M Moutaouekkil

Abdelkrim Talbi
email: abdelkrim.talbi@centralelille.fr

E H El Boudouti

Omar Elmazria

Bahram Djafari-Rouhani

Philippe Pernod

Olivier Bou Matar

Acoustic isolation of disc shape modes using periodic corrugated plate based phononic crystal

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

Introduction:

The Phononic crystals are created by periodic arrays of elastic structures displaying a strong contrast in their elastic properties and density. These materials can be arranged into one-dimensional (1D), 2D and 3D structures. The ability to control the propagation of elastic waves with such composite materials has attracted a considerable attention during the last two decades from science and technology points of view [START_REF] Deymier | Acoustic Metamaterials and Phononic Crystals[END_REF]. Similarly to photonic crystals, the interest in phononic crystals has been generated by their unique properties such as the formation of band-gaps, near zero group velocity, and anomalous dispersion (negative refraction). These properties make phononic crystals a viable choice for use in vibration and noise reduction applications [START_REF] Kosevich | [END_REF]3] as well as in the design and implementation of components for Radio Frequency Micro-Electro-Mechanical Systems (RF MEMS) including filters, resonators, and advanced signal processing functions [4][5][6][7][8][9][10][11][12]. The existence of band-gaps in electroacoustic devices combined with phononic structures has been demonstrated both theoretically and experimentally [4][5][6][9][10][11][12]. The control of propagating waves can be achieved by modifying portions of the phononic structure to induce a line or point defect state. The acoustic energy with frequencies in the band gaps may be localized in the defect and therefore the propagation can be engineered. In the case of locally resonant structural unit cells, the phononic crystals can exhibit band-gaps with a lattice constant smaller than the relevant wavelength [8][9][10][11][13][14][15][16]. The eigen-frequencies of the localized modes generally depend on the precise geometrical properties (such as size or shape) and the composition of the supporting structure. Many authors have studied the defect states in such phononic crystals and demonstrated their usefulness as waveguides, filters, and cavity modes [14][15][16]. In this study, we introduce a new design of cavity resonator design based on 1D phononic crystal structure. The structure is made of a corrugated AlN thin membrane; the central micro-strip line supports periodic gold disc shaped thin layer (Fig. 3). The structure is completely different to cavity designs presented in most previous works where the cavity is obtained by removing a portion of the crystal or by changing the geometric parameters of the unit cell. In our case, the phononic crystal design remains unchanged and a disc shaped resonator was introduced as a defect. The design combines the advantages of: i) micro-machined electroacoustic devices based on the S0 Lamb wave mode. ii) 1D phononic crystal that provides the suppression of mechanical energy leakage from the disc resonator to the supporting structure. iii) disc shape resonator structure that supports radial contour modes like whispering gallery and breathing modes characterized by their high Q factor owing to their in-plane modal vibration. The proposed design is based on materials of practical interest in electroacoustic devices technology. The membrane is made of AlN thin films that has been considered in recent years as a viable technology for the fabrication of radio frequency passive components for use in telecommunication applications. The choice of the S0 Lamb wave mode to transduce the mechanical resonance of the disc shape resonator is motivated by its excellent characteristics in the case of AlN materials including smooth dispersion curves, high acoustic wave velocity up to 10 000 m/s and relatively high electro-mechanical coupling coefficient up to 3.5% [17][START_REF] Soltani | IEEE International Ultrasonics Symposium[END_REF].

Figure 1(a) shows a schematic design of a phononic structure unit cell that contains a micro-strip deposited on a piezoelectric membrane. The geometrical design parameters are defined as follows: a is the lattice constant, e is the thickness of the AlN membrane, and (h1, w) are respectively the (height, width) of AlN. The numerical results including dispersion and transmission curves are calculated by the finite element method (FEM) using Comsol Multiphysics software. For the dispersion curves, the Bloch periodic boundary conditions were applied to the unit cell shown in Fig. 1(a). The dispersion curves will be presented in terms of the reduced frequency (f.a) versus the Bloch wave-vector inside the first Brillouin zone along X direction (Fig. 2(a)), where f and a represent the frequency and lattice constant respectively. For the transmission spectra, a finite system along the x direction containing five unit cells and infinite along the y-direction is considered (Fig. 1(b)). Perfectly Matched Layers (PMLs), which can absorb waves and avoid reflection, are applied on each side of the structure along the finite-length direction. The incident wave is a S0 Lamb wave of the plate launched by applying a prescribed harmonic acceleration ax in the (y,z) plane at the left side of the crystal and propagating along the x axis. The transmitted acceleration value is detected and recorded in the far field on the right side of the crystal. The transmission coefficient is normalized to the acceleration field propagating in the homogeneous plate.

We first calculate the band structure of a phononic crystal composed of AlN membrane and only micro-strips. Figure 2(a) shows the calculated band structure along the X direction. The geometrical parameters are chosen in order to obtain wide band-gaps (i.e., e/a = 0.22, h1/a = 0.32, w/a = 0.68) and to be compatible with standard micromachining process for operation frequency in the GHz range. We propose now to use the property cited above for the design of a new kind of resonator cavity structure. The cavity design is shown in Fig. 3(a). The super cell is composed of a periodic structure that contains one line of AlN micro-strip with a disc shape layer surrounded from each side by two lines of AlN micro-strip without disc. In this section, we will keep fixed the membrane and AlN micro-strip thicknesses (e/a = 0.22, h1/a = 0.32 and width w/a = 0.68) and we will add a periodic disc cap layer made of gold on the top of the central micro-strip. The cap layer is characterized by its height h2 = 0.07a and radius r1 = 0.16a. Our goal consists in considering the effect of a thin layer presenting a strong contrast in elastic and density properties on the evolution of band-diagrams and transmission spectra. Figure 4(a) shows the band structure of the phononic crystal computed using the super-cell model. First, we can notice that the two band-gaps observed for the case h2 = 0 (Fig. 2(a)) still exist with approximately the same width. Secondly, Fig. 4(a) shows the existence of some nearly flat branches (labeled 1, 2 and 3) inside the upper band gap. The mode labeled 1 corresponds to the bending mode as shown by the total displacement field distribution (Fig. 4(c)). The behavior of the displacement field distribution for the modes labeled 2 and 3 is similar to the whispering gallery modes (WGMs) with quadrupolar shape (Fig. 4(c)). Figure 4(a) clearly shows that the three modes are mainly confined in the disc shaped layer enabling the possibility to engineer the properties of these kind of modes by tuning the geometrical parameters of the latter including thickness, radius, and shape. Fig. 4(b) shows the transmission coefficient as a function of the reduced frequency for a phononic crystal strip composed of five unit cells (Fig. 3(b)). This figure clearly shows two transmission dips in the frequency domains [1560-2200 m/s], and [3500-5120 m/s] which are consistent with the band-gaps calculated from the band structure (Fig. 4(a)). We can also notice the existence of two peaks located at 3418 m/s and 4391 m/s respectively. The frequencies of these peaks are in accordance with the flat modes labeled 1, 2 in Fig. 4(b). However, due to its symmetry, the flat mode labeled 3 vibrating along the [110] direction (Fig. 4(c)) does not present any coupling with the S0 mode launched in the x direction, which explains its absence in the transmission spectrum (Fig. 4(b)). Also, we studied the quality factor of the mode labeled 2, in the cavity design, as a function of the phononic crystal size. The size is defined as the number of disc-free lines surrounding the central micro-strip with Au disc shaped layer. As we know, the actual Q factor is based on several energy loss mechanisms, such as thermo-elastic damping, surface loss, and anchor loss. In this study, we consider only the Q factor related to mechanical energy leakage (support loss) from the disc resonator to the supporting structure that serves for us as a reference for the design of the confined radial contour modes. The Q factor is calculated using the ratio between the central frequency and the full width at half maximum of the transmission peaks. Figure 5 shows the results for one and two microstrips surrounding the cavity layer. First, we can notice that as the number of phononic crystal layers increases, the location of the resonant frequency peak remains unchanged. Secondly, we can notice that the quality factor drastically increases by increasing the phononic crystal size giving rise to an efficient acoustic isolation as it is described in the displacement field displayed in Fig. 5(b). In comparison to previous cavity designs reported in the literature and using similar calculation method [5,14,16], the proposed structure enables to achieve the much higher Q factor with minimal phononic crystal size.

Conclusion:

We have proposed an alternative and useful platform to obtain highly confined disc shape radial contour modes, characterized by their high Q factor and surface mode nature. The structure is composed of a corrugated piezoelectric membrane and disc shape thin films deposited on the micro-strip surface. This work can be useful for designing advanced electroacoustic waves devices exhibiting performances that may surpass their conventional micro/nano electromechanical systems for sensing applications.

Fig. 1

 1 Fig. 1 (a) Schematic representation of the unit cell. (b) Schematic setting used for the computation of the transmission through a phononic crystal containing five unit cells.

Figure 2 (

 2 b) shows the corresponding normalized transmission spectrum along the X direction.

Fig. 2

 2 Fig. 2 (a) Band structure of a phononic crystal composed of corrugated AlN membrane. (b) Transmission spectrum for the S0 mode through a phononic crystal containing five unit cells.

Figure 2 (

 2 Figure2(a) shows two band gaps: an upper band-gap (the widest) located in the frequency range 3500 m/s < f a < 5100 m/s where the dispersion curves fold back at the limit of the Brillouin zone (Bragg condition). The lower band-gap appears in the frequency range 1500 m/s < f a < 2300 m/s (Fig.2(a)). The opening of this gap results from the crossing of two Lamb mode dispersion curves, namely the first crossing between A0 and S0 modes. As indicated in Fig.2(b) strong dips are observed in the transmission spectrum and correspond very well to the stop band frequencies shown in Fig.2(a).We propose now to use the property cited above for the design of a new kind of resonator cavity structure. The cavity design is shown in Fig.3(a). The super cell is composed of a periodic structure that contains one line of AlN micro-strip with a disc shape layer surrounded from each side by two lines of AlN micro-strip without disc. In this section, we will keep fixed the membrane and AlN micro-strip thicknesses (e/a = 0.22, h1/a =

Fig. 3

 3 Fig. 3 (a) Schematic representation of a supercell. (b) Schematic setting used for the computation of the transmission through a phononic crystal containing five unit cells.

Fig. 4

 4 Fig. 4 (a) Band of a phononic crystal constituted of a periodic repetition of a super cell (b) Transmission spectrum for the S0 mode through a phononic crystal containing five unit cells. (c)Total displacement field distribution for flat modes labeled 1, 2 and 3 in (a).

Fig. 5

 5 Fig. 5 (a) Evolution of the quality factor as a function of the size of the structure (b) Total displacement field distribution for the flat modes labeled 2 at  point in Fig4(a).

