the yields to ∼80% of the theoretical limit."

Recently, an interesting study was conducted by researchers from Pisa [START_REF] Galletti | From giant reed to levulinic acid and gamma-valerolactone: a high yield catalytic route to valeric biofuels[END_REF]. Using a high-yield catalytic route, they developed a process to produce LA and GVL directly from a plant. As giant reed is considered to be one of the suitable biomass sources for energy production, they improved their process on it by using a bifunctional (acid and hydrogenating) ruthenium-based catalytic syst em.Only5barf orH 2 and a temperature of 70 ∘ C were required to perform hydrogenation. Initial results were very promising: almost 80% of GVL in mol (or [START_REF] Hayes | Exploring the oxidative decompositions of methyl esters: methyl butanoate and methyl pentanoate as model compounds for biodiesel[END_REF].6% in weight) was produced, and the authors concluded that this indicates the great potential of GVL for biofuel production.

All the cited studies on the different processes to produce valerates are summarized in Table 3.5.

Outlook

Due to the properties of valerates, modern cars should be able to use valerates as additives in gasoline or diesel blends without any modification to their engines; moreover, the existing network of fueling stations could be used for their distribution. To use valerates as future fuels, however, further experiments are required to evaluate their real potential. Moreover, converting lignocellulose on a sufficiently large scale to be economically attractive and with significantly reduced CO 2 emissions is still challenging. The only company to consider the production of valerates from GVL by developing the new process so far is Shell (http:// www.greencarcongress.com/2010/05/valerates-20100511.html). During the FP7 project DIBANET (Development of Integrated Biomass Approaches NETwork, 2008-2012), the United Kingdom, Brazil, and Chile were involved in developing novel sustainable technologies for the production and use of levulinic acid to make diesel-miscible fuels (via the esterification of ethanol with levulinic acid over solid acid catalysts), but not the production of valerates. The available level of technology is not high: as several steps of the processes are still at the optimization stage, the economic viability of the fuel production process has not yet been assessed.

Biofuel can be used as an additive to replace ethanol, for example, without any problem, but it is still not possible to determine whether it is less expensive and better for the world biomass than ethanol production. Moreover, it is still necessary to decide which plant, such as giant reed, would be the most appropriate to produce valerates.

Conclusions

Since Lange et al. announced their new process in 2010 to produce levulinic acid derivatives from lignocellulose, valerates have been studied in order to assess their capacity as potential fuels for car engines. These fuels are more suitable than GVL because they can provide biofuels of similar properties and that can be either blended with gasoline or diesel or used as fuels themselves. Recent works have focused on determining properties such as ignition delay, laminar burning speeds, and kinetic schemes to ensure their suitability as fuels. Few studies show that blends of valerates can be used as fuels in SI or compression engines without any drawback, but more real road experiments are needed to improve the real ability of valerates to be used as substitute fuels. As propyl valerate has properties between gasoline and diesel types, studies are also needed to improve it as a potential fuel.

Figure 3 . 1 Figure 3 . 2

 3132 Figure 3.1 Roadmap for the conversion of lignocellulosic biomass (rectangles) to chemicals (ovals) and fuels (pentagons), via the intermediate formation of C5 and C6 sugars (hexagons), suggested by Azadi et al.( R e p r oduced with permission from Azadi et al. [1] of Royal Society of Chemistry.)

Figure 3 . 3

 33 Figure 3.3 Optimum ignition conditions for valerates as fuel compared with PRF.

Figure 3 . 4

 34 Figure 3.4 Experimental values of laminar burning velocities of ethyl and methyl pentanoate/air mixtures at T = 423 K (a) as a function of the equivalence ratio at 1 bar (filled symbols) and 3 bar (open symbols).

Figure 3 . 7 Figure 3 . 8

 3738 Figure 3.7 Efficiency and CO 2 emissions as a function of IMEP for EV, MV, PRF as fuel, and 20% EV and MV blends. The open symbol is for 1500 rpm and the filled one for 2500 rpm.(Reproduced with permission from Contino[START_REF] Contino | Engine Performances and Emissions of Second-Generation Biofuels in Spark Ignition Engines: The Case of Methyl and Ethyl Valerates[END_REF] of SAEInternational.)

Figure 3 . 9

 39 Figure 3.9 Example of cylinder pressure and HRR evolutions for MV, EV, and PRF95 (intake pressure = 0.6 bar, IMEP = 4.5 bar).

Figure 3 . 10

 310 Figure 3.10 Estimated ignition delay for MV and EV at different temperatures.

Figure 3 . 11 Figure 3 . 12

 311312 Figure 3.11 Specific consumption as a function of the low heating value for the three different fuels for both conditions.

Figure 3 . 13

 313 Figure 3.13 Ethylene, methane, and benzene emissions for all fuels and under both engine conditions.

Figure 3 . 14

 314 Figure 3.14 Compression-ignition single-cylinder bench.

Figure 3 . 15

 315 Figure 3.15 Indicated efficiency as a function of IMEP for diesel and blends with 20% of BV and PenV.

Figure 3 . 16

 316 Figure 3.16 Ignition delay determined by CA5-SI 1 for BV and PenV in comparison with diesel.

Figure 3 .

