Yannick Dusch

Nicolas Tiercelin

Alexey Klimov

Vasyl Rudenko

Yury Ignatov

Sami Hage-Ali

Philippe Pernod

Vladimir Preobrazhensky

Giant magnetostrictive nanostructured films with auto induced spin reorientation transition

In various micro and nanosystems applications comprising magnetic films, the polarizing field still needs to be integrated. We hereby present a solution for self biasing of magnetic films using micropatterned permanent magnets. Micromagnetic simulations were used as a designing and optimization tool to create a biasing structure. Samples were elaborated with varying geometric parameters using classical silicon microfabrication techniques. Nanostructured TbCo/FeCo magnetostrictive thin films were sputtered over coercive FePt filled trenches etched in silicon. Magnetic and magnetoelastic characterizations confirmed numerical simulations. In particular, non-linear actuation of a self-biased magnetostrictive cantilever has been obtained at zero external polarizing field.

I. INTRODUCTION

It was shown that nanostructured giant magnetostrictive films 1-4 under Spin Reorientation Transition (SRT) can be made highly sensitive to magnetic excitations and exhibit strong non-linear behavior [5][START_REF] Benyoussef | Magnetics Conference[END_REF][START_REF] Tiercelin | [END_REF] . This feature of SRT conditions opens route toward, for example, original magnetoelectric microsensors, microactuators or RF devices [8][9][10][11] . In particular, magnetoelectric effect is dramatically enhanced near SRT in composite magnetostrictive/piezoelectric layered structures [12][13][START_REF] Tiercelin | Selected papers from the Symposium F "Multiferroics and Magnetoelectrics Materials" of the E-MRS Conference[END_REF] . Such critical state can be obtained when the bias field H Bias directed along the hard axis of magnetization (HA) reaches the anisotropy field H a of the layer (field-induced SRT).

Polarization of magnetic layers in Micro and Nano-Electro-Mechanical-Systems (MEMS and NEMS) can be obtained by several means, depending on the requirements of the application. Macroscopic magnets can be used in research or industrial environments but prevent any size reduction of the systems. Spintronic devices or NEMS can benefit from thin exchange coupled layers. Nevertheless, due to the short length of the interactions, such nanostructures are hard to implement for thick active layers in the 100nm -1µm range. The use of permanent magnet-induced boundary fields has also been investigated using SmCo 15 or CoPt [START_REF] Kitada | [END_REF] and was proved efficient for biasing magnetoresistive layers up to 200nm and several hundred oersteds. In any case, the typical length of the system along the biasing direction did not exceed a few hundred microns.

a) Electronic mail: yannick.dusch@centraliens-lille.org

We hereby propose the use of micropatterned L1 0 -FePt sputtered films to polarize magnetic thin films with larger in-plane dimensions.

• Part II will explain the benefits of SRT.

• Part III will deal with the biasing structure design and simulations.

• Technological process and results are given in IV and discussed in V

II. PROPERTIES OF NANOSTRUCTURED GIANT MAGNETOSTRICTIVE THIN FILMS UNDER SRT

Geometry of the basic unimorph actuator under consideration is presented in fig. 1. It consists in a cantilever with magnetostrictive multilayer deposited on the surface. Orientations of the bias H s and alternating h magnetic fields and magnetization M relatively to the easy axis (EA) of the multilayer are also shown in the figure. The magnetic free energy of the system can simply be written as the sum of the Zeeman energy and the anisotropy energy restricted at its first term:

F = -M (H s cos(ϕ) + hsin(ϕ) + 1 2 H a sin 2 (ϕ))) (1)
where H a is the in-plane anisotropy field. This energy can then be used to understand the behavior of the magnetization angle ϕ. When the bias field is perpendicular to the EA and strong enough (H s > H a ) magnetization is parallel to H s and this orientation is stable. Application of an alternating field with an amplitude of a few Oersteds perpendicularly to H s leads to a linear oscillation of the magnetization with a small angular amplitude (Fig. 2a). The torsion elastic vibrations are linearly excited in such conditions. In the point of SRT (H s = H a ), the magnetic subsystem becomes unstable. The amplitude of magnetic oscillation increases (Fig. 2b) and nonlinearity manifests itself. When H s < H a equilibrium orientation of magnetization turns towards the anisotropy axis (angular phase) and linear oscillation near the new equilibrium position takes place when amplitude h is not too high (Fig. 2c). Rotation of magnetization leads also to appearance of longitudinal components of magnetostrictive stress and as a result to excitation of flexural deformations of cantilever. The dependence of magnetization angle on instantaneous value of alternating field is shown in Fig. 2d. As expected for the SRT, this kind of behaviour is consistent with the second order phase transitions theory described by Landau [START_REF] Landau | Course of Theoretical Physics; statistical physics[END_REF] . Near the SRT, an increase of amplitude of the alternating field leads to a dramatic change of the thermodynamic potential (see Fig. 3b) and the magnetic oscillation presents a switching character of its orientation between positions defined by the amplitude h: This switch is accompanied by a related switch of the magnetostrictive stress (as also observed in [START_REF] Peuzin | Proceedings of the French Journée microsystèmes du CNRS[END_REF] ). The spectrum of magnetic stress near SRT contains a great number of harmonics with high amplitudes. Each one can be used for resonance excitation of elastic modes. These properties are to be used in original MEMS or electronic devices. The following part describes the found solution for an integrated bias field structure.

III. NUMERICAL SIMULATIONS

As shown on fig. 4, the biasing structure consists in parallel FePt trenches etched in a silicon substrate on top of which a Ta spacer and a (TbCo(5nm)/FeCo(5nm))*n multilayer are deposited. The multilayer exhibits uniaxial magnetic anisotropy. The easy axis of magnetization (EA) is obtained in the multilayer thanks to sputtering under magnetic field. Magnetostatic simulations of the flux density show that alternate polarized areas are created in the active layer, thanks to the coupled or isolated flux closure (fig. 5). This leads to a striped magnetic structure in the active layer (part 1 and part 2, Using the open source micromagnetic simulation software Magpar 21 , we investigated the effects of several biasing structures on a magnetic thin film with in-plane uniaxial anisotropy. It appeared that the structure presented above offered a good tradeoff between the obtained polarization along HA and technological simplicity. Fig. 6b presents a typical result of the numerical simulations, clearly showing the stripped pattern of magnetization on top of the active layer. Magpar has then been used to carry out numerous simulations with varying geometric parameters (FePt/silicon width ratio, trenches width, FePt thickness, Ta gap thickness) to optimize the strength and the homogeneity of the bias field.

IV. TECHNOLOGICAL PROCESS AND REALIZATION

Filled trenches of hard magnetic material have already been realized with SmCo and NdFeB, but the process involved a critical phase of Chemical-Mechanical-Planarization (CMP) [START_REF] Walther | Current Perspectives: Perpendicular Recording[END_REF] . We present here a simpler process for FePt, based on lift-off.