Acknowledgments: We acknowledge support from the French "Agence Nationale de la Recherche" through the project grant N ° ANR-12-BS09-0015-01.


Norbert Mercier
email: norbert.mercier@u-bordeaux-montaigne.fr

Loïc Martin

Sebastian Kreutzer

Virginie Moineau

Dominique Cliquet

Dating the palaeolithic footprints of 'Le Rozel' (Normandy, France)

Keywords: OSL dating, Le Rozel, Neandertal, footprints

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.

Introduction

The archaeological site of 'Le Rozel', located on the western part of the Cotentin peninsula (Normandy, France; Fig. 1) exhibits a long series of Mousterian occupations from the Upper Pleistocene period. The site was discovered in the 1960s and its importance immediately recognised (Scuvée, 1967(Scuvée, , 1969)). However, detailed investigations were not undertaken before the 1980s (Scuvée and Vérague, 1984). They revealed that the site preserved a long stratigraphic sequence which constitutes a valuable archive for reconstructing Upper Pleistocene environments in this part of Europe (Van Vliet-Lanoë et al., 2006). For that reason, in 2000, a series of sediment samples originating from the lower part of the stratigraphic sequence had been dated using multi-grain aliquots of quartz [START_REF] Folz | La luminescence stimulée optiquement du quartz : développements méthodologiques et applications à la datation de séquences du Pléistocène supérieur du Nord-Ouest de la France[END_REF]. These first results indicated that the lower part of the sequence covers the Marine Isotope Stage (MIS) 5 [START_REF] Folz | La luminescence stimulée optiquement du quartz : développements méthodologiques et applications à la datation de séquences du Pléistocène supérieur du Nord-Ouest de la France[END_REF]Fig. 1). In 2012, another large excavation under the supervision of D. Cliquet discovered numerous footprints in association with flint artefacts and fossilised remains of animals [START_REF] Cliquet | Néandertal au Rozel[END_REF].

Such artefacts are typical for the Middle Palaeolithic period and believed having been produced by Neanderthals since, during this period, modern humans (i.e. Homo sapiens) were not supposed to live in Western Europe. Within five succeeding field seasons, a total number of 450 prints (including handprints) had been identified and studied. Today the site constitutes the largest known series of palaeolithic human prints [START_REF] Cliquet | Néandertal au Rozel[END_REF]. The importance of this discovery led to a new dating study focused on the archaeological layers containing the prints, for which the results are presented here. Conversely to the previous OSL study, the singlegrain technique has been applied to quartz grains, and comparisons with K-feldspars ages were systematically undertaken for the sediments sampled.

Site stratigraphy and samples location

Figure 2 shows a synthetic profile revealing the stratigraphic sequence. At the base, the sequence (Unit D1) is composed of large rounded pebbles which are interpreted as the beach remnants formed during MIS 5e (Van Vliet-Lanoë et al., 2006). The upper part of unit D1 as well as the overlying units D2 and D3 are composed of sands or silt sediments. These units are interpreted as indicators of past climatic variations characterising the transitions from MIS 5d to MIS 5a (ca. 109-82 ka; cf. MIS scale by [START_REF] Lisiecki | A Pliocene-Pleistocene stack of 57 globally distributed benthic δ 18 O records[END_REF]. Intercalated small solifluction layers (D3a1-D3c) have been identified in Unit D3 which also contains several archaeological layers rich in lithic artefacts, animal bones and footprints. To account for its archaeological relevance, our dating study focused on this unit (D3). In total six sediment samples were taken within this unit. All our samples (black dots on Fig. 2) are located in a stratigraphical higher position than the samples OSL-dated in 2000 (open dots on Fig. 2: [START_REF] Folz | La luminescence stimulée optiquement du quartz : développements méthodologiques et applications à la datation de séquences du Pléistocène supérieur du Nord-Ouest de la France[END_REF], and should thus be younger.

Sample preparation and dosimetry

Sample preparation

Samples were prepared under orange, subdued, light conditions. The sediment was split into two parts: 100 g were kept for high resolution gamma-ray spectrometry analysis while the other fraction was prepared using conventional sample preparation methods for luminescence dating (e.g., [START_REF] Preusser | Luminescence dating: basics, methods and applications[END_REF]. Granulometric analyses of our samples done with sieves suggested a great homogeneity of all samples (their massic fractions were very similar: ca. 5 % for <200 µm; ca. 20% for 200-250 µm and ca. 75% for >250 µm); thus, they all consisted mainly of fine and medium sand. The 200-250 µm fraction was finally chosen for the sample preparation. After sieving, this fraction was treated with HCl (10%), then H 2 O 2 (30%) and a part of it was then treated with HF (40%, 40 min) to dissolve feldspar grains and then rinsed in HCl (10%) and demineralised water. The etched fraction was later used for OSL quartz. The other part was kept untreated and later used for IRSL measurements on feldspar grains. For this series of analyses, feldspar grains were extracted from the untreated HF fraction using heavy liquids at a density of 2.56 g/cm 3 .

Field dosimetry

On site, in situ gamma-ray measurements were performed. Therefore, a LaBr gamma probe (connected to a Canberra Inspector 1000 electronic handheld), calibrated using the threshold technique [START_REF] Mercier | Field gamma dose-rate measurement with a NaI(Tl) detector: re-evaluation of the "threshold" technique[END_REF] was used. The holes left in the profile by the sampling have been used after they have been slightly enlarged to allow the insertion of the probe. The measured gamma dose-rates are given in Table 1, and range from 226-364 µGy/a. The cosmic dose-rate was not measured on site but estimated according to the depth of the sample position [START_REF] Prescott | Cosmic ray contributions to dose rates for luminescence and ESR dating: large depths and long-term time variations[END_REF]; its value was estimated to 150±30 µGy/a.

Laboratory dosimetry

High resolution low-level gamma-ray spectrometry was performed on the preserved fractions after the sediments were dried and stored in sealed plastic boxes for at least three weeks. U, Th, K contents were found to be similar for all samples (Table 1), ranging from 0.39-0.48 ppm for U, from 1.02-1.61 ppm for Th, and from 0.66-0.83 % for K. No radioactive disequilibria were detected in the U-series chain. The measured water contents ranged from 8-12% and a mean value of 10% was taken for the dose rate calculation. The gamma dose-rates determined from the U, Th, K contents give values close to those measured on site with the LaBr probe, indicating that the sediments are homogeneous in terms of radioelements distribution at a scale of at least ten of centimetres. The U, Th, K data also allowed to compute the infinite matrix beta dose-rate of each sample (Table 1) using the dose rate conversion factors by [START_REF] Guérin | Dose-rate conversion factors: update[END_REF], and the attenuation factors by [START_REF] Guérin | On the use of the infinite matrix assumption and associated concepts: a critical review[END_REF]. However, such calculation assumes that all radioelements are homogeneously distributed in the sediment at a scale much lower than the range of the particles depositing the dose, i.e. here 2-3 mm for beta-particles. This assumption is only partly true for our samples. The sediments contain feldspar grains which may have a high Kcontent, acting as hot-spots, especially if their proportion in mass is low [START_REF] Guérin | On the use of the infinite matrix assumption and associated concepts: a critical review[END_REF]. Moreover, the granulometric distribution of our sediments which is characterised by a large fraction above 250 µm, may also affect the beta dose rate received by the grains used for the D e estimation. To tackle these impacts, grains from sample S1-2 (from the fraction untreated with HF) were analysed with scanning electron microscopy (SEM): the proportion of K-feldspar grains was determined and their internal K-content measured. An averaged K-content of 10±2% was obtained for the investigated grains. To better assess the impact of these feldspathic grains on the beta dose rate, in a second step a model of the sediment was created with the software DosiVox (Martin et al., 2015a). The model considers the granulometric distribution of the sample, the proportion of feldspar grains as well as their mean K-content.

The numerical simulation by DosiVox indicates that quartz grains with a grain size of 200 µm have been exposed to a beta dose-rate (due to the found K content), which is on average ca. 7% higher than the value computed by the infinite matrix assumption. Nevertheless, taking into account the contribution of U and Th to the total beta dose rate received by these quartz grains, the resulting total beta dose rate represents already 59% of the total dose rate (including gamma and cosmic doses). Thus, we deduced that the difference in dose rates between the infinite matrix model (in which the radioelements are homogeneously distributed, exactly as they would be if the sediment were a liquid) and a model in which the feldspar grains (rich in K in comparison to the sediment) are explicitly represented, does not exceed 4%. However, the simulation also shows that a small proportion of grains received a beta dose rate much higher (almost two times higher) than the mean value (a similar result had already been obtained by Martin et al. (2015b) for a series of sediment samples). The heterogeneity in the beta dose rates received by the 200 µm grains may then contribute significantly to the over-dispersion characterising the D e distribution of this sample. Nevertheless, this conclusion is not necessarily valid for to other samples. The result depends on the proportion of feldspathic grains and on the granulometric distribution and, is thus sample dependent.

Luminescence measurements

Equipment

Both multi-grains and single-grain luminescence analyses were performed. All multi-grain measurements were carried out on a Freiberg Instruments lexsyg SMART reader [START_REF] Richter | Lexsyg smart -a luminescence detection system[END_REF]. The reader was equipped with an Hamamatsu H7360-02 photomultiplier tube and a Sr-90/Y-90 -source delivering ca. 11 Gy/min to 90-180 µm quartz grains (Risø calibration quartz, batches 90 and 106). For quartz, green LEDs (525 ∆ 25 nm) delivering a maximum power density of 70 mW/cm 2 were used and the luminescence signal in the UV was detected through a Schott BG-3 (3 mm) in conjunction with a Chroma BP365/50 EX interference filter. Feldspars were measured on the same machine using IR stimulation (850 ∆ 3 nm, max. 300 mW/cm 2 ) and the signal was detected in the blue-violet range through a Schott BG-39 (3 mm) in combination with an AHF BrightLine HC 414/46 interference filter.

For quartz single-grain measurements, a Risø TL/OSL DA-20 reader [START_REF] Bøtter-Jensen | Advances in luminescence instrument systems[END_REF][START_REF] Duller | Distinguishing quartz and feldspar in single grain luminescence measurements[END_REF] was used. This device was equipped for stimulation with a 10 mW Nd:YVO 4 solid-state diode-pumped laser emitting at 532 nm (max. 103 mW/cm 2 ). The signal was detected through a 7.5 mm Hoya U-340 filter in front of an EMI 9235QB15 photomultiplier tube. The inbuilt Sr-90/Y-90 -source allowed irradiations with a dose rate of ca. 8.3 Gy/min to 200-250µm quartz grains.

