Mylène Hugoni
email: mylene.hugoni@univ-lyon1.fr

Arthur Escalas

Cécile Bernard

Sébastien Nicolas

Didier Jezequel

Fanny Vazzoler

Gérard Sarazin

Christophe Leboulanger

Marc Bouvy

Patrice Got

Sarazin

Marbec Bouvy

Marc ; Ird

Marbec Ader

D Jézéquel

M Bouvy

M Troussellier

H Agogué

Spatiotemporal variations in microbial diversity across the three domains of life in a tropical thalassohaline lake (Dziani Dzaha, Mayotte Island)

Keywords: Extreme environment, Soda lake, Metabarcoding, Eukaryotes, archaea, bacteria Extreme environment / Soda lake / Metabarcoding / Eukaryotes / Archaea / Bacteria

Abstract

Extreme environments, like soda lakes, represent excellent models to study how drastic environmental conditions shape microbial diversity. In these ecosystems, microorganisms significantly contribute to biogeochemical cycles, but their community structure and spatiotemporal dynamics remain largely unexplored. In this study, we monitored the 3-domainsof-life composing the microbial communities of Lake Dziani Dzaha (Mayotte), a tropical saline alkaline lake. Using a diversity partitioning approach, we revealed that most of the microbial diversity was hosted in local microbial communities, with a comparatively lower contribution of between-communities differences to the overall diversity. Nonetheless, the diversity of the whole system was clearly impacted by the presence of chemoclines, inducing a stratification of the water column into different ecological niches, allowing significant communities differentiation across spatio-temporal scales. A detailed analysis of Bacteria, Archaea and Eukaryota showed that depth, season, and sampling year impacted differentially the establishment of each domain of life. Indeed, photosynthetic microorganisms were abundant in surface layers while deeper layers were dominated by chemotrophic microorganisms from Firmicutes and Bacteroidetes phyla, and by putative methanogenic lineages such as Woesearchaeota. Our findings highlighted the importance of considering multi-domain microbial processes and interactions in time and space to better understand their impact on ecosystem functioning. or Mexico and in dry steppe regions like in Russia [START_REF] Sorokin | Microbial diversity and biogeochemical cycling in soda lakes[END_REF][START_REF] Grant | Bacteria, Archaea and Viruses of Soda Lakes[END_REF]. The name "soda" is derived from the chemical composition of their waters, which are considered alkaline because of the high concentration of dissolved inorganic carbon and the presence of sodium as the major cation, so that upon nearly complete evaporation Na 2 CO 3 (called soda) could precipitate. These characteristics are often associated with elevated pH values (9.5 to 12) and high salinity waters (>50 psu). As a result of such drastic environmental conditions, soda lakes are inhabited by microorganisms adapted to high alkalinity and salinity, unlimited supplies of dissolved inorganic carbon and sometimes low oxygen availability. These adaptations relied on molecular mechanisms [START_REF] Ochsenreiter | Diversity of Archaea in hypersaline environments characterized by molecular-phylogenetic and cultivation studies[END_REF][START_REF] Mesbah | The halophilic alkalithermophile Natranaerobius thermophilus adapts to multiple environmental extremes using a large repertoire of Na(K)/H antiporters[END_REF], as for example modifications of their membrane structure, the use of transporter proteins or the synthesis of osmo-protectants [START_REF] Sorokin | Microbial diversity and biogeochemical cycling in soda lakes[END_REF][START_REF] Grant | Bacteria, Archaea and Viruses of Soda Lakes[END_REF]. Previous studies clearly showed that salinity is one of the key environmental factor shaping the composition and structure of aquatic microbial communities on a global scale [START_REF] Lozupone | Global patterns in bacterial diversity[END_REF][START_REF] Canfora | Salinity and bacterial diversity: to what extent does the concentration of salt affect the bacterial community in a saline soil?[END_REF]. As a consequence, the microbial diversity in soda lakes is limited to salt-tolerant specialists that are key players of biogeochemical cycles occurring in those ecosystems (e.g. carbon, nitrogen and sulfur cycles).

In spite of apparent extreme conditions, soda lakes are considered among the most productive aquatic ecosystems, especially in tropical areas with elevated temperature and high incident solar radiations. Prodigious rates of photosynthetic primary production were [START_REF] Ballot | Phylogenetic relationship of Arthrospira, Phormidium and Spirulina strains from Kenyan and Indian waterbodies[END_REF][START_REF] Lewis | Rationale for control of anthropogenic nitrogen and phosphorus to reduce eutrophication of inland waters[END_REF]. The primary productivity can reach up to 10 gC.cm -2 .day -1 , delivering fixed carbon to haloalkaliphilic communities, as aerobic and anaerobic chemoorganotrophic Bacteria and Archaea [START_REF] Melack | Photosynthetic rates of phytoplankton in East African alkaline, saline lakes1[END_REF][START_REF] Grant | Alkaliphiles: Ecology, diversity and applications[END_REF].

Most of the studies investigating microbial communities in soda lakes revealed dense populations of primary producers affiliated with unicellular and filamentous Cyanobacteria, such as the genera Arthrospira, Cyanospira, Geitlerinema, Leptolyngbya or Anabaenopsis [START_REF] Grant | Bacteria, Archaea and Viruses of Soda Lakes[END_REF][START_REF] Krienitz | Tiny and Tough: Microphytes of East African Soda Lakes[END_REF]. At higher salinity (>50 psu), unicellular green algae like Picocystis salinarum or Dunaliella viridis were also retrieved [START_REF] Krienitz | Tiny and Tough: Microphytes of East African Soda Lakes[END_REF]. Studies focusing on prokaryotes reported the dominance of Alphaproteobacteria, Gammaproteobacteria, Firmicutes and Bacteroidetes [START_REF] Dimitriu | Spatial and temporal patterns in the microbial diversity of a meromictic soda lake in Washington State[END_REF][START_REF] Sorokin | Microbial diversity and biogeochemical cycling in soda lakes[END_REF][START_REF] Aguirre-Garrido | Bacterial Diversity in the Soda Saline Crater Lake from Isabel Island, Mexico[END_REF], associated with abundant Euryarchaeota in hypersaline soda lakes [START_REF] Ochsenreiter | Diversity of Archaea in hypersaline environments characterized by molecular-phylogenetic and cultivation studies[END_REF][START_REF] Mesbah | Novel and unexpected prokaryotic diversity in water and sediments of the alkaline, hypersaline lakes of the Wadi An Natrun, Egypt[END_REF][START_REF] Vavourakis | Metagenomic Insights into the Uncultured Diversity and Physiology of Microbes in Four Hypersaline Soda Lake Brines[END_REF]. Although salt-adapted organisms derive from all the three domains of life, most studies investigated the prokaryotic fraction of the microbial assemblage [START_REF] Ghai | New Abundant Microbial Groups in Aquatic Hypersaline Environments[END_REF][START_REF] Ventosa | Microbial diversity of hypersaline environments: a metagenomic approach[END_REF][START_REF] Kambura | Bacteria and Archaea diversity within the hot springs of Lake Magadi and Little Magadi in Kenya[END_REF], while very few considered the eukaryotic diversity associated with those ecosystems [START_REF] Krienitz | Picocystis salinarum (Chlorophyta) in saline lakes and hot springs of East Africa[END_REF].

Over the past decade, high-throughput sequencing technologies have been successful in describing relative low-diversity ecosystems such as extreme environments, by giving snapshots of the overall community structure and gaining new insights into uncultivated microorganisms genome [START_REF] Ghai | New Abundant Microbial Groups in Aquatic Hypersaline Environments[END_REF]Narasingarao et al., 2012;[START_REF] Vavourakis | Metagenomic Insights into the Uncultured Diversity and Physiology of Microbes in Four Hypersaline Soda Lake Brines[END_REF]. Lake Dziani Dzaha, located in Mayotte Island, is a small crater lake (ca. 0.24 km 2 ) with shallow water (mean depth: 3 m, except for a pit at 18 m depth). Its probable seawater 6 origin makes it a peculiar soda lake, which water composition has been modified by biological and geothermal activities up to current conditions: extremely high alkalinity (0.23 mol/L), elevated salinity (ranging from 34 to 71 psu) and pH (9.1 to 9.4). This lake presents extremely and constantly high rates of organic matter production and mineralisation (Leboulanger et al., 2017). The alternation of a rainy (Nov.-Apr.) and a dry season (June-Oct.) induces a saline and seasonal stratification of the water column, caused by the dilution of the upper layer by rainfalls, which creates a chemocline at around 2.25 meter depth. This stratification usually persists until August, when a combination of temperature decrease and salinity increase by evaporation lead to an increase of the density of the surface layer. The water column is permanently anoxic below about 1 to 2m depth, irrespectively of the water column stratification, with rare episodes when anoxia reaches the surface of the water column. A second chemocline was systematically identified in the pit at a depth around 14m, below which H 2 S/HS -, NH 4 + /NH 3 and CH 4 concentrations were systematically high and reached values of up to 5, 4 and 1 mM, respectively. In this ecosystem, the aquatic food web is very simple and characterized by permanent cyanobacterial blooms (mainly Arthrospira), high prokaryotic biomass depending on the season, and an absence of metazoans apart from endemic flies (Leboulanger et al., 2017).