Prototypes were realized on Si wafers by usual microfabrication techniques in a cleanroom environment. Silicon is first etched through an aluminum mask by means of Deep Reactive Ion Etching (DRIE) down to 2µm. A 100nm Ta adhesive layer as well as a thick (2µm) FePt layer are then deposited by RF Sputtering. Lift-off is used to remove the excess material. FePt is obtained by the RF sputtering of a composite target under Ar flow at 5.10 -3 mbar. Sputtering is decomposed into 15min runs followed by a rest period of 4min to prevent detrimental effects of temperature, such as internal stress. A 100nm Ta non-magnetic spacer (also used to prevent oxydation of FePt during annealing) is added on top of the structure before annealing at 750 • C during 30min under secondary vacuum (1.10 -6 mbar) to obtain the L1 0 phase of FePt. This process led to a coercive field H c = 1T . The nanostructured active layer is deposited by RF sputtering under an homogeneous magnetic field (obtained by permanent magnets placed on the substrate holder). Alternating the sputtering of TbCo and FeCo composite targets led to 25 exchange-coupled 10nm bilayers (250nm thick). FePt is finally polarized along HA. A typical result of this process is shown on fig. 7. The vertical structure at the interface between FePt and Si is due to DRIE combined with masking effects.

Two sets of samples have been elaborated: 25 samples with centimeter dimensions on a 3" wafer with different geometric parameters (L = 20, 50, 100, 200, 400µm and L F eP t /L = 0.7, 0.6, 0.5, 0.4, 0.3) and 5 samples fabricated on a thin (150µm) 2" silicon wafer to obtain centimetersized cantilevers for magnetoelastic characterizations.

V. RESULTS AND DISCUSSION

A. Magnetic characterizations

First measurements were made using a Vibrating Sample Magnetometer (VSM) equipment (ADE EV9 Series) with sub-µemu resolution. Fig. 8 presents VSM measurements of the magnetization of a sample with the following characteristics: L = 50µm, L F eP t = 25µm, FePt thickness e F eP t = 2µm, Ta spacer thickness e spacer = 100nm, active layer thickness e = 250nm. The contribution of FePt has been removed beforehand on the curve. As shown on fig. 8, the global hysteresis curve M (H ext ) of the biased active layer along HA is composed of two shifted contributions (compared to the unbiased reference), each accounting for half of the magnetic stripes. Both shifts are almost symmetrical with a bias field of approximately 500Oe. As, in some cases, slope changes are difficult to observe, we also used the derivatives of the hysteresis Longitudinal Magneto-Optic Kerr Effect (LMOKE) measurements have been carried out to investigate the magnetic microstructure on the surface of the nanostructured active layer and validate the interpretation of the VSM measurements. Due to size limitations of the experimental setup, measurements could not be carried out on every sample. Nevertheless, results obtained for L = 100µm, L F eP t = 50µm confirmed our interpretations. The hysteresis curves for each part of the magnetic structure can be seen on fig.9. As expected, when FePt is magnetized, two adjacent stripes (namely part 1 and part 2) show opposite offsets along HA. Here, the offsets are respectively 100Oe and 200Oe.

As stated above, the bias field must be equal to the anisotropy field to obtain the properties of SRT. Nevertheless, the biasing structure has been designed to provide a bias field superior to the anisotropy field. In such situation, the polarization can be taylored using minor magnetization cycles of FePt. Indeed, it is possible to reduce the bias field by reducing the remanent magnetization of the permanent-magnet elements. Fig. 10 and Fig. 11 illustrate the method: each half-loop lessens the shift of the magnetization cycle for both stripes. When FePt is fully demagnetized, the bias disappears.

B. Magnetolelastic characterizations

Magnetoelastic characterizations have been carried out by a laser deflection technique on a centimeter sized silicon cantilever on top of which the biasing structure has been realized. The cantilever is placed inside the core of a driving coil producing a dynamic magnetic field along the EA of the active layer. The cantilever is then placed under an homogeneous static magnetic field created by an electromagnet along HA. The flexural or torsional vibration amplitude of the free tip is measured by the deflection of a laser beam on a 2D Position Sensing Diode (PSD). As predicted by theory 8 , thanks to giant nonlinearity near the SRT, subharmonic magnetic excitation at f r /2, with f r a resonant frequency of the cantilever, results in an amplified mechanical vibration at f r near the SRT point (H Bias ≈ H a ). Fig. 12 shows the results for a 2cm × 0.5cm × 150µm cantilever for the second flexural mode at f r = 3124Hz.

As expected, non-linear actuation of the system occurs for shifted values of the external magnetic field, compared to an unbiased sample, and even exists without any ex- ternal field, as the bias field is close to the anisotropy field H a = 300Oe.

C. Perspectives

The fabrication process presented above has proved efficient for our purposes. However, other structures can be considered. Following the same steps, we also investigated the potentialities of a simpler structure, presented on fig. 13. The main asset of this structure is to reduce the technological complexity by suppressing the etching step.

First micromagnetic simulations have proved the viability of this approach. Fig. 14 presents a simulation of such structure with the folowing parameters:L = 50µm, L F eP t = 25µm, FePt thickness e F eP t = 2µm, Ta spacer thickness e spacer = 100nm, active layer thickness e = 250nm.

The technological realization is pending.

VI. CONCLUSIONS

In this paper, we have proposed an integrated permanent magnet based microstructure for the polarization of nanostructured magnetic thin films exhibiting a Spin Reorientation Transition. Micromagnetic simulations proved to be efficient as a sizing and optimization tool for such structures. Several samples have been successfully elaborated thanks to a MEMS-compliant process. In the case of a giant magnetostrictive thin film, integrated (VSM) as well as local (LMOKE) magnetic characterizations confirmed the numerical studies. It was also found that the bias field could be taylored to fulfill the SRT requirements thanks to the minor magnetization cycles of FePt. Moreover, magnetoelastic measurements showed that, thanks to the integrated polarization, subharmonic actuation of a cantilever could be obtained, thus demonstrating the nonlinear behaviour expected in the vicinity of the SRT, without any external static field. Other structures are currently investigated to optimize the technological process. These results pave the way for the development and the integration of innovative and multifunctional Micro-Magneto-Mechanical-Systems (MMMS) and Micro-Magneto-Electro-Mechanical-Systems (MMEMS).

FIG. 1 .

 1 FIG. 1. Unimorph geometry : clamped silicon cantilever coated by a nanostructured magnetostrictive film.

FIG. 2 .

 2 FIG. 2. Free energy of the system as a function of the magnetization angle ϕ, for several values of the excitation field h(t) and for tree different positions of Hs: (a) Hs > Ha, (b) Hs = Ha, (c) Hs < Ha. In this simulation 5 , Ha = 244Oe

FIG. 4 .

 4 FIG. 4. Schematic view of the biasing structure 19 .

FIG. 6 .

 6 FIG. 6. (a): Schematic illustration of the magnetization curve of the active layer when the polarizing field is superior to the anisotropy field. (b): Top view of the simulated active layer with Hext = 0Oe, LF eP t = 25µm and L = 50µm. Arrows indicate magnetization.

FIG. 8 .