Quartz measurements

Preliminary tests were carried out on multi-grain aliquots. It was first checked that the quartz extracts (200-250µm fractions) did not give significant signals when stimulated with IR (measured IR/OSL ratio lower than 2%). Moreover, comparisons of the OSL signals from our samples and from the Risø calibration quartz indicated that the fast component was dominant. Dose recovery tests (DRT) were then performed using different preheat temperatures on a series of aliquots of sample S3. Artificial bleaching was carried out with a Hönle Sol500 solar simulator. For measurements, a single-aliquot and regenerative dose (SAR) protocol [START_REF] Murray | Luminescence dating of quartz using an improved singlealiquot regenerative-dose protocol[END_REF][START_REF] Duller | Distinguishing quartz and feldspar in single grain luminescence measurements[END_REF] was used. The measurement sequence included a systematic measure of thermal transfer, recycling ratio and a IR depletion test included at the single grain level [START_REF] Duller | Distinguishing quartz and feldspar in single grain luminescence measurements[END_REF]. The data were analysed with Analyst [START_REF] Duller | The Analyst software package for luminescence data: overview and recent improvements[END_REF]v4.31).

The DRT results are shown on Fig. 3 indicating no trend with increasing temperature, but a plateau over the investigated temperature range. Finally, a preheat temperature of 260°C for 10 s, and a cutheat temperature of 160°C for 0 s were chosen for subsequent measurements. ) to 47% (sample S1-2) but the Abanico plots [START_REF] Dietze | The abanico plot: visualising chronometric data with individual standard errors[END_REF] do not show any trend which might indicate poor bleaching of the selected quartz grains, whatever is the OD value (Fig. 4). To support this observation, the Finite Mixture Model was applied to samples S1-2 and S3 using the function calc_FiniteMixture (Burow, 2017), with a sigma-b value of 0.14 (similar to the OD value determined with the DRT test). The results indicate that the De distributions are best represented by 2 components with one component gathering together 69% (sample S1-2) and 70% (sample S3) of the population. But for sample S1-2, the main component is the first one, while for sample S3, it is the second. This seems indicate that partial bleaching is not the source of scatter of the individual De values.

The study by [START_REF] Guérin | Testing the accuracy of a single grain OSL Bayesian central dose model with known-age samples[END_REF] suggested that the CAM under-estimates the mean D e and also returns a D e -error which is not comparable to the error associated with the dose rate value [START_REF] Guérin | How confident are we in the chronology of the transition between Howieson's Poort and Still Bay[END_REF]. These authors estimated that the difference between the CAM and the Bayesian model ('baSAR') by Combès et al. (2015), which is supposed to overcome the inherent problems affecting the CAM and assumes a Cauchy distribution of the individual D e values instead of a log-normal distribution for the CAM, was significant in the temporal range of 4-46 ka. For the samples from Le Rozel, we then computed D e values with the baSAR model, in using the R (R Core Team, 2017) function analyse_baSAR()proposed by [START_REF] Mercier | Bayesian statistics analysis in the R Luminescence package : the analyse_baSAR function[END_REF] and available in the 'Luminescence' package (Kreutzer et al., 2012;[START_REF] Kreutzer | Luminescence: Comprehensive Luminescence Dating Data Analysis[END_REF]. To compute the central dose (cf. Combès et al., 2015;[START_REF] Mercier | Bayesian statistics analysis in the R Luminescence package : the analyse_baSAR function[END_REF], we applied a single saturating exponential dose response curve and did not include the recycling points in the calculation. Similar conditions were chosen for D e values which had been used for calculating the CAM. In the temporal range covers by our study (between 70 ka to 90 ka), the comparison of the two sets of results indicates that the baSAR D e values are between 4 % to 17% higher than the CAM D e values (Table 2). Since the baSAR model has been shown to be less sensitive to outliers than the CAM [START_REF] Guérin | Testing the accuracy of a single grain OSL Bayesian central dose model with known-age samples[END_REF], we preferred the D e values derived from the baSAR model and their associated uncertainties to compute the quartz OSL ages given in Table 2.

Feldspars measurements

Since feldspar grains were also present in our sediment samples, we tested the post IR IRSL approach by Thomsen et al

Feldspars -tests

The bleachability of the pIRIR 225 signal was evaluated by exposing aliquots of sample S3 (natural dose ca. 200 Gy) to our solar simulator for durations of {0, 1, 5, 22,48} h. This device provides an intensity of ~800 W/m 2 which is six times higher than the natural sunlight. In our case, after 22 hours, the natural dose had been reduced by 98.5%. The residual dose was estimated to ca. 2 Gy (Fig. 5). After 48 hours, the dose reduction reached >99%. These results indicate that the pIRIR 225 signal can be well bleached by solar light exposure, but these experiments do not inform on potential residual doses at the time of deposition. Consequently, we did not subtract any residual dose when calculating ages from the pIRIR data.

Fading tests were performed with the same sample. Five aliquots were bleached for 48 hours with the solar simulator, before being irradiated with 150 Gy. Prompt preheat and measurements following [START_REF] Auclair | Measurement of anomalous fading for feldspar IRSL using SAR[END_REF] were applied. The pIRIR 225 signals were measured after different delays (0, 24, 300 h). The fading rate, normalized to 2 days (g 2d ) was 2.36±0.6 %. The large relative uncertainty (~25%) reflects the apparent different behaviours of the aliquots. Fig. 6 shows for 4 out of 5 aliquots a significant decrease of the normalised pIRIR 225 signal if one compares the 24h and 300h points to the 0h point, but a similar decrease (expected on a logarithm scale) is not visible between the 24h and 300h points. The reason of this behaviour was not further investigated but might be related to a not corrected sensitivity change or another process as a short-term fading. Only for one aliquot the normalised signals followed a logarithmic scale as expected.

Feldspars -Dose recovery test and equivalent doses

A dose recovery test was done with five aliquots of sample S3 bleached for 48 h with the solar simulator and irradiated with 183 Gy. A SAR pIRIR protocol similar to [START_REF] Buylaert | Testing the potential of an elevated temperature IRSL signal from K-feldspar[END_REF] was used for estimating the D e . The sequence was composed of seven cycles with regenerative doses of {45, 153, 275, 450, 0, 45} Gy and, as for the previous tests performed with feldspars, used a test dose of 15 Gy and all preheats were set at 250°C for 60s. The dose recovery test ratio was close to unity (0.96±0.05) indicating that this protocol allows recovering a known dose similar in size to the expected naturally absorbed dose. For each sample, this protocol was applied to a series of 20 aliquots (except sample S3 for which 26 aliquots were measured). Fig. 7 shows a typical dose-response curve of the normalised pIRIR 225 signal. For the six samples, the mean D e values are similar, ranging from ~143 Gy to ~152 Gy (Table 2). Table 2 also contains mean D e values calculated after the dose rate correction (DRC) method [START_REF] Lamothe | Towards a prediction of longterm anomalous fading of feldspar IRSL[END_REF] has been applied to individual aliquots, considering the measured fading rate (g 2d =2.36±0.6). Fading-corrected mean D e values are given in Table 2 and are on average 36% higher than the uncorrected values. This large difference is caused mainly by the fading rate which leads to a significant increase of the Ln/Tn ratio, and to a less extent by the curvature of the growth curve.

Ages calculation and discussion

Ages were calculated both for quartz and feldspars data (Table 2). For quartz, ages range from 70 ± 10 ka to 86 ± 9 ka (MIS 4 to MIS 5c) but do not exactly follow the stratigraphic order. However, considering the associated errors, they are all indistinguishable. This relatively low scatter was expected since all samples have been taken in a unit with a presumably high sedimentation rate, otherwise, the footprints would have not been preserved. These new OSL ages closely associated with the footprints are younger than the results obtained in 2000 for sediment samples taken lower in the stratigraphy (Fig. 2), and which gave ages concordant with MIS 5, as expected. Our data also indicate that large OD values do not necessarily characterise poorly bleached grains: for instance, sample S1-2 (OD value of 47±6%) gives an OSL age in good agreement with the other samples exhibiting lower OD values. We thus conclude that micro-dosimetric heterogeneities account for a part of the observed OD values, as demonstrated by the numerical simulation using DosiVox, and that this particular contribution is sample dependent. By contrast, the feldspar ages (Table 2) are older than the quartz ages, ranging from 114 ± 11 ka to 126 ± 12 ka, but five out of six of them are in the range 122 ± 12 ka to 126 ± 12 ka. These ages are likely over-estimated and consequently too old in comparison of the stratigraphical evidence, in particular, the presence of the Eemian deposit (MIS 5e) in unit D1. Two reasons may explain this over-estimation: (1) No residual dose was subtracted and even though the measured pIRIR 225 signal proved itself as well bleachable in the laboratory, it might be higher in nature (insufficient bleaching). ( 2) The fading correction used a rate which might not be representative of the true fading affecting our samples. More work (single grain measurements on feldspars, long-term fading measurements) will be necessary to explore these uncontrolled parameters.

Conclusion

New luminescence dating results were presented for the archaeological site 'Le Rozel'. We applied single-grain OSL on quartz separates and pIRIR 225 measurements on K-feldspar extracts. Despite the encountered inconsistencies between OSL quartz and pIRIR 225 ages, the OSL ages calculated in applying the baSAR model to individual single-grain data were found in agreement with the previously obtained dating results as well as with the sedimentological data. It believes that poor bleaching of K-feldspar grains and the use of an inappropriate fading rate may explain the large over-estimation of the pIRIR results. We also noticed that high OD values -up to 47% -obtained when measuring single-grains of quartz Bleaching was with a Hönle SOL500 solar simulator.

Figure and table captions:

Figure 6: Fading test results. The signal loss was measured using the prompt pIRIR 225 signal and delay times of 24 h and 300 h. Table 1: Radioactive (U, Th, K) contents of the sediment samples deduced from spectrometric analyses. The annual dose rate includes a cosmic contribution of 150±30 µGy/a and the annual dose rate for feldspars includes an internal beta contribution assuming a K-content of 10±2% for feldspar grains. A water content of 10±2% was assumed for all samples.

Table 2: Equivalent doses, overdispersion (OD) and ages for the 6 samples of this study. All quartz results have been obtained in analysing single grains. The quartz OSL ages were obtained considering the baSAR D e values. For feldspars, multi-grains analyses were done. A fading correction using the DRC method [START_REF] Lamothe | Towards a prediction of longterm anomalous fading of feldspar IRSL[END_REF] was applied to the individual aliquots.

D3a1

after Van Vliet-Lanoë ( 2006

Figure 1 :

 1 Figure 1: Location of the Le Rozel site in Normandy (France).

Figure 2 :

 2 Figure 2: Stratigraphic profile of the Le Rozel sequence. Black dots indicate the location of the samples dated in this study. Open dots are sediment samples OSL-dated by[START_REF] Folz | La luminescence stimulée optiquement du quartz : développements méthodologiques et applications à la datation de séquences du Pléistocène supérieur du Nord-Ouest de la France[END_REF].