Thus, this singular ecosystem can be considered as an excellent microbial model to examine the genetic structure and dynamics of microbial communities.

Results

Physico-chemical characteristics of the water column

This study was conducted in the pit zone of the lake, characterized by the maximum depth registered (18m). The surface layer of the water column was oxic down to 2m while the conditions were completely anoxic all year long below that limit (Figure 1).

Microbial community structure in lake Dziani Dzaha

This work investigated the spatial and temporal changes in the microbial communities diversity of the three life domains from the pelagic ecosystem of the lake Dziani Dzaha.

The relative importance of these two dimensions of the microbial dynamics differed among the considered life domain (Bacteria, Archaea, Eukaryota).

Depth was the main factor influencing the composition of prokaryotic communities, notably for Bacteria for which it explained 47% of variation in community composition (Table 1). For Archaea, the influences of season and year on community composition were closer to the effect of depth (15, 12 and 21% of variation, respectively, Table 1). On the contrary, the composition of eukaryotic microbial communities was mostly influenced by the sampling season and to a lesser extent by year and depth (35, 12 and 6% of variation, respectively, Table 1). The differences in the relative importance of time and space effects on microbial communities composition are presented in Figure 2.

When considering all samples together, the richness in normalized datasets consisted in 242 bacterial, 109 archaeal and 87 eukaryotic OTUs. When pooling the three domains together, total microbial richness ranged from 221 to 359 OTUs per sample, with an average of 301±37 OTUs. Then we used a diversity partitioning approach to explore the multiple facets of microbial diversity across multiple scales. We estimated the total microbial diversity (i.e. γ-diversity) associated with each domain of life using Rao' quadratic entropy (Table 2). When using presence-absence data, we found that bacterial communities exhibited the highest γ-diversity in the system, with 230.6 OTUs, followed by Archaea with 97.9 OTUs and Eukaryota with 41.9 OTUs. When using relative abundance data, we observed that archaeal communities were the most diverse (γ -diversity = 8.9), followed by bacterial (γ -diversity = 3.7) and eukaryotic (γ -diversity = 1.4) communities. This change in the diversity estimates between the two methods is due to the fact that the distribution of abundance between OTUs was more even in archaeal communities compared with bacterial and eukaryotic ones, which were dominated by a single OTU representing most of the dataset (i.e. Arthrospira fusiformis and Picocystis salinarum, respectively).

An additive decomposition of γ-diversity was used to determine whether the total observed diversity aroused from the average diversity within communities (i.e.

α LocalCommunities ) or the differences between communities across seasons (i.e. β InterSeason ) and across depth (i.e. β InterDepth ) (Figure 3.A and B). Overall, local communities represented most of the total diversity (α LocalCommunities > 76.5% on average). When using presenceabsence data, we observed that β-diversity (β InterSeason + β InterDepth ) represented a higher proportion of γ-diversity in eukaryotic communities (36.6%), while it contributed in a smaller proportion in archaeal (20.2%) and bacterial (14.6%) communities. When using abundance data, we observed higher contributions of β-diversity to γ-diversity for Archaea (34.9%) and Bacteria (31.6%) while the value for Eukaryota dropped to 3%. Further, we found that differences along the depth profile (β InterDepth ) contributed more to the total diversity than inter-season differences (β InterSeason ), with 20.4 and 3.1% of γ Diversity , respectively.

The present work showed that the diversity distribution along the depth profile differed greatly between the three domains of life ( between OTUs in these communities was more balanced as the depth increased. The decomposition of diversity reveals that there was a very low degree of differentiation between communities at the top of the water column while deeper communities tended to be more variable. On the contrary, archaeal communities exhibited maximum diversity in the first meter and a sharp drop of diversity below this depth. This reverse pattern corresponded to the increasing dominance of a smaller number of archaeal taxa with increasing depth. For archaeal communities, we observed a higher β-diversity in the upper layers but there was always a certain degree of differentiation from a given depth across time (year and season). Eukaryotic communities showed a very low and constant diversity along the depth profile (i.e. due to the hyper dominance of Picocystis OTUs). The proportion of eukaryotic β-diversity observed was strikingly lower than for other domains and this was the case at every depth.

Sampling seasons also have a different impact on the diversity estimated for the three domains of life (Figure 3.D). Bacterial communities appeared to be more diverse during the stratified period, with γ-diversity estimates more than twice higher in this season.

This was notably due to more dissimilar communities, with β-diversity representing 36.7% of γ-diversity during the stratified period compared to only 15.5% during non-stratified one.

The diversity of archaeal and eukaryotic communities was more stable across seasons and exhibited smaller changes in their composition, notably for eukaryotic organisms where βdiversity represented less than 3% of γ-diversity. 4).

Microbial community composition in lake Dziani

Discussion

The present work constitutes the first characterization of the whole microbial assemblage associated with the tropical lake Dziani Dzaha, by including both prokaryotic (Archaea and Bacteria) and eukaryotic compartments. The use of high-throughput Illumina sequencing, through two consecutive years and during stratified and non-stratified periods, gave the opportunity to fully describe microbial taxonomic groups inhabiting a simple functional microbial network where most grazers were absent.

Our study provided new insights into the biodiversity of microbial communities at three different scales including diversity (i) of local communities (α-diversity), (ii) between communities (β-diversity) and (iii) of the whole system (γ-diversity). We showed that α-LocalCommunities contribution to γ-diversity was important (about 76.5%) outweighing β-InterSeason and β-InterDepth, thus supporting the idea of consistently high diversity across local microbial communities (OTU richness = 301±37 OTUs on average). However, βdiversity represented a variable part of γ-diversity depending on the domain of life and the type of matrix considered (i.e. presence-absence vs abundance matrix). A striking example was the difference in the contribution of β-InterDepth to γ-diversity observed in eukaryotic communities with presence-absence (32.2%, Table 2) versus abundance data (2.1%). This reflected the fact that, although the list of detected OTUs might change between depths, the abundance distribution across these OTUs at each depth was so skewed toward a single OTU (Picocystis salinarum), that the communities could almost be considered as composed the other hand, for prokaryotic communities, change in the identity of detected species was relatively small compared to the total diversity (i.e. β-diversity represented 20.2% and 14.6% of γ-diversity with presence-absence data in Archaea and Bacteria, respectively).

However, the distribution of abundance among the OTUs varied greatly according to depth and season (i.e. contribution of β-diversity was 34.9% and 31.6% for Archaea and Bacteria, respectively). Overall, these trends suggested that while eukaryotic communities were relatively more variable in their composition, prokaryotic communities were more dynamic in terms of changes in OTUs abundance across season and depth. Moreover, the diversity decomposition according to the season revealed that γ-diversity was higher during the stratified period, especially for Bacteria, which is in accordance with the presence of environmental clines in the water column. In fact, these clines generated different ecological niches through changes in H 2 S, O 2 or pH, and ultimately allowed higher communities differentiation. Some differences in γ-diversity were also observed according to depth, with decreasing bacterial and increasing archaeal γ-diversity. Those results were confirmed through the analysis of community composition along the depth profile during the stratified period compared to the non-stratified one. Indeed, the structure and composition of microbial assemblages were highly influenced by the sampling year, the season and the depth considered, and thus ultimately by the physico-chemical structure of the water column. During the stratified period, the community composition differed between surface water samples (0.5m and 1m depth) and water samples from 2.5 to 11m, suggesting that the oxic zone associated with the seasonal chemocline at 2m impacted the community structure for both prokaryotes and microbial eukaryotes. Moreover, a shift in bacterial community structure was also reported at the permanent chemocline situated at As observed in other soda lakes, photosynthetic organisms dominated the microbial assemblage [START_REF] Grant | Bacteria, Archaea and Viruses of Soda Lakes[END_REF][START_REF] Krienitz | Tiny and Tough: Microphytes of East African Soda Lakes[END_REF], particularly in upper layer. In lake Dziani Dzaha, the photosynthetic communities were dominated by Cyanobacteria from the Arthrospira genus (also named Spirulina) and Eukaryota from the Picocystis genus. Arthrospira consisted in alkaliphilic filamentous Cyanobacteria, which formed dense masses seasonally or permanently [START_REF] Ballot | Phylogenetic relationship of Arthrospira, Phormidium and Spirulina strains from Kenyan and Indian waterbodies[END_REF][START_REF] Sili | Arthrospira (Spirulina)[END_REF].

