Maxime Tisserant

Philippe Janssen

André Evette

Eduardo González

Paul Cavaillé

Monique Poulin
email: monique.poulin@fsaa.ulaval.ca

Diversity and succession of riparian plant communities along riverbanks bioengineered for erosion control: a case study in the foothills of the Alps and the Jura Mountains

Keywords: Bioengineering, Mixed techniques, Ripraps, Riverbank stabilization, Vegetation succession, Willow fascines

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Most streams and associated riparian zones worldwide have been altered by 'hard' civil engineering structures such as dams, weirs, levees, dikes and other erosion protection structures. These structures are needed to control flooding and prevent channel migration in the presence of agriculture or urban and transport infrastructures in floodplains, but at the same time they drastically modify natural river dynamics [START_REF] Feld | From natural to degraded rivers and back again: a test of restoration ecology theory and practice[END_REF][START_REF] Nilsson | Fragmentation and flow regulation of the world's large river systems[END_REF]. Associated changes in abiotic and biotic conditions including water quality have resulted in several directives to stimulate stream restoration in Europe, notably the Floods Directive of 2007, the European Water Framework Directive of 2000, and the Habitat Directive of 1992 [START_REF] Gumiero | Linking the restoration of rivers and riparian zones/wetlands in Europe: Sharing knowledge through case studies[END_REF][START_REF] Carvalho | Protecting and restoring Europe's waters: An analysis of the future development needs of the Water Framework Directive[END_REF]. In that regard, recent literature reviews revealed that restoration actions that modify the prevalent water and/or sediment regime are increasingly and efficiently used to restore riparian vegetation, for example, by operating dams to satisfy plant requirements, or by removing or relocating levees and dikes [START_REF] González | Restoration of riparian vegetation: A global review of implementation and evaluation approaches in the international, peer-reviewed literature[END_REF]2018). Yet, such restoration strategies could conflict with the human infrastructures in close proximity. Where erosion control is of primary concern to ensure public safety, soil bioengineering could represent a good compromise between civil engineering and ecological restoration.

Soil bioengineering is in fact often viewed as riparian ecosystem restoration, sensu lato, because it promotes the recruitment and growth of native plant species along stabilized riverbanks [START_REF] Li | Soil bioengineering and the ecological restoration of riverbanks at the Airport Town, Shanghai, China[END_REF] and, more generally, because it facilitates the partial recovery of some of the main ecological functions previously provided by now degraded riverbanks, i.e. biodiversity support, ecological corridor, and decontamination [START_REF] Karle | Stream and floodplain restoration in a riparian ecosystem disturbed by placer mining[END_REF][START_REF] Sudduth | Effects of bioengineered streambank stabilization on bank habitat and macroinvertebrates in urban streams[END_REF]. As a nature-based solution, soil bioengineering uses the physical properties of living plants to minimize the negative impacts of artificial bank stabilization on stream ecosystems [START_REF] Rey | Soil and water bioengineering: Practice and research needs for reconciling natural hazard control and ecological restoration[END_REF].

It has been used for centuries in Europe [START_REF] Evette | History of bioengineering techniques for erosion control in rivers in western Europe[END_REF] and consists in copying natural systems by integrating vegetation into engineering design in order to protect hill slopes, embankments and human structures from erosion and other undesired geomorphological processes (e.g., sediment deposition, channel incision and channel migration; [START_REF] Gray | Biotechnical and soil bioengineering slope stabilization: a practical guide for erosion control[END_REF][START_REF] Shields | Rehabilitation of an incised stream using plant materials: the dominance of geomorphic processes[END_REF]. The positive effects of soil bioengineering on riparian habitats in terms of biodiversity support (fishes, macroinvertebrates) have been empirically demonstrated by several studies [START_REF] Sudduth | Effects of bioengineered streambank stabilization on bank habitat and macroinvertebrates in urban streams[END_REF][START_REF] Cavaillé | Influence of riverbank stabilization techniques on taxonomic and functional macrobenthic communities[END_REF][START_REF] Schmitt | River bank stabilisation by bioengineering: potentials for ecological diversity[END_REF][START_REF] Janssen | Soil bioengineering techniques enhance riparian habitat quality and multi-taxonomic diversity in the foothills of the Alps and Jura Mountains[END_REF].

However, the effects on plant biodiversity itself have received less attention (but see [START_REF] Cavaillé | Biodiversity assessment following a naturality gradient of riverbank protection structures in French prealps rivers[END_REF][START_REF] Schmitt | River bank stabilisation by bioengineering: potentials for ecological diversity[END_REF]. In particular, it is not known whether the successional dynamics of plant communities on bioengineered banks resemble those of natural riverbanks. Yet, knowing the ability of these nature-based solutions to initiate vegetation succession is essential to assess whether they meet the self-organization requirement necessary to declare full recovery in restoration projects (see International principles and standards for the practice of ecological restoration in [START_REF] Gann | International principles and standards for the practice of ecological restoration[END_REF].

Plant communities in riparian areas are mostly shaped by flood disturbance: species associated with early stages of riparian succession frequently encounter physical and physiological constraints such as anoxia, shear stress or submersion, rather than limited light and plant competition, as in later stages of succession [START_REF] Corenblit | Reciprocal interactions and adjustments between fluvial landforms and vegetation dynamics in river corridors: A review of complementary approaches[END_REF][START_REF] Corenblit | Engineer pioneer plants respond to and affect geomorphic constraints similarly along water-terrestrial interfaces worldwide[END_REF]. The first phases of succession in riparian systems are typically characterized by the colonization of pioneer species like willows, poplars/cottonwoods, and herbaceous species with ruderal, light-demanding, short-lived characteristics and affinity for hydric conditions [START_REF] Mccoy-Sulentic | Changes in community-level riparian plant traits over inundation gradients, Colorado River, Grand Canyon[END_REF][START_REF] Muñoz-Mas | Exploring the key drivers of riparian woodland successional pathways across three European river reaches[END_REF]. As succession advances and fluvial landforms age, aggrade and disconnect from the stream channel, flooding disturbance is replaced by inter-specific interactions (e.g., competition, facilitation) as the main driver of vegetation change [START_REF] Tabacchi | Development, maintenance and role of riparian vegetation in the river landscape[END_REF]2019).

According to the passive relay floristic approach (i.e. Field of Dreams hypothesis sensu [START_REF] Palmer | Ecological theory and community restoration ecology[END_REF], the active introduction of early successional woody species, such as Salix spp. (willows), which are also ecosystem engineer species [START_REF] Gurnell | Plants as river system engineers[END_REF], should affect the riverbank physical environment and foster the development of plant communities during secondary succession [START_REF] Lennox | Development of vegetation and aquatic habitat in restored riparian sites of California's north coast rangelands[END_REF][START_REF] Mcclain | Successional models as guides for restoration of riparian forest understory[END_REF].

Active revegetation may be seen as an "assisted" succession for the over-and understory composition of riparian vegetation. It is a common practice in invasive species management projects following the removal of undesired plants [START_REF] González | Vegetation response to invasive Tamarix control in southwestern US rivers : A collaborative study including 416 sites[END_REF][START_REF] Ruwanza | The effectiveness of active and passive restoration on recovery of indigenous vegetation in riparian zones in the Western Cape, South Africa: A preliminary assessment[END_REF] or after abandonment of agriculture in the floodplain, when a limited inflow of propagules occurs [START_REF] Battaglia | Sixteen years of old-field succession and reestablishment of a bottomland hardwood forest in the Lower Mississippi Alluvial Valley[END_REF][START_REF] Bunting | Long-term vegetation dynamics after highdensity seedling establishment: implications for riparian restoration and management[END_REF][START_REF] Bourgeois | Threshold dynamics in plant succession after tree planting in agricultural riparian zones[END_REF]. Active revegetation by seeding or planting cuttings (or stakes) helps recruit other native and typically riparian species, with different techniques leading to different plant communities [START_REF] Van Looy | Restoring river grasslands: Influence of soil, isolation and restoration technique[END_REF]. In riparian areas stabilized by soil bioengineering techniques, shrubs are frequently assembled into fascines or brushlayers, which consist respectively of branches tied together in linear cylindrical bundles or in multiple layers, placed on streambanks with or without a rock embankment in the lower part of the bank, depending on local constraints [START_REF] Li | Biotechnical engineering as an alternative to traditional engineering methods: A biotechnical streambank stabilization design approach[END_REF]. We suggest that such bioengineering practices also represent a type of assisted succession. As is the case for active revegetation, different bioengineering techniques have been shown to strongly influence the resulting plant community [START_REF] Cavaillé | Biodiversity assessment following a naturality gradient of riverbank protection structures in French prealps rivers[END_REF][START_REF] Schmitt | River bank stabilisation by bioengineering: potentials for ecological diversity[END_REF]. To our knowledge, however, how succession is modulated by bioengineering alone, i.e. "pure" bioengineering, or combined with hard civil engineering, i.e. "mixed" bioengineering, has not been reported in the scientific literature.

This study aimed to investigate if soil bioengineering can foster succession of riparian plant communities through the active introduction of early successional shrub species on riverbanks. Specifically, we examined how plant community composition varied between sites where pure versus mixed soil bioengineering techniques were implemented, and compared to sites with civil engineering stabilization structures of different ages in the French and Swiss foothills of the Alps and the Jura Mountains.

Many soil bioengineering structures have been successfully applied to foothill streams of these regions where bank erosion is an important issue in proximity to roads and other infrastructure. We hypothesized that by adding pioneer engineer species, soil bioengineering bypasses the natural establishment of pioneer and ruderal species, and fosters a faster transition to a dominance by post-pioneer competitive species.