 3 Figure 3.17 CO, unburnt HC, and NO emissions as a function of IMEP.

Figure 3 . 18

 318 Figure 3.18 FSN values as a function of IMEP for both blends.

Table 3 . 1

 31 Properties of valerates as fuels.

	Fuel	Structure	MW
			(g

/mol) O 2 (wt%) LHV (MJ/kg) AFR st (kg/kg) T b (K) BRON Lange et al. [9] DCN ASTM D7668 H vap (kJ/kg at 298 K) Density (kg/l)

		Region of CA50 from 0 to 1 CAD
	1. 6 1. 5 1. 4	BV	EV iso-octane	MV
	1. 3 1. 2	PenV
				PRF80 PRF90
				PRF60
		PRF40
		PRF20
		n-heptane
	Methyl	116	27.5 28.8 9.52 410 115	n.a.	371	0.875
	valerate
	Ethyl	130	24.6 30.3 10.09 415 100	17.1	361	0.874
	valerate
	Propyl	144	22.2 31.5 10.55 440	90	n.a.	277	0.870
	valerate
	Butyl	158	20.2 32.6 10.92 460 n.a.	24.5	335	0.868
	valerate
	Pentyl	172	18.6 33.5 11.24 479	10	30.3	257	0.874
	valerate

  analyzer with an accuracy of

	Electric motor
	p	p
		Intake plenum		Flow meter and controller
	T	T	Fuel
	Exhaust gas		vaporizer	Flow meter
	analyser			and controller
	CO, CO 2 , O 2 , NO x , HC	Flow meter and controller
	Crankshaft	Pressurized
	position sensor	fuel tank	Air

Figure 3.6 Single-cylinder SI engine bench.

Table 3 . 2

 32 Operating conditions for unregulated pollutant emission study.

	Case	Regime	Intake	Optimized	Equivalence
		(rpm)	pressure	IMEP	ratio
			(bar)	(bar)
	Case 1	2000	0.64	5	1
	Case 2	1700	0.5	3	0.81

Table 3 . 3

 33 Summary of the studies focused on the global performance of pure valerates and blend in IC engines.

	Reference	Engine type	Operating	Concentration	Key conclusions	Mechanisms
			conditions	in blend		involved
				(or neat use)
	Lange et al. [9]	SI engine (10	Road	15% of EV in	No difference in	Global study
		vehicles)	(500 km/day)	commercial	fuel
				gasoline	consumption
					No effect on
					global behavior
					(fuel tank,
					emissions, etc.)
	Contino et al.	SI engine (0.4 l,	From 2 to 9 bar	20% MV and	No visible effect	Higher laminar
	[17]	single cylinder)	IMEP, 1200 rpm	EV in PRF95	for blended fuels	burning speed
					(efficiency, CO 2 ,
					NO, CO, UHC)
					For pure fuel	Higher research
					higher CO 2	octane number
						and ignition
						delay
	Mounaïm-	SI engine (0.5 l,	5barIMEP,	100% EV	Higher	Higher laminar
	Rousselle et al.,	single cylinder)	2000 rpm		consumption	burning speed
	private
	communication		3barIMEP,	100% MV	Less UHC, CH 4 ,	Higher Research
	(2014)		1700 rpm		benzene	Octane Number
					emissions but	and ignition
					higher ethylene	delay oxygen
					and	contents
					formaldehyde
	Contino et al.	CI engine (0.4 l,	From 2 to 9 bar	20% of BV and	No visible effect	Cetane number
	[17]	single cylinder)	IMEP, 1500 and	PenV in diesel	for blended fuels	Higher ignition
			2500 rpm		(efficiency, CO,	delay
					NO, CO, UHC,
					FSN)
	fuel, in particular above 6 bar IMEP, are very small and would probably be further
	reduced by proper optimization.

Table 3 . 4

 34 Key performance indicators for the Lange et al.[START_REF] Lange | Towards 'bio-based' nylon: conversion of gamma-valerolactone to methyl pentenoate under catalytic distillation conditions[END_REF] three-step process.

	Step	LA to GVL	GVL to VA	VA to valerate
	Process	Hydrogenation	Hydrogenation	Esterification
	Catalyst	Pt/TiO 2	Pt/ZSM-5	Acidic resin
	Selectivity (%)	>95	>90	>95
	Conversion (%)	>90	>50	>50
	Residence time (h)	10	1	0.02

Table 3 . 5

 35 Different processes to obtain valeric esters.

	Reference	Reactor	Operating	Concentration	Catalyst	Main	Maximum yield
		type	conditions	in solvent	(if present)	reaction	and associated
				(or neat use)			operating
							conditions/
							catalyst
	Lange et al.	Flow	Temperature	Ethanol	Pt or Pd/	Hydrogenation	20-50%
	[9]	reactor	275-300 ∘ C		TiO 2	+ esterification	selectivity
	GVL to EV		Pressure 10 bar
			Residence time
	Luo et al. [34] LA to EV		Temperature 200 ∘ C	Dioxane	Ru/TiO 2		VA + valerate 45.8%
			Pressure 40 bar				conversion
			H 2
			Residence time
	Pan et al. [35]		Temperature	Ethanol	Ru/SBA-	Hydrogenation VA + EV
	LA to EV		240 ∘ C		SO 3 H		94% conversion
			Pressure 40 bar
			H 2
			Residence time
	Kon et al.		Temperature		Pt/HFMI
	[29]		200 ∘ C
	LA to VA or		Pressure 8 bar H 2
	EV		Residence time
	Dong et al. [30]	25 ml round	Temperature 80 ∘ C	Ethanol	ProHSO 4	Esterification	99% conversion 100%
	VA to EV	bottomed	Pressure				selectivity (two
		flask	Residence time				phases)
			7h

Acknowledgments

The research leading to the authors has received funding from the European Research Council under the European Community's Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement no. 291049 -2G-CSafe.