Interestingly, a recent characterization using a polyphasic approach of strains isolated from lake Dziani Dzaha, reported that Arthrospira strains were affiliated to Arthrospira fusiformis and Picocystis strains to Picocystis salinarum (Cellamare et al., Submitted). In lake Dziani Dzaha, Arthrospira fusiformis shows an unusual straight morphotype suggesting that it might be adapted to the peculiar environmental conditions identified in this lake. This is also consistent with the retrieval of 15.2% of total sequences on average corresponding to Picocystis salinarum, although the lake was considered as dominated in biomass by Cyanobacteria (Leboulanger et al., 2017). P. salinarum and A. fusiformis are highly productive primary producers often reported as numerically abundant in microbial communities of saline habitats, such as soda lakes of the East African Rift Valley [START_REF] Krienitz | Picocystis salinarum (Chlorophyta) in saline lakes and hot springs of East Africa[END_REF] or Mono Lake, USA [START_REF] Hollibaugh | Stratification of microbial assemblages in Mono Lake, California, and response to a mixing event[END_REF]. A recent study conducted on bioreactors inoculated with alkaline sediments fed by Arthrospira biomass showed that the produced organic matter was hydrolyzed mainly by Bacteroidetes ML635J-40 aquatic et al., 2015). This microbial consortium is highly relevant in the case of lake Dziani Dzaha, where the Methanomicrobia is strongly dominated by the genus Methanocalculus. In addition, the enrichment in Methanocalculus with depth is concomitant to the enrichment in Bacteroidetes affiliated with Bacteroidia_ML635J-40 aquatic group. This group has been formerly identified in soda lakes and alkaline environments such as the Mono lake [START_REF] Humayoun | Depth Distribution of Microbial Diversity in Mono Lake, a Meromictic Soda Lake in California[END_REF], Magadi lake [START_REF] Baumgarte | Microbial Diversity of Soda Lake Habitats[END_REF] and the Lonar crater lake [START_REF] Wani | Molecular analyses of microbial diversity associated with the Lonar soda lake in India: an impact crater in a basalt area[END_REF]. Previous work conducted on soda lake sediments reported the presence of the genus Methanocalculus responsible for hydrogenotrophic methanogenesis able to use both CO 2 and formate to produce CH 4 in highly saline conditions [START_REF] Zhilina | Methanocalculus natronophilus sp. nov., a new alkaliphilic hydrogenotrophic methanogenic archaeon from a soda lake, and proposal of the new family Methanocalculaceae[END_REF][START_REF] Sorokin | Methanosalsum natronophilum sp. nov., and Methanocalculus alkaliphilus sp. nov., haloalkaliphilic methanogens from hypersaline soda lakes[END_REF]. Syntrophic acetate-dependent methanogenesis has been reported in a co-culture of a novel high-salt tolerant and obligatory syntrophic member of Clostridiales and Methanocalculus natrophilus [START_REF] Sorokin | Methanogenesis at extremely haloalkaline conditions in the soda lakes of Kulunda Steppe (Altai, Russia)[END_REF].

Our results clearly showed that multi-domain metabarcoding approaches could reveal biological processes observed in natural ecosystems that also occurred in experimental conditions.

In addition to microorganisms responsible for organic matter recycling, sulfur cycle related organisms were also retrieved in the water column of lake Dziani Dzaha. Firmicutes Dethiobacter alkaliphilus strain which is anaerobic, sulfidogenic and chemolithotrophic [START_REF] Melton | Draft genome sequence of Dethiobacter alkaliphilus strain AHT1T, a gram-positive sulfidogenic polyextremophile[END_REF]; this strain is phylogenetically close to C. contubernalis (also isolated from a soda lake in Russia [START_REF] Zhilina | Candidatus Contubernalis alkalaceticum," an Obligately Syntrophic Alkaliphilic Bacterium Capable of Anaerobic Acetate Oxidation in a Coculture with Desulfonatronum cooperativum[END_REF]). Among the later candidate division, C.

contubernalis alkalaceticum was isolated and demonstrated as one partner of the sulfidogenic association with a hydrogenotrophic, alkaliphilic sulfate-reducing Desulfonatrum and/or Desulfonatrovibrio [START_REF] Zhilina | Candidatus Contubernalis alkalaceticum," an Obligately Syntrophic Alkaliphilic Bacterium Capable of Anaerobic Acetate Oxidation in a Coculture with Desulfonatronum cooperativum[END_REF]. In this syntrophic association, C. contubernalis alkalaceticum is able to oxidize acetate (an important terminal product formed and accumulated in the course of fermentation of organic matter by the anaerobic microbial community), ethanol, serine or fructose. Previous studies demonstrated the competition potentially occurring between methanogenic and sulfidogenic microorganisms [START_REF] Visser | Competition of methanogenic and sulfidogenic bacteria[END_REF]. In natural conditions, and in the presence of nonlimited levels of sulfate, methanogens are generally poor competitors compared with sulfato-reducers, especially in marine sediments, while methanogens tend to be the dominant scavengers of hydrogen and acetate in low-sulfate environments [START_REF] Raskin | Competition and coexistence of sulfatereducing and methanogenic populations in anaerobic biofilms[END_REF]. In lake Dziani Dzaha, sulfate concentrations were relatively low in the surface layers (3.5 mM), that is above the 2m deep seasonal chemocline during the stratified period and above the 14m depth permanent chemocline during non-stratified periods. Additionally, sulfate was not detected below these two chemoclines and H 2 S/HS -was present instead. Other less documented phyla were detected in lake Dziani Dzaha and could represent a gene reservoir for undeciphered functional diversity. Indeed, Woesearchaeota DHVEG-6 were initially described in anoxic environments such as saline and sediments habitats [START_REF] Dojka | Microbial Diversity in a Hydrocarbon-and Chlorinated-Solvent-Contaminated Aquifer Undergoing Intrinsic Bioremediation[END_REF][START_REF] Großkopf | Novel Euryarchaeotal Lineages Detected on Rice Roots and in the Anoxic Bulk Soil of Flooded Rice Microcosms[END_REF] and were recently demonstrated as inhabiting surface waters of oligotrophic alpine lakes, suggesting a wide range of environmental adaptations [START_REF] Ortiz-Alvarez | High occurrence of Pacearchaeota and Woesearchaeota (Archaea superphylum DPANN) in the surface waters of oligotrophic high-altitude lakes[END_REF]. Moreover, a recent study showed that Woesearchaeota probably encompasses two phyla, splitted into Pacearchaeota and Woesearchaeota (Castelle et al., 2015). Genome analysis of the Woesearchaeota AR20 revealed the absence of most of the core biosynthetic pathways, suggesting a parasitic or symbiotic lifestyle for this microorganism (Castelle et al., 2015). Thus it could be interesting to build ecological interaction networks to investigate the potential consortia of OTUs affiliated with Woesearchaeota along with their putative bacterial hosts. Other partial genomes affiliated with Pacearchaeota (AR13) and Woesearchaeota (AR3 and 4) are predicted to have saccharolytic and fermentative lifestyle, consistent with environmental conditions retrieved in the water column of lake Dziani Dzaha. Another less abundant group, named WSA2 and belonging to Euryarchaeota, was also identified in the water column, and was recently attributed with a peculiar methanogenic metabolism by metagenomes analyses [START_REF] Nobu | Chasing the elusive Euryarchaeota class WSA2: genomes reveal a uniquely fastidious methyl-reducing methanogen[END_REF] coenzyme M indicating that they might require organic carbon sources to grow in a heterotrophic way; however, this carbon way is very rare for methanogens, suggesting that WSA2 might cooperate with other active methanogens. Taken together, these features are congruent with a lifestyle adapted to organic-rich anaerobic environments, such as wastewater treatment sludge [START_REF] Wilkins | Pyrosequencing of mcrA and Archaeal 16S rRNA Genes Reveals Diversity and Substrate Preferences of Methanogen Communities in Anaerobic Digesters[END_REF] or lake Dziani Dzaha water column, where fermentation and methanogenesis might produce the required carbon sources, amino acids, ammonia and putatively free coenzyme M.