Conversely, we hypothesized that civil engineering facilitates the recruitment and establishment of opportunistic (notably non-native) and fast-colonizing species and leads to a different and slower successional trajectory than bioengineering. For simplicity, the term bioengineering is used instead of soil bioengineering in the sections below.

Material and methods

Study area and sampling design

The study area is located in the French and Swiss foothills of the Alps and the Jura Mountains, within the Rhône River watershed (Figure 1). This region is characterized by a limestone substratum and a temperate climate. We selected 23 streams, extending between the Drôme River (44°43'N; 4°58'E) in the southern part of the study area and the Doubs River (47°21'N; 7°10'E) in the northern part, at elevations ranging from 134 to 700 m a.s.l. All of the streams studied belong to the same vegetation zone, i.e., "lower and mid-mountain: collinean and montane vegetation belts" [START_REF] Ozenda | An ecological map of Europe: why and how?[END_REF], and to the same major group of stream types in Europe, i.e., mountain streams [START_REF] Sandin | Stream and river typologiesmajor results and conclusions from the STAR project[END_REF].

In 2011, 42 riverbank sites were sampled to assess the response of plant communities to different types of engineered riverbank stabilization structures for erosion control over time (a complete description of sampled sites, including year of completion, country, river and absolute elevation, is provided in Appendix S1). We selected three types of stabilization structures from among those most commonly used (Figure 2): "pure" bioengineering protection (i.e. willow fascines on the lower part of the bank, brushlayers and cuttings of willow species on the middle part and herbaceous seeding on the upper part of the bank, 15 sites); "mixed" protection (i.e. a technique combining hard civil engineeringriprapon the lower part, brushlayers and cuttings of willow species on the middle part and herbaceous seeding on the upper part, 13 sites); and "riprap" protection (i.e. hard civil engineering protection on the entire bank, 14 sites).

Willow species used in bioengineering techniques (fascines and cuttings) were Salix viminalis L., S. purpurea L., S. triandra L., S. myrsinifolia Salisb. and S. pentandra L.

We used a space-for-time substitution approach to construct a chronosequence of 14 years (the number of sites was distributed evenly across years and stabilization structures, Appendix S1).

Vegetation survey

Riparian vegetation was sampled between May and July 2011 using the Line Point Intercept method [START_REF] Bonham | Measurements for terrestrial vegetation[END_REF] to detect the presence and frequency of occurrence (i.e. density) of plant species. At each site, three 25-m transects (lower, middle, upper) were set parallel to the stream channel. The lower transect was placed close to the water line at low-flow discharge. The middle transect was placed at an elevation determined according to the biannual flood recurrence water level, estimated visually using the presence and occurrence of wetland species, signs of recent flooding disturbance (i.e., plant debris; bent branches) and the morphology of the channel. The upper transect was placed near the edge of the riverbank and we assumed that it did not flood regularly. All sites were sampled during low-flow conditions, so that transects near the low-flow water level would be comparable across sites. At each transect, sampling points were established every meter for a total of 75 points per site. At each sampling point, all plant species intercepted by a vertical rod or its upward projection were recorded and identified. All specimens were determined to the species level, except for Rubus spp. and Festuca spp., which were considered at the genus level because of uncertain identification and potential hybridization. We then used the total number of taxa and their density (number of points where present divided by 75 and multiplied by 100 %), pooling the three transects together for each site as dependent variables in subsequent analyses, but for simplicity we will use the term species instead of taxa throughout the paper. Species density may exceed a hundred percent, because of vertical overlap of individuals at each sampling point.

Plant species groups

We first calculated the richness and density of total, native and non-native species. Nonnative species represent potential threats to native riparian plant communities and can pose challenges to restoration measures [START_REF] Richardson | Riparian vegetation: degradation, alien plant invasions, and restoration prospects[END_REF][START_REF] González | Regeneration of Salicaceae riparian forests in the Northern Hemisphere: A new framework and management tool[END_REF].

Species origin was determined based on their chorology, i.e. introduced species originated from America, Africa and Asia, according to the Baseflor database [START_REF] Julve | Baseflor. Index botanique, écologique et chorologique de la flore de France[END_REF] as well as information available from the DAISIE database (http://www.europealiens.org/). We then considered the richness and density of hygrophilous and shadetolerant species, based on Ellenberg's indicator values [START_REF] Ellenberg | Zeigerwerte von Pflanzen in Mitteleuropa[END_REF] extracted from the Baseflor database [START_REF] Julve | Baseflor. Index botanique, écologique et chorologique de la flore de France[END_REF]. Species having indicator values for soil moisture requirements ≥ 6 were considered hygrophilous; species having indicator values for light requirements ≤ 6 were considered shade-tolerant (Appendix S2). These classification criteria are derived from data examination and consistency between moisture (F) and light (L) Ellenberg indicator values, the wetland indicator status of the US National Wetland Inventory [START_REF] Reed | National list of plant species that occur in wetlands : Northeast (Region 1)[END_REF] and the light requirement classification in the TOPIC database [START_REF] Aubin | TOPICtraits of plants in Canada[END_REF]. Finally, we considered the richness and density of ruderal and competitive species using Grime's CSR scheme [START_REF] Grime | Evidence for the existence of three primary strategies in plants and its relevance to ecological and evolutionary theory[END_REF], extracted from the list of CSR categorical strategies, adapted from [START_REF] Pierce | A global method for calculating plant CSR ecological strategies applied across biomes world-wide[END_REF].

Finally, species were grouped as hygrophilous, ruderal, shade-tolerant, and competitive to compare succession over time among stabilization structures. In riparian zones, hygrophilous species tend to occur in the lowest elevated and more frequently flooded fluvial landforms, typical of early stages of the biogeomorphological succession (e.g., point bars, off-channel depressions, abandoned channels, [START_REF] Corenblit | Control of sediment dynamics by vegetation as a key function driving biogeomorphic succession within fluvial corridors[END_REF].

Ruderal species are well-adapted to low stress and high disturbance environments and also characterize pioneer communities in the early stage of vegetation succession (González et al., 2017a). Shade-tolerant species arrive later, as the overstory canopy develops [START_REF] Mcclain | Successional models as guides for restoration of riparian forest understory[END_REF]. Competitive species are well-adapted to low stress and low disturbance environments and characterize post-pioneer communities in the mid-to late seral successional stages [START_REF] Johnson | Forest overstory vegetation and environment on the Missouri River floodplain in North Dakota[END_REF][START_REF] Van Pelt | Riparian forest stand development along the Queets River in Olympic National Park, Washington[END_REF].

Environmental variables

We collected measurements of spatial (i.e. altitude, latitude, longitude), geomorphological (i.e. stream width), climatic (i.e. precipitation and temperature) and land cover (i.e. proportion of forest, agriculture and urban areas in the surrounding landscape) environmental variables in addition to characterizing the riverbank condition (age and type of stabilization structure). Spatial and geomorphological variables were measured directly on each riverbank site using a GPS and laser rangefinder. Climatic variables were derived from the WorldClim climatic model [START_REF] Nilsson Hijmans | Very high resolution interpolated climate surfaces for global land areas[END_REF] and adjusted for the effect of altitude following [START_REF] Zimmermann | Variations in the pool (cumulative number of species in all sites) and the mean (±SD) of riparian plant species richness in relation to the type of stabilization structure. Letters indicate homogeneous groups of stabilization structure types after Monte Carlo randomization tests ([END_REF]. Land cover variables were measured within a 500-m-radius around each riverbank site with the QGIS Geographic Information System (QGIS Development Team, 2015). We determined whether environmental variables varied among the three stabilization structures using one-way ANOVAs for each environmental variable with Tukey's HSD post hoc tests. The goal of this analysis was to verify that differences in plant composition were mainly due to the experimental design (riverbank stabilization structures and age) and not to environmental variables. Because we only detected a significant difference in stream width between mixed sites (higher) and ripraps (lower) (One-way ANOVA and Tukey HSD test, Appendix S3) and no differences in any of the other environmental variables were found between the three stabilization structure types, we did not use either environmental variables as a covariable in the statistical analysis of vegetation (see below).

Statistical analysis of vegetation

To determine whether the plant species pool (gamma diversity) differed among stabilization structures, we used species accumulation curves with Monte Carlo randomization tests (n = 999), and the function c2cv in the rich package [START_REF] Rossi | rich: An R Package to Analyse Species Richness[END_REF].

The plant species pool was assessed considering either all species, and by groups (nonnative, hygrophilous, ruderal, shade-tolerant, competitive species).

To determine whether plant species richness and density (for all species and each species group individually) varied in bioengineering stabilization structures compared to ripraps or with their age, or a combination of both factors, we used Generalized Linear Mixed Models (GLMM) with site proximity (see explanation below) as a random effect and the functions glmer and glmer.nb in the lme4 package (Bates et al., 2018). Site proximity was a categorical variable that grouped sites within circular units of 40 kilometers of diameter (Appendix S1). A group of sites could encompass sites in the same reach or in different streams. We chose 40 km because we estimated this distance encompassed homogeneous environmental conditions, and because no sites could belong to two groups using this value. This random effect made it possible to account for spatial autocorrelation between close sites. We developed four a priori models, including the random effect -Structure (riverbank stabilization structure); Age; Structure + Age (additive effect of both factors); Structure*Age (additive effect and multiplicative interaction); and the null model (i.e. the intercept and random effect only model), and fitted Poisson GLMM for species richness and negative binomial GLMM for vegetation density (total and by group). Variance explained by GLMMs was estimated using the marginal coefficient of determination for fixed effect parameters alone [START_REF] Nakagawa | The coefficient of determination R2 and intra-class correlation coefficient from generalized linear mixed-effects models revisited and expanded[END_REF] and the most parsimonious regression model was identified using Akaike's information criterion corrected for small sample sizes (i.e. AICc, [START_REF] Burnham | Model selection and multi-model inference: a practical information-theoretic approach[END_REF]. When the delta AICc with the second best model was > 2, evaluated using the function model.sel in the MuMIn package [START_REF] Barton | MuMIn: Multi-model inference[END_REF], estimated parameters and associated unconditional standard errors were extracted from the top-ranked model only, and when < 2, from the most complex of the top-ranked models [START_REF] Burnham | Model selection and multi-model inference: a practical information-theoretic approach[END_REF].