Abbreviations

LA


D Hrabovský

B D I O U F

L Gabillet

A Audouard

A R F E R T

Dj F B O B O

Exchange anisotropy in Co/NiO bilayers: time-dependent effects

Keywords: . 75.50.Ee Antiferromagnetics -75.60.-d Magnetic domain effects, magnetization curves, and hysteresis -75.70.-i Magnetic properties of thin films, surfaces, and interfaces

The time dependence of the exchange anisotropy was studied in Co/NiO bilayers. In order to only observe the relaxation phenomena inside the antiferromagnetic (AF) layer and to eliminate the dynamic behaviour inside the ferromagnetic (F) layer, we have developed an experimental method where a small a.c. magnetic field is applied perpendicular to the main anisotropy axis. All data are obtained by magneto-optical (m.o.) experiments. We observe a logarithmic time dependence of H ud , the exchange unidirectional anisotropy. We prove that the key parameter for the rate of relaxation is the anisotropy of the AF layer which depends strongly of the preparation method. We use the random field model as proposed by Malozemoff and suppose a breakdown of the AF interface into regular domains of size close to the crystallite size (10 nm width). If we further develop a Fulcomer and Charap relaxation model, we can propose from the distribution of relaxation times an analysis in terms of a spread of AF anisotropy energies. High magnetic pulsed field experiments (55 T) complete the experimental study and the results are analysed assuming that the Zeeman energy balances the anisotropy energy of the AF domains and switches them into the opposite direction.

Introduction

The phenomenon of exchange bias was discovered more than fifty years ago by Meiklejohn and Bean [1]. They observed that fine Co particles, oxidized at their surface, exhibit a shift of the magnetic hysteresis along the field axis, the center of the hysteresis loop being displaced to H =0, as though there were an internal exchange field H ex .Inrecent years, numerous investigations of this effect have been carried out on ferromagnetic (F)-antiferromagnetic (AF) bilayer systems. The hysteresis loop displacement is the most characteristic feature of exchange bias, but also an enhancement of coercivity is often observed. The interfacial exchange coupling gives an efficient method for technical applications like pinning or hardening of some ferromagnetic layer magnetization. Several groups have used FeMn antiferromagnetic films as an exchange biasing layer to study their spin-valve-like response for magnetic sensor applications [2][3][4][5]. One can also use NiO as an antiferromagnet, as already reported by several groups [6][7][8][9][10]. Compared to intermetallic antiferromagnets like FeMn, NiO is an insulator with a good resistance to corrosion and a relatively high blocking temperature T B (the Néel temperature for bulk NiO is 525 K, but clearly lower for thin a e-mail: jfbobo@onecert.fr films). This biasing effect is the consequence of exchange coupling across the AF/F interface. This phenomenon is particularly observed when an external field is applied while cooling the ferromagnetic layer through T N ,t h e Néel temperature of the AF layer. The role of the external magnetic field is subject of discussion. Despite a great variety of works on this subject, the exact mechanism of exchange bias is still controversial, mainly because the observation of the interfacial magnetic structure is difficult. Meiklejohn and Bean developed a simple model to explain the loop shift when ferromagnetic particles are embedded in an AF. The model considers single domain F particle with uniaxial anisotropy -K ua cos 2 θ (θ is the angle between the magnetization MF and the uniaxial axis) and subject to an unidirectional field H ud along the same axis which transfers the exchange coupling to a rigid AF. In the case of an ideal F/AF bilayer system, we suppose an uncompensated interface where only one type of AF sublattice spins is present. In a Stoner and Wohlfarth description the switching fields H c1 and H c2 (in positive and negative direction along the anisotropy axis) do not have the same value because of the additional contribution of the interface coupling and the hysteresis loop is displaced by an amount H bias =1/2(H c1 + H c2 )=-H ud . The bias field estimated in this simple model where the interface is uncompensated is, however, two orders of magnitude larger than experimental values. Mauri [11] also assumes a non compensated interface but the AF spins at the interface reverse simultaneously with the F spins when the F magnetization layer is reversed. In fact he supposes that a planar domain wall parallel to the interface is formed inside the AF layer. Malozemoff [12] supposes that roughness at the interface induces a random exchange field between the two layers, much as in the Imry-Ma random field problem. A minimization of energy argument suggests to break up the AF into magnetic domains (lateral size L and depth h = L/2) due to random fields. Writing the local unidirectional exchange interface energy (expressed in erg/cm 2 )intheformσ l = ±zJ i /a 2 (J i is the individual exchange constant at the interface and the model assumes a simple cubic structure with lattice parameter a and z the coordination number) in the random field problem, the local interface energy will be random and its average value in a region of area L 2 will go down statistically as σ = σ l / √ N where N = L 2 /a 2 the number of sites projected onto the interface plane. This model yields a result very similar to the one of Mauri and explains the order of magnitude of the bias field observed in AF-F interfaces. But in the Mauri model the AF domain wall is parallel to the interface, it is created for one direction of the applied magnetic field and disappears for the opposite direction, exactly as when you exert a rotation strain on a mechanical sample, an elastic stress (a twist) appears to absorb the strain. This dynamic aspect is very interesting. On the contrary, in the Malozemoff model, the AF magnetization breaks down into numerous domains at the interface, most of them being oriented in the same direction as the F magnetization. These domains are a priori static during the reversal of the F layer magnetization, but when the F magnetization remains in reverse position, the AF domains are submitted to a torque that tends to reverse their magnetization. This phenomenon is thermally activated and a relaxation of the exchange anisotropy could be observed, and this will be the presently studied phenomena in Co/NiO bilayers. These last years some experimental studies have demonstrated that the exchange field at the AF/ F interface is time dependent. Several authors have observed a slight decrease or increase in time of the bias depending of the history and final state of the F magnetization. We have observed, in particular when studying magnetic properties of NiO/ Co bilayers, that if we do not pay attention to restore the sample with the same final Co magnetization state the bias is strongly modified a couple of days or a week after. For the two states accessible in zero magnetic field and corresponding to the Co magnetization in the same (forward) or in the opposite (reverse) direction to the bias field, the after-effects are strongly different.