Interestingly, in this ecosystem, the microbial eukaryotic compartment is also characterized by the presence of some taxa affiliated with bacterivorous flagellates like Jakoba jakobida, classically retrieved in marine and hypersaline ecosystems [START_REF] Rodríguez-Ezpeleta | Toward Resolving the Eukaryotic Tree: The Phylogenetic Positions of Jakobids and Cercozoans[END_REF]. Some other taxa were affiliated with ciliates, such as Spirotrichea.

Taken together, our results suggest that in this extreme ecosystem the trophic network can be clearly defined as microbial, but is not exclusively composed of prokaryotes. In this microbial trophic network, Eukaryota might play important roles by controlling prokaryotic and Picocystis salinarum communities through grazing pressure. Moreover, we could certainly explain the ecological success of Arthrospira fusiformis by the absence of metazoan predators, like shrimps or flamingos, characteristic of other hypersaline ecosystems [START_REF] Krienitz | Tiny and Tough: Microphytes of East African Soda Lakes[END_REF].

Conclusions

Soda lakes are extreme environments where highly adapted microbial communities flourish. Understanding their microbial ecology is key in providing insights into ecosystem 3-domains-of-life metabarcoding approach, how total microbial diversity is impacted by season and inter-annual variations, across a vertical gradient of the water column. By decomposing biodiversity at fine scale in lake Dziani Dzaha, we highlighted that richness and diversity of Bacteria, Archaea and Eukaryota are differently impacted by the physicochemical structure of the water column. We showed that eukaryotic communities were relatively more variable in their composition compared with prokaryotic communities that were more dynamic in terms of changes in OTUs abundance across season and depth.

Finally, we identified some microbial classes, or even taxa, that could be related to biogeochemical processes occurring in lake Dziani Dzaha and that would need to be confirmed experimentally in the future.

Experimental Procedures

Study site, sampling, and environmental parameters

Lake Dziani Dzaha is an alkaline and saline lake situated on the Mayotte Island (Western Indian Ocean). Its surface is 0.24 km 2 with the mean depth about 2.9 meters except the eastern part of the lake characterized by a pit reaching a maximum depth of 18 m. The elevation of the lake surface is close to the average sea level. This lake occupies a volcanic crater and is characterized by an important salinity (ranging from 34 to 71 psu), a very high alkalinity (0.23 mol/L), and a permanent green color. Four surveys were conducted in order to cover both annual and seasonal variations in environmental conditions. Two contrasted seasons were sampled: the stratified period (April, end of rainy season) and the nonstratified period (October-November, end of the dry season), over two consecutive years, (2014 and 2015). Water samples were collected along a depth profile located at the deepest point of the lake (0.5m, 1m, 2.5m, 5m, 11m, 15m and 17m depth), using a horizontal 1.2L

Niskin bottle. Water samples were processed on return to the field laboratory within 2 hours. Vertical profiles for pH, dissolved O 2 , temperature and conductivity were taken using either a MPP350 probe connected to a Multi 350i data logger (WTW GmbH) or a YSI 6600 probe. The salinity was calculated using conductivity measured in the vertical profiles.

DNA extraction and Illumina sequencing

Because of clogging effect, a prefiltration of water subsample (20mL) through 3µm poresize polycarbonate filters (Millipore) was necessary before collection on 0.2µm pore-size polycarbonates filters (Millipore, pressure <10kPa) and storage at -20°C until nucleic acid DNA extractions were conducted separately on both 3µm and 0.2µm filters, using the Power Water DNA isolation kit (MoBio Laboratories) as described by the manufacturer for maximum yield. The DNA quality was checked by 1% (w/v) agarose gel electrophoresis and quantified using NanoDrop. Amplification of the V3-V5 region of the 16S rRNA genes was performed in triplicate for Bacteria and Archaea, using the universal primers 357F [START_REF] Schuurman | Prospective Study of Use of PCR Amplification and Sequencing of 16S Ribosomal DNA from Cerebrospinal Fluid for Diagnosis of Bacterial Meningitis in a Clinical Setting[END_REF] and 926R [START_REF] Walters | Improved Bacterial 16S rRNA Gene (V4 and V4-5) and Fungal Internal Transcribed Spacer Marker Gene Primers for Microbial Community Surveys[END_REF] and 519F and 915R [START_REF] Hugoni | Temporal dynamics of active Archaea in oxygen-depleted zones of two deep lakes[END_REF], respectively. Amplification of the V4 region of the 18S rRNA genes was performed in triplicate using the universal primer 515F [START_REF] Caporaso | Genomic expansion of domain archaea highlights roles for organisms from new phyla in anaerobic carbon cycling[END_REF] and the eukaryotic primer 951R (TTG-GYR-AAT-GCT-TTC-GC). Additionally, a DNA extraction was carried out without any biological matrix and considered as a negative control to evaluate ambient contaminations. High-throughput sequencing was achieved after pooling the PCR-triplicates and a multiplexing step, using a HiSeq Rapid Run 300bp PE technology on an Illumina HiSeq 2500 system (GATC Biotech, Konstanz, Germany).

Sequence processing

Bacterial and archaeal 16S rRNA and eukaryotic 18S rRNA paired-end reads from both 3µm and 0.2µm filters were pooled and further merged with a maximum of 10% mismatches in the overlap region using FLASh [START_REF] Magoč | FLASH: fast length adjustment of short reads to improve genome assemblies[END_REF]. Denoising procedures consisted in discarding reads containing ambiguous bases (N) or outside the range of expected length (i.e. 450 to 580 bp for bacterial 16S rRNA, 370 to 580 bp for archaeal 16S rRNA, and 250 to 420bp eukaryotic 18S rRNA). After dereplication, sequences were clustered using SWARM [START_REF] Mahé | Swarm: robust and fast clustering method for amplicon-based studies[END_REF] that uses a local clustering threshold. We removed chimeric sequences using VSEARCH [START_REF] Rognes | VSEARCH: a versatile open source tool for metagenomics[END_REF] but also sequences representing less than 0.005% of the total number of sequences (Bokulich et (data not shown). Taxonomic affiliation was performed with both RDP Classifier [START_REF] Wang | Naive Bayesian classifier for rapid assignment of rRNA sequences into the new bacterial taxonomy[END_REF] and Blastn+ [START_REF] Camacho | BLAST+: architecture and applications[END_REF] against the 128 SILVA database [START_REF] Pruesse | SILVA: a comprehensive online resource for quality checked and aligned ribosomal RNA sequence data compatible with ARB[END_REF]. This procedure was automated in the FROGS pipeline [START_REF] Escudié | FROGS: Find, Rapidly, OTUs with Galaxy Solution[END_REF].

Contaminant OTUs identified from the control samples were removed and samples were randomly resampled to 41,044, 39,960 and 10,868 sequences, for Bacteria, Archaea and Eukaryota, respectively, in order to allow comparisons.

Statistical analyses

For each domain of life (Bacteria, Archaea and Eukaryota), we tested the effect of environmental factors (year, season and depth) on the composition of microbial communities using non-parametric permutation-based multivariate analysis of variance (PERMANOVA, function adonis in R package vegan, [START_REF] Anderson | A new method for non-parametric multivariate analysis of variance[END_REF])) on abundancebased (Bray-Curtis) dissimilarity matrices. We also realized an ordination of the samples using NMDS approach on Bray-Curtis dissimilarity matrices (function metaMDS in R package vegan).

We used an additive diversity-partitioning framework [START_REF] Belmaker | Regional Variation in the Hierarchical Partitioning of Diversity in Coral-Dwelling Fishes[END_REF] to decompose the total observed diversity and express it as the sum of the diversity observable at various scales. In a first step, we decomposed the total diversity (γ-diversity) into the sum of inter-season differences, inter-depth differences and diversity in local communities with:

γ-diversity = β-InterSeason + β-InterDepth + α-LocalCommunities.
The approach is presented in greater details elsewhere [START_REF] Escalas | A unifying quantitative framework for exploring the multiple facets of microbial biodiversity across diverse scales[END_REF][START_REF] Escalas | Functional diversity and redundancy across fish gut, sediment, and water bacterial communities[END_REF]. This decomposition was performed on diversity estimated using Rao's quadratic entropy on presence-absence and abundance data. This method provides diversity estimates expressed in equivalent number [START_REF] Jost | Partitioning Diversity into Independent Alpha and Beta Components[END_REF] and tend to be influenced by highly abundant species when abundances are taken into account. In a second step, we decomposed the total diversity (γdiversity) along the depth profile and for each season separately into the diversity in local communities and differences across communities: γ-diversity = β-diversity + α-diversity.