We used multivariate generalized linear models to test whether plant species composition varied across stabilization structure and the age of the structure, as well as the interaction between both of these factors, with mvabund package [START_REF] Wang | mvabund -an R package for model-based analysis of multivariate abundance data[END_REF]. This approach makes it possible to test the effects of the predictor variables (stabilization structure and age) on both community-level response and the responses of individual species [START_REF] Warton | Modelbased thinking for community ecology[END_REF]. In this case, we fitted a negative binomial distribution to the abundance data for plant species that were present in more than 5 % of the studied sites (i.e. 105 species). In addition to the model described above, we ran a full model without the five most commonly planted species in bioengineering structures (willows) to assess whether they had a disproportionate weight in the model. More details on the computation of the multivariate generalized linear models (explanatory data analysis, model fitting and checking) are provided in Appendix S4.

We also ran a canonical analysis of principal coordinates (CAP, [START_REF] Anderson | Canonical analysis of principal coordinates: a useful method of constrained ordination for ecology[END_REF] with the Bray-Curtis distance community matrix constrained by the stabilization structures and their age, using the capscale function of the vegan package (Oksanen et al., 2013). Ordinations such as CAP have the advantage of summarizing the main gradients of multivariate variability in a few axes that can be depicted in a multidimensional space (usually bidimensional, two main axes), thus providing an illustrative graphical representation of overall patterns. All analyses were conducted with R version 3.3.2 (R Core Team, 2017).

Results

Effect of the type of stabilization structure and age on species richness and density

Overall, 261 species of plants were recorded at the 42 sites for an average of 25 species per site. Only a small fraction (5.7%) of these species were non-native (15 species), with an average of 1.5 species per site. One third (34%) of the species were hygrophilous (89 species), a similar proportion were shade-tolerant (29%, 75 species), and ruderal (29%, 77 species), while one fourth (23%) were competitive (61 species).

The species pool was 157 species for pure structures, 178 for mixed structures and 114 for riprap structures (Table 1). The species pool for total, shade-tolerant and competitive groups was significantly higher on mixed and pure sites, compared to ripraps. There were more hygrophilous species (accumulated) in pure sites than in ripraps, more ruderal in mixed sites than in ripraps, and more non-native in pure sites than in mixed sites (Table 1). Even though plateaux were not reached (Appendix S5), the accumulation of species slowed down with increasing number of sites and was a good indicator of an appropriate sampling effort. We observed differences in species richness between types of stabilization structures, but some interactions with age were significant for some species groups (Table 2 and3, and Figure 3). Total species richness was higher on mixed and pure than on riprap sites and remained stable with time (Figure 3a, Table 3). This pattern was also reflected in ruderal species (Figure 3d, and Table 3). Hygrophilous species richness was higher on pure and mixed sites, compared to ripraps, and decreased with time on the bioengineered sites, but not in ripraps (Figure 3c and interaction Age:Riprap-Pure, Table 3). For shade-tolerant and competitive species, species richness increased with time on pure bioengineering but slightly decreased on mixed sites; richness of competitive species increased with time on ripraps (Figure 3e, f and interaction Age:Riprap-pure, Table 3). Richness of non-native species did not change over time with any type of stabilization structure, nor did it differ between them (Figure 3b, Table 3).

Plant density also differed greatly among stabilization structures but some interactions with age occurred as well (Table 2 andFigure 4). Plant density was significantly lower on ripraps than on pure and mixed sites for total, ruderal and competitive species (Figure 4a,d,f and Riprap-Mixed and Riprap-Pure, Table 3). Density decreased for hygrophilous and increased for shade-tolerant species on pure sites, compared to ripraps (Figure 4c, e and Age:Riprap-Pure, Table 3). Non-native species did not show differences in density between stabilization structures and age (Figure 4b, Table 3).

Effect of type of stabilization structure and age on species composition

The changes in the entire plant species composition with time since completion of the stabilization work differed among the three stabilization structures (interaction Structure

x Age: Deviance = 328.1, p = 0.006). However, most of the variation in species composition was related to the type of stabilization structure (Deviance = 518.9, p = 0.001), rather than to the age of the structures (Deviance = 191.4, p = 0.019). Pairwise comparisons revealed that significant differences in species composition occurred between mixed and riprap sites (Deviance = 282.0, p = 0.001), and between pure and riprap sites (Deviance = 276.7, p = 0.001), but not between mixed and pure sites (Deviance = 158.9, p = 0.172). The full model run without the five species most commonly planted in bioengineering structures (willows) showed a similar relative contribution of type of stabilization structure and age (Structure: Deviance = 439.3, p = 0.01; Age: Deviance = 170.9, p = 0.04), compared to the models run with the five species, but a decrease of the total deviance of the model (Total deviance = 1649.8, models not shown), compared to the model including the five planted species (Total deviance = 1814.5).

The effect of the stabilization structure on plant composition is well illustrated by the first axis of the canonical analysis of principal coordinates (Figure 5), which clearly separated ripraps (negative end of Axis 1) from bioengineering sites (positive end of Axis 1), while the second axis showed only a slight relationship to the age of the stabilization structure (older sites more positively loaded, Axis 2). Plant communities from ripraps were more clustered (shorter grey lines, Figure 5) than those from pure and mixed sites (longer grey lines, Figure 5), indicating a greater similarity in species composition along the chronosequence for this stabilization structure. Despite the relatively low percentage of variability explained by the ordination (R² adj = 10.3 %, p = 0.001), the individual terms of the CAP model were highly significant (Age: p = 0.021; Structure: p = 0.001).

Univariate tests (Appendix S7) revealed that few species contributed to the multivariate significant effect, i.e. the variation in the abundance of these species captured a large

Discussion

Our results show that plant composition and its trajectory over time differed between soil bioengineering and civil engineering structures. Pure and mixed stabilization structures had higher richness and density of plant species than ripraps, and comprised different species assemblages. Moreover, we found that the successional trajectories of riparian communities differed among the three types of stabilization structures, with more stagnant vegetation on ripraps than on the two other types of sites. As we predicted, these findings show that soil bioengineering not only plays a role in erosion control and riverbank stabilization, but also fosters plant diversity by promoting vegetation succession following the active introduction of pioneer ligneous species.

Bioengineering and ripraps lead to different plant species diversity and composition

Our findings supported those of previous studies [START_REF] Cavaillé | Biodiversity assessment following a naturality gradient of riverbank protection structures in French prealps rivers[END_REF][START_REF] Schmitt | River bank stabilisation by bioengineering: potentials for ecological diversity[END_REF], determining that soil bioengineering techniques enhanced the richness and density of riparian vegetation better than ripraps. Indeed, except for non-native species, total species pool (cumulative) and mean species richness (locally by site) of all species groups were greater on riverbanks stabilized by either pure or mixed structures than on riverbanks entirely stabilized by ripraps. This pattern was especially marked for shadetolerant and competitive species on pure structures. Differences in environmental conditions (light, soil moisture) and in biotic interactions between the pure (and to a lesser extent the mixed) and riprap techniques may explain the pattern. By forming dense thickets on bioengineered sites, Salix viminalis, S. purpurea and S. triandra may decrease flow speed and enhance fine sediment retention [START_REF] Rey | Can bioengineering structures made of willow cuttings trap sediment in eroded marly gullies in a Mediterranean mountainous climate?[END_REF] on the lower part of the riverbank, which in turn should increase seed retention of hydrochorous species and ultimately favour riparian plant diversity [START_REF] Corenblit | Seed retention by pioneer trees enhances plant diversity resilience on gravel bars: Observations from the river Allier, France[END_REF][START_REF] Mikuś | Islands in a European mountain river: Linkages with large wood deposition, flood flows and plant diversity[END_REF]. Also, by modifying local conditions (e.g., reducing light availability and shear stress), the active introduction of ligneous species may favour shade-tolerant and competitive riparian plant species (González et al., 2017a;[START_REF] Lennox | Development of vegetation and aquatic habitat in restored riparian sites of California's north coast rangelands[END_REF], particularly in pure structures where ligneous species are planted across the entire surface, from the bottom to the top of the bank. Our results thus concur with the "Field of Dreams Hypothesis" [START_REF] Palmer | Ecological theory and community restoration ecology[END_REF], which assumes that a more complex vegetation structure established by revegetation efforts will allow other plants to recolonize a restored habitat.

Although we found clear evidence that bioengineering structures favor plant diversity better than ripraps, the findings of our study differ slightly from those reported previously, which showed higher richness on mixed structures compared to pure structures for plants and other trophic groups [START_REF] Cavaillé | Biodiversity assessment following a naturality gradient of riverbank protection structures in French prealps rivers[END_REF]. Mixed structures provide a greater heterogeneity of environmental conditions, with inert materials (riprap) on the lower part of the bank and willow cuttings and plantings on the upper part. Such a combination of techniques will increase species richness only if distinct flora establishes on the riprap area compared to the upper planted part of the riverbank.