In the present paper, we describe the preparation method of samples Glass/NiO/Co and the experimental procedure based on a small a.c. magnetic field applied perpendicular to the easy anisotropy axis, the measurements being done by magneto optical methods. We develop a simple model based on the relaxation of interfa-cial AF magnetic domains to analyze the observed after effects.

Experimental procedure

We have studied various types of Co/NiO samples corresponding to different preparation methods that we have described in detail in a previous paper [13] where we find out conditions for obtaining strong uniaxial anisotropy in the Co layers grown on nickel oxide. NiO was deposited using an RF facing target magnetron, the standard DC magnetron method being used for the Co layer. For deposition of NiO layer, with a constant 1250 Åthickness, two distinct processes were adopted. For the first one the substrate was in a fixed position (FIX), by this way we obtained a well-defined anisotropy in the AF layer, due to oblique incidence deposition, and a subsequently anisotropy in the Co layer deposited on it. We also prepared samples with desired anisotropy by depositing NiO with a rotation of the sample holder, in order to avoid oblique incidence deposition, but the sample holder was equipped with two permanent magnets (MAG) generating an applied magnetic field of 1 kOe. In this last case the morphology of the interface is smoother. Magnetic tunnel junctions [13] of NiO/Co/Al 2 O 3 /Co type made with both processes for the bottom electrode show sharp magnetoresistive responses and yield more than 20% of tunneling magneto-resistance (TMR) at room temperature along the easy axis. We will present here the results observed with three samples FIX60, FIX80, and MAG50 (the sample name indicates the type of growth process and the Co layer thickness in Angstrom unit) selected from many others. The whole magnetic study was realized by magneto optical (m.o.) measurements. To measure the Kerr rotation we used a balanced optical bridge composed of a Wollaston prism to divide the reflected light at the sample surface into two orthogonal polarized beams. Their intensities are detected by two matched Si photodiodes. The differential signal is converted using a 16 bit analog-digital converter. A linearly polarized He-Ne laser was used as a probe. The sample is placed in the center of a copper coil and an accurate current supply generates a magnetic field at its center.

First results on the value of the exchange anisotropy were obtained by classical hysteresis loops measurements. The applied magnetic field was along the easy magnetization axis of the Co film, and the observed Kerr rotation was proportional to the Co longitudinal magnetization (component parallel to the field and to the plane of incidence of the light). For these measurements the applied magnetic field was periodic with a 50 Hz frequency and an amplitude up to 1 kOe, but in order to avoid the warming of the coil, the computer limited the number of periods to six and evaluated the hysteresis loop data during the last period of the magnetic field. Moreover it stopped the magnetic field to manage the final direction of the Co magnetization always in the same direction (positive or negative). At the beginning of the experiments the sample was set up and the Co layer magnetized in the MO signal (a.u.) -400 0 400 Magnetic field H (Oe) t = 0 t = 28 min Fig. 1. Hysteresis loops obtained at t =0a n dt =2 8m i n after reversal of the Co magnetisation at t =0. positive direction, we measured successively the hysteresis loop measurements at regular time intervals and verified that the value of the bias remains constant. After this test and in order to study the relaxation of the bias, we applied, at t = 0, the magnetic field in order that the final state of the Co magnetization was reversed (in the negative direction) and we carried out successive hysteresis loop measurements. Figure 1 presents the hysteresis loops for t =0andt = 28 minutes for sample FIX60 deposited without rotation of the substrate. Note that the bias field has relaxed from a value close to 56 Oe to 37 Oe. This kind of experiment is repeated and the time dependence of the bias is shown in Figure 2. We observe a continuous decrease of the bias when the Co magnetization is in a reversed position (the bias is close to zero after 6 days) and an increase of the bias if the Co magnetization is switched back to the first positive direction.

The analysis of the hysteresis loop was done using the classical model (Meiklejohn and Bean -M.B.) written in the case where a F layer is deposited on an AF layer with an uncompensated interface. Taking into account a ferromagnetic exchange interaction between F and AF spins, the energy of this configuration could be written in the form

E = -H a M F t F cos θ -K ua t F cos 2 θ -J int cos θ (1)
where M F is the F magnetization by unit volume (emu/cm 3 ), H a is the applied magnetic field supposed along the easy axis, K ua is the uniaxial anisotropy by unit volume (erg/cm 3 ), t F is the thickness of the F layer, J int is the exchange interaction energy at the interface by unit surface (erg/cm 2 ). In a Stoner-Wohlfarth (S.W.) model description, the switching fields H c1 (forward) and H c2 (reverse), derived by considering the stability of states θ =0andθ = π are

H c1 = -(2 K ua t F + J int )/M F t F H c2 =(2K ua t F -J int )/M F t F .
We could introduce, as was done by M.B., an uniaxial field H ua =2 K ua /M F and an unidirectional field