This decomposition was performed on abundance data.

Data deposition

The

Table 1. Effect of environmental factors on microbial communities composition

The differences between groups were tested using PERMANOVA analysis on Bray-Curtis dissimilarity matrices.

Table 2. Additive decomposition of microbial diversity

γ -Diversity was estimated using Rao' quadratic entropy and the decomposition was done according to [START_REF] Escalas | Functional diversity and redundancy across fish gut, sediment, and water bacterial communities[END_REF]. Number in parenthesis corresponds to the percentage of the γ-Diversity represented by each component.

  extreme environments widely distributed on Earth, mainly in arid and semi-arid regions, such as the Rift Valley in Africa, United-States, Canada, Iran, China

  Cyanobacteria and/or anoxygenic phototrophic Bacteria

  Figure 3.C and D). The bacterial depth, from very low values near the surface (0 to 2.5m) to a sharp increase at the bottom of the water column (15 to 17m). Thus the distribution of abundance

  OTU (cf. low γ-diversity estimates for Eukaryota in Figure3. B, C and D). On

  . Interestingly, during the non-stratified period the community composition also followed the physico-chemical structure of the water column. It was homogeneous along most of the water column, shifting only at the 14m depth permanent chemocline. Overall, prokaryotic communities composition were mainly influenced by depth while eukaryotic ones were mostly influenced by seasons.

  was biologically produced (hydrogenotrophic pathway) by an archaeal community dominated by Methanocalculus (Nolla-Ardèvol

  represent an important fraction of the relative abundance (i.e. number of sequences) in lake Dziani Dzaha, whereas Deltaproteobacteria were far less represented and can be considered as almost absent. Among Firmicutes and particularly Clostridiales, the main family represented in the lake Dziani Dzaha was Syntrophomonadaceae, which is affiliated with the unknown genera Dethiobacter, Alkaliphilus or Candidatus contubernalis. Recent work isolation and characterization from soda lake sediments (Mongolia) of a

  The low to null sulfate concentrations could explain the low occurrence of sulfato-reducers microorganisms, such as Deltaproteobacteria. The sometimes high concentration of H 2 S compared to sulfate in the anoxic part of the water column during stratified seasons might be due to fermentative pathways performed by heterotrophic microorganisms using R-SH-or alternative processes involved in sulfur cycle in this lake such as reduction of elemental sulfur.

  and stability. The present work is the first to assess, with an in-depth

  2013) along with singletons. The eukaryotic dataset was cured for metazoans sequences

Figure 1 .

 1 Figure 1. Vertical profiles of environmental parameters recorded during the 4

Figure 2 .

 2 Figure 2. Differences in the structure of microbial communities

Figure 3 .

 3 Figure 3. Additive decomposition of microbial diversity

Figure 4 .

 4 Figure 4. Relative abundance (% of sequences) of bacterial, archaeal and eukaryotic

Figure 2 .

 2 Figure 1. Vertical profiles of environmental parameters recorded during the 4

Figure 3 .

 3 Figure 3. Additive decomposition of microbial diversity

Figure 4 .

 4 Figure 4. Relative abundance (% of sequences) of bacterial, archaeal and eukaryotic

Table 1

 1

	Factor	F.value R 2	p.value	F.value R 2	p.value	F.value R 2	p.value
	Year	4.99	0.07 0.020	6.62	0.12 0.004	8.77	0.12 0.001
	Season	6.65	0.09 0.009	7.80	0.15 0.001	25.19 0.35 0.001
	Depth	35.67 0.47 0.001	11.00 0.21 0.001	4.51	0.06 0.006
	Year:Season	1.89	0.03 0.150	3.31	0.06 0.020	4.87	0.07 0.004
	Year:Depth	3.96	0.05 0.038	1.96	0.04 0.114	1.71	0.02 0.151
	Season:Depth	2.14	0.03 0.130	1.63	0.03 0.164	3.64	0.05 0.018
	Year:Season:Depth	0.31	0.00 0.773	0.68	0.01 0.605	3.10	0.04 0.030
	Residuals	NA	0.26	NA	NA	0.38	NA	NA	0.28	NA

Table 2 γ -diversity α-LocalComm. β-InterSeason β-InterDepth

 2

	Presence-absence
	Bacteria	230.6	196.9 (85.4)	3.4 (1.5)	30.3 (13.1)
	Archaea	97.9	78.1 (79.8)	1.3 (1.3)	18.5 (18.9)
	Eukaryota	41.9	26.6 (63.4)	1.8 (4.4)	13.5 (32.2)
	Abundance
	Bacteria	3.7	2.5 (68.4)	0.1 (3.0)	1.1 (28.6)
	Archaea	8.9	5.8 (65.0)	0.7 (7.6)	2.4 (27.3)
	Eukaryota	1.4	1.4 (97.0)	0.01 (0.9)	0.03 (2.1)

Wiley-Blackwell and Society for Applied Microbiology

Acknowledgments

Field permit was granted by the Conservatoire du Littoral et des Rivages Lacustres, Antenne Océan Indien, since lake Dziani Dzaha is currently a protected water body with free public access but restricted activities, under the control of the French agency for littoral ecosystems conservation (http://www.conservatoire-du-littoral.fr/). We thank D. Abrouk and A. Dubost for their help with molecular analyses, and M. Bruto for helpful discussions on the manuscript. The authors wish to thank the Air Austral Airline Company, and Alexandra and Laurent at the "Les Couleurs" Guest House in Mayotte for their valuable assistance and support. This work was granted by the Total Corporate Foundation (project DZAHA, grant number C001493) and the French National Research Agency (project DZIANI, ANR-13-BS06-0001).

Supplementary Figure 1. Additive decomposition of microbial diversity

Decomposition of total diversity (γ-Diversity ) estimated using Rao' quadratic entropy on presence-absence data into local communities diversity (α) and differences between communities (β), along the depth profile (C) and between seasons (D).


Felix Trier

Diogo C Vaz

Pierre Bruneel

Paul Noël

Albert Fert

Laurent Vila

Jean- Philippe Attané

Agnès Barthélémy

Marc Gabay

Henri Jaffrès

Manuel Bibes
email: manuel.bibes@cnrs-thales.fr

Electric-field control of spin current generation and detection in ferromagnet-free SrTiO3-based nanodevices

Keywords: Spin current generation/detection, Spin Hall effect, SrTiO3, two-dimensional electron gas, nanodevices

Spintronics entails the generation, transport, manipulation and detection of spin currents, usually in hybrid architectures comprising interfaces whose impact on performance is detrimental. In addition, how spins are generated and detected is generally material specific and determined by the electronic structure. Here, we demonstrate spin current generation, transport and electrical detection, all within a single non-magnetic material system: a SrTiO3 two-dimensional electron gas (2DEG) with Rashba spin-orbit coupling. We show that the spin current is generated from a charge current by the 2D spin Hall effect, transported through a channel and reconverted into a charge current by the inverse 2D spin Hall effect. Furthermore, by adjusting the Fermi energy with a gate voltage we tune the generated and detected spin polarization and relate it to the complex multiorbital band structure of the 2DEG. We discuss the leading mechanisms of the spin-charge interconversion processes and argue for the potential of quantum oxide materials for future all-electrical low-power spin-based logic.