In our study, ripraps were shown to be inhospitable to most plants, being less densely colonized in general; therefore, they contributed little to increasing the plant richness of mixed sites. This hypothesis of poor colonization of ripraps in our study sites was even confirmed for non-native species, which are normally able to colonize such structures but were mostly absent from ours. For example, civil engineering structures along waterways have been identified as habitats that promote non-native invasive species such as Fallopia japonica [START_REF] Hoggart | Urban river wall habitat and vegetation: observations from the River Thames through central London[END_REF]. Even though we found no statistical evidence that riprap sites were colonized more by non-native species than mixed and pure bioengineered sites, examination of the constrained ordination plot revealed a close association between the occurrence of Fallopia japonica and entirely riprapped riverbanks. Indeed, the mean density of this highly invasive species was twice as high on ripraps (mean ± SD = 10.3 ± 25.5) as on bioengineering structures (pure = 5.4 ± 14.5; mixed = 2.6 ± 6.7). [START_REF] Dommanget | Fast-growing willows significantly reduce invasive knotweed spread[END_REF] reported a poorer performance by F. japonica under a dense canopy cover of Salix species in mesocosm experiments, which suggests that bioengineering could also help limit the propagation of invasive species, more so than ripraps.

Successional trajectories also differ in bioengineered and riprap sites

Much as the type of stabilization structure influenced diversity patterns, time poststabilization was a powerful predictor of plant species richness and density. The occurrence of certain groups of species based on their ecological requirements, i.e. soil moisture and light, as well as competitive strategies, changed along the chronosequence. Specifically, the richness of hygrophilous species decreased over time, notably in the case of bioengineering structures, possibly due to fine sediment aggradation along stabilized riverbanks [START_REF] Corenblit | Control of sediment dynamics by vegetation as a key function driving biogeomorphic succession within fluvial corridors[END_REF] or to a shift in trade-offs from hygrophilous to shade-tolerant species in older sites dominated by dense willow stands [START_REF] Gurnell | Changing river channels: The roles of hydrological processes, plants and pioneer fluvial landforms in humid temperate, mixed load, gravel bed rivers[END_REF]. However, repeated observations on the same sites would have been necessary to confirm this hypothesis. Changes in environmental conditions that accompany aggradation and hydrological disconnection typical of biogeomorphological succession theoretically favor colonization by species with different resource acquisition strategies [START_REF] Corenblit | Control of sediment dynamics by vegetation as a key function driving biogeomorphic succession within fluvial corridors[END_REF]Tabbachi et al., 2019). Nitrogen-demanding species more adapted to drought stress and shade conditions (e.g. Alnus glutinosa, Corylus avellana, Crataegus monogyna, Equisetum arvense) replaced hygrophilous species along succession [START_REF] Januschke | Mountain river restoration measures and their success(ion): Effects on river morphology, local species pool, and functional composition of three organism groups[END_REF]. Our results also showed that shade-tolerant and competitive species responded differently to time post-stabilization, depending on whether they were on pure, mixed or riprap sites. While richness of shade-tolerant and competitive species more than doubled in 14 years on pure sites, they tended to decrease or remain stable on mixed and riprap sites. Overall, we believe that the decrease in hygrophilous species and the increase in shade-tolerant and competitive species over time is related to similar successional trajectories observed in riparian forests that follow a linear succession, i.e. a shift from pioneer phreatophyte species to post pioneer drought-adapted species along succession (e.g. [START_REF] Fierke | Structural dynamics of riparian forests along a black cottonwood successional gradient[END_REF][START_REF] Muñoz-Mas | Exploring the key drivers of riparian woodland successional pathways across three European river reaches[END_REF][START_REF] Van Pelt | Riparian forest stand development along the Queets River in Olympic National Park, Washington[END_REF]. Thus, in accordance with previous studies, our results support the idea that planting ligneous species in riparian zones can foster succession [START_REF] Mcclain | Successional models as guides for restoration of riparian forest understory[END_REF][START_REF] Osman | The effect of plant succession on slope stability[END_REF] and favor biodiversity [START_REF] Lennox | Development of vegetation and aquatic habitat in restored riparian sites of California's north coast rangelands[END_REF], making soil bioengineering a good compromise solution for the restoration of eroding riverbanks. Conversely, ripraps did not show evidence of succession and remained less densely colonized by only a few species, including light tolerant and xerophytic species such as Fallopia japonica, Festuca rubra, Robinia pseudoacacia, and Sanguisorba officinalis (see mean densities in Appendix S7). Ripraps thus remained "blocked" in the early stages of vegetation succession, dominated by pioneer light-demanding and not strictly riparian vegetation [START_REF] Wollny | Dominance of competitors in riparian plant species composition along constructed banks of the German rivers Main and Danube[END_REF]. The fact that the plant community composition in ripraps was rather simple could also explain their higher similarity as a group (as shown on the CAP ordination), compared to the more heterogeneous communities in the other two types of stabilization structures.

Conclusion

Overall, our results illustrated the ecological added-value of soil bioengineering techniques, through the active introduction of native shrubs to support riparian plant species. Previous research highlighted the role of native shrubs as the ecological engineers of river ecosystems. Here, soil bioengineering with Salix spp. promoted vegetation succession on stabilized riverbanks, through the recruitment and establishment of specific plant species groups, mainly shade-tolerant and competitive ones. As a result, soil bioengineering increased riparian plant richness and density, reinforcing the idea that this nature-based solution is a good compromise between erosion control with civil engineering structures and other forms of ecological restoration that cannot be applied in this context. Even though bioengineering can also be designed to resist high shear stress, these techniques should be applied wherever erosion constraints are low and hard civil engineering may be unnecessary.

Conversely, community composition of ripraps did not change over time and remained species-poor, suggesting that civil engineering techniques should only be used in specific contexts where bioengineering techniques cannot be implemented, such as on sites dominated by clay, which represent high constraints for root development, or where scouring conditions are incompatible with the best available bioengineering techniques. Nonetheless, the plant diversity dynamics in ripraps need to be studied for longer periods of time to verify if our findings hold true.

Many questions remain, most importantly, those regarding the contribution of soil bioengineering to regional diversity and factors associated with patterns at the landscape scale. Comparing our results with the regional species pool, for example, would help to quantify the role of stabilization structures in regional biodiversity protection. It is also important to note that succession, particularly in riparian systems, is not always a deterministic linear process, and bifurcations, multiple pathways and regressions are common. It should also be kept in mind that bank erosion is a natural process that promotes dynamic habitats crucial for aquatic and terrestrial biodiversity in stream ecosystems, and in that sense, restoration of entire river segments that embraces channel migration may be preferable over undertaking stabilization work in contexts where public safety is not at risk. Considering natural or near-natural riparian zones as desirable reference endpoints for stabilization structures would be helpful to consider all these aspects in future studies.

  amount of the deviance explained by the model. Cornus sanguinea (Deviance = 23.5, p adj = 0.027), Lonicera xylosteum (Deviance = 23.1, p adj = 0.028), Crataegus monogyna (Deviance = 18.4, p adj = 0.064), Salix purpurea (Deviance = 16.9, p adj = 0.096), Salix alba (Deviance = 15.5, p adj = 0.158) and Salix triandra (Deviance = 12.7, p adj = 0.318) were more closely related to mixed/pure structures than to ripraps. The ligneous species Corylus avellana and Cornus sanguinea were highly associated to old mixed/pure structures (Deviance = 20.4, p adj = 0.033; Deviance = 6.083, p adj = 0.989, respectively, Appendix S7), while Vicia sativa (Deviance = 12.4, p adj = 0.106) was more closely related to young structures (i.e. < 5 years).

Figure captions Figure 1 .

 captions1 Figure captions

Figure 2 .

 2 Figure 2. Schematic drawing of the three types of riverbank stabilization structures: "Pure"

Figure 3 .

 3 Figure 3. Variation in species richness (i.e., number of species) of (a) total, (b) non-native, (c)

Figure 4 .

 4 Figure 4. Variation in species density (frequency of occurrence with vertical overlap) of (a)

Figure 5 .

 5 Figure 5. Biplot of the first two axes of a canonical analysis of principal coordinates (CAP) of

Acknowledgements

This project was funded by a research grant from the Fonds de Recherche du Québec -Nature et Technologies (FRQNT), the Natural Sciences and Engineering Research Council of Canada (NSERC) and Groupe PleineTerre Inc. through a BMP Innovation scholarship to M. Tisserant. We would also like to thank IRSTEA, the French-Swiss Interreg IV Project Geni'Alp, the Agence de l'Eau Rhône Méditerranée Corse, the Auvergne Rhône Alpes Region, the European fund FEDER, the Agence Française de la Biodiversité and the Ministère des Transports du Québec for financial support. We are grateful to Karen Grislis for English revision and to Léon Ducasse, Gilles Favier and Nathan Daumergue for field work. We thank two anonymous reviewers and the editorial board of Ecological Engineering for their constructive comments and insights.

Table 2. Top-ranking models predicting richness and density of total, non-native, hygrophilous, ruderal, shade-tolerant, and competitive plant species in relation to stabilization structure age and type in the foothills of the Alps and Jura Mountains (France and Switzerland), as assessed with Akaike's information criterion corrected for small sample size (AICc). The number of parameters estimated, including the intercept and random effect (k), AICc, AICc weight (W) and marginal coefficient of determination for fixed effects (R²), are provided (details on all a priori models are reported in Appendix S6


Veronica Granata

Lucia Capogna

Filomena Forte

Marie-Bernadette Lepetit

Rosalba Fittipaldi

Anne Stunault

Mario Cuoco

Antonio Vecchione

Spin-orbital nature of the high-field magnetic state in the Sr 4 Ru 3 O 10

I. INTRODUCTION

There is consolidated evidence that transition-metal oxides (TMOs) represent an extremely rich source of new phenomena and quantum phases of matter with a high potential for the development of innovative technologies. The competition of different and complex types of order is typical of TMOs mainly due to the strong entanglement and the frustrated localized-itinerant nature of the charge, spin, and orbital degrees of freedom. Though first thought of as a prerogative of 3d based TMOs [1,2], this class of phenomena seems now to be ubiquitous in 4d and 5d systems [3,4] where octahedral distortions, spin-orbit coupling (SOC), and other magnetocrystalline effects often cooperate to yield novel ordered states and proximity to metal-insulator transition, or even Mott insulating states.