Figure 3 :

 3 Figure 3: Dose recovery tests results performed on multi-grains (quartz) aliquots of sample S3 for preheat temperatures of 200, 220, 240, 260 and 280°C (applied to regenerated doses). Cut heat was 160°C for 0 s (applied to test dose).

Figure 4 :

 4 Figure 4: Abanico plots for samples S1-2 and S3. OD values are 47 % and 29 %, respectively, but no trend which might indicate poor bleaching of grains, is visible whatever is the OD.

Figure 5 :

 5 Figure 5: Decrease of the residual dose in feldspar grains measured with the pIRIR 225 signal. Bleaching was with a Hönle SOL500 solar simulator.

Figure 7 :

 7 Figure 7: Dose response curve of the pIRIR2 225 signal as a function of dose. The open dot corresponds to the normalised natural signal after fading correction with the DRC method.

  Before determining single-grain equivalent dose (D e ) values, a second dose recovery test was performed on 1,200 single-grains of sample S3: 105 out of 1,200 grains (i.e. ~8.7%) passed the chosen selection criteria (thermal transfer < 5%; recycling ratio < 10%; maximum test dose error = 20%). The recovered to given dose ratio was 0.99±0.05, justifying the application of this protocol (preheat treatment at 260°C for 10 s for natural and regenerated signals, cutheat at 160°C for test dose signals). For this DRT test, the over-dispersion (OD) was 14±2 % if a common dose is assumed. For determining individual D e values, 12 single-grain discs of each sample were measured and signals evaluated using the criteria previously determined with the DRT. Additionally, grains giving a natural signal close to or even higher than the maximum regenerated signal were also discarded. Depending on the sample, only between 46 to 55 grains were selected and the Central Age Model (CAM:[START_REF] Galbraith | Optical dating of single grains of quartz from Jinmium rock shelter, northern Australia. Part I: experimental design and statistical models[END_REF] used for calculating D e values (Table 2). As indicated in the same table, OD values range from 29 (sample S3

  ., 2008. Post-IR IRSL (henceforth pIRIR) signals were measured with IR stimulation temperatures of 50°C and 225°C (pIRIR 225 ). The protocol followed the suggestions by[START_REF] Buylaert | Testing the potential of an elevated temperature IRSL signal from K-feldspar[END_REF] After measurement of any natural of regenerative signal, a test dose of 15 Gy was given for normalisation. All preheats were carried out at 250°C for 60s (natural, regenerated and test dose signals). Measurements were done with multi-grains aliquots of 5 mm in diameter and performed in nitrogen atmosphere.

  are not necessarily characterising poorly bleached samples, but may indicate dosimetric heterogeneities at the millimeter scale. Our OSL samples clearly indicate that unit D3 in which were discovered hundreds of human prints is characterised by a high sedimentation rate, what explains the good preservation of these numerous prints. Finally, one concludes that the Le Rozel site was occupied during the outgoing MIS 5 by a group of humans (probably Neanderthals) who left their prints in the archaeological layers.for dosimetry, material research and dating application.Geochronometria 42, 202-209. Scuvée F., 1967. Le Rozel : Trou du renard. Rapport de fouilles ronéoté, 10 p. Scuvée F., 1969. Le Rozel : Trou du renard. Rapport de fouilles ronéoté, 12 p., 5 fig., 7 pl.

	Scuvée F., Vérague J., 1984. Paléolithique supérieur en Normandie occidentale : l'abri-sous-
	roche de la pointe du Rozel (Manche). Cherbourg, LITTUS-C.E.H.P., 150 p.
	Van Vliet-Lanoë B., Cliquet D., Auguste P., Folz E., Keen D., Schwenninger J.-L., Mercier N., Alix
	P., Roupin Y., Meurisse M. et Seignac H., 2006. L'abri sous-roche du Rozel (France, Manche):
	un habitat de la phase récente du Paléolithique moyen dans son contexte géomorphologique.
	Quaternaire 17 (3), 207-258.

Table 1

 1

Table 2

 2

Acknowledgments

The authors are grateful to the LaScArBx (ANR-10-LABX-52) for financial support.

Parisian Bassin

Channel

Le Rozel

Norman-Breton Gulf


See how they fly ! Some considerations on symbolic transfers and territories at the end of Upper Paleolithic

Keywords: Upper Palaeolithic, Magdalenian, Portable art, Symbols

Paleolithic portable art is constitutive of social and cultural identities, as images create a link between territories and men. Therefore, the study of some symbols can lead to a better understanding of the status and the complexity of symbolic territories. In this paper we present the history of diffusion of two symbols from Upper Magdalenian, macrocephalic horses and complex signs coming from a specific site. After a theoretical reflections on the status of symbol, we are considering what criteria should be taken into account for defining each of these symbols and understand how they have diffused -or not -in their immediate or more distant environment. The focus upon designs shareable but that haven't been transferred around suggests new perspectives for thinking the investment of human groups in their symbolic territory, through their artistic production. Therefore, we aim at demonstrating that immobility of images should, as their mobility, be taken in account in the cultural geography of the Upper palaeolithic.

Introduction

Natural spaces and landscapes constitute a general structure of territories culturally transformed by humans. The anthropization of natural lands is being realized according to two complementary dynamics, opposing fixation and mobility of human groups [START_REF] Vialou | Territoires, sédentarités et mobilités[END_REF]. Nature is being sedentarized, especially places of habitat, and is lived and certainly thought differently than the traveled nature, being considered as a network of economy, acquisition, subsistence or exchanges itineraries. The visual appropriation of landscapes by parietal or portable images is carried out according to the same processes. Thus, within the space of Palaeolithic territories, we can dissociate or differentiate the physical immobilization of parietal and rock-art symbols and the mobility of art objects, perhaps together with the symbols they convey. Both are constitutive of social and cultural identities, as images create a link between territories and men and exert on these territories a unique and powerful cultural influence and mediation. Images transcend the primary economic relationship established by men with landscapes. Therefore we consider that sharing and exchange of graphic symbols from one human group to another provides valuable information about social relations through distance. Symbols constitute a mean of clarifying the real nature of networks of exchanges, offering to go beyond the material or technological dimension and highlighting possible fluctuations at the end of the Late Glacial (circa 14 000 yBP). Portable artworks are powerful cultural markers that also fortify thinking on the territorial influence of symbols and, more broadly, on the frames of human and social geographies they help to define. Through the notion of symbolic territory, wondering upon new relations to the daily physical, economic and social space is led possible. Last, images question the modalities of their own diffusion together with phenomena of borrowing, transfer or symbolic convergence, rules governing inter-group exchanges and social relations within groups. Images thus play an essential role in cultural identification and characterization.

Background

If we wish to apply the notion of "symbol" to prehistoric graphic evidences, which are distant and often not very explicit, it is necessary to have a semantic discussion on this term whose definition could be complex.

In linguistics, the term "sign" is generally preferred to "symbol". This word is very early defined (de Saussure, 1912) as an association of a signifier (the form) and a signified (the background, the meaning).

In semiotics, a science dedicated to the analysis of signs, the term takes on a different dimension. In general, visual communication that it carries is recognized as a multiparty association of the signifier (the image in its materiality), a referee or "object" (Peirce, c. 1894) coming from the real or imaginary world (the model) and the signified (the meaning). Several authors have sought to define with precision the functioning of this relation (e.g. Peirce, 1895[START_REF] Morris | Signification and Significance. A study of the relations of signs and values[END_REF][START_REF] Sonesson | Methods and models in pictorials semiotics[END_REF]. The term "symbol" can then be distinguished from the sign, corresponding either to the case of a motivated relation between image and sense, or on the contrary to the case of an arbitrary sign (Peirce, c. 1894). According to the definition of U. [START_REF] Eco | Le signe : Histoire et analyse d'un concept[END_REF], already applied to prehistoric archeology by M.J. [START_REF] Rossano | Making friends, making tools, making symbols[END_REF] and specifically on prehistoric art by G. [START_REF] Sauvet | des objets au Paléolithique, les voies de la recherche, t.2[END_REF], we propose to consider that symbol exists as soon as a specific relationship exists, between an object -whether coming from the real world or part of emotional world of the author, called the referee, a graphic demonstration -the signifier -and a meaning known by the transmitter and surely shared with others persons -the signified. The existence of shared graphic conventions, through perceptual codes or striking characteristics, being described as traits of recognition [START_REF] Eco | Le signe : Histoire et analyse d'un concept[END_REF] or "identification keys" (Man-Estier, 2011, Man -Estier et Paillet, 2013) allows the symbol in question to being appropriated by the group. Thus, one could propose that a paleolithic representation of Deer becomes a "symbol" when some criteria (anatomical, ethological, etc.) of cervids are present and are graphically represented in a particular way. The hypothesis of existence of such symbol seems therefore conceivable only in a case of sufficiently extended and coherent corpus.

We also propose to take some distance with the distinction between figurative and abstract, usually prevailing in the study of prehistoric art [START_REF] Sauvet | des objets au Paléolithique, les voies de la recherche, t.2[END_REF]). Indeed, it seems to us that a "figurative" representation, that is to say referring to a referent coming from the author's environment, can be fundamentally conventional and connotative, just as much as a geometric or abstract pattern. With no doubt it may have had a different meaning than the denoted information offered to view. Moving away from the object to which it refers and from its material dimension, the image becomes a symbol, inaccessible to our understanding. Processing is the same for rock art symbol, that are able to travel as much as portable artworks, despite their fixed conditions (see for instance [START_REF] Bourdier | Rock Art and Social Geography in the Upper Palaeolithic. Contribution to the Socio-Cultural Function of the Roc-aux-Sorciers Rock-Shelter (Angles-sur-l'Anglin, France) from the Viewpoint of its Sculpted Frieze[END_REF][START_REF] Bourdier | Norme et individualité au Roc-aux-Sorciers (Vienne, France) : approche des « mains » du registre animalier au travers de la forme[END_REF]. The message may become even more confusing when the image is surrounded by a multitude of meanings and connotations. Finally how can one attest that a bison image, especially if it gathers several original production standards, really meant "bison" in the mind of its creator?

Goals

From this general definition of "symbol", and by examining two types of conventional and standardized art production, specific of the end of the Upper Palaeolithic (Upper Magdalenian) in the great south-west of France, we wish to evaluate the territorial dynamics of a figurative image (macrocephalic horses) and an apparently non-figurative design (Rochereil complex patterns). These two symbols have been created by Magdalenian groups which have in common, besides their geographical implantation, some raw materials, some lithic and osseous productions and certain know-how. The symbolic material is being analyzed and relocated within the framework of the phenomena of mobility, fixation, diffusion or transfers that regulate visual communication at a territorial scale.