The two-dimensional electron gas (2DEG) that forms at the surface [START_REF] Santander-Syro | Two-dimensional electron gas with universal subbands at the surface of SrTiO3[END_REF] of SrTiO3 (STO) or at its interface with oxides [START_REF] Ohtomo | A high-mobility electron gas at the LaAlO3/SrTiO3 heterointerface[END_REF][START_REF] Chen | Metallic and Insulating Interfaces of Amorphous SrTiO3-Based Oxide Heterostructures[END_REF] or metals [START_REF] Rödel | Universal Fabrication of 2D Electron Systems in Functional Oxides[END_REF] possesses several fascinating properties such as high electron mobility [START_REF] Chen | A high-mobility two-dimensional electron gas at the spinel/perovskite interface of γ-Al2O3/SrTiO3[END_REF] and 2D superconductivity [START_REF] Reyren | Superconducting Interfaces Between Insulating Oxides[END_REF] . Importantly, in this 2DEG inversion symmetry is broken, which allows for the existence of Rashba spin-orbit coupling (SOC) [START_REF] Bychkov | Properties of a 2D electron gas with lifted spectral degeneracy[END_REF] . Another remarkable feature of STO 2DEGs is the strong tunability of their carrier density and related electronic properties with a gate voltage [START_REF] Caviglia | Electric field control of the LaAlO3/SrTiO3 interface ground state[END_REF] . In particular, the electric-field dependence of the Rashba SOC [START_REF] Caviglia | Tunable Rashba Spin-Orbit Interaction at Oxide Interfaces[END_REF] makes the STO 2DEG an attractive platform to design agile spin-orbitronics architectures.

Fig. 1a shows the Fermi surface of a prototypical Rashba 2DEG, with two Fermi contours along which the spin is locked perpendicularly to the momentum k, and having opposite spin chiralities. Firstly, when a charge current is applied along x (𝑗 𝑐 𝑖𝑛𝑗𝑒𝑐𝑡 ), the Fermi contours are displaced by k along -x, which results in the generation of a transverse spin density oriented along y, ∫ 𝑠 𝑑𝑦 ≠ 0, through the direct Edelstein effect 10 (EE). This spin density can then diffuse (with a diffusion constant Ds) and produces a transverse spin current in the material or in adjacent layers. The inverse Edelstein effect [START_REF] Sánchez | Spin-to-charge conversion using Rashba coupling at the interface between non-magnetic materials[END_REF] (IEE) is the reciprocal of the direct EE: the injection of a spin density oriented along y would cause opposite but inequivalent shifts of the Fermi contours along x, leading to the generation of a charge current.

In addition, after the displacement of Fermi contours by k, electrons see their spins precessing around the new expected spin direction, which tilts the spins along +z for ky > 0 and -z for ky < 0, thus creating a spin current polarized along z in the y direction (js); this is the 2D spin Hall effect (2D-SHE) [START_REF] Sinova | Universal Intrinsic Spin Hall Effect[END_REF] . So far in STO 2DEGs, the IEE [START_REF] Lesne | Highly efficient and tunable spin-to-charge conversion through Rashba coupling at oxide interfaces[END_REF] has been more intensely studied than the direct EE [START_REF] Wang | Room-Temperature Giant Charge-to-Spin Conversion at the SrTiO 3 -LaAlO 3 Oxide Interface[END_REF] or the 2D-SHE [START_REF] Jin | Nonlocal Spin Diffusion Driven by Giant Spin Hall Effect at Oxide Heterointerfaces[END_REF] , and has been shown to result in a very efficient spincharge conversion [START_REF] Lesne | Highly efficient and tunable spin-to-charge conversion through Rashba coupling at oxide interfaces[END_REF][START_REF] Chauleau | Efficient spin-to-charge conversion in the 2D electron liquid at the LAO/STO interface[END_REF] . The figure of merit IEE was found to strongly depend in amplitude and sign on a gate voltage as the Fermi energy was varied through the peculiar electronic band structure of the 2DEG [START_REF] Lesne | Highly efficient and tunable spin-to-charge conversion through Rashba coupling at oxide interfaces[END_REF][START_REF] Vaz | Mapping spin-charge conversion to the band structure in a topological oxide two-dimensional electron gas[END_REF] , exhibiting a characteristic crossover in the sign of the effective Rashba SOC [START_REF] Shanavas | Theoretical model for Rashba spin-orbit interaction in d electrons[END_REF] . Those properties, together with the high conversion efficiency, offer interesting prospects for spin-orbitronics devices [START_REF] Manipatruni | Scalable energy-efficient magnetoelectric spin-orbit logic[END_REF][START_REF] Varignon | A new spin for oxide interfaces[END_REF] . Here we take advantage of the ability of STO 2DEGs to efficiently interconvert spin and charge currents, transport spins over long distances and strongly respond to carrier density modulation by electrostatic gating, in order to realize an agile monolithic planar spintronic device free from ferromagnets. LAO//STO Hall bar devices (see Fig. 1c) were fabricated by conventional electron-beam lithography and resist soft-mask lift-off [START_REF] Bjørlig | Nanoscale patterning of electronic devices at the amorphous LaAlO 3 /SrTiO 3 oxide interface using an electron sensitive polymer mask[END_REF] (see Methods). The devices shows n-type metallic transport characteristics, comparable to those of unpatterned interfaces [START_REF] Herranz | High Mobility in LaAlO3/SrTiO3 Heterostructures: Origin, Dimensionality, and Perspectives[END_REF] , with the sheet resistance reducing from 5 kΩ/sq to 300 Ω/sq as the temperature decreases from 300 K to 2 K (see Fig. 1c).

In the absence of ferromagnetic reference contacts, we probe the spin transport in the channel through Hanle experiments (see Fig. 1d). As sketched in Fig. 1b, the application of a charge current along x in one arm of the Hall bar (𝑗 𝑐 𝑖𝑛𝑗𝑒𝑐𝑡 ) generates a spin accumulation oriented along y through the direct EE that diffuses sideways (Ds) in the channel towards the second arm (Fig. 2b). The applied charge current can also generate a spin current polarized along z through the 2D-SHE that similarly is transported towards the second arm (js). At the second arm, the spin current is converted back into a charge current through the IEE or the inverse 2D-SHE (𝑗 𝑐 𝑑𝑒𝑡𝑒𝑐𝑡 ), that we detect as a non-local voltage. Applying a magnetic field along

x (that is, perpendicularly to the spins diffusing in the channel) causes the spins to precess, and thus generates a Hanle effect [START_REF] Abanin | Nonlocal charge transport mediated by spin diffusion in the spin Hall effect regime[END_REF][START_REF] Reyren | Gate-Controlled Spin Injection at LaAlO 3 / SrTiO 3 Interfaces[END_REF] , as sketched in Fig. 1d. During this spin precession, the original spin polarization is lost, consequently lowering 𝑗 𝑐 𝑑𝑒𝑡𝑒𝑐𝑡 and ultimately reducing the non-local voltage measured.

Δ𝑅 𝑁𝐿 (𝐿) = 𝑤 2𝜆 𝑠 𝛾 2 𝑅 𝑠 𝑒 - 𝐿 𝜆 𝑠 ( 1
)
where w is the Hall bar channel width, λs is the spin diffusion length and  is the spin Hall angle. By fitting the amplitude of the Hanle curve with respect to L with Eq. ( 1) (see Fig. 2b), the detected non-local signal indeed seems consistent with spin-charge interconversion and with previous experiments [START_REF] Jin | Nonlocal Spin Diffusion Driven by Giant Spin Hall Effect at Oxide Heterointerfaces[END_REF] . Here, by fitting to Eq. ( 1) we extract a spin diffusion length of λs = 863±56 nm and a spin polarization of  = 12.9±0.6%, in good agreement with previous results [START_REF] Jin | Nonlocal Spin Diffusion Driven by Giant Spin Hall Effect at Oxide Heterointerfaces[END_REF] .

The B-field dependence of the resistance reduction due to the Hanle effect is given by [START_REF] Abanin | Nonlocal charge transport mediated by spin diffusion in the spin Hall effect regime[END_REF] :

𝑅 𝑁𝐿 (𝐵) = 𝑤 2 𝛾 2 𝑅 𝑠 Re (( √1 + 𝑖𝜏 𝑠 Γ𝐵 𝜆 𝑠 ) 𝑒 - 𝐿√1+𝑖𝜏 𝑠 Γ𝐵 𝜆 𝑠 ) ( 2
)
where Γ is the electron gyromagnetic ratio, Γ = 1.76 × 10 11 rad/(s⋅T), and τs is the spinrelaxation time of carriers in the 2DEG. The dotted lines in Fig. 2a We then performed Hanle experiments as a function of the back gate voltage Vg, to probe its influence on the coupled charge-spin and spin-charge conversion processes.