A fascinating example of TMOs is the family of ruthenium perovskites belonging to the Ruddlesden-Popper (RP) series A n+1 Ru n O 3n+1 . The ruthenim based RP represents an astonishing natural success to engineer layered materials that can change drastically their electronic and magnetic properties as a function of the number n of RuO 2 layers within the unit cell [5], as well as by rare-earth substitution for alcaline-earth ions or by partial substitution of inequivalent TM ions [6][7][8][9]. As a result, the Sr n+1 Ru n O 3n+1 are metallic and tend to be ferromagnetic (FM) or metamagnetic [10][11][12][13][14][15][16][17][18], with the exception of the n = 1 member that is a spin-triplet superconductor [19,20]. In contrast, the isoelectronic Ca n+1 Ru n O 3n+1 systems tend to be in proximity to a metal-insulator transition exhibiting antiferromagnetism and rather rich orbital physics [21][22][23][24][25][26][27][28][29][30]. Doping Sr onto the Ca sites leads to insulator-to-metal transition accompanied by a changeover from antiferromagnetic to ferromagnetic dominated spin correlations and the occurrence of static magnetic order over nearly the entire range of (Ca,Sr) substitution [31]. To confirm the wide complexity of the phase diagram, novel spin-orbital correlated phenomena [32,33] can be induced by a tiny partial substitution of inequivalent TM ions in the (Sr,Ca)-RP family as observed, for instance, when Ru ions are replaced by Mn [34][35][36][37][38][39][40], Ti [41], Cr [42][43][44][45][46][47], Fe [48], or other transition-metal elements.

One of the major characteristics of the RP materials is that the physical properties can be critically linked to the number of layers in the unit cell and, hence, to the dimensionality of the electronic environment. Another common aspect is that, for RP members with n different from one, there is a natural emergence of a layer degree of freedom which can label the states where the electrons are located in the unit cell. Such an internal degree of freedom, in analogy with electron spin, can be exploited as a carrier of classical or quantum information and thus it may be a relevant ingredient to explore novel electronic device directions, as for instance already proposed in graphene bilayers [49,50] and metal dichalcogenide bilayers [51]. In this context, trilayered perovskites represent a quite unique system with inequivalent layer components when considering the possible mismatch of the inner and outer layers in the unit cell (see Fig. 1). Hence, the fundamental complexity of the RP ruthenates and the potential interrelation to a layer dependent physics makes Sr 4 Ru 3 O 10 an intriguing representative case in the family of the triple layered oxides. Sr 4 Ru 3 O 10 is an itinerant magnet marked by a strong anisotropy with coexistence of ferromagnetism and metamagnetism. Despite several investigations of the electronic and magnetic properties on this system, there are still unsolved questions both on the microscopic mechanisms that lead to the ferro-meta-magnetic state and on the nature of the resulting phase diagram. There are three key observations that set the Sr 4 Ru 3 O 10 magnetic response [14,52]: (i) a ferromagnetic transition occurs at T Curie ∼ 105 K, (ii) a magnetic enhancement of the susceptibility occurs at T * ∼ 60 K and zero field, and (iii) a metamagnetic transition (i.e., a sharp rising of the magnetization) occurs at T<T * and for fields applied within the ab plane (H ||ab) above ∼2 T. A series of observations contributed to unveil various puzzling features of the metamagnetic phenomena in Sr 4 Ru 3 O 10 . Transport properties showed that the metamagnetic transition lines split as a consequence of a significant spin-orbital coupling [53]. The subtle role of the multiorbital character of the Sr 4 Ru 3 O 10 has been also associated to the occurrence of a double metamagnetic transition in high-quality crystals [54]. Furthermore, close to the metamagnetic transition magnetic domains and electronic phase separation can occur [16,55]. Another important ingredient emerging in the Sr 4 Ru 3 O 10 metamagnetism is provided by the magnetoelastic coupling [56][57][58][59]. In particular, a direct evidence of a strong spin-lattice interaction has been obtained by means of neutron scattering demonstrating how significant structural changes occur concomitantly with the metamagnetic transition [57]. The focus of this work is on the nature of the high-field magnetic state of the Sr 4 Ru 3 O 10 . We employ polarized neutron scattering to analyze the spin and orbital spatial components of the induced magnetization density M(r) at high in-plane magnetic fields above the metamagnetic transition. The analysis indicates that the order relation between spin and orbital moments and their amplitudes in the unit cell are strongly tied to the layers where the electrons are located. We find evidence of a layer dependent magnetic anisotropy with the inner layers having larger spin and orbital magnetic moments than the outer ones in the unit cell. Remarkably, the inner-outer correspondence is robust with respect to temperature variations, being persistent even above T Curie in the paramagnetic state, thus indicating that these features are intrinsic to the high-field magnetic state. In order to investigate the origin of the layer dependent magnetic response, we consider an effective model that describes the coupling between spin and orbital degrees of freedom at different Ru sites in the unit cell. We show that the spin-orbital character of the magnetization in the high field can be ascribed to cooperative effects between octahedral distortions, spin orbit, and Coulomb interactions. The paper is organized as follows. In Sec. II, we introduce the experimental setup and the polarized beam approach. In Sec. III, we present the experimental results, while Sec. IV is devoted to their interpretation and discussion via the effective model. In Sec. V, we provide the concluding remarks.

II. EXPERIMENTAL DETAILS

Single crystals of Sr 4 Ru 3 O 10 were grown in an image furnace [60]. The samples were cut into small rectangular slices with an average size of 5 × 5 × 0.2mm 3 . Similar samples were already used in previous studies [57]. A number of techniques including x-ray diffraction, energy and wavelength dispersive spectroscopy, as well as neutron Laue diffraction have been employed to fully characterize the structure, the quality, and the purity of the crystals. Magnetization measurements on crystals from the same batch identified the ferromagnetic transition at T c ∼ = 105 K and a metamagnetic transition at a field of about 2 T when the temperature is lower than T * ∼ = 50 K and the magnetic field is applied in the ab plane.

Polarized beam measurements were performed on the D3 diffractometer at the Institute Laue Langevin in Grenoble. In such an experiment one measures the flipping ratio R, defined as the ratio of the intensities with neutron polarization parallel and antiparallel to the applied magnetic field. Neglecting corrections such as extinction, half-wavelength contamination, and attenuation, the flipping ratio can be written as [START_REF] Squires | Introduction to the Theory of Thermal Neutron Scattering[END_REF][START_REF] Nathans | [END_REF][63]

R = F N (K) -γr 0 2μ B 2pF N (K)M ⊥ (K) + γr 0 2μ B 2 M ⊥ (K) 2 F N (K) + γr 0 2μ B 2pF N (K)M ⊥ (K) + γr 0 2μ B 2 M ⊥ (K) 2 (1)
where γr 0 = 5.36 × 10 -15 m, and F N (K) and M(K)a r et h e nuclear structure factor and the Fourier transform of the magnetization density at the scattering vector K, respectively. M ⊥ (K) is the component of M(K) perpendicular to the scattering plane, and p is the incident neutron beam polarization.

We observe that at the lowest order of approximation, for small magnetic moments, R -1 is proportional to M ⊥ (K). The data were collected with an incident wavelength λ = 0.825(5) Å and polarization p = 0.95 (1) and with a 0.5-mm erbium filter in order to reduce higher-order contamination in the incident beam. A Heussler monochromator was used.

The crystal was oriented with the [hh0/00l] plane in the scattering plane. An external magnetic field of 9 T was applied in the [h h0] direction prior to cooling and then kept all along while a set of Bragg reflections was measured at 2, 65, and 115 K, which allows us to explore the magnetic configuration within the metamagnetic state, above the metamagnetic transition T * and the Curie temperature, respectively. At each temperature, we measured over 100 Bragg reflections (corresponding to 37 inequivalent reflections) in the spin-up and spin-down configurations by exploiting the optimization technique as described in Ref. [64]. Finally, the software program Sorgam [65] has been used to determine the magnetic form factors from the measured flipping ratios R.

III. RESULTS

In this section we present the main outcome of the polarized neutron-diffraction measurements and the resulting magnetization profile within the unit cell. Figure 2 shows the temperature dependence of the shifted flipping ratio R -1at three significant Bragg reflections.

The R -1 for the (0 0 6) and the (2 2 0) peaks are positive over the whole range of investigated temperatures. On the other hand, for reflection (0 0 4), R -1 undergoes a change of sign when the temperature is raised above T ∼ 60 K.

Assuming that the external magnetic field totally aligns the magnetic moments along the applied direction [h h0], one can show that for reflections of the kind 00l, with even l,the magnetic structure factor M ⊥ (K)inEq.( 1) reduces to

M(00l) = 4m c + 16m e cos[πl(z 2 + z 3 )] cos[πl(z 2 -z 3 )] .
(2) Here, z 2 and z 3 are the fractional coordinates along the c axis of the two unequivalent ruthenia in the external octahedra of the triple layer.