 8 FIG. 8. Hysteresis curve (a) and derivative of the hysteresis curve (b) of the active layer (Solid: biased, dashed: unbiased). Sample Characteristics : L = 50µm, LF eP t = 25µm, FePt thickness eF eP t = 2µm, Ta spacer thickness espacer = 100nm, active layer thickness e = 250nm. 19

FIG. 10 .

 10 FIG. 10. Bias field adjustment by minor magnetization cycles.

FIG. 12 .

 12 FIG. 12.Non-linear Magnetoelastic actuation measurement[START_REF] Dusch | [END_REF] (Solid: biased, dashed: unbiased). Clamped cantilever: 2cm × 0.5cm × 150µm.Excitation of the second flexural mode @ fr = 3124Hz, excited with fex = fr/2 = 1562Hz.

FIG. 14 .

 14 FIG. 14. Simulation of magnetization in the structure described in fig.13 (transverse view). Arrows indicate the main direction of magnetization.

H. Le Gall, J. BenYoussef, N. Tiercelin, P. Pernod, V. Preobrazhensky, and J. Ostorero, Magnetics, IEEE Transactions on, Magnetics, IEEE Transactions on DOI -10.1109/20.908746 36, 3223 (2000), ISSN 0018-9464, 10.1109/20.908746.

ACKNOWLEDGMENTS

This work is part of the French ANR PNANO-Project NAMAMIS. The authors would like to thank the Direction Générale de l'Armement(DGA-France) for the Ph.D. funding of Mr Y. Dusch, the French Ministry of foreign affairs (MAE) for the Ph.D. funding of Mr. Y. Ignatov, and Région Nord-Pas-de-Calais for the postdoctoral funding of Dr. V. Rudenko. In addition, the authors would like to thank Pr. D. Givord for fruitful discussions.


Eric Raile

Arun Khatri-Chhetri

Julien Demenois

Emmanuel Torquebiau

Matthieu H Arnoult

Thomas Eglin

Dominique Masse

Mohamed Habibou Assouma

Vincent Blanfort

Claire Chenu

Lydie Chapuis-Lardy

Jean-Michel Medoc

Saidou Nourou Sall

Barriers and Strategies to Boost Soil Carbon Sequestration in Agriculture

Keywords: climate change mitigation, climate change adaptation, food security, innovation, policy, stakeholders, territory

The Paris Agreement calls for limiting global warming below 2 • C. The "4 per 1,000 Initiative: Soils for food security and climate" was launched in 2015 to increase soil organic carbon sequestration with three objectives: mitigation of climate change, adaptation to climate change and improved food security. One of the challenges of the Initiative relates to its feasibility in contrasted biophysical, social and economic environments, questioning the adoption rate of required new practices. We conducted participatory multi-stakeholder workshops in France and Senegal to collect knowledge and perception of farmers, NGOs, agro-industries, administrations, donors and researchers on barriers and coping strategies for 4 per 1,000 innovations. Results in both countries reveal the predominance of social and economic barriers such as lack of knowledge or training, increased difficulties of fieldwork, workload, risk handling, funding and social pressure. Biophysical constraints such as limited potential of soil organic matter storage or rainfall scarcity and variability appear more important in Senegal. Identified actions to foster the sequestration of soil carbon call for an improved policy context leading to innovations in land planning, stakeholder communication, demonstration facilities, capacity building or financial support. Fewer constraints and coping strategies mention technical issues, showing that fostering agricultural soil carbon sequestration is more a question of enabling environment than technical innovations or farmers' willingness for change. We conclude that actions to support the 4 per 1,000 Initiative need to include a variety of stakeholders such as extension services, private sector, civil society, local institutions, policy makers, consumers, and not only farmers.

INTRODUCTION

The Paris Agreement, at the 21 st Conference of Parties (COP21) of the United Nations Framework Convention on Climate Change (UNFCCC), calls for limiting global warming well below 2 • C, and to pursue efforts to limit the temperature increase even further to 1.5 • C. To achieve this, major greenhouse gas (GHG) emission reductions are needed together with technologies that result in net removal of CO 2 from the atmosphere [START_REF] Meinshausen | Greenhouse-gas emission targets for limiting global warming to 2[END_REF][START_REF] Lomax | Investing in negative emissions[END_REF]IPCC, 2018). In this context, the "4 per 1,000 Initiative: Soils for Food Security and Climate" (http:// 4p1000.org) was launched with the objective of a net increase in soil organic carbon (SOC) stocks at an aspirational annual rate of 4%• (or 0.4%) to contribute to climate change mitigation while improving soils' capacity for climate change adaptation and their contribution to food security objectives, known as a "3-fold objective." Carbon is indeed the main component of soil organic matter, which is known to play a central role in soil fertility, and therefore crop productivity [START_REF] Lal | Carbon sequestration[END_REF]. SOC sequestration is defined as "the process of transferring CO 2 from the atmosphere into the soil of a land unit, through plants, plant residues and other organic solids which are stored or retained in the unit as part of the soil organic matter (humus). Retention time of sequestered carbon in the soil (terrestrial pool) can range from short-term (not immediately released back to atmosphere) to long-term (millennia) storage" [START_REF] Olson | Experimental consideration, treatments, and methods in determining soil organic carbon sequestration rates[END_REF].

While the 4 per 1,000 Initiative may reconcile mitigation and adaptation, and therefore Northern and Southern interests and visions regarding climate policies [START_REF] Kam King | Soil sciences and the French 4 per 1000 initiative-the promises of underground carbon[END_REF], it is also clear that for many farmers, especially smallholders in developing countries, climate change mitigation is not a priority in the short term [START_REF] Luedeling | Carbon sequestration potential of parkland agroforestry in the Sahel[END_REF]. Farmers' priorities are to get immediate benefits from farming to ensure income or food security [START_REF] Masson-Delmotte | Food first! Theorising assets and actors in agroforestry: risk evaders, opportunity seekers and "the food imperative" in sub-Saharan Africa[END_REF]. Therefore, beyond its technical feasibility, one of the main challenges to be addressed by the 4 per 1,000 Initiative relates to its implementation in contrasted social and economic environments, including a diversity of livestock and agricultural production systems. Increasing organic matter in soils via management practices not only encompasses soil carbon related questions, but also agronomic and environmental dimensions, as well as social, economic, and ethical ones [START_REF] Chenu | Increasing organic stocks in agricultural soils: knowledge gaps and potential innovations[END_REF][START_REF] Rumpel | The 4p1000 initiative: opportunities, limitations and challenges for implementing soil organic carbon sequestration as a sustainable development strategy[END_REF]. Farmers may not have sufficient financial resources or a workforce to implement existing technical options, even though they do exist (e.g., agroforestry; [START_REF] Corbeels | Is the 4 per thousand initiative for soil organic carbon storage achievable in sub-Saharan Africa? Insights from agroforestry and conservation agriculture[END_REF]. [START_REF] Soussana | Matching policy and science: rationale for the '4 per 1000 -soils for food security and climate' initiative[END_REF] confirms that "additional studies are needed to refine and improve our understanding of the conditions which foster (. . . ) soil carbon sequestration". This shows that soil carbon sequestration raises questions of both scaling out (i.e., reaching similar stakeholders) and scaling up (i.e., reaching different stakeholders), as defined by [START_REF] Douthwaite | Impact pathway evaluation: an approach for achieving and attributing impact in complex systems[END_REF]. It can therefore be hypothesized that boosting soil carbon sequestration in agriculture is more related to the transformation and adjustment of current practices or to locally designed innovations rather than to the simple dissemination of generic technical options.