Representative results for three gate voltages are displayed in Fig. 3a, and the gate dependence of ΔRNL is plotted in Fig. 3b. ΔRNL shows a highly non-monotonic dependence with

Vg, exhibiting a maximum at Vg ≈ +10-40 V. By fitting the non-local resistance data simultaneously to Eqs. (1-2), we extract λs, τs (see Supporting Figure S2) and , plotted in Fig. 3c. The non-monotonic dependence of ΔRNL with the back-gate voltage appears to originate from a large modulation of  between 5-40%, with a maximum at Vg ≈ +10-40 V. Remarkably, this maximum practically coincides with the Lifshitz transition [START_REF] Joshua | A universal critical density underlying the physics of electrons at the LaAlO3/SrTiO3 interface[END_REF] occurring at Vg ≈ +50 V for ns  1.310 13 cm -2 , as deduced from the analysis of the Hall resistance (see Supporting Figure S1), and corresponding to the onset of the occupancy of the first heavy dxz/yz sub-band (with carrier density n2 in the inset of Fig. 3c). λs and τs both show an overall positive correlation with Vg (see Supporting Figure S2), reaching their largest values for the largest Vg. This increase is consistent with the onset of population of the dxz/yz sub-bands, which are known to result in higher electron mobilities [START_REF] Bell | Dominant Mobility Modulation by the Electric Field Effect at the LaAlO 3 / SrTiO 3 Interface[END_REF] . Furthermore, the spin-diffusion length and the electron mobility display a strong correlation (see Supporting Information), as expected from the standard driftdiffusion equation within the Elliot-Yafet mechanism of spin-relaxation.

While these data indicate a strong spin-charge interconversion efficiency, highly tunable by an electric field, they cannot discriminate between EE and 2D-SHE as the underlying mechanism, since in both cases the applied magnetic field (along x) is perpendicular to the expected spin direction (along y for EE and along z for 2D-SHE). To address this issue, we have performed similar experiments with the field applied along y, see Fig. 3d-f. The shape of the obtained Hanle curves is comparable to those obtained with the field along x, which indicates that the precessing spins are initially perpendicular to both x and y, i.e. oriented along z and identifies the 2D-SHE as the dominant mechanism for charge-spin interconversion. This is confirmed by measurements with the field applied along z (see Supporting Figure S3)) that show an inverted Hanle shape, expected when the spins have an initial average orientation parallel to the external magnetic field, in the presence of spin-randomizing processes.

The gate dependence of the Hanle signal with the field along y is shown in Fig. 3d-e, and bears a strong resemblance to that measured with the field along x, with a maximum for Vg ≈ 50-75 V. We fitted independently the Hanle curves for this measurement geometry using Eqs. (1-2) and the extracted . Its gate dependence (Fig. 3f) shows a maximum value of about 40% at Vg ≈ 25-35 V, and strongly resembles its counterpart with B along x. This further confirms that the 2D spin Hall effect is the main mechanism at play, and that  can be identified as a spin Hall angle. Its value, amounting to a maximum of about 45%, is among the highest reported for oxide materials [START_REF] Everhardt | Tunable charge to spin conversion in strontium iridate thin films[END_REF][START_REF] Vaz | Oxide spin-orbitronics: New routes towards lowpower electrical control of magnetization in oxide heterostructures[END_REF] and larger than typical values found in heavy metals. To further understand the nature of this large spin Hall angle [START_REF] Tanaka | Intrinsic spin Hall effect and orbital Hall effect in 4 d and 5 d transition metals[END_REF] and pinpoint the 2D spin Hall effect as the origin of the spin current generation, we have performed a theoretical modelling of LAO//STO (see Methods and Supporting Section S1) [START_REF] Abanin | Nonlocal charge transport mediated by spin diffusion in the spin Hall effect regime[END_REF] . We theoretically determine the spin Hall conductance of the 2DEG, given as the product of the effective spin Hall angle by the sheet conductance σxy = σs, using a tight-binding (TB) form and compute the eigenenergies and eigenvectors for each wavevector k in the Brillouin Zone (BZ) relevant to the electronic bands of LAO//STO (see Fig. 4a) [START_REF] Cancellieri | Polaronic metal state at the LaAlO3/SrTiO3 interface[END_REF] Rashba effect [START_REF] Sinova | Universal Intrinsic Spin Hall Effect[END_REF] . The fluctuations that are seen in σxy at higher energy are associated with the Lifshitz transition [START_REF] Joshua | A universal critical density underlying the physics of electrons at the LaAlO3/SrTiO3 interface[END_REF] and the filling of dxz/yz states where the system becomes strongly multiorbital with a complex intertwining of the bands [START_REF] Vivek | Topological states at the (001) surface of SrTiO 3[END_REF] .

In order to directly compare our experimental results with the calculations, we relate the chemical potential and the sheet conductance from the TB model, and plot the spin Hall conductance as a function of the sheet conductance (see Supporting Fig. 1) for both the experimental results and the TB calculations (see Fig. 4c). It is evident from Fig. 4c that both the presence and magnitude of the non-monotonic behaviour of the spin Hall angle observed experimentally is reasonably well captured by the TB calculations, qualitatively and quantitatively. Based on this agreement, we see fit to conclude that the 2D spin Hall effect is indeed the origin of the generated spin current in our LAO//STO Rashba nanodevices.

Theoretically, the 2D-SHE is well described via the linear response theory and Kubo's formula giving the transverse conductance 𝜎 𝑥𝑦 𝑧 = 𝜎 𝑥𝑦 Σ + 𝜎 𝑥𝑦 C , that comprises two-parts: a bare (source) term, 𝜎 𝑥𝑦 Σ , little dependent on the spin-flip processes, and a second contribution given by the so-called vertex corrections, 𝜎 𝑥𝑦 C (see Supporting Section S2). The latter expresses the role of the spin-diffusion processes on the spin-accumulation appearing via IEE mechanisms and initially generated from 𝜎 𝑥𝑦 Σ . However, it is generally proposed (see e.g. Ref. [START_REF] Dimitrova | Spin-Hall conductivity in a two-dimensional Rashba electron gas[END_REF] ) that in homogeneous Rashba 2DEGs, both terms exactly cancel each other in the case of klinear splitting departing from the exact LAO/STO case. However, our double crossbar geometry makes these devices essentially inhomogeneous, avoiding in fine the cancellation of the spin-Hall conductance 𝜎 𝑥𝑦 𝑧 . This arises because the devices are patterned into lateral spin-diffusive channels, thus introducing a strong spin-flip contribution to the equation dynamics linking spin-current and spin-accumulation trough the spin relaxation time 𝜏 𝑠 . It follows that the spin-accumulation profile throughout the lateral channel is strongly affected by 𝜏 𝑠 , resulting in a significant reduction of both the spin-accumulation responsible for IEE and vertex corrections (also at the region of the injected current). As claimed in Refs. [START_REF] Seibold | Intrinsic spin Hall effect in systems with striped spin-orbit coupling[END_REF][START_REF] Kato | Anomalous Hall effect in spin-polarized twodimensional electron gases with Rashba spin-orbit interaction[END_REF] , we here conclude that due to spin-flip processes along the lateral direction |𝜎 𝑥𝑦 C | < |𝜎 𝑥𝑦 Σ |, which results in a non-zero spin Hall conductance. A possible longer spin-relaxation time along the direction normal to the layer, as already experimentally evidenced in other types of confined Rashba system [START_REF] Ghiasi | Charge-to-Spin Conversion by the Rashba-Edelstein Effect in Two Dimensional van der Waals Heterostructures up to Room Temperature[END_REF] may enhance the characteristic spin-diffusion length and size of SHE-ISHE compared to IEE in-plane effects.

In summary, we have realized spin transport and demonstrated the electric-field control of spin-charge interconversion in nanodevices built from a single material system, the 2DEG that forms at the LAO//STO interface. The conversion process proceeds through the direct and inverse 2D spin Hall effects, and the spin Hall angle can be electrically tuned from 10 to over 40%. Our results now call for additional experiments with local top gates [START_REF] Hurand | Field-effect control of superconductivity and Rashba spin-orbit coupling in top-gated LaAlO3/SrTiO3 devices[END_REF] , in which one could selectively tune spin generation, transport and detection. More importantly, they highlight the potential of oxide interfaces for low-power spin-orbitronics [START_REF] Manipatruni | Scalable energy-efficient magnetoelectric spin-orbit logic[END_REF] , beyond conventional materials systems.