For l = 6, the two terms contributing to the intensity of M(K), i.e., the one from the central octahedra m c and the one from the external ones m e , are in phase and therefore add up, whichever the value of the two single terms. In contrast, for l = 4, the two terms are in antiphase. As a consequence, for the (0 0 4) reflection R -1 may change sign, which is indeed observed close to T ∼ 60 K, suggesting a temperaturedependent transfer of the magnetization from one site to the other in the unit cell. In the case of the (2 2 0) reflection, all the moments contribute in phase to M(K) and cannot undergo any cancellation due to interference. In order to give a quantitative picture of such redistribution of spectral weight, we have determined the spatial dependence of the magnetic density below and above the temperature where R -1 changes its sign. Figure 3 shows the spatial contour plot of the spin density within the RuO layers in the unit cell at two representative temperatures, i.e., T = 2 and 115 K. The spin densities were obtained from the measured magnetic structure factors by maximum entropy reconstruction [START_REF]Maximum Entropy and Bayesian Methods[END_REF]. At both temperatures, a set of 37 independent structure factors was used. Figure 3 reports the projections onto the (a + b,c) plane, which was perpendicular to the applied magnetic field. As expected, the main densities are concentrated on the Ru sites, while weaker densities are observed on the oxygen sites. A clear unbalance between the Ru sites also appears clearly in the maps, the densities on the inner Ru ions being higher than those of the outer Ru sites. We do notice that the unbalance is slightly more pronounced in the low-temperature regime.

The magnetic moments for the different ions were refined by means of the program Fullprof [START_REF] Carvajal | [END_REF]. The structural and extinction parameters, obtained from the data collected at the D10 diffractometer of the Institute Laue Langevin, Grenoble, were not varied in the flipping ratio refinement.

For the magnetization density, we have adopted the dipole approximation with the magnetic form factor being only dependent on the magnitude of the scattering vector (spherical distribution):

f |K| 2 = l=0,2,4,6 W l J l |K| 2 . (3)
Here, J l ( |K| 2 ) are spherical Bessel functions of order l, tabulated in the form of approximations inside Fullprof [68], and W l are the refinable parameters. Since no radial functions are available for the valence state +4, we have used those of TABLE I. Refined magnetic moment at three different temperatures for the ruthenium and oxygen atoms. Ru 1,4 refer to the inner RuO layers, while Ru 2,3 are in the outer ones (see Fig. 1). A magnetic moment was also allowed on the oxygen ions. Both the total and orbital components are presented. O a and O b refer to the apical and basal oxygen sites. the ion Ru +1 , which have been already shown to be a good approximation in analogous observations [69].

T (K) 2 65 115 M(μ B )M tot M orb M tot M orb M tot M orb Ru 1,
In the refinement we retain the first two terms, i.e., the ones with coefficients W 0 and W 2 which correspond to the total and the orbital component of the magnetic moments, respectively. In 3d transition-metal systems, the strong crystalfield (CF) interaction dominates over the spin-orbit interaction and the orbital moment is typically quenched. For the layered ruthenates with 4d electrons the spin-orbit coupling is expected to be not negligible and in turn it results in a nontrivial orbital contribution to the total magnetization.

Due to the large unit cell, the refinement procedure has been performed by reducing the number of inequivalent ions contributing to the neutron response. The twelve ruthenium atoms sit in four different crystallographic sites that we indicate as Ru 1 ,R u 2 ,R u 3 , and Ru 4 . In order to reduce the free parameters, we sort them into two types: the ruthenium atoms in the central octahedra of the unit cell (Ru 1 and Ru 4 ) and those in the external octahedra (Ru 2 and Ru 3 ). As we shall show below, this is physically plausible and consistent with the observed response. Indeed, since the Ru 1 and Ru 4 have similar surrounding anions, their magnetic moments can also be constrained to have the same amplitude, and the same would hold for the Ru 2 and Ru 3 .

Furthermore, a magnetic moment was also allowed to occur at the oxygen ions in the RuO 6 octahedra. The presence of unpaired electron density on O b (the basal ligands) and on O a (the apical ligands) is found to be quite high. Unlike the case in the compound Ca 1.5 Sr 0.5 RuO 4 [70], we observe a sizable moment not only on the basal oxygens but also on the apical ones.

Given the number and the multiplicity of the oxygen sites, we conclude that a significant fraction of magnetization density in the unit cell is transferred from the ruthenium atoms to the oxygens. This is not surprising as the large bandwidth of the Ru-4d orbitals [5,71] close to the Fermi level allows for a significant overlap with the oxygen 2p bands that is typically larger than that in the 3d oxides.

In Table I we present a summary of the magnetic configurations on the inequivalent Ru and O sites for the three investigated temperatures. The amplitude of the orbital contribution μ L is significant if compared to the total moment on both types of Ru sites. More specifically, the contribution of the inner layer is found to be larger with respect to the outer, and it is robust to the temperature increase. We observe that, approximately within the estimated errors, the orbital moments of the inner Ru ions as well as the oxygen moments do not vary with temperature. We have tested the statistical fit by imposing constant values as a function of temperature for both the orbital ruthenium moments and the oxygen ones. We point out that the resulting chi square turns out to be slightly greater than that obtained by keeping all the parameters unconstrained.

As far as the total magnetic density is concerned, we can state that a significant layer dependent magnetic anisotropy takes place, which traces back to the unbalance between the larger central and weaker outer components, both in the spin and orbital channels. Moreover, the percentage variation between the two clearly indicates that, by lowering the temperature, part of the magnetization is transferred from the ruthenium in the inner octahedra to those in the outer ones.

IV. EFFECTIVE MODEL AND DISCUSSION

In this section we discuss the microscopic ingredients and the physical mechanisms which are relevant to understand the spin and orbital magnetic response of Sr 4 Ru 3 O 10 . Then, we introduce and solve an effective model to present the specific magnetic density configuration that can be obtained in the high-field magnetic state and discuss the connection with the experimental outcome.

A. Mechanism for inequivalent spin-orbital response at the Ru sites

As shown in the previous sections, spin-polarized neutron diffraction provides direct evidence of a sizable orbital component and a net unbalancing of the total magnetic density, both in the orbital and spin sector, between Ru ions belonging to the central and the outer planes of the unit cell.

There are various degrees of freedom to take into account for analyzing the magnetic response. The first important microscopic ingredient is provided by the different octahedral configurations for the surrounding ions of the Ru sites belonging to the inner and the outer layers of the unit cell. Indeed, the octahedral distortions can affect in a distinct way the crystal field potential experienced by the Ru-t 4 2g electrons close to the Fermi level. In the case of tetrahedral distortions of the RuO 6 octahedra, an inverted hierarchy of the d xy and d xz,yz levels occurs depending on the flat or elongated nature of the deformation and, accordingly, a tendency to a positive or negative orbital polarization p = n xy -1 2 (n xz + n yz ) can be obtained (see Fig. 4). Apart from the structural feature, the breaking of the orbital rotation symmetry due the CF splitting together with a sizable spin-orbit coupling, expected to be relevant in 4d systems, are the other basic elements to be added to properly describe how the variation of the local spin and orbital moments can set the magnetic response [72].

Based on these considerations, we propose and analyze a possible scenario where the magnetic response of each Ru site in the inner and outer layers crucially depends on the specific character of the tetrahedral deformations, i.e., the degree of flattening/elongation, and its competition with local Coulomb interaction and spin-orbit coupling.

The mechanism for having an inequivalent magnetic response at different Ru sites is illustrated by the sketch in Fig. 4. The key observation is that the local configurations at the Ru sites, as shown in the middle panels of Fig. 4, can have an orbital polarization for which the competition between the Coulomb interaction and the spin-orbit coupling in the presence of the crystal-field potential can be significantly different. We first consider the case of flat octahedra, which is reported in the upper panels of Fig. 4. In this case the local configurations at the Ru site, which is representative of the ground state with four electrons in the t 2g sector (i.e., Ru-4d 4 ), can have a preferential occupation of the d xy orbital as due to the CF potential. In the absence of any applied magnetic field, the in-plane L x,y components of the orbital angular momentum L and the corresponding SOC activated terms (L x S x + L y S y ) are mainly inhibited by the CF splitting. On the other hand, the out-of-plane L z and the related L z S z term of the SOC can be equally hindered by the Coulomb interaction that tends to favor a fully aligned spin-triplet state. Hence, in the regime where all these energy scales are of the same order of magnitude and thus compete, the response to an applied field is expected to be mainly isotropic, in both the orbital and spin channels.

In the elongated case (lower panel of Fig. 4), the hierarchy of the t 2g orbitals is different and the minority spin prefers to occupy the d xz,yz sector. While the L x,y can be still inhibited by the CF, the L z and the relative SOC term L z S z are now unaffected by the local Coulomb interaction. The result is that there is an emergence of a local easy polarization axis both for the spin and the orbital components, which can lead to an anisotropic response to an applied field in the case of Ru sites belonging to elongated octahedra. Then, we are brought to deduce that the in-plane magnetic moments would be harder to be polarized at the Ru sites having elongated octahedra since in this case the applied field is orthogonal to the easy orbital axis z. On the contrary, there will be a greater susceptibility to an in-plane magnetic field at the Ru sites with flat octahedra, as in this case the magnetic isotropy makes the moments more easily oriented.

B. Model

In order to quantitatively support the physical scenario introduced above, we consider a model Hamiltonian with two inequivalent Ru atoms that includes all the local interactions of the electrons in the t 2g sector and allows for an effective charge transfer between them.

The inequivalent Ru sites are indicated with Ru fl and Ru el to label the compressive and the elongated distortions of the corresponding octahedra. The Hamiltonian H for the correlated electron in the t 2g manifold is expressed as a sum of different contributions:

H = H kin + H el-el + H CF + H SO + H xy . ( 4
)
The first term in Eq. ( 4) is the kinetic contribution between the t 2g orbitals on different Ru sites, H el-el is the local Coulomb interaction expressed in term of the couplings U and J H , H CF stands for the crystalline-field potential via the parameter , H SO indicates the spin-orbit term through the coupling λ, and H x,y describes the in-plane applied Zeeman field B (see the Appendix for details).