H ud = J int /M F t F which translates the effect of the interface cou- pling into H c1 = -H ua -H ud and H c2 = H ua -H ud .
Due to the contribution of the interface exchange coupling, the two switching fields are not equal and the hysteresis loop is displaced by an amount -H ud = -J int /M F t F which appear inversely proportional to the F layer thickness as expected for an interfacial effect. From hysteresis loop measurements the exchange anisotropy (uniaxial and unidirectional parts) is deduced from the two coercive fields H c1 and H c2 . Moreover the coercive fields depend strongly on the rate at which the applied field is varied. Many phenomena must be taken into account like nucleation or propagation processes and thermal activation, and a S.W. model is generally not convenient for describing the reversal process. Moreover the hysteresis loops depend on dynamic effects (magnetic viscosity) in the F layer resulting from the rate of change of the applied field. In order to observe only the relaxation phenomena inside the AF layer, the dynamic behavior inside the F layer must be eliminated. For these reasons we have developed an experimental method close to that proposed by Krivotorov [14], probably being more efficient because the magnetic state of the F layer is unchanged during exchange anisotropy relaxation measurements. In the Krivotorov's experiments a small a.c. magnetic field is applied perpendicularly to the main easy anisotropy axis in the plane of the Co/CoO sample and by help of a technique based on the anisotropic magnetoresistance effect (AMR) they obtain the a.c. response of the Co magnetization whose amplitude depends on the exchange anisotropy field H ex = H ua + H ud . We have developed an equivalent method based on magneto optical (m.o.) measurements. The anisotropy axis of the sample is oriented perpendicularly to the incidence-reflection plane of the laser beam (see Fig. 3), the a.c. magnetic field (amplitude 10 Oe, frequency 60 Hz) is applied in this plane and in the plane of the sample, by this way the longitudinal Kerr effect (obtained by help of a numerical lock-in amplifier) gives directly the component of the magnetization along the applied a.c. magnetic field (perpendicular to the easy magnetization axis). In our measurements the magnetization of the Co layer is locked in one of the two stable positions corresponding to θ =0orπ and we observe a small a.c. Co magnetization component resulting from the a.c. applied field. From the amplitude of this component we could deduce the exchange anisotropy field and study its time dependence. With this method, we separate the time dependent effects in the AF layer from dynamic effects in the F layer. Using the expression (1), completed by the term -H ac M F t F sin θ, we could deduce from the measurements of M ac the value of H ex by the simplified formula (we suppose small angles and a zero dc magnetic field)

M ac = M F H ac /(H ua + H ud )( 2 )
analogous to expression (2) in Krivorotov's paper. The smaller important is the exchange field, the smallest is the amplitude of transversal magnetization oscillations.

For larger amplitudes of oscillation a numerical calculus replaces this simplified formula. phenomenon. These values of H ua and H ud can be compared to those obtained, before any relaxation, by the classical hysteresis cycle method (see Fig. 2). We deduce from the shift of the hysteresis loop a slightly different value of the unidirectional field, H ud ≈ 50 Oe. As explained above, the hysteresis loop method supposes that the S.W. model is appropriated to describe the switching of the Co magnetization, however, this is not the case. Moreover, for 65 <t<100 seconds, we observe in Figure 4 the onset of the relaxation of H ud .A tt = 100 seconds, switching back the Co magnetization to the positive direction, we observe H ex = 930 Oe. Considering that the uniaxial anisotropy has a constant value, we could deduce the unidirectional field H ud (100) = 71 Oe value obtained after the relaxation of the AF domains during 35 seconds. The second preliminary study concerns the same sample, but 3 days after that the Co layer was saturated in the reverse direction. We consider that H ua has not changed and that H ud has relaxed during this time towards a value corresponding to some more complex and stable state of the NiO layer obtained after three days of reverse orientation of Co. Measurements presented Figure 5 show that H ex ≈ 869 Oe. When reversing at t = 60 s the Co magnetization in the forward direction, a very small change . Same experiment as in Figure 6, but with opposite initial cobalt magnetization. Contrary to sample FIX60 (Fig. 5), it could be observed that the unidirectional field H ud has changed its sign after several days with a reverse Co magnetisation, proving a larger relaxation rate of the bias field.

of the exchange field is observed. As previously, we can deduce both values of the uniaxial and unidirectional field H ua ≈ 875 Oe and H ud ≈ 6 Oe. We observed that H ua has kept the same value (the discrepancy between 875 and 859 Oe is not significant) but the unidirectional field has relaxed during the three days to some value close to zero. Moreover, we observed for 60 <t<95 s , when the Co is back in a forward position, that H ud begins to increase to recover a positive value.

The same preliminary study was realized with sample MAG50 corresponding to a lower anisotropy of the antiferromagnetic layer. Results are presented in Figures 6 and7. We observed that, after several days with a reverse magnetization of the Co layer, the unidirectional field H ud has changed its sign which proves that the NiO magnetization was partially reversed.

After these preliminary studies, we have investigated the relaxation of H ud (t) following the experimental protocol:

1. saturation of Co in the positive direction during several days to recover the magnetic state S1 observed after the preparation of the samples, 2. reversal of the Co magnetization in the negative direction at t =0, 3. measurements of M ac (t)f o rt>0, H ud (t) being deduced using expression (2).