MATERIALS AND METHODS

With the aim of identifying potential barriers to the adoption of 4 per 1,000 practices and actions to overcome these barriers, we conducted two participatory multi-stakeholder workshops in France and Senegal in April and June 2018. Our objective was to collect knowledge and the perceptions of farmers, NGOs, agroindustries, administrations, donors, agricultural organizations, agricultural school teachers, and researchers on barriers and coping strategies for 4 per 1,000 innovations. The choice of the participatory multi-stakeholder workshops, to collect people's points of view, was based on the assumption that the explicit use of group interaction produces additional information and insights-an approach commonly used in participatory appraisal methods (e.g., [START_REF] Pretty | A Trainer's Guide for Participatory Learning and Action[END_REF][START_REF] Narayanasamy | Participatory Rural Appraisal Principles, Methods and Application[END_REF]. Group discussions focusing on a common topic and convening different categories of people help in identifying priorities and interests [START_REF] Chambers | Participatory rural appraisal (PRA): challenges, potentials and paradigm[END_REF]. Informal group facilitation with an "attitude" [START_REF] Groot | Demystifying Facilitation of Multi-Actor Learning Processes[END_REF], intended not to influence people and to provide them with time to think, discuss, hesitate, or to change their mind before giving a final answer, generates valuable qualitative data.

Invitations to the workshops were sent to eighty five key informant participants (not including the authors of the present paper) identified through the networks of the authors, without any pre-requisite regarding their knowledge of the 4 per 1,000 Initiative, to confront viewpoints and to deliver concrete propositions for action. Participants were invited due to their professional positions and we therefore assumed that their technical background was not a limiting parameter. Thirtyseven key informant participants (not including the authors of the present paper) confirmed the invitation and were able to participate in the 2 day workshops.

The workshop participants were split into working groups that were defined prior to the workshops in order to have a balanced distribution of the different categories of stakeholders per group. Different working groups focused on different farming systems. The rationale of working on farming systems was to facilitate the mobilization of field experience of the different participants and to ensure convincing contributions. The modus operandi for each working group allowed all participants to express themselves, regardless of their number in their stakeholder category.

Farming Systems in France

For France, each group had to choose a type of farming system among the nine case studies defined in the report "Agriculture, Forest, Climate. Towards strategies of adaptation" carried out by the French Ministry of Agriculture (Centre d'Etudes et de Prospective, 2013). In this report, each case study was described based on technical, economic, and environmental variables, including SOC. The following four case studies were chosen by the participants: (i) Polyculture-breeding in Meuse, (ii) Cattle breeding in Creuse, (iii) Field crops in Cher, and (iv) Vineyards in Beaujolais. A brief description is given below, and a comprehensive description of these farming systems can be found in Centre d'Etudes et de Prospective (2013).

Polyculture-Breeding in Meuse

Polyculture-breeding in Meuse (North-Eastern France) is a farming system focused on cow milk production in permanent grasslands, combined with additional fodder from corn silage. The typical farm size is around 100 ha with about half the area used for corn-wheat-barley-rape rotations which provide additional income as well as straw and supplementary fodder when necessary. At low elevation (<200 m asl), with an annual rainfall of 800 mm, cold winters and dry summers, cereal yields are moderate because of shallow soils, albeit with a good carbon content. About 17% of the income comes from subsidies. [START_REF] Noë | Drivers of long-term carbon dynamics in cropland: a bio-political history (France, 1852-2014)[END_REF] indicates a moderate increase in SOC stocks in the topsoil of cropland (0-30 cm) of + 1 to 2 % year -1 for the period from 2000 to 2014 for this area. In this area, [START_REF] Pellerin | Stocker du Carbone dans les sols Français -Quel Potentiel au Regard de L'objectif 4 pour 1000 et à Quel Coût? Synthèse du rapport d'étude[END_REF] assesses an additional potential of SOC sequestration of 0.9% year -1 for permanent grasslands and 5.2% year -1 for croplands.

Cattle Breeding in Creuse

The cattle breeding farming system in Creuse (Central France) is based on cattle meat production with weanlings fattening in grasslands. Cereal silage (from only 5% of about 100 ha average farm size) provides additional fodder. Soils are sometimes hydromorphic with a 3% soil organic carbon content. Under high rainfall (at least 1,100 mm/year) and at an elevation of 700 to 1,000 m asl., the plant-growing season is never longer than 6 months. About 35% of the income comes from subsidies. [START_REF] Noë | Drivers of long-term carbon dynamics in cropland: a bio-political history (France, 1852-2014)[END_REF] indicates a relatively high increase in SOC stocks in the topsoil of cropland (0-30 cm) of + 2 to 3 % year -1 for the period from 2000 to 2014 for this area. In this area, [START_REF] Pellerin | Stocker du Carbone dans les sols Français -Quel Potentiel au Regard de L'objectif 4 pour 1000 et à Quel Coût? Synthèse du rapport d'étude[END_REF] assesses an additional potential of SOC sequestration of 0.9% year -1 for permanent grasslands.

Field Crops in Cher

The field crops farming system in Cher (Central France) is characterized by small farms (∼25 ha) producing corn and rape (with wheat-barley rotations), without irrigation. Good soils with about 2.4% organic matter content have a high agronomic potential. The climate has oceanic influence due to western winds and the annual rainfall is 600 to 700 mm, at an elevation of <500 m asl. Farms show good economic conditions. Le [START_REF] Noë | Drivers of long-term carbon dynamics in cropland: a bio-political history (France, 1852-2014)[END_REF] indicates a moderate increase in SOC stocks in the topsoil of cropland (0-30 cm) of + 1 to 2% year -1 for the period from 2000 to 2014 for this area. In this area, [START_REF] Pellerin | Stocker du Carbone dans les sols Français -Quel Potentiel au Regard de L'objectif 4 pour 1000 et à Quel Coût? Synthèse du rapport d'étude[END_REF] assesses an additional potential of SOC sequestration of 5.2% year -1 for croplands.

Vineyard in Beaujolais

The vineyard farms of Beaujolais are situated in Eastern France, north to the city of Lyon. The Beaujolais wine farming system studied here represents about a quarter of the farms in the area, with a farm size around 14 ha producing about 500 hl of wine per year, mostly (95%) for bulk sale to wine merchants, the rest being bottled at the farm. Shallow, stony soils hold a low organic carbon content (<2%). Rainfall is about 500 mm year -1 , with dry, cold winters and warm summers with frequent storms. The fluctuating wine market makes income irregular. Le [START_REF] Noë | Drivers of long-term carbon dynamics in cropland: a bio-political history (France, 1852-2014)[END_REF] indicates a low increase in SOC stocks in the topsoil of cropland (0-30 cm) of 0 to 1% year -1 for the period from 2000 to 2014 for this area. In this area, [START_REF] Pellerin | Stocker du Carbone dans les sols Français -Quel Potentiel au Regard de L'objectif 4 pour 1000 et à Quel Coût? Synthèse du rapport d'étude[END_REF] assesses an additional potential of SOC sequestration of 3.7%year -1 for vineyards related to inter-rank plant grass cover.