The complete Hamiltonian embodies five interaction parameters. We follow local-density approximation predictions [5] and assign, in the calculations, the values t = 0.4eV and fl /t =-0.3, el /t = 0.225 to the CF parameters of the central-flat and outer-elongated octahedra, respectively. In the second instance, we will also vary the CF parameters, in order to simulate possible magnetoelastic effects driven by the applied field. Concerning the Coulomb interactions, we consider the ratio U/J H = 5.0 and analyze the regime of intermediate electronic correlations set by U/t = 5.0 [ 73]. We also include the SOC term the amplitude of which is λ/t = 0.14, in the range of values that is expected to hold for Sr-based ruthenates [74]. It is worth pointing out that the interplay of the Coulomb and spin-orbit interactions has an important role in determining the magnetic responses. Indeed, a choice of a different regime of amplitudes for U and λ would significantly modify the local configurations contributing to the ground state and in turn alter the resulting spin and orbital response.

C. Ground-state properties: Zeeman field response and role of distortions

In this subsection, we analyze the ground-state properties by solving the model Hamiltonian in Eq. ( 4) by exact diagonalization in a physical regime that is relevant for the Sr 4 Ru 3 O 10 compound.

In Figs. 5(a1) and 5(a2) we present the field dependence of the local in-plane orbital m L and spin m S components of the total magnetic density at the flat and elongated Ru sites, upon the application of an in-plane Zeeman field. As one can notice, the magnetic response is dominated by configurations where the spin moment is larger than the orbital one (in absolute value) and the spin-orbital moments at the flat Ru sites overcome those associated with the elongated octahedra. The evolution of the magnetic moments is marked by two different regimes. In the low-field region B/t 0.03,m L and m S have opposite signs, while they are parallel oriented above this threshold. This behavior is expected due to the spin-orbit coupling that tends to form a local J = 0 singlet with J = L + S and thus contributes to have the spin and the orbital angular moments in an antialigned orientation within the ground state. The spin magnetic moment m S grows linearly with the field and promptly exhibits a larger contribution of Ru fl . These features are easily reconciled within the scheme depicted in Fig. 4. Indeed, for elongated octahedra, the existence of the easy orbital axis z makes the spin-orbital response at low fields quite stiff. In contrast, in the flat case, there is no privileged quantization axis and both the in-plane spin and angular magnetic moments have a comparable response to the applied field. We point out that, in this window of parameters, the spin and orbital moment are not fully polarized as expected when the field is much smaller than the other involved energy scales. The amplitude of the spin magnetic moment reaches the value 1μ B while for the orbital part one gets 0.4μ B and 0.3μ B , respectively.

Next, we consider the possibility to tune the CF strength to mimic an effective magnetoelastic coupling or a physical situation where a structural change occurs with the application of a magnetic field.

In the regime of high magnetic fields, there are no available ab initio data or complete information on the unit-cell atomic positions, and thus the theoretical estimates of the CF parameters are lacking. We also notice that it is not possible to extract any indirect estimate of the CF parameters from the performed neutron measurements, since they were collected in an experimental configuration which was optimized to study the magnetic structure and not aimed at determining the nuclear structure. Hence, we referred to recent neutron-scattering experiments [57], demonstrating that a significant shrinking of the unit cell along the c axis occurs concomitantly with the metamagnetic transition. On the basis of this experimental observation, we infer that the reduction of the c-axis parameter should naturally lead to an overall compression of the apical Ru-O distances. Due to the symmetry between the two Ru sites forming the cluster under examination, the variation of the Ru-O apical bond length can be simulated by an increased CF potential for the Ru site of the flat octahedral only, without loss of generality. Hence, we have selected the regime in which the crystal-field potential for the Ru site of the flat octahedra increases. In Figs. 5(b1) and 5(b2) we report the evolution of the orbital and spin contributions to the magnetic density in the case of a more pronounced compressive potential, i.e., fl /t =-0.45, while el is kept unchanged. The increased value of fl /t modifies the behavior of the response both at low and high fields. In particular, the orbital moment shows a reduction of both the flat and elongated components, with a major percentage reduction of the former which indeed is hindered by the crystal-field potential (see Fig. 4). In contrast, the slope of the spin curve for flat octahedra shows an appreciable upturn, which is indicative of a stronger spin susceptibility. Interestingly, at high fields there is an increase of the spin unbalance between the magnetic moments at the two Ru sites indicating that the relation between the spin response and the octahedral deformation can be highly nontrivial particularly concerning the amplitude of the effects. Furthermore, the specific relation between spin and orbital moments at the two inequivalent Ru sites is strongly dependent on the strength of the spin-orbit and Coulomb interactions. A decrease of these interactions will affect both qualitatively and quantitatively the response to an applied field.

D. Temperature dependence of the spin and orbital magnetic moments

To conclude this section, we present the thermal evolution of the spin and orbital densities as a function of the microscopic parameters involved in the model, by mainly focusing on the regime of moderate-to-strong Coulomb correlations, intermediate spin-orbit coupling, and high magnetic fields, where the theoretical outcomes at T = 0 exhibit the best agreement with the low-temperature experiments. The comparison is made both on the absolute amplitude of the spin-orbital moments and the degree of unbalancing between the flat and elongated layers. The study performed at finite temperature strengthens and, at the same time, enriches the scenario we propose by revealing interesting features of the layer dependent magnetic anisotropy. One of the main findings is that this effect is stable over a wide range of temperatures. On a general ground the spin and orbital densities exhibit a small amplitude change by raising the temperature. Nevertheless, we underline a distinct response of the spin and orbital component in the high-temperature regime. Concerning the spin density, the response is generally not much affected both in the flat and elongated cases, though, in a wide range of parameters, it tends to exhibit a maximum and then it gradually decreases, as expected, due to thermal fluctuations. The specific spin response is strongly related to the competing ferro-and antiferromagnetic correlations in the ground state of the small cluster and somehow overestimates the strength of the short-range correlations with a resulting smooth increase at small temperatures. In contrast, the orbital moment appears to be promptly reduced in both channels. Furthermore, the degree of the anisotropy for the flat and elongated channels stays almost constant upon temperature. Another interesting aspect emerging in the complete scan of the phase space is that, depending on the regime set by the spin-orbit coupling, one can find that the order relation among the total magnetic densities of the two layers is not preserved when thermally ramping up from low to high temperatures (e.g., above room temperature). Indeed, in the moderate-to-strong spin-orbit regime (i.e., λ/t > λ c ≈ 0.3), we have verified the existence of a characteristic temperature T , above which the moments at the elongated Ru sites carry the larger contribution within the unit cell. We have also analyzed the dependence of T upon the microscopic parameters and found that the value of T turns out to be independent of the applied field B, while it is strongly varying with the Coulomb repulsion U and the spin-orbit coupling. In this respect, we point out that this result adds another constraint to the regime of microscopic interactions that can optimally capture the spin-orbital nature of the high-field magnetic state in the three-layered ruthenate perovskite as described within the proposed model.

As a representative case of the thermal dependence of the magnetic anisotropy we report in Fig. 6 the high-field (i.e., B/t = 0.1) evolution of the spin and orbital components for an optimal set of parameters, i.e., fl /t =-0.45, el /t = 0.225,λ/t = 0.3, and keeping the Coulomb interactions unchanged with respect to the zero-temperature results of Fig. 5, i.e., U/J H = 5.0 and U/t = 5.0. The spin and orbital densities have a small amplitude change (about 10%) by raising the temperature up to T/t ∼ 0.025, which covers the experimental range of investigated temperatures (i.e., for t ∼ 400 meV, T is of the order of 110 K). Such a variation is compatible with the experimental observations and confirms the robustness of the anisotropy with respect to the temperature fluctuations.

V. CONCLUSIONS

In conclusion, by means of polarized neutron-scattering diffraction we have determined the spin and orbital character of the high-field magnetic state of Sr 4 Ru 3 O 10 . Interestingly, the spin-orbital moment distribution in the high-field state is not much affected by temperature, thus indicating that its origin should not be critically related with the ferromagnetic and the metamagnetic phenomena in Sr 4 Ru 3 O 10 .W es h o w that the layer degree of freedom can play a role in the magnetic response of the system with a layer dependent magnetic anisotropy marked by the inner layers exhibiting spin and orbital magnetic moments that are larger than the outer ones. We discuss the origin of this layer dependent magnetic anisotropy in terms of inequivalent distorted octahedra, spinorbit coupling, and local Coulomb correlations. The analysis indicates that local structural changes of the octahedra and spin-orbit cannot account by themselves for the hierarchy between spin and orbital magnetic moments at the inner and outer layers of the unit cell. It is only the cooperative effect between the spin-orbit coupling, the crystal-field potential, and the Coulomb coupling which leads to the unbalance between the spin and orbital moments in the magnetic response at the inequivalent Ru sites. In light of the performed analysis, we argue that the high-field magnetic state for an applied field along the c axis might exhibit an analogous layer dependent magnetic distribution but with an opposite trend between the inner and the outer layers. Such investigation might provide more insight into the fundamental mechanisms that control the ferromagnetic and the metamagnetic behavior in Sr 4 Ru 3 O 10 . Due to the general ingredients of the discussed mechanism, one can also suggest that similar effects can be observed in other systems where inequivalent local orbital polarizations in the presence of competing spin orbit and Coulomb interaction can lead to distinct spin-orbital responses. d † iασ being the creation operator for an electron with spin σ at the i site in the α orbital. The hopping amplitude in H kin is assumed to be t for the orbitals in the t 2g manifold. The second term is the local Coulomb interaction between t 2g electrons:

H el-el = U iα n iα↑ n iα↓ -2J H iαβ S iα • S iβ + U ′ - J H 2 × iα =β n iα n iβ + J ′ iαβ d † iα↑ d † iα↓ d iβ↑ d iβ↓ (A2)
where n iασ ,S iα are the on-site charge for spin σ and the spin operators for the α orbital, respectively. U (U ′ )i st h e intraorbital (interorbital) Coulomb repulsion, J H is the Hund coupling, and J ′ is the pair hopping term. Due to the invariance for rotations in the orbital space, the following relations hold:

U = U ′ + 2J H ,J ′ = J H .
The H CF part of the Hamiltonian H is the crystalline-field potential, controlling the symmetry lowering from the cubic to tetragonal one:

H CF = i i n ixy - 1 2
(n ixz + n iyz ) . (A3)

Positive (negative) values of are related to elongated (flat) RuO 6 octahedron along the c axis and favor the occupation in the d xz,yz (d xy ) sector, respectively. For the present investigation, we consider 1 = fl to be positive while 2 = el is negative.