Hypothesis on the question of symbolic territories have already been proposed, often based on the existence of codes of representations, morphological criteria or shared themes (for instance [START_REF] Bahn | inter-site and Inter-regional links during the Upper Palaeolithic : the Pyrenean evidence[END_REF][START_REF] Feruglio | L'art mobilier magdalénien de la région des Eyzies : sur la piste des liens sociaux en Europe occidentale, in., coll. Grands sites d'art magdalénien[END_REF]Fortea Perez et al., 2004;[START_REF] Fritz | Groupes ethniques, territoires, échanges : la « notion de frontière » dans l'art magdalénien[END_REF][START_REF] Fuentes | The depiction of the individual in prehistory : human representatiobn in Magdalenien societes[END_REF][START_REF] Sauvet | Histoire de chasseurs. Chronique des temps paléolithiques[END_REF][START_REF] Welté | L'art mobilier du Magdalénien supérieur des sites de la vallée de l'Aveyron et d'Europe centrale : relations et/ou convergences ?[END_REF]). We can mention specifically studies on front views animals [START_REF] Sauvet | Crónica de los intercambios entre los grupos humanos paleolíticos. La contribución del arte para el periodo 20000-12000[END_REF] or feminine schematic figures (Aujoulat and Feruglio 2001) at the end of Magdalenian.

Materials

The corpus studied is located in the actual territory of Périgord, which corresponds more or less to the geographical limits of the administrative department of the Dordogne (South-west of France). The chronology is restricted to the end of the Upper Palaeolithic and more precisely the Upper Magdalenian. It is coming from several open air sites along the valleys of Vézère and Dordogne with an epicenter around the rockshelters of La Madeleine and Laugerie-Basse, and the Isle and Dronne valleys, in the northern part of the region, around the small cave of Rochereil (figure 1).

The first of the symbols we have chosen to study is the macrocephalic horse, sometimes referred to as "hypertrophied" or even "barygnath", that is to say, bearing heavy jaws.

Results

macrocephalic horses

This conventional representation (figure 2) is essentially, but not exclusively, concerning horses. Cervids can be found represented with the help of the same formal code. It is characterized by a disproportionate treatment of the animal's forms, mainly its head whose size is exaggerated. It owes its name to this artifact of recognition, even if the morphotype fluctuates, in a certain graphic and expressive continuity, between more or less realistic representations and others that are frankly schematic. Some are also incomplete (heads, anterior part of bodies).

Considering these formal characteristics, J.-M. [START_REF] Appelaniz | Modèle d'analyse d'une école dans l'iconographie mobilière paléolithique : l'école des graveurs de chevaux hypertrophiés de la Madeleine[END_REF] suggests to retain in the macrocephalic corpus only figures which head's length scores at least 1/4 of that of the body. We can add that some extremely dilated heads occupy up to 1/3 of the total length. From this ideal morphotype, macrocephalic horse assumes other formal characteristics. The body is angular, giving the impression of being stretched.

It is often completed by stiff and unfinished anterior and posterior limbs, figured alone or in contiguous pairs, frequently stretched backwards. They dynamically project the animal forward, thus breaking with the stiffness of the legs. When present, the tail is long, narrow and pointed. Rarely, it is completed with a brush or presented disheveled (Lartet and Christy 1865-1875). It is however always detached from the buttock and placed diagonally, in extension. Other technical, graphic and anatomical details complete the typical portrait of the macrocephalic horse. The heads have an angular appearance at the level of the muzzle and the cheek. Their silhouette is polygonal. Frequently, nostril, mouth, eye, and sometimes rock at the back of the latter, as well as the zygomatic, are well indicated. The chin and the cheek are heavy, which underlines the pre-cited "heavy jaw" character. According to E. Lartet and H. Christy, the heads of these animals are heavy and "sounded", that is to say stiff (Lartet and Christy, 1865-1875). On the neckline, the jugular is firmly underlined. Ribs are sometimes indicated by oblique incisions along the back. The mane, bearing an "English style" (Lartet and Christy 1865-1875), frequently stands as a helmet and / or is being separated from the neck by a deep incision. Individuals wear shoulder lines; others have features that mark the belly and the kidneys.

From a technical point of view, contours and details are almost systematically obtained by deep incisions of asymmetric profile. Animal then appears on its medium in a slight or raised relief. Finally, except when mediums are fragmentary, the macrocephalic animals are rarely isolated. They are most often organized in a row of two to five individuals, never opposed. There isn't indication of any particular ethological character. In their individual and collective expression they seem to strictly conform to the constraints of the mediums, on one or two faces of the objects (spear points, chisels). On bored sticks, both faces aren't systematically decorated but the horses are also arranged in file and often occupy the entire length of the body of the object, sometimes even integrating the hole. The macrocephalic horses are thus framed in all available fields. They are even sometimes so reduced, especially on chopsticks, that they lose anatomical details like legs or top of the neckline. This ideal portrait of the macrocephalic horse is then an animal whose fore-hand is hypertrophied, and certainly not a "degenerate" figure [START_REF] Breuil | La dégénérescence des figures d'animaux en motifs ornementaux à l'époque du renne[END_REF][START_REF] Breuil | Exemples de figures dégénérées et stylisées à l'époque du renne[END_REF]. The symbol, with its internal details meets strict formal and aesthetic standards, which seem not to have been questioned during production's period and within its geographical area of influence [START_REF] Rivero | Defining Magdalenian cultural groups in Franco-Cantabria by the formal analysis of portable artworks[END_REF].

Another interesting aspect of the subject is that of medium invested by these representations. They are almost always made of reindeer antlers, on beam or on chopsticks. The corpus recorded 29 spearpoints, 3 chisels and 10 bored sticks (Appellaniz, 1990; Man-Estier and Paillet, 2014). It seems that the medium, limited to a small number of possibilities offered to the artist, plays a role in the composition of the symbolic concept of "macrocephalic horse".

The conventional model of the horse seems to be coming from an artistic production limited in the time of the old and new Upper Magdalenian. According to the research conducted by J.-M. [START_REF] Appelaniz | Modèle d'analyse d'une école dans l'iconographie mobilière paléolithique : l'école des graveurs de chevaux hypertrophiés de la Madeleine[END_REF], this design could find its origin in La Madeleine that gathers the main quantity of material. Moreover, on the basis of an iconographic analysis backed by statistical methods, this researcher has tried to objectify his method of determining the author of this symbol by applying it to what he supposes to be the "school" of the engravers of the Madeleine. This concept of "school" or "workshop" applied to the production of macrocephalic horses is important since it mobilizes other notions such as learning, acquiring and transmitting know-how.

Rochereil complex signs

The observed mobility and the apparent success encountered by macrocephalic horses in southwestern France can be contrasted with the apparent fixation of another system of representation composed of certain structured and original motifs, placed in the blur limits of the figurative and non-figurative, coming from Rochereil (figure 3).

Throughout this second corpus we have been able to individualize a large number of original representations, rather geometric in appearance, structured from oval or rhombus forms. In the body of the pattern, or at its periphery, are aggregated (according to the definition of [START_REF] Sauvet | des objets au Paléolithique, les voies de la recherche, t.2[END_REF], through very varied graphic formulas, internal fills or excrescences. These representations have been interpreted successively as "degenerations" of animal figures [START_REF] Breuil | La dégénérescence des figures d'animaux en motifs ornementaux à l'époque du renne[END_REF][START_REF] Breuil | Exemples de figures dégénérées et stylisées à l'époque du renne[END_REF], phytomorphic or foliaceous motifs, or even animals seen from the front (Man-Estier et al., 2016; Paillet and Man-Estier, 2016). Out of 501 graphic entities, spread over 267 decorated objects (mainly on osseous material), we have identified more than 400 motifs answering the same general set. Their common characteristic lies in the rigorous production standard that seems to govern its composition. They are elaborated from a geometrical body (parenthesis, oval, lozenge ...), endowed with internal graphic elements (lines, unidirectional hatchings, cluster of forms), and external elements concatenated. The latter are generally organized in the form of one, two or three excrescences, juxtaposed with the main body and placed in its prolongation. They can thus be interpreted, according to their shape and the sense of reading given to the image, as horns, legs or even fins seen in front view. Several patterns are also prolonged by a curved line, located in the median axis of the body and which delimits symmetrically the space. We have estimated at more than 4000 the possible combinations of these different elements, to which we must add the innumerable juxtapositions of the motives between them.

The types of mediums invested are less limited than in the previous example. They correspond to a majority of tools or weapons on reindeer antlers (115 objects) (such as spear points, chisels, barbed points), but other media are also concerned. We have counted 4 bored sticks, an ellipse, as well as raw antlers or waste [START_REF] Morris | Signification and Significance. A study of the relations of signs and values[END_REF]. Bones material is also numerous (105 of which only 9 tools). Despite this variability of the mediums, complexity of representation and its relatively coherent formal architecture make us consider these images, in their unity and their variability, as one of these "shareable" symbols, according to the definition proposed above.

Discussion

Therefore we can wonder about the differences of diffusion of these two symbols. Concerning the last, it is indeed very surprising not to find similar patterns within the contemporary and geographically close sites.

With the exception of two objects, one from La Madeleine (Dordogne) and the other from Murat (Lot), our revisions of the classical series did not allow us to identify formal equivalents. Despite an intense and standardized production, even remarkable if it is linked with the site's modest dimensions, the symbol invented at Rochereil didn't spread and doesn't seem to have been shared or borrowed, except may be in a strict domestic context. Its formal and certainly symbolic immobilization, which reflects a form of local idiosyncrasy, is in radical opposition with the extreme mobility of other symbols such as the macrocephalic horse, also existing in Rochereil.

As we mentioned above, macrocephalic horses are also known further away, in Quercy (Tarn valley) and in the Pyrenean foothills [START_REF] Appelaniz | Modèle d'analyse d'une école dans l'iconographie mobilière paléolithique : l'école des graveurs de chevaux hypertrophiés de la Madeleine[END_REF]. But the small number of these documents (12 graphic entities on 3 objects) and especially the modes of representation, quite different from the main corpus (rounded heads, abundant coat, bone mediums...), could carry an hypothesis of diffusion through a new space, distinct from the usually frequented one, by the group at the initiative of the symbol.

In this context, the evolution of image allows us to consider that the transfer of the image and its referent has been accompanied by a loss of its meaning, or at least a loss of the iconographic convention linking the meaning to the image. Independently of this somewhat anecdotal aspect, the appearance of the symbol "macrocephalic horse on reindeer wood", mainly along the valleys of the Dordogne and Vézère can appear as a rather successful example of diffusion. But it wouldn't be silly to take here in consideration also the own will of the producers of the symbol, that is to say the artists themselves but perhaps also the "decision-makers", and therefore considering, after A. Gell (1998) the artwork as a media of social agency. This would allow us to a better understanding of the actual status of this dissemination and its role at the time. Why did some people want to produce similar objects, decorated with the same pattern? Why and how has this symbol been transmitted to other groups? What king of value was associated with it? Even if the answers to these questions are not touchable, we can simply repeat that the mobility of this symbol, which retains an excellent homogeneity despite its travels, is a strong testimony to the existence of cultural territories such as we seek to apprehend.