MATERIALS AND METHODS

Sample growth and device fabrication

To obtain the Hall bar devices, a single unit cell epitaxial LaAlO3 (as confirmed from an in-situ RHEED oscillation) was first deposited using pulsed laser deposition (PLD) on a TiO2terminated SrTiO3 (STO) substrate (10×10×0.5 mm 3 , miscut angle < 0.1 degree) in an oxygen atmosphere of 210 -4 mbar at 730 °C. The LAO was ablated from a crystalline LAO target, with a target-substrate distance of ∼5.5 cm, by a KrF laser (λ = 248 nm) with a repetition rate of 1

Hz and laser fluence of 1 J/cm 2 . After the LAO deposition, the sample was cooled to T = 550 °C at a pressure of pO2 = 0.1 mbar. Once at T = 550 °C, the sample was annealed pO2 = 200 mbar for one hour. Finally, the sample was brought to room temperature by passive cooling at pO2 = 200 mbar. Subsequently, the LAO(1u.c.)//STO sample was then prepared with e-beam PMMA A6 resist soft-mask according to the desired Hall bar design by e-beam lithography using standard exposure and development conditions. The sample was then returned to the PLD chamber for in-situ oxygen plasma cleaning [START_REF] Bjørlig | Nanoscale patterning of electronic devices at the amorphous LaAlO 3 /SrTiO 3 oxide interface using an electron sensitive polymer mask[END_REF] prior to deposition of 30 nm amorphous-LAO (a-LAO) at room temperature and an oxygen pressure <110 -6 mbar. Following this deposition, the remaining PMMA resist was removed by lift-off in organic solvent leaving patterned regions with a-LAO(30nm)/LAO(1u.c.)//STO displaying interface conductivity (which for simplicity in the main text are referred to as LAO//STO). Note that these regions of interface conductivity are interspaced by insulating regions of LAO(1u.c.)//STO. Finally, the sample was mounted on a chip-carrier with a sample-wide back-gate of magnetron sputtered Ti(10 nm)/Au(50 nm).

Transport measurements

Low temperature electrical transport measurements were performed on the patterned Hall bar devices using a standard AC lock-in technique (IAC = 20 nA-2 µA, fAC = 77.03 Hz) in a Quantum Design Dynacool cryostat at temperatures between 2 K and 300 K and magnetic fields between -9 T and 9 T. Prior to any back-gate voltage studies were performed, the LAO//STO devices were subjected to a so-called forming step 37 at 2 K, where the back-gate voltage were cycled several times (>4) between -100 V and +150 V to ensure no irreversible changes would occur in the interface system upon application of the back-gate voltage in the actual experiment. Note that this low temperature forming step was repeated following all occasions the sample was brought above 105 K. Moreover, at each new cooldown, the samples were always cooled with the back-gate electrostatically grounded.

Tight binding calculations

The tight-binding model (see Supplemental Section S1) allows us to compute the eigenvalues We then derive the spin Hall conductivity 𝜎 𝑥𝑦 for each value of the chemical potential following the protocol outlined in the main text. Hall measurements give the change in subband population with respect to the gate voltage. Furthermore, the tight-binding band structure of the material allows us to compute the evolution of the charge filling with respect to the chemical potential. We use the Lifshitz transition as a reference point and assume that the population ratio of the heavy to the light sub-band is the same for both the experimental and numerical values. This yields a correspondence between the chemical potential 𝜇 and Vg and hence between 𝜇 and the sheet conductance 𝜎 𝑠 .

ASSOCIATED CONTENT

Supporting Information is available for this paper at [insert link for SI here].

Figure 1 .

 1 Figure 1. a, Because of the Rashba effect in LaAlO3//SrTiO3 (LAO//STO), the spin degeneracy is lifted, leading to concentric Fermi contours with opposite spin chirality where the spin is locked perpendicular to the momentum. Through the direct Edelstein effect an injected charge current (𝑗 𝑐 𝑖𝑛𝑗𝑒𝑐𝑡 ) along x will generate a transverse spin accumulation along y, ∫ 𝑠 𝑑𝑦 ≠ 0. Additionally, after displacing the Fermi contours by kx, the spins will not be exactly perpendicular to k and will thus start to precess around to local Rashba field to eventually align along the new spin direction. While precessing, the spins acquire a finite component along +z for ky > 0 and -z for ky < 0 ; this is the two-dimensional (2D) spin Hall effect, which ultimately results in a net spin polarization along z. b, top panel, The spin accumulation generated by Edelstein effect will diffuse (Ds) along y in the Hall bar channel, before getting converted back into a detectable

Figure 2 .

 2 Figure 2. a, Non-local resistance, RNL, as a function of the magnetic field, B, for probe spacings between 2 µm and 5 µm at 2 K. The fit of the data to Eqs. (1-2) is shown as dashed lines. b, The non-local resistance amplitude, ΔRNL, as a function of probe spacing, L. c, Table of extracted fitting parameters from the fits in a.

  corresponds to the best fits of the data with Eqs. (1-2). From these fits, we extract the values of λs,  and τs shown in the table of Fig.2c. Overall, we obtain values for λs and  are very consistent with those extracted from the fit of ΔRNL(L) by Eq. (1), and a spin-relaxation time of τs ≈ 2 ps.

Figure 3 .

 3 Figure 3. a, Non-local resistance, RNL, as a function of the magnetic field applied along x, B, for three representative gate voltages at 2 K, for a probe spacing of 2 µm. b, Non-local spin

Figure 4 .

 4 Figure 4. a, Calculated energy dispersion of the spin-split sub-bands along high symmetry crystal directions. b, Calculated spin Hall conductance, 𝜎 𝑥𝑦 𝑧 , as a function of the energy, E. c, absolute value of 𝜎 𝑥𝑦 𝑧 calculated and obtained experimentally from  in Fig. 3c, as a function of the sheet conductance, σs. The experimentally observed maxima of  is reasonably well captured by the calculations.

  . To quantitatively capture the Edelstein effect observed in these STO-based heterostructures, we have furthermore included spin-orbital terms in the TB-calculations. Using the Kubo-Streda formalism in the clean limit we have thus obtained the intrinsic spin Hall conductance of the 2DEG as 𝜎 𝑥𝑦 (𝜇) = 𝑒ℏ ∑ ∫ Ω 𝑛 𝑧 (𝑘)𝑓 𝑛 (𝜖 𝑘 𝑛 -𝜇)𝑑 2 𝑘 𝐵𝑍 𝑛 , where we have summed the spin curvature, Ω 𝑛 𝑧 , over filled states and all k in the BZ. 𝑓 𝑛 is the Fermi function for the band with index n. Subsequently, we computed the evolution of σxy with respect to the chemical potential, µ, (i.e. the energy, E, see Fig 4b). Here we note that the quantized plateaus in σxy present at lower values of the chemical potential correspond to the occupation of consecutive dxy bands and are typical of a

  𝜖 𝑛 (𝑘) and eigenfunctions |𝑛⟩ of the 2DEG at each k-point in the BZ. Using those, we determine the local spin curvature of the 𝑛 𝑡ℎ band at wavevector k: Ω 𝑛 𝑧 (𝑘) = ∑ ⟨𝑛|𝑣 ̂𝑥𝑧 (𝑘)|𝑚⟩⟨𝑚|𝑣 ̂𝑦(𝑘)|𝑛⟩ -(𝑥 ↔ 𝑦) (𝜖 𝑛 (𝑘) -𝜖 𝑚 (𝑘)) 2 𝑚≠𝑛 Where 𝑣 ̂𝛼 = 1 ℏ 𝜕 𝑘 𝛼 ℋ and 𝑣 ̂𝛼 𝑧 = ℏ 2 {𝑣 ̂𝛼, 𝜎 ̂𝑧} are the current and spin current operators, respectively.

Funding Sources

F. Trier acknowledges support by research grant VKR023371 (SPINOX) from VILLUM FONDEN. This work received support from the ERC Consolidator grant no. 615759 "MINT", the French Research Agency (ANR) as part of the "Investissement d'Avenir" program (LABEX NanoSaclay, ref ANR-10-LABX-0035) through project "AXION" and ANR program OISO (ANR-17-CE24-0026-

AUTHOR INFORMATION

Corresponding Author *e-mail: manuel.bibes@cnrs-thales.fr. All correspondence should be addressed to M.B.

Author Contributions

MB and LV designed the experiment and MB supervised the study. FT prepared the samples with the help of DCV. FT performed the transport experiments and analysed them with the help of MB, HJ, AB, AF, LV, JPA and PN. PB and MG performed tight binding and transport calculations. FT and MB wrote the paper with inputs from all authors. 03), TOPRISE (ANR-16-CE24-0017) and the Laboratoire d'Excellence LANEF (ANR-10-LABX-51-01).

ACKNOWLEDGMENT

The authors thank the CTU Minerve Nanotechnology platform where electron beam lithography was performed and B. van Wees for useful comments.