Since we deal with 4d oxides, it is also important to include the spin-orbit coupling

H SO = λ i L i • S i (A4)
where λ is the spin-orbit coupling constant, L i is the total orbital momentum, and S i is the total spin of the t 2g states. Finally, H x,y in Eq. ( 4) describes the Zeeman coupling of the local angular momenta to a magnetic field B applied in the ab plane along the x,y symmetry directions, expressed in units of the Bohr magneton:

H x,y = i (L i + 2S i ) • B x,y .
(A5)

Within the presented analysis, we have neglected the in-plane anisotropy and thus x and y directions are assumed to be equivalent. Such a minimal model contains all the relevant couplings between the local spin and orbital degrees through the spin orbit and the Coulomb interaction as well as the possibility for having charge fluctuations in the t 2g via the kinetic term that links the two atoms.

FIG. 1 .

 1 FIG. 1. Schematic of the crystal structure of Sr 4 Ru 3 O 10 showing the outer and inner RuO layers in the unit cells along the c axis.

FIG. 2 .

 2 FIG. 2. Temperature dependence of the flipping ratio R, diminished by one, of a few significant Bragg reflections in Sr 4 Ru 3 O 10 .

FIG. 3 .

 3 FIG. 3. Spin densities projected onto the (a + b,c) plane, at 2 K (left panel) and 115 K (right panel). Both densities are represented on the same scale, confirming the higher magnetization at low temperature. The middle panel shows the projection of the structure onto the same plane.

FIG. 4 .

 4 FIG. 4. Schematic representation of the mechanisms which activate/suppress the orbital angular momentum components in the absence of an in-plane applied magnetic field, in the case of a flat octahedron (upper panel) and an elongated octahedron (lower panel). Middle panels show representative local configurations that mark the ground state. Right panels describe the orbital polarized configurations that are favored or inhibited with respect to the the crystal-field potential and the Coulomb interaction.

FIG. 5 .

 5 FIG. 5. Evolution of the orbital (a1 and b1) and spin (a2 and b2) components of the magnetic density upon an in-plane applied Zeeman field, for two different values of the compressive crystal-field potential, i.e., (a) fl /t =-0.3and(b) fl /t =-0.45.

FIG. 6 .

 6 FIG. 6. Thermal evolution of the (a) spin and (b) orbital components of the magnetic density for an in-plane applied Zeeman field B/t = 0.1, spin-orbit coupling λ/t = 0.3, and values of the crystal-field potential given by fl /t =-0.45 and el /t = 0.225.

ACKNOWLEDGMENTS

We acknowledge insightful discussions and valuable support during the experiments from Paul Steffens and Laurent Chapon.

APPENDIX

The model Hamiltonian used for the theoretical analysis reads


domain: spi phys

text:
Maxime Duquesnoy
email: maxime.duquesnoy@mirsense.com

Raphaël Lévy

Jean-Michel Melkonian

Guillaume Aoust

Myriam Raybaut

Antoine Godard

Fast and stable photoacoustic gas spectroscopy by frequency tracking of a quartz tuning fork in closed loop detection

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

Trace gas detection can find application in assessment of air quality, detection of pollutants or hazardous gases, control of exhaust gases, monitoring of industrial processes, etc. However, the available gas sensors on the market are either, very sensitive but bulky and expensive, or very compact but with a lack of sensitivity or selectivity. This is also true for devices using laser detection, even though they bring advantages in terms of accuracy, selectivity, speed, and low drift measurements.

Photoacoustic spectroscopy is a technique that could create a compromise between size, sensitivity and cost and allows a simultaneous detection of multiple species. It consists in the excitation of molecules by a modulated laser source, creating a periodical heating of the medium. This heating induces acoustic waves that can be detected by a mechanical transducer, such as a microphone membrane, a cantilever or a tuning fork.

Quartz Enhanced Photoacoustic Spectroscopy (QEPAS) is a particular implementation of photoacoustic spectroscopy in which a quartz tuning fork converts the acoustic waves into a piezoelectric signal. QEPAS is a recent technique which appeared in 2002 [START_REF] Kosterev | Quartz-enhanced photoacoustic spectroscopy[END_REF]. Compared to the other photoacoustic techniques, QEPAS exhibits a better isolation to acoustic and vibrational background. Nonetheless, the use of high quality factor tuning forks (Q > 8000 in air) makes the measurements slow (a few seconds), and the sensor even more sensitive to temperature induced-drifts leading to measurement biases or even signal dropout. In order to circumvent these problems new detection techniques arose such as Beat Frequency QEPAS [START_REF] Wu | Fast and calibration-free trace-gas monitoring based on beat frequency quartz-enhanced photoacoustic spectroscopy[END_REF] or frequency tracking of the tuning fork [START_REF] Rousseau | Quartz Tuning Fork Resonance Tracking and application in Quartz Enhanced Photoacoustics Spectroscopy[END_REF][START_REF] Mordmueller | QEPAS with electrical co-excitation for photoacoustic measurements in fluctuating background gases[END_REF].

We already presented a new detection principle [START_REF] Levy | New signal processing for fast and precise QEPAS measurements[END_REF] allowing to increase the measurement rate and stability. This method relies on the use of frequency counting instead of classical lock-in detection. In this paper we will present a further study of our detection method taking into account improvements we have identified.

Principle of operation

Our measurement method relies on the fact that a force applied to a self-sustained resonator induces a frequency shift which is proportional to that force.

The tuning fork vibration is maintained at resonance by means of an electrical oscillator (see Fig. 1). When the laser is tuned to a gas absorption line, a photoacoustic force is created and applied to the inner surfaces of the beams of the tuning fork with the appropriate phase compared to the oscillator generated force, inducing a frequency shift in the oscillator loop. The technique is linear so that the frequency shift is directly proportional to the gas concentration. This technique also allows differential measurements for the correction of drifts and cancellation of background noises. A proof of principle was presented in [START_REF] Levy | New signal processing for fast and precise QEPAS measurements[END_REF] (see Fig. 2). By exciting the resonator with a custom analogical electrical loop we demonstrated that the method enables differential measurements while tracking the tuning fork resonance frequency, consequently improving the sensor stability over time. In addition, placing the tuning fork at resonance allows making measurements faster, passing from several seconds for classic detection down to 50 ms for our method. However, the sensitivity of the system was NNEA = 3.7 x 10 -7 W.cm -1 .Hz -1/2 which is one order of magnitude worse than the classical method with the same tuning fork [START_REF] Duquesnoy | Quartz enhanced photoacoustic spectroscopy based on a custom quartz tuning fork[END_REF]. In order to improve our detection method, we identified several factors that could lead to an improvement of sensitivity or speed of measurement as well as accuracy. The electrical excitation force of the resonator has to be reduced, what we achieved by modifying the tuning fork electrode pattern and using a numerical electrical oscillator loop based on FPGA (Field Programmable Gate Arrays). Indeed, the excitation electrode surface was minimized while keeping a sufficient excitation force (see Fig. 3). By doing so, we increased the excitation electrode resistance by a factor 5.

First results and future improvements

Fig. 3. Modifications of electrode pattern on two custom tuning forks.

Also, passing from an analogical oscillator loop to a numerical one allows reducing consequently the excitation voltage of the tuning fork which we hope will permit to equal the sensitivity of the classical detection method. By using a commercial lock-in detection HF2LI (Zurich Instruments), we propose to analyze the ultimate sensitivity of our sensor on C 2 H 2 in different configurations as well as the possibility to reduce measurement time.

Fast

  and stable photoacoustic gas spectroscopy by frequency tracking of a quartz tuning fork in closed loop detection Maxime Duquesnoy, Raphaël Lévy, Jean-Michel Melkonian, Guillaume Aoust, Myriam Raybaut, Antoine Godard To cite this version: Maxime Duquesnoy, Raphaël Lévy, Jean-Michel Melkonian, Guillaume Aoust, Myriam Raybaut, et al.. Fast and stable photoacoustic gas spectroscopy by frequency tracking of a quartz tuning fork in closed loop detection. Imaging and Applied Optics. 3D Image Acquisition and Display: Technology, Perception and Applications, Jun 2020, Washington, United States. pp.JTu2A.16, 10.1364/3D.2020.JTu2A.16. hal-03152477

Fig. 1 .

 1 Fig. 1. Schematic of the method principle.

Fig. 2 .

 2 Fig. 2. First measurements made with our method. Measurement of frequency shifts for two different phases, with a frequency drift (left). Differential frequency shift with cancellation of the drift over time (right).