Conclusion

Through these two examples is being constructed the image of a complex symbolic territory at the end of the Magdalenian. The existence of social exchanges at medium distance along the valleys of the Vézère and the Dordogne seems coherent with the spread of the symbol of the "macrocephalic horse". This mobility of the image can be perceived as a vector of unification of systems of representation, each site retaining its originality.

In Rochereil, the coexistence of a symbol coming from elsewhere, well diffused, together with an original endogenous symbol, prompts us to question the functioning of the regional cultural network in the Upper Magdalenian. Without being able to attest that this is a failure of diffusion, its absence elsewhere than on the site princeps prompts us to reconsider our way of perceiving the exchanges of content and production.

Only systematic revision of corpus and indexation on extremely fine time scales will be able to remove highlight reality of the areas traveled by symbols, by men, and by ideas. Territory, both symbolic or natural, seems now to need to be perceived as much through the mobility of groups that through the apparent sedentariness that emerges from some productions, at least on the short time scale of a man's life.

  It seems we can propose to link this pattern to the sequence of the Late Glacial such as it is known within the site of La Madeleine (layer F, dated between 16236 and 13991 years cal BP (D'Errico et al. 2011 and Bouvier, 1977)). In the current state of knowledge, there are 108 representations of macrocephalic horses, spread over 42 objects, and coming from 9 sites in Dordogne and Gironde: La Madeleine, Laugerie-Basse, Limeuil, Le Soucy, le Morin, Raymonden, Jolivet, Rochereil, La Peyzie (Appelaniz, 1990 ; Deffarge et al. 1975 ; Man-Estier and Paillet, 2014, Paillet, 2014a, Sieveking, 1987). Three more distant sites (Montastruc and Fontalès in the Tarn-et-Garonne and Mas-d'Azil in Ariège) offered other horses (4 at Montastruc, 5 at Fontalès and 3 at Mas d'Azil) evoking the macrocephalic representations, but whose formal characteristics and technical choices do not quite correspond to the referential corpus (Appelaniz 1990, Aujoulat and Feruglio, 2011). The second type of representations we are willing to study comes from the little cave of Rochereil (Grand-Brassac, Dordogne). The site was excavated in the first half of the 20th century (Jude, 1960) and since 2011 has been subject of a Collective Research Project (Paillet 2014b ; Paillet and Man-Estier 2013, 2014) aiming at a new evaluation of ancient series (lithic and osseous material), fauna and numerous nonutilitarian productions. The corpus gathers today nearly 270 portable art objects. The archeostratigraphic context of these productions (layer A of the old and new Magdalenian superior) is contemporary with layer F of the Madeleine (age of 15027 -14081 years cal BP : Mallye et al., 2014).

Figure 1 -

 1 Figure1-map of thes site mentionned in the text (CAD E. Man-Estier). 1.Abri Morin, 2.Le Soucy, 3.Limeuil, 4. Laugerie-Basse, 5. La Madeleine, 6. Jolivet, 7. Raymonden, 8. La Peyzie, 9. Rochereil.

Figure 2 -

 2 Figure 2 -macrocephalic horses exemples from La Madeleine (up) and Rochereil (bottom), pictures trustees of the British Museum (up), MNHN -JCDomenech (bottom).

Figure 3 -

 3 Figure 3 -complex signs from Rochereil, tracings P. Paillet.

Figure 3 -

 3 Figure 3 -complex signs from Rochereil, tracings P. Paillet.


Meriem Elhosni
email: meriem.elhosni@univ-lorraine.fr

Omar Elmazria

Sébastien Petit-Watelot

Laurent Bouvot

Sergei Zhgoon

Abdelkrim Talbi

Michel Hehn

Keltouma Aït Aïssa

Sami Hage-Ali

Daniel Lacour

Keltouma Ait Aissa

Frederic Sarry

Olivier Boumatar

Magnetic field SAW sensors based on magnetostrictive-piezoelectric layered structures: FEM modeling and experimental validation

Keywords: SAW, magnetic field sensor, wireless, FEM Modeling

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.

Introduction

Because surface acoustic wave devices (SAW) exhibit a high sensitivity to various physical and chemical parameters, they offer innovative and very promising solutions in a wide range of sensing applications [START_REF] Lonsdale | Method and apparatus for measuring strain[END_REF][START_REF] Wohltjen | Surface Acoustic Wave Probe for Chemical Analysis -Introduction and Instrument Design[END_REF][START_REF] Staples | Electronic Nose Simulation of Olfactory Response Containing 500 Orthogonal Sensors in 10 Seconds[END_REF]. In addition to being small, simple and robust, these devices have the advantage of being passive (batteryless), remotely queried (wireless), packageless (when needed), and inexpensive if they are fabricated at a large scale [START_REF] Reindl | Passive Radio Requestable SAW Water Content Sensor[END_REF][START_REF] Kalinin | Application of passive SAW resonant sensors to contactless measurement of the output engine torque in passenger cars[END_REF][START_REF] Bhattacharjee | Packageless SAW Devices with isolated Layer Acoustic Wave (ILAW) and wave guiding Layer Acoustic Waves (WLAW)[END_REF][START_REF] Legrani | Packageless temperature sensor based on AlN/IDT/ZnO/Silicon layered structure[END_REF]. Their use as passive and wireless sensors allows them to operate in rotating parts or in extreme conditions such as high temperature (up to 1000°C) or radioactive environments, in which no other wireless sensor can operate [START_REF] Reindl | Passive radio requestable SAW water content sensor[END_REF][START_REF] Aubert | In situ high-temperature characterization of AlN-based surface acoustic waves devices[END_REF]. Practical SAW sensor systems have been reported, such as temperature, chemical and pressure sensors [START_REF] Kalinin | Application of passive SAW resonant sensors to contactless measurement of the output engine torque in passenger cars[END_REF][START_REF] Aubert | Surface acoustic wave devices based on AlN/sapphire structure for high temperature applications[END_REF][START_REF] Talbi | ZnO/quartz structure potentiality for surface acoustic wave pressure sensor[END_REF].

Recent developments have enabled the elaboration of magnetic field SAW sensors by combining magnetostrictive and piezoelectric materials [START_REF] Kadota | Sensitivity of surface acoustic wave magnetic sensors composed of various Ni Electrode structures[END_REF][START_REF] Zhou | Theoretical and experimental study of multilayer piezomagnetic structure based surface acoustic wave devices for high sensitivity magnetic sensor[END_REF][START_REF] Weiler | Elastically Driven Ferromagnetic Resonance in Nickel Thin Films[END_REF][START_REF] Hauser | Wirelessly Interrogable Magnetic Field Sensor Utilizing Giant Magneto-Impedance Effect and Surface Acoustic Wave Devices[END_REF]. Magnetic SAW devices such as a SAW delay line made of TbCo2/FeCo/Y-cut LiNbO3 [START_REF] Zhou | Theoretical and experimental study of multilayer piezomagnetic structure based surface acoustic wave devices for high sensitivity magnetic sensor[END_REF] and SAW resonators with Ni electrodes/quartz [START_REF] Kadota | Sensitivity of surface acoustic wave magnetic sensors composed of various Ni Electrode structures[END_REF] were reported. However additional efforts need to be made in order to increase the sensitivity to the magnetic field of such structures. Systematic fabrication, test and demonstration of SAW sensors performances are time consuming and expensive, especially when layered structures are considered, and when the sensitivity to external parameters is investigated. Thus, accurate simulation models are required to design optimal SAW magnetic field sensors based on resonators or delay lines. For such devices, the finite element analysis (FEM) is a useful and efficient tool, notably because of the relative ease of implementation of complex geometries. In our study, a single half-period structure has been studied, and the application of inverted periodical boundary conditions allowed us to compute the derived infinite geometry [START_REF] Lebrizoual | FEM modeling of surface acoustic wave in diamond layered structure[END_REF]. It should be noted that if extremely precise data are required, FEM will use very important computational resources. This work presents an accurate and fully coupled model enabling the investigation of magnetoelastic SAW devices sensitivity to an externally applied magnetic field. This model is then validated experimentally. Both the direction and the intensity of the applied magnetic field are considered. The magnetic field dependence of SAW resonators is demonstrated, leading to possible applications as either magnetic field sensors or externally controlled frequency-tunable resonators. This paper is organized as follows: in section 2, we describe the development of a numerical model to study magnetic field SAW sensors, which is, in a first step, successfully confronted to experimental results previously published by Kadota &al. [START_REF] Kadota | Sensitivity of surface acoustic wave magnetic sensors composed of various Ni Electrode structures[END_REF]. In section 3, we use this model to study extensively a new layered structure, in terms of insertion loss, sensitivity to the magnetic field in two in-plane directions, the quality factor and to describe the impact of using harmonics. In section 4 we describe the fabrication and characterization of the new layered structure and provide additional demonstration of the validity of the developed numerical model. To finish, section 5 describes new strategies to yield highly sensitive and high Q wireless magnetic field sensors.

Model validation

A FEM computational study was performed using COMSOL Multiphysics considering a magneto-elastic wave in a ferromagnetic film deposited on a piezoelectric substrate.

We consider a magnetoelastic wave in a ferromagnetic thin film deposited on a substrate and magnetized to saturation. In this case, the equations for the mechanical and magnetic systems, the equations of Landau-Lifshitz and motion equations are ( [START_REF] Zhou | Multilayer magnetostrictive structure based surface acoustic wave devices[END_REF]):

𝜌 "²$ % "& ' = "* %+ ", + (1)
"𝑴 "& = -𝛾µ 1 2𝑴 × 𝑯 𝒆𝒇𝒇 7 (2)
Where 𝛾 the gyromagnetic ratio, 𝑢 9 is is is the ith component of the particle displacement, and 𝑥 ; denotes the Eulerian coordinates. The effective magnetic field 𝑯 𝒆𝒇𝒇 and 𝑇 9; is the stress tensor given by [26]:

𝑯 𝒆𝒇𝒇 = 𝑯 - = > ? "@ "𝑴 (3) 𝑇 9; = "@ "A %+ (4)
where 𝑯 is the Maxwellian magnetic field, and 𝐸 CD is the strain tensor

𝐸 CD = = E F "$ G ", H + "$ H ", G J (5)
U is the local internal energy density written as U=Uan+Ume+Ue, , Uan is the magnetocrystalline anisotropy energy, Ume is the magneto-elastic coupling energy and Ue is the elastic Energy.