Farming Systems in Senegal

For Senegal, a selection of farming systems was done prior to the workshop based on expert knowledge from colleagues in Senegal, including past or on-going projects related to soil carbon sequestration in the country. The following four case studies were chosen: (i) Peri-urban agriculture in the Niayes, (ii) Irrigated agriculture in the Senegal River valley, (iii) Agroforestry in Faidherbia albida parklands, and (iv) Rain-fed agriculture and extensive livestock integration. A brief description is given here. Soil organic content values are given, when possible, as approximate values obtained from available publications on similar soil types in the area.

Peri-Urban Agriculture in the Niayes

The coastal peri-urban agriculture farming systems of the Niayes supply the Senegalese capital Dakar and its suburbs with vegetables and fruits. It is a succession of sandy dunes and interdune depressions where the water table regularly outcrops, and the soil has a high salt content. Urban development and rising standards of living have also created a demand for animal products. Livestock farms contribute to the supply of manure and slurry to horticultural farms. Organic residual products and biowastes represent significant volumes. [START_REF] Soumare | Effects of Casuarina equisetifolia composted litter andramial-wood chips on tomato growth and soil properties in Niayes, Senegal[END_REF] reports a soil organic content of 1.2% for the Niayes area. The urban sprawl of the city of Dakar exerts a strong pressure on this peri-urban farming area. Climate is tropical semi-arid with a single rainy season from July to October. Based on Zomer et al. ( 2017), an indicative additional potential of SOC sequestration for the Niayes area should be around 2 to 3% year -1 .

Irrigated Agriculture in the Senegal River valley

Irrigated rice cultivation in the Senegal River valley is strongly influenced by the structural organization of cultivated areas and the social organization of producers [START_REF] Gal | Gestion collective des systémes de culture en situation d'incertitude: cas de l'organisation du travail en double culture dans le delta du fleuve Sénégal[END_REF]. Farms are part of local irrigation schemes and farmers are grouped in peasant organization for water management, agricultural inputs, and mechanization of work. Tillage and harvesting operations are mechanized in large areas, where the most common method of planting is broadcast sowing in water, and weed control is either manual or chemical. For small perimeters, transplanting is the most general rule as well as manual weeding. Soils are mainly Vertisols with swelling clays and frequent high salinity [START_REF] Boivin | Les sols de la moyenne vallée du fleuve Sénégal: caractéristiques et évolution sous irrigation[END_REF]. Two cropping seasons are generally carried out: the hot dry season, from February to July, and the wintering season, from July to November-December. Based on Zomer et al. ( 2017), an indicative additional potential of SOC sequestration for the Senegal River valley area should be around 1 to 2% year -1 .

Agroforestry in Faidherbia albida parklands

Faidherbia albida is a leguminous tree widely distributed in semiarid West Africa, as a scattered tree in cropland (agroforestry "parklands"). The best-known peculiarity of F. albida is its reverse phenology [START_REF] Wickens | A study of Acacia albida Del. (Mimosoideae)[END_REF]. Trees are in leaf, growing, and fruiting during the dry season, whereas leaves are shed after the first rains and growth resumes only at the end of the wet season. This phenology is advantageous for agroforestry, because competition with associated crops growing during the wet season (mainly pearl millet and groundnut in Senegal) is minimized. F. albida is thus a multipurpose tree widely grown for soil fertility improvement but also for fodder production (nitrogen-rich pods) in rural communities. Most parkland soils are Arenosols with low carbon content. Participants to the workshop mainly rely on their experience in the central part of Senegal (Niakhar; rainfall ∼ 500 mm) where parklands of F. albida (12.5 m high; 7 trees ha -1 ; 5% canopy cover) are part of the local agro-silvopastoral systems. In agroforestry "parklands, " Corbeels et al. ( 2018) assess a mean additional potential of SOC sequestration slightly above 4% year -1 , ranging from 3 to 22% year -1 .

Rain-Fed Agriculture and Extensive Livestock Integration

Extensive livestock breeding in Senegal has been a traditional activity based on common use of resources (water, rangelands) in which managed herd movements are necessary for sustainability.

The highly seasonal rainfalls brought by the convective storms of the West African monsoon, drive resource production in these rangelands with poor soils showing low soil carbon content.

Livestock mostly adapt to the local resource availability and graze under the guidance of a herder or freely within communally exploited grazing areas [START_REF] Ickowicz | Crop-livestock production systems in the Sahel-increasing resilience for adaptation to climate change and preserving food security[END_REF]. Extensive breeding varies largely by the diversity of animal species, herd size, herding practices, and by the amplitude of their mobility. Agriculture is primarily rain-fed. It has undergone significant changes in the past 50 years. From food and family farming, it has been strongly oriented toward cash crops (peanuts and cotton). The groundnut industry, which has long been the engine of the Senegalese economy, is going through a major crisis. Production is increasing, however, in the cereal (millet, rice, and corn), pulses (peanut, cowpea), fruit and vegetable, and cassava sectors, meeting growing local demand. In rain-fed agriculture, if the three principles of conservation agriculture (i.e., minimum or no tillage/crop residue mulching/intercrop or crop rotation) are implemented, Corbeels et al. ( 2018) assess a mean additional potential of SOC sequestration above 4% year -1 , this being however highly variable.

Workshop Organization

Each group first had to identify the main sources of GHG emissions corresponding to the studied farming system, and to identify potential practices for soil carbon sequestration. For France, participants were invited to refer to the report "How can French agriculture contribute to reducing greenhouse gas emissions? Abatement potential and cost of ten technical measures" published in 2013 by INRA [START_REF] Pellerin | Quelle Contribution de l'Agriculture Française à la Réduction des Emissions de gaz à Effet de Serre? Potentiel d'Atténuation et Coût de Dix Actions Techniques[END_REF]. For Senegal, each group comprised a specialist of the studied farming system to help in the identification of sources of GHG emissions and therefore potential 4 per 1,000 practices. Next, each working group was asked to identify: (i) barriers to adoption of innovations contributing to the objectives of the 4 per 1,000 Initiative, and (ii) actions to overcome these barriers. All barriers and actions were classified by participants into major "categories" representing scientific disciplines or fields of action.

Data Analysis

Barriers and solutions identified were categorized, using keywords (e.g., technical, financial, social. . . ). Visualization of the occurrence of barriers and actions for each farming systems was performed running a Correspondence Analysis (CA) on data from Tables 1, 3 converted in contingency tables, using the R.3.5.3. environment for statistical computing [START_REF] Core | R: A Language and Environment for Statistical Computing[END_REF].