In Figure 8 we present the results obtained for the three samples FIX60, FIX80 and MAG50. In order to compare the relaxation process for the different samples, H ud (t) was normalized by the value of H ud (0). We observe that H ud is roughly constant during the first instants of measurements 0 <t<t 1 (t 1 is sample-dependent but is always of the order of magnitude of ten seconds). For t 1 < t<t exp we observe a logarithmic time dependence of H ud that could be written as H ud (t) -H ud (t 1 )=-K Log t/t 1 . The time t exp corresponds to the end of the M ac acquisition measurements. Clearly several experiments were done with a greater t exp (for example 12 hours) and seems to prove a logarithmic time dependence for larger time range but the signal to noise ratio of dH/dt becomes smaller and smaller and prevents a precis analysis of the time dependence of H ud for longer times. The various parameters characteristic of the samples FIX60, FIX80 and MAG50 are summarized in Table 1. For each of them, the values of the relaxation speed K, uniaxial and unidirectional fields H ua and H ud are presented for the relaxation from the state S1 which is the quasi stable state obtained after preparation of the samples. Table 1 also shows the main parameters deduced from a next experimental step where the relaxation is studied from an intermediate state, called S2 for simplification, carried out several days after reversal of the Co magnetization. The relaxation is then studied when reversing one more time the Co magnetization in the positive direction, the system coming back to state S1. We observe a value of the slope K larger in the case of NiO deposited with rotation of the substrate, this sample corresponding to lower anisotropy of the NiO layer. The values of H ud are close to zero after 2 hours of measurements, the unidirectional field H ud (t) changes its sign and the reversal of a large part of the AF domain magnetization is achieved. On the contrary, for a sample without rotation of the substrate, the unidirectional field H ud (t)is

4Analysis

As proposed by Malozemoff, and due to random field created by roughness, we assume the formation of regular AF domains, at the interface. Let us justify, in our case, this Malozemoff approach. Miltényi et al. [21] have proposed that the exchange bias is due to magnetic domains in the volume of the AF layer. This hypothesis is asserted by an experimental study on systems AF/F with diluted AF. In this case, the number of domains depends of the defect density inside the bulk AF layer, each defect being a pinning center for a domain wall (and not on disorder or defects at the interface). Results obtained by A. Mougin et al. [22] on irradiation effect on exchange bias systems are consistent with the Miltényi model. But in our case the structure of magnetic domains is linked to the preparation process of the NiO layer, and we have shown [13] that for non rotating substrate, the inclined deposition induce columnar growth with 10 to 15 nm wide grains (the grains crossing the whole AF layer with a rather constant dimension). We consider that the AF domains size is correlated to the crystallite size and the problem of exchange bias differs, in our case, from the phenomena observed in diluted AF. We suppose, as in the Malozemoff model, that the magnetic configuration in the bulk AF layer (125 nm thick) is fixed when the Co is reversed. The torque exerted by the reversal of the F magnetisation involve only the drag of an interfacial part of the AF domains. With this hypothesis, each domain presents a weak net magnetic moment resulting from the non total compensation of the spins. As a consequence of the preparation method (cooling with an applied magnetic field) most of these magnetic moments are oriented along the easy anisotropy axis and are ferromagnetically coupled with the adjacent Co layer magnetization. It induces a bias field and the hysteresis cycle is not centered at H =0 .W h e n the Co magnetization is reversed (due to negative applied magnetic field) most of the AF domains are submitted to a torque that tends to reverse their magnetization in the same direction as the Co layer. This phenomenon is thermally activated and explains the after-effects observed concerning the bias field. Following the presentation of Fulcomer and Charap [15] we consider that the AF domains are identical and non-interacting and that they are exchange coupled to the magnetization of the Co film. The total energy E AF for one of these identical domains can be written:

E AF = K AF a V sin 2 γ + J × S cos γ
where γ is the angle between the AF moment and the common AF and F easy axis, K AF a is the unit volume anisotropy of the AF layer, V is the AF domain volume, S is the contact area between AF domain and Co film, J is the unit area interface exchange coupling constant (in the paper of Malozemoff J is called σ)a n dJ results from the incomplete compensation of the AF moments at the interface and can be written as inversely proportional to √ N ,w h e r eN is the number of interface spins in an AF domain. For JS < 2 K AF a V , there are two equilibrium states for the AF domain magnetization which are γ =0 (state 1) and γ = π (state 2), separated by a maximum of the total energy equal to

E max = K AF a V 1+ JS/2 K AF a V 2 .
The switching of the AF domain magnetization above E max is activated by thermal fluctuations. The barrier energies are of distinct amplitudes when going from state 1 to state 2 and inversely

∆E± = K AF a V 1 ± JS/2 K AF a V 2 .
The probability to overcome the barrier is thermally activated and consistent with an Arrhenius law τ = τ 0 exp (+∆E/kT )w h e r eT is the temperature of the experiment, ∆E the barrier energy and τ 0 being a characteristic attempt time for spin reversal. ∆E being stronger when going from state 2 to state 1, the AF domain magnetization approaches a new equilibrium corresponding to AF moments in the same direction as the Co magnetization. The two process 1→2a n d2 →1 are characterized by two relaxation times τ 1 and τ 2 and finally the total time constant τ will be given by the expression

1/τ =1/τ 1 +1/τ 2 =1/τ 0 [exp(E 1 -E max )/kT +exp(E 2 -E max )/kT ].
The unidirectional field (or bias field) evolves in time according to

H ud (t) -H ud (∞)=[H ud (0) -H ud (∞)] exp(-t/τ )
where H ud (0) and H ud (∞) are the initial and final fields.

As often in similar systems an appropriate size, volume or energy distribution leads to a logarithmic time dependence. The unidirectional magnetic field can be then expressed in the form:

H ud (t) -H ud (t 1 )=[H ud (0) -H ud (t 1 )] × τmax τmin ρ(τ )exp-t/τ dτ = S log t/t 1 ( 3
)
where S is the viscosity characteristic of the relaxation rate. The time dependence of H ud observed experimentally in various cases (see Fig. 8) is well described by a logarithmic function of time. These results are in agreement with the existence of a distribution of domain sizes or energies. The parameters τ max and τ min , determining the range of time constant distribution, can be obtained by fitting the experimental H ud (t) to the above equation under the assumption ρ(τ )=1 /τ and are presented in Table 2 [16].

Discussion

The Fulcomer and Charap model [15] can be developed or applied to our system when assuming some hypothesis.