When linearizing the equations ( 1) and (2) around a ground state position, we obtain the dependence between elastic constants and the magnetic field. ∆𝐶 9; is the term dependent to the magnetic field ( [START_REF] Bou Matar | Band gap tunability of magneto-elastic phononic crystal[END_REF]). The elastic constant 𝐶 M 9;

of the magnetic film are dependent of the applied magnetic field H.

𝐶 M

9; = 𝐶 9; + ∆𝐶 9; [START_REF] Bhattacharjee | Packageless SAW Devices with isolated Layer Acoustic Wave (ILAW) and wave guiding Layer Acoustic Waves (WLAW)[END_REF] The numerical model was generated using the AC/DC and the structural mechanics modules of COMSOL Multiphysics. To introduce the coupling between the two domains, appropriate terms are added to the subdomain variables. The coupling magnetostriction equations are ( [START_REF] Slaughter | Coupled Structural and Magnetic Models: Linear Magnetostriction in COMSOL[END_REF]):

𝑇 = 𝐶 N 𝑆 -ℎ𝐵 (7) 𝐻 = -ℎ𝑆 + 𝜈 T 𝐵 (8)
Where 𝑇 is the stress, 𝐶 N is the compliance matrix at constant flux density, 𝑆 is the strain, ℎ is the piezo-magnetic coupling coefficients. 𝐻 is the variable magnetic field, 𝐵 is the flux density, and 𝜈 T is the inverse of the permeability at constant strain.

A FEM computational study was performed using COMSOL Multiphysics. In a magnetostrictive thin film, a coupling between the AC/DC module and the structural mechanics module was implemented. To verify if the magnetoelastic interaction calculation in our model is correct, a half period of Ni-IDT/quartz SAW resonator [START_REF] Kadota | Sensitivity of surface acoustic wave magnetic sensors composed of various Ni Electrode structures[END_REF] was first studied (Fig. 1).

Fig. 1 The sensitive element consists of IDTs made in nickel. We investigated the magnetic sensitivity of the SAW sensor by studying the relative frequency shift to the external magnetic field for different IDT features. Figure 2 shows the dependence of the sensitivity to the metallization ratio of the IDTs in X and Y directions, i.e. parallel and perpendicular to the direction of propagation of the acoustic wave, respectively.

As one can observe, the higher the metallization ratio, the higher the sensitivity, particularly in the Y direction. For this reason a metallization ratio of 80%, which is elevated but still compatible with a practical implementation, was used as in [START_REF] Kadota | Sensitivity of surface acoustic wave magnetic sensors composed of various Ni Electrode structures[END_REF] to study the magnetic characteristics of the SAW sensor.

Fig. 2 Using a 80% metallization ratio, the relative frequency shift (Fig. 3) and the quality factor (Fig. 4) versus the magnetic field intensity were then calculated for each direction (X, Y, Z) and compared to the experimental results published by Kadota et al. [START_REF] Kadota | Sensitivity of surface acoustic wave magnetic sensors composed of various Ni Electrode structures[END_REF]. The obtained results are highly consistent with the experimental ones, thus confirming the validity of our model. As an example, at B=120 mT, Δf =100ppm and 95 ppm for the experiment and the simulation, respectively. As one can observe in figure 4, the sensor is more sensitive to the magnetic field in the X direction. However, the theoretical and experimental results show that the quality factor (Q) is also strongly affected by the magnetic field intensity and direction. Figure 5 shows that the Q value decreases with the intensity of the magnetic field applied in the X direction and reaches a minimum value of 2500 for B=38 mT. This value is too low to enable a remote interrogation of the SAW sensor, thus complicating any use in wireless applications. In the Y-direction, the Q factor gradually increases when magnetic field intensity increases. This explains why this structure was considered as a suitable candidate for testing as a wireless sensor of the magnetic field only in the Y direction. Note that in simulated results, Q is estimated by the inverse of the fractional width between frequencies where the real part of the admittance Y becomes the half height of its peak [START_REF] Hashimoto | Surface Acoustic Wave Devices in Telecommunications[END_REF]. According to previously published paper [START_REF] Yamaguchi | Variable SAW delay line using amorphous TbFe2 film[END_REF] the variation of frequency (i.e. phase velocity) and Q factor versus magnetic field intensity shown in Fig. 3 and Fig. 4 respectively are attributed to the ΔE effect, which is a change in Young's modulus E under magnetic fields, and to a dynamic magnetoelastic coupling, which is the interaction between acoustic waves and magnetic moments. Indeed, as described by P. Smole et al. [START_REF] Smole | Magnetically tunable SAWresonator[END_REF], applying an external field in hard axis direction leads primarily to a decrease in the elastic modulus towards a local minimum. A further increase of the external field causes a proportional growth of the elastic modulus up to a saturation value where the E modulus is approximately the same as in the initial state. Thus, the Q factor behavior follows the Young Modulus one. Considering the previously performed optimization of the ZnO and Ni layers regarding the SAW sensor sensitivity to the magnetic field and the electromechanical coupling coefficient (K 2 ), their thicknesses were fixed at 250 nm and 200 nm, respectively [START_REF] Elhosni | FEM modeling of Multilayer Piezomagnetic Structure Based Surface Acoustic Wave Devices for Magnetic Sensor[END_REF].

Theoretical study of

As shown in figure 6, the S21 frequency response of the optimized structure was calculated for each step in our device modeling: IDT/LiNbO3, ZnO/IDT/LiNbO3, and finally Ni/ZnO/IDT/LiNbO3. As one can observe, the insertion loss (IL) of the device is slightly affected by the presence of the ZnO and Ni layers. These changes in the insertion losses are due to the dependence of the considered structures on the propagation loss and on the K 2 value.

To quantify the contribution of K 2 and quality factor (Q) to insertion losses, these parameters were also calculated at different steps. Table 1 summarizes the calculated values of K 2 , IL, Q and of the center frequency.

Table 1 Fig. 6 The wideband S11 frequency response of the optimized Ni/ZnO/IDT/LiNbO3 delay line structure was then calculated and the results are shown in figure 8-a. The peaks obtained at 162MHz, 460 MHz and 810MHz were respectively identified as the peak of the fundamental Rayleigh mode (H1), of its third spatial pseudo-harmonic (H3) and of the fifth one (H5). The term "pseudo" is used because the frequency values of H3 and H5 are not the exact multiples of H1, which is due to the acoustic wave velocity dispersion induced by the multilayer configuration in the considered structure [START_REF] Talbi | Sezawa Mode SAW Pressure Sensors Based on ZnO/Si Structure[END_REF][START_REF] Elmazria | Effect of diamond nucleation process on propagation losses of AlN/diamond SAW filter[END_REF]. The identification of the mode and of the spatial pseudo-harmonics is made by analyzing the distribution of the particles displacement. Figure 8-b shows the 2D presentation of the calculated particles displacement distributions in the Ni/ZnO/LiNbO3 layered structure obtained for the H1, H3 and H5 spatial pseudoharmonics. The wavelength related to each spatial pseudo-harmonic is clearly observed: the penetration depth of the acoustic wave is inversely proportional to the considered frequency (i.e. the order of the harmonic). Thus, we can expect that, for high frequencies, the sensitivity to magnetic field of the structure will be enhanced. Indeed, the acoustic wave is more confined to the surface and subsequently in the sensitive layer. For all the spatial harmonics, the magnetic sensitivity was calculated, when the direction of the applied magnetic field is parallel to the direction of acoustic wave propagation (i.e X direction). Figure 8-a shows that when the magnetic field intensity increases, the resonance frequency of the device first decreases, then reaches a minimum for H= 0.18Tesla, and then increases, trending towards the initial value. We can consider that the studied device could be advantageously used as a magnetic field sensor in the range of intensity between 0 and 160mT in the X direction.

The Ni/ZnO/IDT/LiNbO3 structure shows a relative sensitivity of 0.69ppm/mT for the fundamental mode. This sensitivity is enhanced by a factor 3 when we consider the third spatial pseudo-harmonic (2.1ppm/mT) and by a factor 5.2 for the fifth one (3.6ppm/mT), as it is shown in figure 9-a. As expected, the sensor sensitivity is enhanced with the order of the considered spatial pseudo-harmonic (i.e. operating frequency). Note that here the sensitivity is expressed in (ppm/mT) in a relative fashion, and if we consider the absolute sensitivity in (Hz/mT) corresponding to the actual frequency shift, the enhancement is of a factor 26 for the fifth harmonic.

The magnetic field was then applied in the Y direction, perpendicular to the acoustic wave propagation. The results obtained for the fundamental mode and for the two nearest spatial pseudo-harmonics are shown in figure 8-b.

Similarly to the X direction, the sensitivity increases when the considered operating frequency increases. As we can see, the frequency shift in the Y direction is smaller than the one in the X direction. However, the range of sensitivity that could be considered for sensor applications is almost three times wider in the Y direction (from 0 to 500mT). Moreover, when we compare the frequency shifts for two directions of the magnetic field, X and Y (Fig. 9), we can see that the Y-direction frequency shift presents a better linearity with respect to the field intensity. Even more important for applications is the absence of ambiguous sensor readings that appear in X-direction (i.e. same central frequency for two different magnetic field intensities).

Fig. 8 Fig. 9

Quality factor

As mentioned before, the quality factor is a critical parameter for SAW devices. The sensor accuracy is directly depending on Q value and in wireless configuration the query distance is also limited by the Q value. A minimum value of 3000 is often required. Q variations versus applied magnetic fields in the X and Y directions were extracted from admittance-frequency response and calculated for all the spatial pseudo-harmonics H1, H3 and H5.

The obtained results, summarized in figure 10, show that the Q value decreases with the intensity of the magnetic field in the X-direction and reaches a minimum value of 800 for B=200mT. When the magnetic field is applied in the Y direction, the Q value increases with the magnetic field intensity. A slightly larger value of 2279 is obtained for the fifth harmonic at 600 mT. In many cases, this value is not sufficient for many wireless SAW sensor applications.

Fig. 10 4. Experimental results

Electrical characterization

To confirm our theoretical predictions, a Ni/ZnO/IDT/LiNbO3 structure optimized by FEM modeling was fabricated. In the first step, the aluminum IDTs of the delay line were fabricated on the surface of a 128°Y-X LiNbO3 substrate using photolithography and wet etching processes. The spatial period of the IDTs that defines the working wavelength was fixed to 24 µm. Then, according to the modeling results, a 250 nm-thick insulating ZnO layer was deposited over the IDTs and the LiNbO3 substrate by RF magnetron sputtering. Finally, a 200 nm thick Nickel film was deposited on the ZnO surface using RF magnetron sputtering. Depositions parameters for ZnO and Ni are described in previous work [START_REF] Elhosni | FEM modeling of Multilayer Piezomagnetic Structure Based Surface Acoustic Wave Devices for Magnetic Sensor[END_REF].