RESULTS

Barriers to Adoption of 4 per 1,000 Practices

For virtually all cases, the number of identified barriers is surprisingly high and diversified. Despite the different case studies addressed and the different socio-economic contexts between France and Senegal, social and economic contexts were identified as the major barriers to the adoption of 4 per 1,000 practices in both countries and most farming systems (Table 1).

The first and second principal components of the CA explained, respectively, 41.55 and 22.52% of the total inertia (Figure 1). Axis 1 was positively correlated with "Environmental" and "Organizational" barriers and was negatively correlated with "Political" and "Capacity building" barriers. Thus, vineyards in Beaujolais were mainly characterized by "Environmental" and "Organizational" barriers, while polyculture-breeding in Meuse and agroforestry in Senegal were correlated with "Political" and "Capacity building" barriers. According to the results of the CA (Figure 1), most of the farming systems shared barriers related to Axis 1 (Figure 1). Axis 2 was positively correlated with "Cultural" barriers. As livestock and agroforestry in Senegal were the only two farming systems in the upper part of the diagram, the "Cultural" barrier made these farming systems specific. Most farming systems shared "Social, " "Economic, " "Technical" and "Biophysical" constraints (Table 1). These constraints therefore appeared near the center of the CA diagram and did not help in differentiating the farming systems.

The compilation of detailed answers appearing in Table 2 shows that frequently mentioned topics refer to: "Lack of knowledge, " "Lack of training and capacity building, " "Difficulties of fieldwork and workload, " "Risk/change aversion, " "Social pressure" or "Legal, political, and professional compliance." In both countries, economic, social, and capacity building appeared as major barriers related to an enabling environment. Biophysical barriers (e.g., low capacity of soil carbon storage in sandy soils, availability of organic matter, monsoon variability, fire, erosion) were also identified, mainly in Senegal. In France, the absence of additional income (i.e., economic barrier) resulting from the implementation of 4 per 1,000 practices was considered an impediment to their adoption. In Senegal, land availability and tenure can also be a constraint.

Actions to Overcome Barriers to the Adoption of 4 per 1,000 Practices

As for barriers, the number of proposed actions to overcome the identified barriers to 4 per 1,000 is high and diversified, ranging from training needs to fund raising or the need for new fodder sources. Identified actions to foster soil carbon sequestration mainly consisted in economic, political, and capacity-building actions (Table 3), in both countries. The first and second principal components of the CA explained, respectively, 31.65 and 29.74% of the total inertia (Figure 2). Axis 1 was positively correlated with "Regulations" and "Organizational" actions and was negatively correlated with "Communication" and "Demonstration" actions. Axis 2 was positively correlated with "Consultation" and "Research" actions and was negatively correlated with "Organizational" actions. Most farming systems shared "Capacity building, " "Political, " and "Economic" actions (Table 3). These actions therefore appeared near the center of the CA diagram and did not help in differentiating the farming systems.

One striking result was the difference of potential actions between farming systems in France and in Senegal. Indeed, all French farming systems were gathered on the diagram (Figure 2), while the Senegalese farming systems were more scattered in several parts of the diagram. According to the results of the CA (Figure 2), most of the farming systems in France shared actions related to "Communication, " "Demonstration, " and "Economic" actions (Figure 2). Furthermore, the diversity of actions identified was higher for farming systems in Senegal, ranging from "Regulations" and "Organizational" (i.e., periurban agriculture in the Niayes) to "Research" actions (i.e., agroforestry in Faidherbia albida parklands).

Specifically, actions such as "Adopting territorial approach to improve land planning, " "Coordination between stakeholders and actions, " or "Building networks of demonstrators from researchers to farmers, or from farmers to consumers" (Table 4) show a concern for interactive, perhaps collective, solutions where different persons are connected. Labeling and communication actions on value chains and marketing were mentioned in France, while diagnostic studies, or the need for research and organizational support, were highlighted in Senegal.

DISCUSSION

Results from the two workshops showed that most barriers to the adoption of 4 per 1,000 practices were more related to farmers' enabling environment (e.g., legal compliance, governance, lack of training and capacity building, lack of economic incentives) than to technical issues. Even though this result might have been influenced by the technical knowledge of the participants, it is consistent with other analyses (e.g., [START_REF] Amundson | Soil carbon sequestration is an elusive climate mitigation tool[END_REF] showing that while the 4 per 1,000 calculus (i.e., offsetting the annual increase of CO 2 by soil carbon sequestration) is physically true, it is unlikely to be politically and economically possible everywhere, especially as the potential for additional carbon storage in the soil is different from one farming system to another, and one region to another. Overcoming most of these barriers is therefore not in the control of farmers themselves. Consequently, actions to scale up the 4 per 1,000 Initiative should target stakeholders far beyond the farmers.

It is well-known that research, education, and extension are usually not sufficient to bring knowledge, technologies, and services to farmers and entrepreneurs, or to help them innovate (World Bank, 2012). From a worldwide survey conducted in the framework of an international research cooperation project on soil carbon sequestration in agriculture CIRCASA (2019), it appears that a high proportion of farmers do apply organic amendments (manure, compost) to increase SOC. Economic barriers do not necessarily explain the limited rate of adoption of new techniques. For instance, in France, part of the GHG mitigating potential in agriculture related to SOC is estimated to have a low cost (e.g., agroforestry, intercropping) or even to generate benefits (e.g., longer grazing period, de-intensification of grassland management) for farmers [START_REF] Pellerin | Identifying cost-competitive greenhouse gas mitigation potential of French agriculture[END_REF]. In the case of France, the integration of GHG mitigation benefits in the production system was also seen possible through some of the proposed actions in economics, e.g., value chain design, marketing, labeling, which can all lead to giving carbon an economic value and thus increasing farmer income. In the case of Senegal, no such actions appeared in our results and the benefits of GHG mitigation rather materialize in terms of improved adaptation and resilience of the farming systems.