The main one concerns the size of the AF domains and this point will be discussed at first. In a second part, taking into account the distribution of τ (relaxation characteristic time) which results from the experimental study, we try to deduce most of the characteristics of the NiO/Co systems. As in most of the models, the ferromagnetic layer is regarded as a single domain. This assertion is not obvious because the F domain size, during magnetization reversal, has been observed to be much smaller in an exchange biased bilayer than in a single F layer. Nevertheless we have observed for systems Glass/ NiO/ Co [17] F domains of sufficient large size (in the range 1 µm-1 mm) compared to the size of the AF domains to consider the F layer as single domain. Moreover we consider that the domain size of NiO may be strongly correlated to the crystallite size. By HREM we have noticed regular columnar grains of 10 to 15 nm wide. The NiO films are in our experiments 125 nm thick, but taking into account the work of Malozemoff the reversal does not concern the whole AF film, only a thickness of order of 5 nm (the half width of the domains) is involved. Consequently the mean AF domain volume could be estimated to V = 0.5 × 10 -18 cm 3 . This small size of the AF domains is confirmed by the work of Wang et al. [18]. When they pattern in micronic dots a NiO/NiFe bilayer, if the NiO film is epitaxially deposited the exchange field increases when reducing the pattern size proving that, in this case, the AF domains are larger than one micron. On the contrary, the exchange field of patterned polycrystalline NiO on Si does not depend of the pattern size, demonstrating a considerably smaller AF domain size, close to the grain size. The order of magnitude of the AF domain size can be also approached considering that the domains tend to contract, as explained by Malozemoff, until the size equals the wall width, whose classical expression is δ = π A AF /K AF a . Taking into account the absolute values of the exchange constants A 1 =1 .6 × 10 -7 erg/cm between first neighbours, A 2 =6 .7 × 10 -7 erg/cm between second next neighbours and a mean anisotropy constant K AF a =3 .3 × 10 6 erg/cm 3 , we obtain the value δ = 14 nm. This value is consistent with the above mentioned order of magnitude obtained when considering that the domain is similar to the grain size (10 to 15 nm). Nevertheless the breakdown of the AF layer, close to the interface, into small conventional magnetic domains is clearly a strong simplification of the physical reality. Due to interface roughness there is a strong magnetic frustration in the AF layer leading to magnetic disorder at the interface as in any system with random anisotropy. The after effects reported above, when we reverse the Co magnetization, is characteristic of frustrated spin system. Complex transitions between metastable states are thermally activated and the simple model of regular AF domains at the interface is a rough approximation. If one further allows that the interface exchange coupling constant J between the Co layer and a perfectly uncompensated AF plane is close to the value J 0 = 10 erg/cm 2 [19], one can expect, as in the Imry-Ma random field problem, that the effective coupling energy per unit area would go down statistically as J = J 0 / √ N where N is the number of Ni magnetic sites at the interface between the AF domain and the Co layer. Taking into account the mean surface of each AF domain at the NiO/Co interface we can deduce an averaged coupling energy associated with an AF domain surface: J S =0.2 × 10 -12 erg.

We now discuss the experimental results in terms of relaxation time range. As shown in Figure 8, the typical relaxation time range characteristic of the decrease of H ud (t) is roughly equal to 1 <τ <1000 s. Taking into account τ 0 =1 0 -9 s, and JS =0 .2 × 10 -12 erg, assuming that all the AF domains are equal in size and a distribution of anisotropy energy, we can deduce the range of anisotropy energies 0.72 × 10 6 <K AF a < 0.84 × 10 6 erg/cm 3 .T h e s e values are completely in the order of magnitude that we would expect taking into account that K AF a (associated to magnetocrystalline anisotropy) of NiO is at maximum equal to 3.3×10 6 erg/cm 3 . Note that we have not observed a possible texture in the NiO film and that consequently the easy (111) planes are randomly distributed. We recall that the anisotropy is in our case, and for non rotating substrate, the result of oblique incidence deposition. In case of a rotating substrate the anisotropy results from magnetoelastic effects due to deposition under 1 kOe applied magnetic field. When comparing these results with results obtained by Dubourg [17] in the case of a purely rotating substrate we observe that he obtained a value roughly ten times smaller K AF a =0.1 × 10 6 erg/cm 3 .

High magnetic field experiments results and analyze

These experiments were done subsequently to our recent results [20] for various exchange-biased systems exposed to pulsed magnetic fields. A 55 T magnetic field pulse was applied on the same series of samples in two directions, namely along the exchange unidirectional field and opposite to it. In the first case, and for sample FIX60, no change in exchange bias was detected after the pulse, its value remaining 56 Oe (as observed by hysteresis cycle measurements). In the second case, where the 55 T pulsed field reverses the Co magnetization, we observed, a ss h o w ni nF i g u r e9 ,a ni m m e diate bias field decrease to zero, the decay time being probably reduced to the field pulse duration (less than 500 ms).

This evidences that, during the high magnetic field pulse, the Zeeman energy on non-compensated moments of the AF domain balances or overcomes the anisotropy energy barrier and switches some of the AF domain magnetization into the opposite direction.

It has to be noted that used m.o. method does not allow to reveal constant contribution to the magnetization (magnetic moment from non-compensated AF domains), and hysteresis loops in Figure 9 are manually centered along vertical axis.