The magnetization of the Ni thin film has been measured with a vibrating sample Magnetometer (VSM). The obtained results along X and Y axis are displayed in figure 9 and they confirm that the deposited Ni film is sufficiently isotropic in X and Y plane. Frequency responses of the realized delay line SAW structure Ni/ZnO/IDT/LiNbO3 in transmission configuration (S21) were measured using Network Analyzer (Agilent PNA 5230A, Santa Clara, CA) and RF probe station RF (PM5Suss Micro-tech PM5). As shown in figure 10, measurement was made before and after ZnO and Ni films depositions. We can observe that after adding the two layers (ZnO and Ni) the fundamental peak shift from 164.9 MHz to 159.4 MHz, the third pseudo-harmonic from 498.8 MHz to 465.5 MHz and the fifth one from805.1MHz from to 753 MHz.

In order to prepare test samples for magnetic characterization, the SAW delay line structure Ni/IT/ZnO/LiNbO3 is bonded to copper-coated printing circuit board (PCB), suitable for microelectronics applications. The connections are established between the PCB and the SAW device using a 20 µm diameter gold wire (Fig. 10). Four RF connectors (SMA) are used in order to characterize simultaneously two independent SAW devices. The S21 frequency response of the mounted device was measured with a network analyzer (see Figure 14). The insertion loss (IL) of the device is slightly affected by the mounting process (+2.8 dB for the fundamental peak). Note that after packaging, only the fundamental and the third pseudo-harmonics appear clearly at 159.4 MHz and 465.5 MHz.

Thus, for experimental magnetic characterization, only those two frequencies will be considered.

Magnetic characterization

A magnetic field with controlled intensity is applied to the packaged SAW device. The device can be rotated to change the orientation of the applied magnetic field. A Network Analyzer (PNA 5230A) was used to characterize the frequency response of the SAW device and the variation of the center frequency is collected versus intensity and direction of the applied magnetic field. A photo of the experimental set up is shown in Figure 11.

Fig. 11

Note that the maximum external magnetic field reached in our experimental characterization is limited to 0.35mT. The center frequency of the delay line was measured versus the intensity of magnetic field when the field was first applied in X-direction and then in Y-direction. Figure 12, shows the measured and calculated relative center frequency shift (Δf/f) with respect to the applied magnetic field intensity. Both the fundamental wave (H1-159 MHz) and pseudo-harmonic (H3-465 MHz) were investigated. There is a good agreement between calculated and experimental results, which proves that the developed model leads to a correct prediction of the sensor sensitivity to the magnetic field intensity and direction. When the magnetic field is applied in the same direction as the direction of the acoustic wave propagation (X-direction), the experimental results are compared with the theoretical predictions, as shown in Figure12-a, for the fundamental spatial pseudo-harmonic. The Ni/ZnO/IDT/LiNbO3 delay line structure shows a sensitivity of 0.65ppm/mT, a value that is enhanced by a factor 3 when it is studied at the third harmonic (2.1ppm/ mT).

When the magnetic field is perpendicular to the acoustic wave propagation (Fig. 12-b) the experimental results confirm the calculated ones. As we can see in figure 18-b, the shift in the Y-direction is smaller than the one in the X direction. However, the range of sensitivity that could be considered for sensor applications is wider in the Y direction (0 to 500mT). Moreover, the absence of ambiguous sensor readings that appear in X-direction is confirmed here experimentally, and it is very important for sensor applications.

Fig. 12 5. Discussion: toward more sensitive magnetic field sensors

The obtained sensitivity and quality factor values are still limited and various paths can be envisioned to enhance them. A strength of our structure is the possibility to use different strategies, separately or altogether to improve the sensor performances. Thus, the sensor sensitivity to magnetic field intensity can be improved by: -Using a more sensitive layer, such as a strongly magnetostrictive layer for example: CoFeB, CoFeTb or the stacks similar to (TbCo2/FeCo) multilayers [START_REF] Zhou | Theoretical and experimental study of multilayer piezomagnetic structure based surface acoustic wave devices for high sensitivity magnetic sensor[END_REF]. However, the knowledge of physical constants of such layers is required before for theoretical studies and optimization.

-Using higher frequency device leading to better confinement of the acoustic wave near the surface and subsequently inside the sensitive layer.

-Using insulating layer with different properties that presents a higher acoustic velocity, leading to a better confinement of the acoustic wave particularly in the sensitive layer.

Here we will consider the combination of the last two approaches. As insulating layer, we may use alumina (Al2O3) that presents a lower density and an acoustic velocity that is more than two times higher than that of ZnO. We will consider a device operating at 815 MHz in order to make a qualitative comparison with the spatial pseudoharmonics 3 and 5 in the two structures previously studied in this paper, Ni/Quartz and Ni/ZnO/IDT/LiNbO3 respectively.

First, we considered alumina (Al2O3) as an insulating layer instead of ZnO and kept all geometric parameters of the structure unchanged. Calculated results (Fig. 13) show that the particles displacement is larger when considering the structure with Al2O3 layer.

Fig. 13

By substituting ZnO with Al2O3 the sensor sensitivity was also enhanced by a factor 9 in the X direction (Fig. 14-a)

for a comparable operating frequency. The enhancement factor is equal to 6.25 in the Y direction (Fig. 14-b). This new structure also exhibits a higher quality factor compared to the structure using ZnO as insulator (Fig. 15-a).

When the magnetic field is applied in the Y direction (Fig. 15-b), the quality factor increases when the magnetic intensity increases and its value is always over than 5000, making this structure very interesting for wireless magnetic sensing applications. Work is in progress to realize the simulated structures and experimentally confirm the predicted results.

Conclusion

To conclude, a theoretical model for the prediction of a SAW sensor sensitivity with respect to the intensity and the direction of externally applied magnetic fields was developed and validated experimentally. For the validation of our model, we used experimental results available in literature as well as our own experimental results.

This study confirms that the realization of magnetic wireless sensors combining high sensitivity and high quality factor is achievable by using a layered SAW structure. Three different structures were investigated, demonstrating that a careful choice of properties of considered piezoelectric, insulating and sensitive magnetoelastic layers is very important for the final performance of the sensor. Note that for more clarity for reader, the first and the second curves were shifted by 120 and 60 dB respectively.

Figure captions

Fig. 3

 3 Fig.3

Fig. 4

 4 Fig.4

Ni/ZnO/IDT/LiNbO3 structure 3 . 1

 31 Frequency response of the structure with no magnetic fieldAfter validating our model by analysis of the matching with known results, we extended the use of this model to new structures in order to enhance the sensor sensitivity. A delay line made of a Ni/ZnO/IDT/LiNbO3 layered structure was considered (Fig.5shows a half-period of an IDT). The purpose of this design is to add additional degrees of freedom in the structure by separating the Ni sensitive layer and the metallic IDT layer. The Ni sensitive layer has now a 100 % metallization ratio and the IDTs are made with aluminum, whose conductivity is almost 2.5 times higher than the one of nickel. The IDTs spatial period was fixed to 24µm. Thus the elastic wavelength (l) related to central frequency of the fundamental is equal to 24 µm. If we consider the harmonic n, the related wavelength is ln= l/n. Thin film of zinc oxide (ZnO) was used as insulating layer in order to avoid the shorting of the IDTs by the nickel layer.

Fig. 5

 5 Fig.5

Fig . 7 -

 7 Fig .7-a, Fig .7-b

Fig. 9

 9 Fig.9

Fig. 10

 10 Fig. 10

Fig. 14

 14 Fig.14

Fig. 15

 15 Fig. 15

Fig. 1 :Fig. 2 :Fig. 3 :

 123 Fig. 1: Schematic cut view of Ni-IDT/quartz structure.

Fig. 4 :Fig. 5 :Fig. 6 -

 456 Fig. 4: Calculated quality factor (Q) versus the magnetic field intensity of a Ni-IDT/quartz resonator.

Fig. 7 :Fig. 8 :Fig. 9 :Fig. 10 :

 78910 Fig. 7: Calculated sensitivity of the Ni/ZnO/IDT/LiNbO3 structure to an applied magnetic field in the X (close symbols) and Y (open symbols) directions for the fundamental (square) the third (circle) and the fifth (triangle) harmonics

Fig. 11 :

 11 Fig.11: Experimental setup used to characterize the sensitivity of magnetic SAW sensor: (a) Magnetic filed generator, (b) Packaged SAW device under test inside the gap, (c) Network analyzer connected to the SAW device.

Fig. 12 :Fig. 13 :Fig. 14 :Fig. 15 :

 12131415 Fig.12: Comparison between calculated and measured relative frequency shift (Δf/f) versus the magnetic field intensity applied in the X direction (a) and the Y direction (b). Both fundamental (H1) and spatial pseudo-harmonic (H3) frequencies are investigated.

Fig. 1 :Fig. 2 :Fig. 3 :

 123 Fig. 1: Schematic cut view of Ni-IDT/quartz structure.

Fig. 4 :Fig. 5 :Fig. 6 -Fig. 6 -Fig. 7 :Fig. 8 :Fig. 9 :

 4566789 Fig. 4: Calculated quality factor (Q) versus magnetic field intensity of layered magnetostrictive-piezoelectric Ni-IDT/quartz sensor.

Fig. 10 :

 10 Fig. 10: Frequency response of IdT/LN structure (top), Ni/ZnO/IDT/LiNbO3 characterized before (middle) and after packaging (dottom).

Fig. 11 :Fig. 12 :Fig. 13 :Fig. 14 :Fig. 15 :

 1112131415 Fig.11: Experimental setup used to characterize the sensitivity of magnetic SAW sensor: (a) Magnetic filed generator, (b) Packaged SAW device under test inside the gap, (c) Network analyzer connected to the SAW device.

Table caption Table 1 .

 caption1 Calculated electro-mechanical coupling coefficient and insertion loss for the considered structures

	Structure	K 2 (%)	calculated IL (dB)	Q	central frequency
	IDT/ LiNbO3	0.049	-10	1850	165MHz
	ZnO/IDT/ LiNbO3	0.052	-9	1487	164MHz
	NI/ZnO/IDT/ LiNbO3	0.035	-11.4	1180	162MHz

Aknowledgement

This work was supported in parts by the Institut Jean Lamour 7198, Université de Lorraine -CNRS, by the Ministry of Science and Education of the Russian Federation (123/14-544), International Research University Moscow Power Engineering Institute, 14 Krasnokazarmennaja, 111250 Moscow, by the International Associated Laboratory LEMAC/LICS -IEMN UMR CNRS 8520.