Fostering dynamic interactions and interconnections between farmers [START_REF] Klerkx | Evolution of systems approaches to agricultural innovation: concepts, analysis and interventions[END_REF], [START_REF] Foran | Taking complexity in food systems seriously: an interdisciplinary analysis[END_REF] requires bringing together education, extension, and business development services on the one hand, with organizations, agricultural research system, policy makers, the private sector, and consumers on the other. Stakeholder engagement is a [START_REF] Corbeels | Is the 4 per thousand initiative for soil organic carbon storage achievable in sub-Saharan Africa? Insights from agroforestry and conservation agriculture[END_REF]. For instance, between industrialized systems in Northern countries and extensive pastoral or agro-pastoral and family systems in Southern countries, there is a highly diversified range of livestock systems that differ markedly in terms of mitigation innovations [START_REF] Vigne | Contraintes sur l'élevage dans les pays du Sud: les ruminants entre adaptation et attenuation[END_REF]. Such discrepancy between farming systems in Northern and Southern countries in the potential actions to boost soil carbon sequestration was confirmed in our study, as all French farming systems were gathered on Figure 2, while the Senegalese farming systems were more scattered. The most concrete example of institutional innovation to foster stakeholder collaboration is through multi-stakeholder innovation platforms at community and national levels [START_REF] Schut | Innovation platforms: experiences with their institutional embedding in agricultural research for development[END_REF]. The farm is not the appropriate scale for a variety of stakeholders (e.g., public, private, NGO, farmers) to collaborate and progress toward innovations through interactions and collective action. Participants sometimes mention the development of a "territorial" (i.e., landscape) approach as a more relevant scale where soil and land planning issues can be discussed. Since the "territory" is a set of different land units (fields, dwellings, grazing land, natural areas, etc.) it necessarily has a social dimension [START_REF] Torquebiau | Whither landscapes? Compiling requirements of the landscape approach[END_REF] which is conducive to collective actions such as the introduction of trees, fire management, or livestock practice improvements. It can also be used to design innovations where added value related to SOC storage can be created (e.g., geographical indications), or where the management of organic matter and GHG leakages can be addressed. This is also the scale where new forms of governance are designed that are favorable to development and to solidarity strengthening [START_REF] Caron | Living Territories to Transform the World[END_REF], in contrast to national-level government, which has become too complex and difficult, but also seemingly powerless [START_REF] Toulmin | Foreword[END_REF]. Since the 4 per 1,000 Initiative has a 3-fold objective, it can be expected that the balance between the three components differs from one stakeholder to another and from one region to the next. For instance, smallholder farmers in sub-Saharan Africa may focus more on food security through better adapted practices-and especially the increase of crop and animal productivity [START_REF] Corbeels | Is the 4 per thousand initiative for soil organic carbon storage achievable in sub-Saharan Africa? Insights from agroforestry and conservation agriculture[END_REF]-than on climate change mitigation itself. In such situations, "the territory can also be a form of organization than can internalize certain transaction costs, minimize economic risks" [START_REF] Caron | Why and how the concept of 'territory' can help in thinking rural development[END_REF]. Finally, participants pointed out the real need for a change of mind-set and awareness-raising among institutions, extension organizations, education and training organizations, farmers, and consumers. "Territorial" dynamics have actually been identified as factors of change, modifying social processes and actor behavior [START_REF] Caron | Living Territories to Transform the World[END_REF].

CONCLUSION

The inputs from two participatory multi-stakeholder workshops held in France and Senegal showed that most of the constraints to the adoption of innovations contributing to the objectives of the 4 per 1,000 Initiative were shared by both areas despite their differing environmental and socio-economic contexts. Fostering agricultural soil carbon sequestration is more a question of an enabling environment (e.g., social, economic) than technical innovations or farmers' willingness for change, as a smaller number of constraints and coping strategies mentioned technical issues. As most of these barriers are not in the control of farmers, actions to scale out and to scale up the 4 per 1,000 Initiative need to target stakeholders beyond farmers themselves and call for an improved policy context leading to innovations in land planning, stakeholder communication, demonstration facilities, capacity building, or financial support. A "territorial approach" appears to be the appropriate scale to address the governance challenges related to the 4 per 1,000 Initiative. In summary, actions to support the 4 per 1,000 Initiative need to include a variety of stakeholders such as extension services, the private sector, civil society, local institutions, policy makers, consumers, and not only farmers. Scaling out and scaling up the 4 per 1,000 Initiative is not a process which differs from other agricultural innovations. Experiences related to sustainable intensification of agricultural systems, for instance, could be useful to feed the current discussions on the dissemination of the 4 per 1,000 Initiative.

Financial-

  Compatibility with the Common Agricultural Policy (CAP) Political Cattle breeding in Creuse, France -Introduce intermediary crops with legumes -Introduce mixed species cover crops (méteil) -Increase crop area from 4.5 ha to 9 ha to decrease straw and legumes purchase and transport -Reduce tillage frequency to one every 5 years -Increase proportion of legumes -Increase cattle loading by 20% -Increase length of grazing period -Concentrate spreading of organic manure on crops and temporary grasslands -Fattening weanlings in grasslands -Introduce hedges -Introduce apple trees in permanent grasslands -Net Soil Organic Carbon balance to be assessed -Calculate new ratio production of grasslands vs. cattle needs -Higher exposure to climatic conditions -Compatibility between production of cereals, fodder and hay -Needs to fatten the weanlings -Redesign the farming system and especially the number of training related to the introduction and management of cover crops Capacity building -Social pressure from neighbors and family -Risk aversion related to changes of practices Social -No additional income for soil carbon sequestration and improvement of the quality of the products (e.g.of varieties resistant to mildew -Quality of organic inputs -Lack of references for new techniques -Compliance with norms (e.g., AOC labels) Technical -Poor soils typical of vineyard in France -Root spreading of the trees -Competition for water Biophysical -Increased difficulty of work and workload -Limited capacity of negotiation of the farmers -Difficulty to implement collective action -Social pressure from the profession Social -No additional income/payment related to environmental services Economic -The monoculture of wine grape since centuries lead to negative environmental impacts Environmental -Organization of the vineyard sector Organizational (Continued)Frontiers in Sustainable Food Systems | www.frontiersin.org

  FIGURE 1 | Correspondence Analysis on identified barriers to adoption of 4 per 1,000 practices in eight different farming systems in France and Senegal. Farming systems are in blue. Category of barriers are in red.

FIGURE 2 |

 2 FIGURE 2 | Correspondence Analysis on potential actions proposed by stakeholders to boost soil carbon sequestration in eight different farming systems in France and Senegal. Farming systems are in blue. Category of actions are in red.

-

  to overcome constraints of knowledge and opinion from farmers at the scale of farmers' group: broad political context to stimulate change Political -Carry out a feasibility study to identify the problems at the scale of the farm: local diagnosis models and address the transition Political -Carry out a pre-study to have a clear picture of the current situation Study -Communicate on value chains and low carbon farms Communication Field crops in Cher, France -Improve marketing Economic -Training for non-farmers -Training on soil management -Provide online training (video, MOOC) activity in territorial management policies (e.g., Climate Plan) Political -Develop communication related to soil carbon sequestration and vineyard Communication -Develop field visits, demonstrations, field advice and share experiences Demonstration -Include soil carbon sequestration in AOC labels certification Labeling -Study the environmental impact of organic inputs Study Peri-urban agriculture in the Niayes, Senegal -Develop soil carbon monitoring -Develop knowledge and tools for carbon balance evaluation -Develop skills on soil organic matter management and transformation processes (safety, agronomic qualities, GHG balance) -Improve composting and bio-digestion -Assess safety and agronomic qualities of organic wastes (compliance with standards, measurement tools) -Define and implement suitable transformation processes Technical -Organize the collection and transport of organic wastes -Sort organic urban wastes at source Organizational -Assess waste deposits (location, amount), use and economic viability Study -Control quality standards, regulations, certification Regulations Irrigated agriculture in the Senegal River valley -Change in pre-irrigation practices to reduce tillage -Spatial planning for reintroduction of trees in the landscape -Public policy of self-sufficiency in rice Political -Data collection following IPCC Tier 2 or Tier 3 research and characterization Research (Continued)Frontiers in Sustainable Food Systems | www.frontiersin.org

TABLE 1 |

 1 Categories of barriers identified by stakeholders for the adoption of 4 per 1,000 practices in eight different farming systems in France and Senegal.