By these high magnetic field experiments we can expect a new possible estimate of the energy barrier and have a confirmation of the previous model. At first we can evaluate the mean magnetic moment associated with the non compensation of the AF domain volume whose size was discussed earlier. We know the average number N of spins in a volume corresponding to the AF magnetic domains N =2 .5 × 10 4 . The statistically non-compensated magnetization of each AF domain could be written in the form M =2µ B √ N =29× 10 -22 JT -1 . When a 55 T high magnetic field pulse is applied along the uniaxial axis but opposite to the unidirectional field, we have observed an immediate bias field decrease to zero. An estimate of the Zeeman energy of the AF domain (vol- This energy is larger than the barrier energy due to the anisotropy. It could explain the immediate reversal of a lot of AF domains in the direction of the Co magnetization inducing the observed decrease of the bias field.

The method consisting to apply a series of pulsed magnetic field of increasing amplitude could be an efficient experimental process to probe the distribution of barrier energies. This conclusion could be debated, if we consider that, in high magnetic field, the spin flop phase could be induced in a large part of the antiferromagnetic domains. This effect, probably favor the simultaneous reversal of AF domains with the Co magnetisation in the direction of the applied magnetic field.

7Conclusion

We have developed a magneto-optical method to study the relaxation of the exchange anisotropy. The results obtained with Co/NiO systems show a systematic logarithmic time dependence of the unidirectional field H ud .T h e relaxation rate of H ud is directly correlated to the uniaxial anisotropy of the AF layer which results of the deposition method. For example, when NiO is obliquely deposited, the characteristic time of relaxation is very long, the bias tends to a value close to zero after about several days when the Co magnetization is reversed. Assuming the analysis developed by Malozemoff based on random field model and the model of Fulcomer and Charap, we propose a possible first description of this phenomenon. Clearly real systems are more complex and the AF/F interface presents more the characteristics of a frustrated spin system.

Fig. 2 .

 2 Fig. 2. Time dependence of the bias field HB after reversal of the Co magnetisation (at t =0a n dt = 140 sec). The arrows indicate the direction of the Co magnetisation.

Fig. 3 .

 3 Fig. 3. Experimental configuration for the a.c. perturbation method: position of sample, of the laser beam and of the two applied magnetic field components H dc (static) and Ha.c. (alternate).

Fig. 4 .Fig. 5 .

 45 Fig. 4. Exchange field Hex vs. time for sample FIX60. The arrows indicate the direction of the Co magnetisation. 1000 950 900 850 800 750 700 Anisotropy field H ex (Oe)

Fig. 6 .Fig. 7

 67 Fig. 6. Exchange field Hex vs. time for sample MAG50. The arrows indicate the direction of the Co magnetisation.

Fig. 8 .

 8 Fig. 8. Comparison of normalised unidirectional field H ud vs. time for samples FIX60 FIX80 and MAG50. Solid lines are fits to equation (3).

Fig. 9 .

 9 Fig.9. Comparison of hysteresis loops for sample FIX60, before and after a reverse pulsed field.

3Results

  Before presenting the direct relaxation study of the exchange anisotropy field H ex , we have realized a series of preliminary measurements in order to test the a.c. method chosen to obtain H ua and H ud . They are to carry carry out, by m.o. measurements, the amplitude of the transversal a.c. magnetization component M ac and using expression (2) we deduce H ex . Figures4 and 5present the exchange field versus time for the sample FIX60. The sample was prepared with the Co magnetization saturated in the forward direction, H ua and H ud are in the same direction corresponding to the more stable state of the AF layer and H ex = H ua + H ud = 941 Oe. At t = 65 seconds (see Fig.4), we switch the Co magnetization in the reverse direction, the interface coupling changes its sign and the exchange field becomes H

	Anisotropy field H ex (Oe)	1000 950 900 850 800 750 700
		40	80	120	160
			Time (s)

ex = H ua -H ud = 777 Oe (we have supposed that H ud was not modified during the short time of the Co reversal). By this simple way we can deduce both values of the uniaxial and unidirectional field H ua = 859 Oe and H ud = 82 Oe before any relaxation

Table 1 .

 1 Table of parameters Hua and H ud resulting of the preliminary studies (short reversal).sample state Hua (Oe) H ud (Oe) K (Oe/dec) Knorm close to zero only after several days. These results demonstrate that the behavior of H ud (t) depends strongly on the anisotropy of the AF layer. As already discussed, a difficult experimental problem is met when analyzing the behavior of H ud (t)f o rav e r yl o n gt i m e( ac o u p l eo fd a y s or a couple of weeks) after the reversal of the Co magnetization. Moreover most of our tentatives to obtain the final value of H ud seem to indicate that it is obvious to consider that the final AF state is symmetric with respect to the state at t = 0 before reversal. Clearly the time dependence of the exchange field results from the relaxation of the AF domains dragged by the reversal of F magnetization and excited by thermal activation. The initial state can be considered as a quasi stable state after the sample preparation process. When switching the Co magnetization a torque appears due to F coupling which tends to reverse progressively the various AF domains. But taking into account numerous crystallites of different size due to the sputtering technique used for preparation but also the roughness of the interface we have to consider that the various intermediate states of AF layer are very complex and numerous, similarly as in frustrated spin systems such as spin glasses, and it is difficult to suppose an exact symmetry of the system even after a very long time.

	FIX60 S1	865	86	18.7	0.22
	S2	832	4.7	-34.2
	FIX80 S1	515	53	10.4	0.20
	S2	503	-11	-19.8
	MAG50 S1	851	160	51.0	0.32
	S2	881	-116	-98.0

Table 2 .

 2 Table of parameters Hua and H ud resulting of the preliminary studies (short reversal).

	sample	τmin (s) τmax (s)	K (Oe/dec)
	FIX60	12.1	2.28 × 10 10 18.7
	FIX80	4.4	1.55 × 10 11 10.4
	MAG50 8.7	2.33 × 10 7	51.0