	Farming System in France

TABLE 2 |

 2 Identified soil organic carbon sequestration practices in eight different farming systems in France and Senegal, with barriers potentially affecting these practices.

	Farming system Identified soil organic carbon sequestration	Identified barriers	Category of barrier
		practices
	Polyculture-	1st option:	-Extrusion of linen	Technical
	breeding in	-Diversification of crops (linen, alfalfa, protein) to offer	-Choice of tree species for agroforestry
	Meuse, France	more autonomy to livestock breeding	-Improvement of soil cover
		-Improvement of grassland and development	-Reduction of soil tillage
		of agroforestry Improvement of soil cover and	-Adapted tools for improvement of soil cover/reduction of tillage
		reduction of tillage	-Adapted seeds for improvement of soil cover/reduction of tillage
			-Technical know-how for agroforestry	Capacity building
		2nd option:	-Availability of agronomic and zootechnical knowledge and
		-Increase of the grassland area (including legumes)	advice to diversify the crops
		-Increase of pasture -Valorization through high added value market -Evolution of herd genetics (mixed race with lower milk production) (2 years) -Introduction of hedges Reduction of calving age	-Available workforce missing -Opinion ("social visa") from farmers and neighbors -Fragmentation of the plots -Access to high added value market soybean for animal feed -Lack of competitiveness of self-produced legumes vs. imported	Social Economic
			-Initial investment for agroforestry
			-Financial problem during period of reconversion

TABLE 2 |

 2 Continued

	Farming system Identified soil organic carbon sequestration	Identified barriers	Category of barrier
		practices
	Peri-urban	-Intensification of organic wastes recycling through	-Organic matter treatment techniques	Technical
	agriculture in the	the production of compost, the use of sludge and	-Safety of organic products because of the contents in trace
	Niayes, Senegal	mechanization	metallic elements
		-Use of organic fertilizers	-Sandy soils with limited potential of SOC storage	Biophysical
		-Introduction/association of trees and shrubs -Use of biochar	requires the control of the composting process -Lack of workforce as composting is hard to implement and	Social
			-Organization of the organic matter collection, waste treatment	Organizational
			sector as the resources are scattered
			-New skills required	Capacity building
			-Lack of knowledge of organic matter resources to intensify
			recycling of organic matter
			-Land pressure related to urbanization, risk of conversion of	Economic
			agricultural land to urban areas
	Irrigated	-Implementation of alternate wetting and drying	-Irrigated systems depend on large quantities of fertilizers and	Technical
	agriculture in the	irrigation technique to decrease water consumption	pesticides, herbicides
	Senegal River	as well as N 2 O and CH 4 emissions	-Trees are systematically logged because of the risks associated
	valley	-Improved management of inputs: mixture of organic	with birds
		and chemical fertilizers	-No quantification of carbon flows and stocks and
		-Diversification of production with inclusion of N-fixing	sequestration balances
		legumes and fresh legumes in counter-season	-Alluvial soils are difficult to work when dry and require	Biophysical
			mechanization
			-In the delta, the salt water table rises if a permanent water slide
			of 10 or 15 cm is not maintained throughout the growing season
			-Irrigation canals, pumps, etc. require heavy work	Social
			-Organic matter (straw) is no longer available in plots but is sold	Economic
			to cover financial needs
			-Irrigation canals, pumps, etc. require maintenance costs
	Agroforestry in	-Increase the stem density of Faidherbia albida trees	-Difficult to increase stem density (plow/reduction of cultivated	Technical
	Faidherbia albida	-Bury organic matter in the soil	areas)
	parklands in	-Introduce hedges of shrubs and trees	-Optimal density of trees not known; farmers not convinced by
	central Senegal	-Reduce fire occurrence	an increase
		-Decrease livestock number	-Lack of space for productive hedges
		-Incorporate clay in the soil	-Difficulty to stop burning
		-Import organic matter from urban areas	-Equipment needed for burial of organic matter / transport and
		-Introduce N-fixing species in the rotation	incorporation of clay
			-Availability of convenient clay sources	Biophysical
			-Transition from subsistence agriculture to cash farming requires	Capacity building
			a change of logic
			-Perception from other farmers	Social
			-Overall objective is to have many animals (prestige, savings)
			-Workforce needed to harvest woody organic material prior to
			burial / for installation and maintenance of hedgerows
			-Potential land conflict. To whom belongs the hedge?
			-Cost of substitute products for the modification of animal diet	Economic
			-Slaughter of young animal is culturally, and economically difficult
			as young animals are seen as "savings on feet"
			-Overall objective is to have many animals (prestige, savings)	Cultural
			-Subsidy for chemical fertilizers	Political
	Rainfed agriculture	-Cattle herding in cultivated plots	-Insufficient number of animals or lack of animal feeds	Technical
	and extensive	-Use of organic amendment for crops	-Competition for crop residues
	livestock	-Use of crop residues	-Unpredictable inter-annual variability of rainfall forcing herds to	Biophysical
	integration,	-Housing of cattle and use of biodigestors to produce	go far
	Senegal	biogas and reduce the pressure on fuel wood	-Lack of local qualified workforce for biodigestors technology	Social
			-Increased land pressure and degradation of resources
			(demographic growth)

(Continued) Frontiers in Sustainable Food Systems | www.frontiersin.org 6 April 2020 | Volume 4 | Article 37

TABLE 2 |

 2 Continued

	Farming system Identified soil organic carbon sequestration	Identified barriers	Category of barrier
	practices
		-Current low level of cattle housing	Economic
		-Low means for organic matter collection (transport, labor)
		-Cost and availability of fertilizers
		-Low income diversification
		-Cost of biodigestor technology
		-Availability of organic matter for biodigestors	Organizational
		-Organic amendment requires large amount of manure
		-Cultural barrier to use excrements (e.g., pigs, humans)	Cultural

TABLE 3 |

 3 Categories of potential actions proposed by stakeholders to boost soil carbon sequestration in eight different farming systems in France and Senegal.

	Farming System in France

TABLE 4 |

 4 Identified actions to overcome barriers to soil organic carbon sequestration in eight different farming systems in France and Senegal (see Table2for corresponding practices and barriers).

TABLE 4 |

 4 Continued

	Farming System	Proposed actions

Frontiers in Sustainable Food Systems | www.frontiersin.org

April 2020 | Volume 4 | Article 37

FUNDING

This work was funded through the EIT Climate-KIC project no. 180507 Action plan to scale out the 4 per 1,000 Initiative.

DATA AVAILABILITY STATEMENT

All datasets generated for this study are available on https://dataverse.cirad.fr with the following doi: 10.18167/DVN1/LRPTHE.

AUTHOR CONTRIBUTIONS

JD and ET contributed to the conception and design of the study and wrote the first draft of the manuscript. MAr, TE, and DM wrote sections of the manuscript. All authors contributed to manuscript revision, read, and approved the submitted version.

Conflict of Interest:

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.